August, 1974
A GUIDE TO MODELS
IN GOVERNMENTAL PLANNING
AND OPERATIONS
prepared for
Office of Research and Development
ENVIRONMENTAL PROTECTION AGENCY
Washington, D.C. 20460
Contract No. 68-01-0788
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EPA Review Notice
This report has been reviewed by the policies of the Environmental Protec-
Office of Research and Development, tion Agency, nor does mention of trade
EPA, and approved for publication, names or commercial products consti-
Approval does not signify that the con- tute endorsement or recommendation
tents necessarily reflect the views and for use.
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Abstract
This report "A Guide to Models in
Governmental Planning and Opera-
tions" is directed towards the majority
of governmental (Federal, State and
local) officials and their staffs who are
confronted with the continuing task of
selecting solutions, i.e., of making deci-
sions in societal areas. The report is
divided into 12 major chapters: 1. In-
troduction to Decision Models—a
primer on the basics of models and
model building, 2. Models and Policy
Making, 3. Models in Air Pollution, 4.
Models in Water Resources, 5. Models
in Solid Waste Management, 6. Urban
Development Models, 7. Models in
Transportation, 8. Models in Law En-
forcement and Criminal Justice, 9.
Models in Educational Planning and
Operations, 10. Models in the Field of
Energy, 11. Models in Planning and
Operating Health Services, 12. Econo-
metric Models for Policy Analysis.
Each chapter is basically self-con-
tained, with model concepts and termi-
nology introduced in the primer. The
Guide is an attempt to present to a
non-technical, governmental-oriented
audience an overview of what models
are, and how they have been used in a
number of important social-urban areas.
It represents a source from which gov-
ernment officials and others can obtain
an understanding of this approach to
decision making.
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Contents
Chapter
Preface vii
1 Introduction to Decision Models 1
2 Models and Policy Making 39
3 Models in Air Pollution 61
4 Models in Water Resources 103
5 Models in Solid Waste Management 139
6 Models in Urban Development 165
7 Models in Transportation 201
8 Models in Law Enforcement and Criminal Justice 231
9 Models in Educational Planning and Operations 277
10 Models in the Field of Energy 317
11 Models in Planning and Operating Health Services 347
12 Economic Models for Policy Analysis 375
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Preface
The Guide is directed towards a spe-
cific audience—the majority of govern-
mental (Federal, State and local)
officials and their staffs who are con-
fronted with the continuing task of
selecting solutions, i.e. of making deci-
sions, in societal areas: If you are a
part of our audience, we assume you
have had limited scientific experience,
but your elective or appointed tasks
require you to resolve the conflicting
objectives inherent in society's prob-
lems; problems which have scientific
and technical implications, e.g. air pol-
lution control systems, or which may be
better solved by methodologies foreign
to your experiences and training, e.g.
the use of optimization procedures for
routing refuse trucks.
From the realms of military, space
and industrial problem solving, a body
of knowledge, under the generic title of
models, has been developed and has
proven of great aid to decision making
in those areas. This knowledge and its
methodologies is now being adapted
and applied to a broad range of do-
mestic governmental problems. In these
applications, some look at models and
model building as an "aqua regia" which
cart dissolve all of society's problems;
while to others, models are mysterious
academic exercises and have not proven
themselves in the arena of social action.
This Guide is written from the perspec-
tive of a middle ground—to the extent
that we understand the convoluted na-
ture of these social problems and the
needs of the decision makers, and to the
extent that we have concomitant under-
standing of the power and limits of
.models, then models can aid the gov-
ernmental decision maker to improve
his ability to make more informed and
effective decisions.
Our approach to imparting to you
what we feel is an appropriate level and
scope of information on models is to
first present a primer (Chapter 1) on
the basics of models and model build-
ing. This primer should supply the
reader with a foundation for reading
and understanding the remaining chap-
ters which describe models in specific
problem settings.
The primer is just that—it is tutorial,
and not a handbook of models, nor a
state-of-the-art in models; it is not ex-
haustive. In terms of our audience, the
primer presents definitions, examples
and discussions in a relatively nontech-
nical manner, but of sufficient strength
so that the readers may not only under-
stand the chapters which follow, but
hopefully they will then be able to com-
municate better with model developers.
The succeeding Chapters 3-11 de-
scribe the use of models in a variety of
social-urban fields; air pollution, water
resources, solid waste, urban develop-
ment, transportation, law enforcement
and criminal justice, education, energy
and health services. Each chapter is
basically self-contained, but unless you
have some knowledge of modeling, it
requires prior reading of the primer.
In addition, each author presents infor-
mation on models which complement
the material in the primer. Thus, for
example, the section on "General
Themes in Urban Modeling" of the
"Urban Development Models" chapter
describes modeling concerns which are
applicable to most modeling situations;
also, the chapter on "Models in Air
Pollution" includes a technical discus-
sion on stochastic models which is of a
general nature. Most chapters have ele-
ments on model building which should
reinforce the concepts and understand-
vn
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ing of readers in their pursuit of just
how can models aid them within their
decisionmaking framework. Thus a
reader interested in models and, for
example, air pollution, will not do jus-
tice to the total material if only the
primer and the chapter on air pollution
is read. Do read all, or at least read the
nontechnical parts of all chapters so
that each author's viewpoint and con-
cerns are assimilated into a total view-
point.
As econometric models are of general
interest and are applicable to many
areas, a somewhat more detailed de-
scription of econometric models for
policy analysis is included as Chapter
12.
The fields selected for description in
terms of the use of models were chosen
for one of two reasons: (1) the field
was well-developed and could contribute
valuable lessons, or (2) the field is
important even though use of models is
embryonic and discussion here could
foster wider use. Each author describes
the critical decisions of his field, the
models which have proven of value in
analyzing some of the decisions, and
specific applications. This approach is,
not adhered to strictly in that each
author was allowed to define and de-
limit the scope of his field and to
present his discussion based on his in-
sights and understanding. Thus, in some
instances, authors add their assessments
and critiques if such discussions would
add to the reader's knowledge and if
such assessments could be made in a
succinct fashion.
Some chapters are more mathemati-
cal than others. We felt that a set
chapter format would be too restrictive
for the authors and too limiting for the
reader. A reader not interested in the
mathematical presentations can skip
those sections and still obtain valuable
insights into models in governmental
operations; the more technically in-
clined reader should allow more time
to the pursuit of models, especially
while reading the primer and the chap-
ters on air pollution and econometric
models.
In the structuring of a book for gov-
ernmental decision makers, we must
pay some attention to the scope of our
definition of decision maker and de-
cision problems. We sometimes inter-
change these concepts with policy mak-
ers and policy problems, or strategic
vs. tactical, or planning vs. operations,
high level vs. low level, etc. The primer
sets the basic definitions for decision
makers and their problems from a very
general point of view. We find many
applications of models to the decision
problems described in the Guide. How-
ever, there is a concern that models are
not being used to analyze significant
policy problems at the highest levels of
government, even though the applica-
tion of models here can be of great
value. The reasons for this lack of use
and an approach to overcoming the
deficiency are addressed in (Chapter 2)
"Models and Policy Making."
In sum, the Guide is an attempt to
present to a nontechnical, govern-
mental-oriented audience an overview
of what models are, and how they
have been used in a number of im-
portant social-urban areas. It represents
a source from which government
officials and others can obtain an under-
standing of this approach to decision
making.
SAUL I. GASS
ROGER L. SISSON
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Acknowledgments
The following publishers have given
their kind permission to use the cited
materials:
From AN INTRODUCTION TO
MACROECONOMICS by K. C.
Kogiku, Copyright 1968 by McGraw-
Hill Book Company, used with per-
mission of McGraw-Hill Book Com-
pany, pp. 43-53.
From THE ELEMENTS OF INPUT-
OUTPUT ANALYSIS by William
H. Miernyk, Copyright 1957 by
Northeastern University, Copyright
1965 by Random House, Inc., Re-
printed by permission of Random
House, Inc., p. 54.
Thanks are due to the many other
authors whose reports on their research
and applications of models served as
the basis for most of the material in
the Guide. The staffs of MATHE-
MATICA, Inc. (Bethesda, Maryland)
and its subsidiary, Government Studies
and Systems, Inc. (Philadelphia, Penn-
sylvania), were responsible for the crea-
tion, organization and editing of the
Guide. Appreciation is also due to the
following EPA personnel: Dr. Peter
House, Director, Environmental Studies
Division; Dr. Philip Patterson, Project
Officer; and Mr. Gene Tyndall. Finally,
sincere thanks to Ms. Carrie Scannell
and Ms. Sally Whipp of MATHE-
MATICA, Inc. for their assistance in
preparing the many versions of the
manuscript to typed copy.
IX
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The Authors
INTRODUCTION TO DECISION
MODELS
ROGER L. SISSON is the Associate
Director of Government Studies and
Systems, Inc. He received his M.S. in
Electrical Engineering from M.I.T. in
1950. His professional work is in design
and use of planning systems for public
institutions and in the development and
application of models to support policy
decision making.
MODELS AND POLICY
PLANNING
PETER W. HOUSE is Director of the
Environmental Studies Division, Wash-
ington Environmental Research Center,
U. S. Environmental Protection Agency.
He received his Ph.D. degree in Public
Administration from Cornell University.
For the past six years he has been in-
volved in the design and construction
of large-scale, policy-oriented models
for the Federal government, including
the CITY models and the RIVER
BASIN MODEL.
GENE TYNDALL is Chief of the Plan-
ning Coordination Division in the Office
of the Secretary of Transportation. He
received his B.A. in Economics from
the University of Maryland and M.B.A.
from George Washington University.
He has over eight years experience in
the design, development and application
of management science techniques to
policy-level problems, of which the past
three have been within the Federal gov-
ernment.
MODELS IN AIR POLLUTION
NOZER D. SlNGPURWALLA, Ph.D., is
Associate Professor of Operations Re-
search at George Washington Uni-
versity. He specializes in applied
probability and statistics with particular
emphasis on models for air pollution
and reliability. He is co-author of a
forthcoming book entitled Statistical
Methods for the Analysis of Reliability
and Life Data, John Wiley and Sons,
Inc.
MODELS IN WATER RESOURCES
DAVID HUNTER MARKS is Associate
Professor of Civil Engineering at the
Massachusetts Institute of Technology,
where he is a member of the Water
Resources Division and Director of
the Civil Engineering Systems Labora-
tory. He holds a B.C.E. and M.S. from
Cornell University and a Ph.D. in En-
vironmental Engineering from Johns
Hopkins University. His teaching and
research is in both the water resources
and systems areas; he is the author of
numerous papers on water resource
systems, water quality and environ-
mental management and is co-author
with Richard de Neufville of System
Planning and Design: Case Studies in
Modeling, Optimization and Evaluation
to be published by Prentice Hall.
MODELS IN SOLID WASTE
MANAGEMENT
JON C. LIEBMAN is Professor of
Environmental Engineering at the Uni-
versity of Illinois at Urbana-Champaign.
He received the B.S. degree in Civil
Engineering from the University of
Colorado, and the M.S. and Ph.D. from
Cornell University. He is the author of
a number of papers on modeling of
solid waste collection, and has served
as a consultant in this area.
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MODELS IN URBAN
DEVELOPMENT
JAMES C. DHLS is Assistant Professor
of Economics and Public Affairs at
Princeton University where he teaches
courses in urban economics and in
housing policy. He has an A.B. degree
in economics from Harvard College and
M.A. and Ph.D. degrees in economics
from the University of Pennsylvania.
PETER HUTCHINSON is Assistant to
the President's office, Irwin Manage-
ment Company. He has an A.B. degree
from Dartmouth College and a Master
of Public Affairs degree from Princeton
University.
MODELS IN TRANSPORTATION
and
MODELS IN THE FIELD OF
ENERGY
KENNETH W. WEBB is a private con-
sultant and a former staff member of
the Urban Institute. He has an M.A. in
Statistics from George Washington Uni-
versity. His research in transportation
includes the study of network simula-
tion with exploding queues and demand
peaking. In addition, he has written on
critical problems of transportation
modeling with regard to social effects.
He has consulted with a major oil
company on scheduling, manufacturing
and related problems. In addition, he
has designed a technology assessment
approach to total energy studies.
MODELS IN LAW ENFORCEMENT
AND CRIMINAL JUSTICE
SAUL I. GASS is a Vice President and
Director of the MATHTECH Division,
Washington, D. C. office of MATHE-
MATICA, Inc. He has a B.S. in edu-
cation and M.A. in mathematics from
Boston University, and a Ph.D. in
Engineering Science—Operations Re-
search. University of California, Berke-
ley. He was a member of the Sci-
ence and Technology Task Force of
the President's Commission on Law
Enforcement and the Administration of
Justice, and has conducted research
efforts dealing with the application of
operations research and computers to
the law enforcement area.
MODELS IN EDUCATIONAL
PLANNING AND OPERATIONS
EDMOND H. WEISS is a Senior Asso-
ciate, Government Studies and Systems,
Inc., in Philadelphia. He holds a Ph.D.
from Temple University and an M.A.
and B.A. from the University of Penn-
sylvania. Dr. Weiss is a consultant in
planning and management systems for
education, and is an elected member of
the board of education in Willingboro,
New Jersey.
MODELS IN PLANNING AND
OPERATING HEALTH SERVICES
BOYD Z. PALMER is a Senior Opera-
tions Research Analyst at Government
Studies and Systems, Inc. He has a
B.A. in Mathematics and Physics from
Earlham College and an M.S. in Opera-
tions Research from Case Institute of
Technology. He has developed models
for use in Comprehensive Health Plan-
ning, and has directed a project to de-
sign a simulation model of health serv-
ices in an urban area.
ECONOMETRIC MODELS FOR
POLICY ANALYSIS
E. PHILIP HOWREY is Professor of
Economics at the University of Michi-
gan. He earned an A.B. degree from
Drake University and a Ph.D. from the
University of North Carolina. His re-
search and consulting activities have
been in the area of national and re-
gional econometric models.
XI
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Chapter 1
Introduction to Decision Models
By
Roger L. Sisson
SUMMARY . 3
I. THE DECISION PROCESS AND THE ROLE OF MODELS 4
Who are the Decision Makers? 5
Styles of Decision Making 5
Operational and Strategic Situations 5
Decisions in Relation to Organizational Levels 6
Scope of Decision Making 6
Recurring or One-Shot Decisions 6
The Nature of the Phenomena About Which Decisions are Made 6
Concept of a Model 7
The Basic Decision Process 9
II. TYPES AND CHARACTERISTICS OF MODELS 9
Descriptive Models 10
Physical Models 10
Symbolic Models 11
Simulation Models 11
Use of Models 11
Prediction and Optimization Models 13
Deterministic and Probabilistic Models 13
Dynamic, Semi-Dynamic and Recursion Models 14
Continuity 14
Feedback 14
Degree of Aggregation 14
Representing Behavior in the Model 15
Some Standard Model Forms 15
Simulation 16
Econometric Models 19
A Simple Econometric Model 20
Input-Output Models 23
Mathematical Programming 24
Decision Trees 25
1
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III. How MODELS ARE CREATED AND TESTED 26
Recognizing the Need for a Model 26
Problem Definition 28
Choice of Analysis Method 28
The Basic Steps in Model Design 29
Model Specification . 30
Analysis of Data Requirements and Availability of Sources 31
Creation of the Model 32
Computation: Programming and Debugging 32
Model Verification and Validation 32
Model Use 32
Analysis and Presentation of Results 33
Implementation 33
Documentation 33
IV. PROBLEMS IN USING MODELS . 34
Defining Measures of Effectiveness 34
Aggregation 34
Data Acquisition . 34
Verification and Validation 35
Cost and Personnel Requirements 36
Setting Up the Model 36
Interpreting Results 36
REFERENCES . . 36
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Introduction to Decision Models
SUMMARY
Most of this book is directed toward
decision makers who have some infor-
mation about models and wish to learn
what kinds of models, relevant to their
areas of interest, are available and what
success has been obtained with them.
We recognize that there are also a large
number of public administrators who
would like the basic information about
models. The purpose of this chapter,
therefore, is to provide a very brief,
general background about models and
how they help decision makers.
Modeling is a sophisticated combina-
tion of art and science. No one should
expect to be able to understand it, even
as an informed observer, without many
weeks of study and actual practice in
design and application. We do believe,
however, that the flavor of modeling
can be obtained by reading this chap-
ter plus one or more of the subsequent
chapters, those which are in areas of
your interest. Every effort has been
made to keep the subsequent chapters
as free of jargon and mathematical
notation as possible. This chapter uses
technical symbolism only for one ex-
ample.
In order to keep the total book
within bounds it was not possible to
develop extensive examples in this ini-
tial chapter. We hope the interested
reader will read this chapter in con-
junction with discussions in subsequent
chapters which will serve as examples.
Excellent texts which are available and
are referenced throughout the chapter
should also be used by the serious stu-
dent in conjunction with this text.
This book deals with government
decisions which are consciously made
in complex and changing situations.
The decisions usually are to allocate
resources or to establish regulations or
legislation. These are made by elected
officials or by the heads of departments,
i.e. by policy makers. We also deal with
models to support some key decisions
made by agency and bureau heads and
program managers.
Models are computational proce-
dures designed to help the decision
maker and his staff predict the conse-
quences of proposed alternatives. In
some cases the model includes an op-
timizing procedure which computes the
optimal'alternative.
Section I of this chapter categorizes
decision processes and develops the
role of models in supporting decision
making. Section II is a classification of
types and characteristics of models pre-
sented in part to explain the terminol-
ogy used by modelers. The discussion
includes a description of the symbolism
by which models are expressed and of
the procedures by which they are used
to predict or optimize. Several model
types of most use in policy making are
described.
It is important for decision makers
to know how analysts develop and use
models. In fact, for proper results, it is
necessary for the decision maker to
interact with the analyst while the
models are being developed and used
so that he fully understands the results.
Section III describes how models are
created, how data is obtained, how the
models are tested and used in order to
help compare alternatives and perhaps.
equally important, to provide insights
for the decision maker.
The final section of this chapter re-
views some of the critical problems that
can arise in the use of models.
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If the reader has had no earlier con-
tact with the concept of modeling, we
hope that a thoughtful reading of this
chapter will enable him to read at least
the non-technical parts of the remain-
ing chapters. We also hope it will en-
courage him to delve into technical
areas of interest both within this book
and to read some of the references.
I. THE DECISION PROCESS AND
THE ROLE OF MODELS
The major theme of this Guide is the
use of analytical aids in the process of
making decisions. The making of a
decision—the choosing among alterna-
tives—can be viewed in many ways:
as a psychological event, as a socio-
logical drama, or as a process of
data and information manipulation. If
viewed in the latter way, the case we
are considering, it becomes reasonable
to consider mathematical, logical, com-
putational and informational processing
aids for improving the quality of the
decision. We further assume that the
decision maker is conscious of making a
choice, although this is not always true.
Among the mathematical-information
aids, we shall be concerned with those
termed models which are used to evalu-
ate alternative decisions, and which can
be applied to a wide range of important
situations.
Where decision making is more than
just impulse and guess work, it is pre-
ceded by some sort of analysis. If the
analysis is made entirely by intuitive
cogitation, then the concept of a model
is not applicable. If, however, the anal-
ysis preceding the decision is an explicit
activity, capable of being described,
then models can improve the analysis
and the results of the decision.
Decision making, especially where
more than one person is involved, does
not always occur at a sharply defined
point in time. Some decisions evolve.
Nevertheless, if any formal study pre-
cedes the period of decision, then a
model may be of assistance in produc-
ing information for'weighing the avail-
able alternative choices and probable
result. Thus, this book deals with proc-
esses that involve the sequence of
events: analysis, decision, action.
We illustrate the process for two de-
cision situations which are of major
concern to all levels of governmental
planning and operations: resource allo-
cation and regulation setting. In most
decision situations an allocation of
some resources must be made, Figure 1.
The resources may be dollars (budget),
manpower, facility or equipment ca-
pacity. The allocation may divide the
available resources among a number of
potential resource users such as agen-
cies, programs, projects, services, de-
partments, locations, client groups, or
even individual clients. The allocation
may also establish the resources to be
available in various time periods.
A second type of decision, creating
or changing regulations, often precedes
and constrains the resource allocation
problem, Figure 2. Examples of such
decisions are: set acceptable pollutant
levels or establish prices for scarce
resources.
We next discuss some of the char-
Types of Recipients
Resources
to be
allocated,
e. g. dollars,
manpower
Decision
Process
"^
i^
Project
JProject
Client
Groups
Locations
FIGURE 1—Resource Allocation Decision Situation
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Regulation Decision Situation
Regulations
Resources
Allocation
Decisions
FIGURE 2—Regulation Decision Situation
acteristics or dimensions of decision
makers and decisions.
Who are the Decision Makers?
In government the decision makers
are usually well identified. They include
elected officials, agency, department
and bureau heads and program man-
agers. Congress and other legislative
bodies obviously make many important
decisions, both regulations and alloca-
tions. Elected officials are sometimes
distinguished from other decision
makers by calling them policy makers.
In the chapter on "Models and Policy
Making," policy makers are defined as
the group of persons who make the
principal decisions which guide the
public sector, and the process of policy
making is defined as those actions taken
by elected officials or their immediate
staffs. The process of policy making at
this highest level is differentiated from
that at the department level by the
scope of the problems and issues and
the necessity to take into account the
basic values of the whole society. This
book emphasizes policy decisions.
Governmental decision makers may
act individually, but more often than
not they involve their staff and advisors.
In some cases a task force has decision-
making power, but usually the mission
of a task force or a committee is to
perform the analytic work preceding a
decision.
Styles of Decision Making
Another dimension of the decision
process is style, ranging from the least
analytic to the most. Some decisions
are made naively, even impulsively with
no conscious thought involved. Deci-
sions by experts or by good managers
are presumed to involve some cogita-
tion or judgment; some mental analysis.
Models are valuable in supporting
those decisions which must be made in
relation to complex and changing situ-
ations, where even informed judgment
will not lead to the best possible re-
sults. Certainly, many situations facing
government are of this nature. Models
are important for many situations in
government where it is either impos-
sible or beyond fiscal feasibility to pilot
test a range of ideas; that is, to perform
experiments on proposed alternative
programs to confirm which decision
would be best. Nevertheless, where
feasible, experiments are justified to
provide a basis for decisions which have
major, long-term effects on the clients
of the jurisdiction involved. This is be-
coming an accepted approach in some
social welfare areas and there have
been experiments to evaluate alterna-
tive welfare, medical insurance, and
housing subsidy plans.
Operational and Strategic Situations
A distinction is usually made be-
tween decision problems of an opera-
tional or tactical scope and those of a
strategic or policy nature. Policy deci-
sions almost always change relation-
ships between other decision makers.
Policy decisions directly or indirectly
change who can decide what. The most
useful way of recognizing the distinc-
tion between strategic and operational
is by determining whether the actions
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which result from the decision can be
reversed (or the effects of these actions
compensated for) in the relatively short
run, say within a year. The decision to
assign an employee to a particular posi-
tion within an office is a reversible,
operational decision, since the em-
ployee can, without too much difficulty,
be reassigned in the next month or the
next year. On the other hand, consider
a decision by a State to initiate a major
rehabilitation service which requires
the acquisition (long term lease or
purchase) of a facility, the hiring of
employees with at least implicit tenure
and the raising of public expectations.
This is obviously a long term, strategic
commitment. It would be hard to re-
verse this decision within a month or
even within several years of the date
the program is initiated. It is important,
of course, to make good decisions in
either case.
Decisions in Relation to
Organizational Levels
Generally, operational decisions are
made at the lower levels and policy
decisions at the higher levels of any
organization. The right to make policy
decisions is restricted in most organiza-
tions to certain top level positions
through mechanisms such as budget
approval, or limitations on the amount
of money that can be committed on
any one decision, or by the imposition
of special review committee structures.
Decisions at lower levels tend to be
prestructured by custom or by written
procedures which are established by
higher level decision makers to insure
that routine decisions are made the way
they want without having to review
every one. Where a decision-making
process can be completely defined, it can
often be automated with the aid of
modern computers.
Scope of Decision Making
Another dimension to the decision
process is the scope of the implications
of the decision. Some decisions involve
only a specific person or work unit.
A decision on how to locate offices
within space assigned to a department
has practically no consequences beyond
that department. At the other extreme
are all the global decisions made, say,
by the U.S. about foreign commitments
and activities. Scope is not always lim-
ited just because the level of govern-
ment is low. For example, a decision
made by a planning committee of a
township in regard to sewage disposal
can affect the environmental quality
throughout a whole region.
There are also differences in "func-
tional" scope, represented by the dif-
ference between "policy setting" and
"planning." We have defined a policy
decision as one that changes the struc-
tural relationships between decision
makers. Obviously the creation of a
new department or agency is a policy
decision. The introduction of major
new legislation which, by implication,
causes changes or additions in organi-
zation is also a policy. The introduc-
tion of national health insurance, for
example, would be a policy decision,
because it would have significant effect
on the organizational arrangements
both in health insurance and in health
delivery. Planning decisions, although
having long-term consequences do not
affect organizational interrelationships.
Recurring or One-Shot Decisions
Some decisions are made very rarely
(yet usually are the most critical), such
as decisions to institute a new program,
to construct a major facility or to
change a basic policy. Others are made
annually such as to allocate funds
through a budget. Some are made more
often, such as to pursue particular
alleged offenders of a pollution law.
Since using a model may require a
major initial investment in design, test-
ing and data collection, it is sometimes
hard to justify its use for a one-shot
decision. The justification in these cases
lies in the importance of the decision.
The Nature of the Phenomena About
Which Decisions are Made
Because we understand the physical
world much better than we understand
human behavior, it is useful to distin-
guish decisions which have the effect of
-------
allocating physical resources from those
which allocate human resources. It is
also useful to distinguish those cases
where human behavior significantly in-
fluences the decision from those where
it does not. Most decisions made by
government agencies are somehow in-
fluenced by human behavior, and this
is one of the reasons why decision
making and the use of supporting
models is difficult in public administra-
tion.
An analogy might be appropriate
here. In the physical world we know
that if an object, Figure 3, is at rest
and forces are applied to it in the di-
rection and magnitude of the vertical
and horizontal arrows, the resultant
effect is that the object will move in
the direction of the diagonal arrow.
Our physical model predicts the result
with certainty. However, if a sailor just
in from a six month sea duty is the
"object" and the forces are the attrac-
tion of two pretty girls in two direc-
tions, we cannot predict the resultant
action of the sailor. We must approach
the use of models for prediction of
human behavior with caution!
With the above characterization of
decisions in mind, we next turn to the
nature of models and their relationship
to the decision process.
Concept of a Model
A model is a way of abstracting the
real world so that, not only the static
picture of the world is obtained, but
also the dynamic (time) interrelation-
ships are represented. With an appro-
priate model of a real world situation,
we should then be able to predict cer-
tain outcomes or determine how the
real world would behave if we imple-
mented a particular alternative deci-
sion. In some instances, our model will
enable us to select the best or optimum
Object
Force 2
Force 1
decision. This book is concerned with
models as they are used in decision-
aiding analysis. Therefore, "model"
never means "example" or exemplary
case. In the literature, especially in the
social fields, the word "model" is often
used in this second meaning: as in a
"model reading program," a "model
environmental control policy." Such
examples may be useful in defining a
possible alternative, but are not models
for prediction or optimization.
The models of use in informed
decision-making tend to be quantitative.
The interrelationships depicted by the
model can be expressed in numerical
terms, e.g. the relationship between a
coal burning source and resultant pol-
lution per ton of coal burned. How-
ever, appropriate methodology also
exists for representing many qualitative
factors.
Models have two major components:
variables and relationships. In many
real situations, it is possible to enumer-
ate thousands of relationships and/or
variables. The skill of the model builder
enables him to capture the essence, only
the important variables and relation-
ships, so as to produce a meaningful
and useful model. The creative input
to the modeling process, the art of
model building, is in translating a per-
ception of the world into the essential
relationships and variables, and thus
into a model which is tractable and,
hopefully, computationally manageable.
In the model, the variables represent
either (1) values; numbers which are
real world levels, counts, measure-
ments, budget allocations, physical
quantities, the results of survey instru-
ment measurements, etc., or (2) codes
which identify projects, items, units,
people, groups, proposals, etc. The
codes in turn can take on values such
as zero if a project is not to be funded
and a value of one if it is to be funded.
The relationships (equations, con-
straints) are expressed as procedures
for computing the values of certain
variables, given values of others; usu-
ally for computing the values of vari-
ables at a future time given the values
-------
at a present time. These computational
processes represent the real interactions
characterizing physical interconnections
(the wear on a vehicle as it is used),
economic relationships (the relation-
ship between the demand for an item
and its price), behavioral interactions
(the effect of information produced by
one group on the actions of another
group) and many others.
A model represents some segment of
reality. H is important to recognize the
boundaries which define what is to be
represented by the model. The included
activities or structures are usually re-
ferred to as the system being analyzed.
Sometimes these are further divided
into related activities or subsystems.
The boundaries may demarcate geo-
graphic or political limits, a temporal
span, client groupings, funding arrange-
ments, or behaviors or several of these.
That which is outside the system is
termed its environment.
In nearly all models it is found that
the variables can be classified into four
categories.
(1) Controllable Variables. These
are variables whose values can
be determined by the decision
process. (For example, in a
vehicle replacement problem,
the factor we can determine or
control is when to trade in the
old unit for a new one.)
(2) Uncontrolled Variables. Many
of the variables in a situation
are not under the control of the
decision maker (otherwise the
problem would be trivial).
Uncontrolled variables include
physical phenomena (wear on
a vehicle and, therefore, fre-
quency of maintenance), vari-
ables which result from the
actions of others or certain eco-
nomic parameters, which are
determined by the actions of the
production and consumption
processes in the country (e.g.,
price of a new vehicle).
(3) Results or Output Variables.
These are variables characteriz-
ing the results of processes in
the real world. (In the vehicle
replacement situation a main
output is the total cost of op-
eration).
(4) Utility or Value Variables. The
decision maker will set a utility
or value on the results of the
process.
Uncontrolled variables are of two
types: those whose values are com-
puted in the modeling process and those
which are inputs to the model. The lat-
ter represent the effect of the environ-
ment on the system; the action of the
world outside penetrating the system's
boundaries. For the model to operate,
it is clearly necessary to obtain esti-
mates of the values of these input vari-
ables over the time span of interest. In
some cases, these are known from ex-
isting data (such as the average cost of
a particular kind of maintenance opera-
tion). In other cases, data about the
future is required (such as the amount
of trash that will be generated in a
given area per week over the next five
years). Estimating values of these un-
controllable variables may be done by
other agencies, such as economic agen-
cies or the Census Bureau. Or the
analyst may use forecasting processes
subsidiary to the model itself. Some
modeling theorists believe that every
model should be self-contained and
should not require subsidiary forecasts
or inputs. Such models, which include
their environments, are termed holistic
[13].
With any uncontrolled variable there
is a certain degree of uncertainty: the
estimates are never exact. Sometimes
the estimates are sufficiently accurate
and have a sufficiently small amount of
variation so that we can assume they
have a specific value. This leads to
what are called deterministic models,
the uncontrolled variables are assumed
to be determined.
More often some of the uncontrolled
variables are difficult to estimate or
there is a variability which exists in the
real world. (The amount of refuse gen-
erated in an area is not constant but
varies from week to week.) In these
circumstances, the most accurate model
(not necessarily the most useful) will
-------
represent the variables as statistical
quantities and take the variations spe-
cifically into account. These are known
as probabilistic or stochastic models.
The utility or value variables are
computed by a formula from the result
variables; the formula is called the
objective-function. Note that the as-
sumption is that there is one measure
of value. In some studies this value is
measured in dollars, however, in many
situations, particularly in governmental
applications, the measure of value is
more complex. Indeed, in many cases
there is no single measure of the utility
of the outcomes (this is termed a
"multi-objective" situation). Whatever
is chosen as an indication of value
however, it is an important variable to
be computed in the modeling process.
The controllable variable values which
give the best available utility are said
to be the optimum.
The Basic Decision Process
In most cases the model builder as-
sumes the decision problem to be of
the following nature: Find the values
of the controllable (decision) variables
which produce the greatest utility
(value) as measured by the utility vari-
able^) given the assumptions about the
uncontrolled variables. For example,
what is the best time to replace a ve-
hicle to obtain the least total cost—
the utility measure—given data about
vehicle price and depreciation, main-
tenance requirements and cost and
vehicle usage? The utility is com-
puted from the result or output vari-
ables (costs, in the example) estimated
by the modeling process.
Decision Theory is a title given to
the general mathematical study of this
class of problems. Operations Research
is the study of specific applications of
decision theory using mathematical
tools. Management Science is the appli-
cation of the results of decision theory
and of operations research studies to
specific management situations. (The
terms management science and opera-
tions research are often used inter-
changeably, so that the definitions just
given are not always clear cut unless
the context is specified.)
Let us consider the model-builder in
a practical situation. He must first
identify the variables and then con-
struct relationships (equations, compu-
tational processes) that interconnect
the variables. In the most ideal case his
work is facilitated by two sorts of
theory: (1) theories about the physical
and behavioral phenomenon in the
situation, derived from physical, psy-
chological, and sociological research;
and (2) theories about the structure of
the specific management process de-
rived from operations research work.
The theoretical results, if available,
indicate to the model builder what are
the most important variables, what are
the relationships between them (in
precise, computationally feasible form)
and what procedures can be used to
find the decision (controllable) values
which will give the greatest utility.
All modeling processes allow us to
compute present and future values of
operating or result variables. Some
allow us to compute the utility-optimiz-
ing controllable values. The latter is
known as optimization; and (when
considering situations over time) the
former is called prediction.
II. TYPES AND CHARACTER-
ISTICS OF MODELS*
The basic types of models available
to an analyst can be classified by the
manner in which they are expressed:
descriptive, physical, symbolic and pro-
cedural. The latter two forms include
those models which are more relevant
to government planning and operations.
Any explanation of modeling meth-
odology has two parts. The first part
describes the form in which the model
is to be expressed; the second part
describes the way in which the model is
to be used to make predictions (or
optimize) and to aid in the decision-
making process. Factors used to evalu-
ate modeling methods include the rela-
* This section adapted from Emshoff, Sis-
son, Design and Use of Computer Simulation
Models, New York, Macmillan, 1970.
-------
live cost of the use of the models, the
ease with which the models may be
communicated among technical people
and from technical people to practi-
tioners, and any special limitations on
the application of the models. Table 1
is a taxonomy of model types based on
these factors.
Descriptive Models
Descriptive models (which are ex-
pressed in native language) have many
limitations, perhaps the greatest being
that the method of prediction is usually
internal and thus cannot be communi-
cated nor easily replicated. The advan-
tage of descriptive models is that the
cost of making predictions is extremely
low; therefore, they are the most com-
monly used model for decision making.
The high powered, successful indus-
trialist of our folklore probably had an
intuitive sense for forming descriptive
models and for manipulating the re-
lated information to yield effective
decisions.
Physical Models
Physical models range from floor
plan layouts to complicated aircraft
wind-tunnel models. The method of
optimizing with physical models is to
search among alternative designs in the
following way:
• Performance criteria are estab-
lished.
• Estimates provide an initial com-
bination of controllable decision
variables.
• The model is then used to predict
the value of the performance cri-
teria under these conditions.
• A search rule, which incorporates
all results to date, resets the con-
trollable variables. The rule for
search is designed to move the
controllable variables in directions
that will lead to the greatest im-
provement in performance.
• When maximum performance is
found, the search has found an
optimum, and the values of con-
trollable variables that give this
optimum are the desired operating
conditions.
One significant advantage of the
physical model is the ease with which
its structure can be communicated to
people with a nontechnical background.
However, for modern decision-making
purposes it suffers from an inability to
represent information processes. Fur-
thermore, there is often a high cost in
the construction of a physical model,
and, usually, the model can be used
only for the particular problem for
which it was designed.
Table 1. Taxonomy of Model Types
Model
(Form of
expression)
Descriptive
(Native
language)
Physical
Symbolic
Procedural
Method of
Prediction
Judgment
Physical
manipulation
Mathematical
Numerical
approximation
Simulation
Method of
Optimizing
7
Search
Mathemati-
cal
Mathemati-
cal
Search
Cost
Low
High
Low
Medium
High
Ease of Communication
Tech-
nical
Poor
Good
Good
Fair
Non-
technical
Poor (appears
good but often
misunder-
stood)
Good
Poor
Good
Limitations
Cannot repeat
the prediction
process
Cannot repre-
sent informa-
tion processes
Needs previ-
ously developed
mathematical
structure
General
properties not
easily deduced
from the
model
10
-------
Symbolic Models
Decision analysis has made major
progress by the use of symbolic models,
[5]. These models employ concise
mathematical symbols to describe the
status of variables in the system and to
describe the way in which variables
change and interact. Predictions or
optimal solutions are obtained from
these symbolic representations by
means of mathematical, computational
and logical procedures, called deduc-
tive methods. The cost of using sym-
bolic models is often low as most
models of this type can be solved by
standard computational procedures.
The conciseness inherent in symbolic
models makes them particularly suit-
able for communication among tech-
nical people. On the other hand, the
symbolism is not familiar to the average
decision maker, and so communication
between the technical person and the
nontechnical person is difficult. (This
situation is improving, however, as
more people are becoming trained in
the use of mathematics and in symbolic
and computer languages.)
Simulation Models
The fourth model type identified in
Table 1 is procedural; however, it is
generally referred to as simulation. The
model is actually a procedure expressed
in precise symbols; the term simulation
refers to the method by which the model
is used to make predictions. In a sense,
every model is a simulation of reality,
but in this book, in consonance with
current modeling usage, the term is re-
stricted to mean the procedural model
and its execution process.
By means of a series of elementary
operations on the appropriate variables,
a procedural model expresses the dy-
namic relationships hypothesized to
exist in the real situation. These opera-
tions are usually stated in a computer-
like flow chart, but may also be ex-
pressed in the form of decision tables or
other procedural languages. The predic-
tion of outcomes is made by actually
executing the procedural steps with ap-
propriate initial data and parameters.
The execution process may be carried
out clerically, but it is generally done
using a computer. The computer is
programmed to perform the procedure
(which is the model); running the pro-
gram creates the prediction. Concisely,
then, a simulation is a model of some
situation in which the elements of the
situation are represented by arithmetic
and logical relationships and processes
that can be manipulated (on a com-
puter) to predict the dynamic proper-
ties of the situation.
In contrast to symbolic models, the
problems usually attacked by simulation
procedures do not lend themselves to
solution by standard computational
techniques. Thus for simulation as with
other model forms that do not utilize an
explicit mathematical calculus, appro-
priate combinations (solutions) of con-
trollable variables must be found by a
search process or some other form of
enumeration. Simulation is expensive in
terms of both the model preparation
time (although this has been reduced
significantly by use of simulation lan-
guages) and the cost of the computer
time necessary to make the predictions
during the search for the optimum. An
important by-product of a simulation
model is that, properly written, it fa-
cilitates explanation to people with a
nontechnical background. Simulation
models can be created for almost any
situation in which a researcher can state
precisely the relationships among vari-
ables, although it may be difficult to
obtain the data for such models.
This book is about symbolic mathe-
matical and simulation models and
their use in a wide range of govern-
mental decision-making settings.
Use of Models
Models may serve different purposes
in relation to specific analyses. At least
the model should be a predictor to help
the analyst predict the values of the
output variables (given the assumed un-
controllable input variables and specific
controllable or decision variables). The
model is used to answer "what if" ques-
tions of two types: (1) "what if we set
the decision variables at certain values?
11
-------
(e.g., 'what if we traded the vehicle
every five years')?" and (2) "what if
an uncontrollable takes on a different
value?" (e.g. 'what if maintenance rates
increase at 10% per year instead of
6%?'). The total decision problem is,
of course, to find the optimizing values
of the decision variables. If the analyst
has only a predictive model, then he
must use the predictor to search for the
satisfactory values- of the controllable
variables as described above. It is never
possible to try out all possible combina-
tions of values of the controlled varia-
bles. There are just too many in any
real situation. One can try a large num-
ber at random and pick the one pre-
dicted to have the highest utility, but
there are more organized ways for
searching for best values [11].
An optimizing procedure has two
characteristics: (1) it is a well defined
series of steps which, for real problems,
can be executed in a reasonable amount
of computational time; (2) there is a
mathematical proof which guarantees
that the optimum solution is found at
the end of the computational process.
There are some intermediate analytic
tools where the procedures do not meet
criteria (2), but can be shown to yield
good, nonoptimum values. These are
called heuristic procedures in that they
involve special logical, mathematical
and sometimes intuitive steps which are
based on the structure of a particular
problem and which have not been
shown to lead to an optimum solution.
Table 2 is a brief summary of some
decision situations for which models
have been developed. It is not meant to
be all inclusive. Most of the standard
models and their uses are described in
other chapters. An informed decision
maker should know enough about mod-
eling to recognize a situation for which
a model might exist. Models most rele-
vant to policy making are described at
the end of this section. The informed
manager should also understand the de-
ductive methods used to compute model
predictions, particularly calculus [14]
Table 2. Summary of Types of Decisions For which Models Have Been
Developed
Situation
Queuing, waiting
for service
Facilities that
wear out
Items stored for
future use
Allocation of
resources to
activities
Market place
distribution of
goods, money
or services
Determine whether
to obtain more
information before
a decision (by
survey or
experiment)
Competition for
limited resources
Decision
How much service
capacity and how
organized, priority
rules
Timing of mainte-
nance and repair
Amount and timing
of orders
How much of each
resource to allocate
to each activity
Price constraints,
market regulations,
subsidy levels, etc.
Amount to spend
on information
acquisition
Strategy to employ
Organizational
Level of User
Low
Low
Low
Medium
High
High
High
Model Name
Queuing, Sequenc-
ing, Simulation
Replacement
Inventory, Simula-
tion
Mathematical Pro-
gramming, (Linear,
Nonlinear, Goal) ,
Dynamic Program-
ming
Econometrics, Input-
Output, Industrial
Dynamics, Simula-
tion, Markov
Decision Trees,
Bayesian Analysis
Game Theory
12
-------
and the statistical methods used to esti-
mate factor values [15, 16]. Typical de-
cision problems which exemplify the
use of models are:
• A local sanitation agency operates
vehicles to collect refuse. One op-
erational decision it must make is
when to replace a vehicle. If the
vehicle is allowed to get too old,
maintenance costs become high.
But there is a real cost in purchas-
ing a new unit in terms of both the
purchasing process and early, large
depreciation in value. Thus there
should be some best or "optimum"
period after which the vehicle
should be replaced. This is a rela-
tively well-defined operational de-
cision for which models are rou-
tinely used, [1].
• A metropolitan air conservation
commission has the problem of set-
ting air pollution regulations affect-
ing the sulfur content of coal
burned in the area. A "linear-
programming" model was used to
evaluate the economic feasibility
of controls on coal by examining
all sources of coal pollutants in the
area's airshed, [2].
• A Federal Agency must consider
the question of setting the ceiling
price of natural gas. This is a prob-
lem in economics and use of an
"econometric" model can be of
value, [3].
Models vary greatly in terms of the way
they are constructed and the way they
operate. We next define a series of mod-
el characteristics. Knowledge of these
can help one to understand or select a
proposed model for a particular appli-
cation. These characteristics are used to
describe the models in the other chap-
ters of this book.
Prediction and Optimization Models
As we have pointed out the ideal
model has two aspects or parts, the first
part represents the real world and al-
lows us to predict how that world
might unfold (given certain assumptions
about both uncontrollable inputs and
about the decision or controllable vari-
ables). The second part then selects
from the feasible range of controllable
variable values the particular ones that
optimize or give us the most desirable
results. (The two parts are not always
clearly separate.) Some models accom-
plish both aspects and are called opti-
mizing models. Other models (because
of limitations on the state of the art or
the skill of the modeler) contain only
the predictive process. Usually a study
of the outputs provided by the model
will indicate quickly whether it makes
a prediction or finds an optimum. As
some optimization models, as well as
most other types of models, cannot al-
ways represent institutional and orga-
nizational constraints in an explicit
manner, these type of constraints must
be considered when attempting to apply
a particular solution.
Deterministic and Probabilistic
Models
In deterministic models it is assumed
that the exact values of all variables can
be computed and values of all param-
eters are known. In a probabilistic
model, at least some variables or param-
eters have an unpredictable random-
ness and must be represented as statis-
tical variables. If the model is dynamic
it might be termed stochastic, i.e., the
model includes random variables that
depend on some parameters, often a
time variable.
Probabilistic quantities, although not
known with certainty, are not complete
mysteries. What we do know about
them is usually characterized by a dis-
tribution. This tells us how often the
probabilistic quantity is likely to have a
certain value. A simple distribution is
shown in Fig. 4.
This variable has a value of four 50%
of the time, three 40% and five 10%
50--
40- -
30..
20
10--
0
345 ^variable
FIGURE 4—Frequency Distribtuion
13
-------
of the time. Distributions are charac-
terized by measures like the mean or
average; and by measures of the spread
of the distribution about the mean like
the variance or the standard deviation.
Dynamic, Semi-Dynamic and
Recursion Models
Most decision-making situations re-
quire a model which represents situa-
tions which change over time. Thus
most models are dynamic in the sense
that time is explicitly represented and
the variables change with simulated
time as they would (if the model is cor-
rect) in the real world. Most such
dynamic models are completely self-
contained, i.e. the model and other va-
riables change from time period to time
period automatically. There are a few
models however, which are only semi-
dynamic. That is the model computes
the transition from one time period to
the next, but then the analyst may in-
spect the output and adjust certain in-
puts and parameters within the model
before the next time period is computed.
This is done largely with the large, more
complex, econometric models designed
to represent the economics of an entire
nation. The complexity occurs largely
because the model has to represent the
various markets. The analyst introduces
factors into the model which are not
automatically modeled; factors having
to do with legislative and executive fiscal
and regulatory actions, strikes, or other
relatively unpredictable events. The offi-
cial designation of these semi-dynamic
models is quasi-equilibrium models.
Continuity
Another characteristic of models,
closely related to the level of aggrega-
tion, is the continuity of the variables.
Continuity, simply stated, means that
the variables move smoothly from one
value to another and do not jump
around, i.e. they can take on all frac-
tional values as well as integers. Many
elements which are actually discrete,
that is, can take on only unit values
like 1,2,3, , can be represented as
continuous. For example, the popula-
14
tion of the nation actually consists of
whole people but for national planning
purposes can be considered as an aggre-
gated continuous variable since we are
not interested in the exact value. Many
factors, however, cannot be represented
as continuous. For example, in assign-
ing individuals to jobs either the assign-
ment is made or not. The discontinuity
must be incorporated into the model.
Feedback
Feedback is a property of a model
and presumably of the situation it repre-
sents. Suppose a situation involves a
cause-effect chain:
B
D
but B is determined not only by A but
also by D
B
D
The D,B path is the feedback loop. For
example, suppose consumer attitudes
cause business levels which cause tax
increases, but tax increases cause
changes in consumer attitudes. We then
have feedback. If the feedback adds to
the earlier effect it is positive feedback
and often causes oscillations or cyclical
changes in activity. If it subtracts it is
negative feedback, and tends to increase
the system stability. Control theory is
the study of feedback systems, [13].
Degree of Aggregation
An important characteristic of a
model is the level to which it aggregates
real world phenomena. Obviously this
characteristic can be evaluated only in
relation to the kinds of situations to
which the model applies. For example,
let us consider models intended to assist
in making decisions about welfare allo-
cations. The most detailed model would
represent every individual who could
come into the welfare process. (In order
to represent the future, the model would
have to simulate the birth and life of
people as yet unborn.) The most aggre-
gate model would represent the entire
body of welfare recipients in the nation
as a single entity; perhaps by one vari-
able such as their income level (as is
-------
done in some econometric models). In
between is a range of model structures
which are more aggregate than the in-
dividual level but less than single rep-
resentation. A welfare model may be
disaggregate in terms of geographic
areas, in terms of social-economic char-
acteristics, in terms of current welfare
status, in terms of basic need, in terms
of age groups, etc. Obviously the more
aggregate models are simpler in that
they have fewer variables and few inter-
relationships. Thus aggregate models
are less expensive to use; they require a
less extensive data collection and pre-
processing, and they operate quickly
when computerized. On the other hand,
aggregate models stand a greater chance
of being unrealistic for they deal with
artificial groupings and not with direct
representations of reality. In fact, a
good deal of the art of modeling is in
how to aggregate so as to gain the bene-
fits of an efficient model and yet retain
useful and realistic representations.
Obviously the selection of the level
of detail in the model also depends
upon the nature of the decision. If we
want to make decisions about the allo-
cation of funds to specific agencies, we
must, of course, use a detailed model.
Representing Behavior in the Model
Some of the relationships in a model
may represent the behavior of people,
e.g., the way people decide what job to
take, the way in which a student learns,
the decision-making behavior of a for-
eign power, or the choice of transporta-
tion mode. In order to obtain a mathe-
matical or simulation model of such
behavior it is necessary to have a basis
of understanding the behavior. Often
such understanding does not exist, em-
pirically or theoretically.
In order to perform research on the
behavioral situation, the analyst tries to
study it in the real world by observation
and surveys. But often this is expensive
or infeasible. The analyst might then
try to use a partial simulation in which
the behavior is acted out by a real per-
son, but the rest of the situation is
simulated. When humans are used as
elements of a modeling process, the
model is called a game.
In a few cases the game may involve
the actual persons. For example, the an-
alyst may have welfare recipients mak-
ing decisions. More often however, he
chooses a surrogate (a college student
for example) to play the role of the
person being modeled.
Thus, in a game model many of the
aspects of reality are modeled by com-
putations; only certain of the behavioral
relationships are modeled by the hu-
man. Game models are rarely useful in
support of actual decision making be-
cause they involve too many unknown
assumptions and uncertainties. Their
main use is in training, research, or for
communication purposes.
The word gaming usually means the
use of game models as defined above.
Sometimes, however, it refers to the use
of a predictive model to try out (search
for) different alternatives. In contrast,
theory of games is a particular mathe-
matical theory which can be applied to
situations in which there are two or
more parties competing for resources.
To date there has been limited applica-
tion of the theory of games in the pub-
lic area.
Some Standard Model Forms
A manager should be acquainted with
the more common forms of models,
just as he should be acquainted with the
techniques of personnel management,
leadership or any other, phase of his
trade. In this section we will introduce
in as easy way as possible the most
common policy-decision-supporting
models, i.e. those of simulation, econo-
metric, input-output, mathematical pro-
gramming and decision trees. There are
several texts [5, 6, 1] that contain sim-
ple explanations of models for opera-
tional decisions.
Although some of the discussion
which follows next is of a technical na-
ture, it is felt that a close reading of
these model examples will enable the
reader to obtain a better understanding
of the material presented in this book.
As we have mentioned, a model can
have two parts: (1) the part that repre-
15
-------
sents the real world processes and al-
lows the examination of the effects of
changes in them and (2) the process for
optimizing. Policy situations are very
complex and for them only part (1), a
representation that facilitates prediction,
is often all that is possible. We do not
yet know how to optimize in any for-
mal way for most situations. Let us look
at the policy decisions and how the
models relate to them; see Table 3.
The four kinds of decisions shown in
Table 3 fall into two basic groups:
(1) the establishment of a new program
or constraint (including forecasting to
support such decisions) and (2) the al-
location of resources to existing pro-
grams. The latter decisions tend to be
much more specific, because the nature
of the programs are already defined
and their consequences are often clear
either from past experience or by logic
and deduction. In allocation there are
many complications, and we do not
wish to imply that allocation of re-
sources is simple, but it is less difficult
than the other group.
Most policy-supporting modeling
techniques fall into the general class of
simulation. The other model forms,
such as the econometric, differ from
general simulation only in that they
employ one or more theoretical rela-
tionships and, therefore, have a more
definite structure. The theory generally
deals with assumptions about how
groups of people will behave under spe-
cified circumstances. Perhaps the most
well-known of these is the supply-
demand relationship of economics,
which says that in a market situation,
as a product or service becomes scarce,
people will bid for it so as to increase
its price (and conversely).
In the case of model forms relevant
to policy decisions it is almost always
the case that the method of producing
the prediction is to execute on a com-
puter the relationships made explicit by
the model. That is, the computer is used
to calculate the model relationships
which in turn simulate (as best the
modeler can arrange it) the real process.
In the next few pages we will describe
16
briefly each of the important model
forms and try to show:
— the basic assumptions or theoie-
tically derived structure.
— how the model is constructed.
— how the parameters of the model,
that is, the constants, are esti-
mated.
— how assumed programs, alloca-
tions or changes are input into
the modal (to make it represent a
particular alternative to be stud-
ied).
— how the model is used or com-
puted in order to make a predic-
tion of what would happen given
the alternative.
Simulation
Simulation (which was described
above) is actually a general technique
for creating models and, in a sense, is
more general than any particular model
form [4]. In simulation the analyst
programs a computer directly to repre-
sent the situation under study. The only
limitation to the situations that can be
modeled are those which the analyst
imposes upon himself because he lacks
an understanding of the relationships
within the real situation. In addition to
most physical, chemical and biological
processes, human behavior can be mod-
eled if the analyst dares hypothesize
how the behavior of people can be rep-
resented. Researchers have modeled
such phenomena as:
— the results of election campaigns,
— the effect of advertising and pric-
ing of Pharmaceuticals on the
physicians' behavior in buying
them,
— an urban area including the ma-
jor functions such as industrial
growth, residential growth, trans-
portation, commerce and pollu-
tion,
— the whole world (of course, at an
aggregate level).
Many of the models discussed in other
chapters of this book are simulations.
The essence of simulation, and in-
deed most of these modeled forms dis-
cussed in this section, is the following:
the analyst can understand by observa-
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17
-------
tion, analysis or theory the relationships
between two or three factors. That is,
he can understand small bits of the to-
tal process. He, or the decision-maker
or anyone else has a difficult time, how-
ever, understanding the whole process
and making predictions about it. In the
simulation process these understandings
of the small parts of the system are as-
sembled in a precise way into a com-
plete model. The model then is more
likely to make a good overall predic-
tion because it is based on a series of
small, good understandings rather than
one large, poor one.
In the most basic form of simulation
time is represented as discrete points
(not a continuous process). The world
is viewed as a series of snapshots, with
the program computing the changes be-
tween snapshots. The time interval can
be any size (minute, year, decade) or
even unequal, e.g. to the next significant
event. The computations can represent
any change large or small. In one form
of simulation, called continuous, time
is always advanced in equal steps, small
compared to the phenomena under
study and the computations assume
that all variables change by a small
amount each period, an amount deter-
mined by explicit rate-of-change varia-
bles (which themselves can change a
little each time interval). Continuous
models are often useful in studying
long-term aggregate system behavior.
One of the most difficult aspects of a
simulation model is to determine its
validity. Since the model may be pre-
pared on the basis of one (or a small
group of) analyst's understanding of the
important relationships, its validity may
be more uncertain than models which
are based on more widely understood
and accepted relationships (that is, on
proven theory).
Because of the generality of simula-
tion there are no basic assumptions in-
herent in the technique. The assump-
tions are those which the analyst
incorporates and, therefore, it is very
important for any user of simulation
results to be fully briefed on those as-
sumptions.
The construction of simulations fol-
lows the process to be discussed in Sec-
tion III. The analyst first studies the
situation and gets firm in his own mind
the variables and relationships involved.
He then expresses these in a form which
facilitates the preparation of a computer
program. One such representation is the
computer flow chart; a series of boxes
which describe the computations which
represent the relationships in the model.
An aid to preparing the computer pro-
gram is a simulation language; a lan-
guage, in the usual sense, with verbs
and nouns and rules of grammar. A lan-
guage is designed to help the analyst de-
scribe a certain class of situations. The
most common simulation languages are:
— DYNAMO [13], for preparing
continuous simulation models of
socio-economic systems,
— CSMP [4], for preparing continu-
ous models; originally intended
for representing physical (me-
chanical, chemical, electrical)
systems, but useful for some eco-
nomic models,
— GPSS [4], for discrete models in-
tended for representing opera-
tional situations (e.g. traffic),
— SIMSCRIPT [4], actually a lan-
guage to aid the analyst; not really
a user-oriented language,
A user of a simulation model should
understand the essence of the simula-
tion language, if used, so that he can
communicate with the analyst about the
assumptions in the model. Most of these
languages have been designed to be
relatively easily understood because
their purpose is to describe the world
from the decisionmaker's viewpoint, not
from the programmer's.
Any of the available techniques may
be used to estimate the values of the
parameters in a simulation model. In
the complex situations which policy-
makers face, it is usually difficult to use
any of the formal methods of estima-
tion. Either there is not enough histori-
cal data available, it is not in the right
form, it is too expensive to obtain, or
the agencies which have the data cannot
make it available. Under these circum-
18
-------
stances the art of guessing at the values
of the parameters should not be be-
littled. Guessing at a series of param-
eters and then using these in a well
thought-out model to make a prediction
probably leads to better predictions (and
ones which are easier to understand and
test) than simply guessing at the over-
all prediction itself.
Alternative cases are set up by rede-
signing that portion of the simulation
which represents the changes that
would result from the proposed alterna-
tive. This can be a time-consuming task,
but is facilitated if the model is ex-
pressed on a simulation language. When
the simulation program has been de-
signed a computer program is prepared
to carry out the procedures. This may
be done by the analyst or a programmer.
Where the model has been prepared in
a simulation language, the translation
to the computer program is automatic.
The program is tested; the data repre-
senting the parameters and the initial
state is fed into the computer; the com-
puter program is executed for as many
time periods as desired. The output of
the computer is the desired prediction.
The simulation may be re-run a large
number of times in order (1) to get a
better statistical representation of the
prediction and (2) to examine a num-
ber of different alternatives.
Econometric Models
Econometric models are, in a sense,
simulations in which most of the key
variables and most of the relationships
between them are derived from eco-
nomic theory [23]. The other difference
is that econometricians usually insist
that the parameters in the model be de-
rived from carefully designed statistical
estimating procedures which use past
economic data as a basis. This fact, on
one hand, tends to increase the model's
validity, but, on the other, limits the
scope, since economic historical data is
readily available only for certain ag-
gregate phenomena. Econometric an-
alysts also are willing to make adjust-
ments to the model between each year
simulated on the basis of special in-
formation (e.g. predicted legislative
changes); so that there is some human
"tuning" of the model as it computes
predictions.
A market is a situation in which
prices, established by many individual
transactions, cause supply and demand
to come into useful relationship. There
are markets in consumer goods, indus-
trial capital goods, investment funds
(with interest rates being the price) and
in labor (with wage rates as the price).
Many State and Federal govern-
mental policies, as expressed in legisla-
tive acts, executive orders or commis-
sion rulings, are designed to alter or
constrain relationships in a market situ-
ation. Thus, models which can represent
and predict the consequences in such
situations are particularly valuable in
governmental planning. Econometric
models fill this role.
"Economists construct . . . models
to study the behavior of various
economic units in the activities of
producing, exchanging, and con-
suming economic goods. Economic
units are households, firms, gov-
ernments, etc. Macroeconomic
models are economic models that
concentrate on various groups of
economic units using aggregative
measures such as national income,
total employment, and the price
level. Each of these economic
units may have definite motives
such as maximizing satisfaction or
maximizing profits. . . . Macro-
economic models examine how the
interactions of various sectors with
different behavior patterns deter-
mine the aggregative magnitudes
of the total economy. Some mac-
roeconomic models go even fur-
ther and explore the possibilities of
influencing the aggregates to attain
desired goals by public policy ac-
tions." [23, p. 1]
The basis for the development of an
econometric model is assumptions
about how economic units behave.
"There are many simple theories
based on assumed motives of vari-
ous groups within the economy.
After all, assumptions come cheap.
If we know exactly what each
19
-------
group's motives are, then we can
fairly safely deduce the conse-
quence of interactions of these
forces. But not all motives are ap-
parent. For prediction we must de-
pend on observed behavior. A case
in point is the controversy con-
cerning the consumption function,
which over the years has produced
a variety of explanations" [23].
Consumption can be assumed propor-
tional to absolute income, income rela-
tive to others, preceived long term in-
come, etc. Many econometric models
have evolved over the past forty years.
At first they were largely used for theo-
retical development. Since about 1945,
they have been used for predictions in
support of policy-making, although, for
most applications they are in an ad-
vanced research or developmental stage.
Early models represented a nation as a
whole and were useful only for overall
Federal policy analysis. Current models
contain tens or hundreds of '"sectors."
A sector is an identifiable part of the
economy: an industry, a governmental
function, a group of households. Thus
modern models should be useful for
analysis of rather specific proposals.
Most models are for analyzing long-
term consequences of policy changes.
The scope of a model in regard to the
sectors of activity covered depends upon
the purpose of the analysis. Models to
assist in studying the effects of a river
basin development concentrate on en-
ergy production, those for natural gas
fuel policy on the gas and petroleum
sectors.
A Simple Econometric Model [23]
An econometric model views the na-
tion (or region) by a series of flows
shown in Figure 5. All flows are mea-
sured in dollars. As an example of an
econometric model, we consider the
simpler flow shown in Figure 6.
Personal consumption and industrial
investment are the only sectors repre-
sented. The sum of these two demands
is always met by the output of the na-
tion—the national produce (gross and
net being the same).
The behavioral assumptions are that
each group of actors (consumers, in-
dustrialists) make demand decisions
based only on past production levels.
Expe ndi tu res
Purchases of good
and services, G
I Interest paid
by consumers
FIGURE 5
(Adapted from the chart "The Flow of Income and Expenditures in the United States 1964,'
published by the Twentieth Century Fund, Inc., 1965. The chart reproduced with minor change1.
with the kind permission of the publisher.
20
-------
Consumers look at the last data avail-
able, the last period's production:
Ct = c0 + Cl Yw
Ct is the consumption in period t.
Yt_! is the national product in the
previous period (one before t).
c0 is the basic consumption (say,
for "necessities") unaffected by
past production levels.
cx is the marginal propensity to con-
sume; that is, the increase in spending
that occurs for a unit increase in dis-
posable income, which in turn, in this
case, is equal to the national product
since there are no corporate retained
earnings nor taxes. (This assumption on
the way consumption changes with dis-
posable income is only one of several
that have been hypothecated, and is
only an example.) cx is assumed to be
greater than zero (never spend less when
disposable income increases) and less
than one (never increase spending more
than the increase in disposable income) .
Now we model the investment sub-
system decisions :
It is the demand or requirements by
industry for goods, in period t, meas-
ured in terms of output.
i0 is the basic requirement, unaffected
by previous rates of production (e.g.,
for replacement of equipment).
Yt_! — Yt_2 is the change in product
based on the latest information available
(change from next-to-last to last pe-
riod).
it is the increase in investment (hence
output) for a unit increase in the
change in output. Notice that this be-
havior is related to changes, not levels.
Businessmen are assumed to be opti-
mistic and demand more when the prod-
uct has been increasing rapidly, less
when increasing slowly and actually
have a negative demand (reduce out-
put) when the product has been decreas-
ing. (Many other assumptions are pos-
sible.)
The third relationship represents the
market place; it says that supply equals
demand:
Yt = Ct + It-
Note that prices are not specifically rep-
resented, but are implied to have worked
to bring about this equilibrium.
We now have the relationships needed
to compute the way the product Y
Disposable
Personal
Income
(Business
Decisions)
FIGURE 6—Flow for Simple Econometric Model
21
-------
changes with time. If we assume con-
tinuity (very small, short periods) we
can use calculus to compute the "time
path" of Y. Or we can "simulate" by:
(a) assuming an initial value of Yt-1
and Yt_2 and then
(b) compute Ct from the first rela-
tionship
(c) compute It from the second
(d) compute Yt from the sum of the
amounts computed in (b) and
(c) and
repeat b, c, d for as far into the future
as we want to predict.
If we use calculus or run simulations
with different parameters, we will see
that there are four general shapes to the
time path: (Figure 7):
(1) stable change to a new level,
(2) stable change to a new level with
cycles or oscillations,
(3) unstable with cycles; product
ever increasing,
(4) unstable without cycles.
The cycles are due to the fact that
businessmen are assumed to act on
changes and hence can overshoot the
investment requirements.
All dynamic econometric models use
the form of reasoning of this example.
They just introduce many more subsys-
tems and relationships. Typically they
involve 15 to 150 equations.
Econometric models are so complex
that the process of constructing them
has become a discipline in itself. For
most policy analysis, existing models
are used. Construction of a model pro-
ceeds as described for simulation mod-
els, except that the designer consciously
invokes economic principles in prepar-
ing the equations. He also estimated the
parameters carefully, as we have said,
using formal statistical methods; often
developed by the econometrician.
Alternatives are introduced into the
model by changing the appropriate
parts and parameters. (If the models
available do not explicitly contain the
sectors affected by the proposed
changes, a new model must be de-
veloped; a major effort. Since most
existing economic models do not sepa-
rate certain public functions, such as
health, their use by government policy
analysts has been limited.)
The econometric models are used in
the same way as simulation models; the
computer computes the predictions year
by year.
National
product-
dollars
t
time
FIGURE 7
22
-------
Input-Output Models
The basis of an input-output model is
a table which shows the relationships,
in dollar terms, between the inputs and
outputs of each sector of the economy
[36]. It is a highly-structured form of
an econometric model (see Table 4).
The entries in the table show for exam-
ple, how much of the output of the steel
industry is used by the automobile
manufacturing industry and how much
of its output is used in transportation
services that are used by the steel and
other industries. Also shown are the
ultimate demand: inventory accumula-
tion, exports, government and private
purchases and capital formation. Inputs
in form of payments from such sources
into the economy are represented.
Input-output models are used to an-
swer certain specific but important eco-
nomic policy questions. For example,
they can be used to make comparisons
between nations. This could help under-
developed countries determine the types
of investments which would be most ef-
fective in stimulating growth. The input-
output model can be used for studying
the level or nature of the aggregate de-
mand that would be required to achieve
full employment (although full em-
ployment depends on other factors not
always represented in the input-output
model). These models are particularly
useful in making a consistent short-term
forecast; consistent in the sense that the
inputs and outputs to each sector have
the proper relationship to each other.
France uses an input-output model as
one tool for making forecasts of the re-
quirements of each industrial sector.
Input-output models can be used to
study the effects of public programs
such as public works or space programs
on employment in industrial production.
To use input-output models for long-
term forecasting requires some sophisti-
cation because they are basically static
models. Some method of changing the
factors within the model to reflect
changes in technological developments,
for example, are required if proper
long-range forecasts are to be made.
Input-output models have been used
to study regions of smaller size than the
Table 4. Hypothetical Input-Output Transactions Table
Sector Purchasing
(in Billions $)
Processing Sector
Final Demand
>* Outputs1
(1) Industry A
(2) Industry B
(3) Industry C
(41 Industry D
(5) Industry E
(6) Industry F
(7) Gross inventory
depletion (— )
(8) Imports
(9) Payments to
government
(10) Depreciation
allowances
(11) Households
(12) Total Gross
Outlays
(11
A
10
5
7
11
4
2
1
2
2
1
19
64
(2)
B
15
4
2
1
0
6
2
1
3
2
23
59
(3)
C
1
7
8
2
1
7
1
3
2
1
7
40
(4)
D
2
1
1
8
14
6
0
0
2
0
5
39
(5)
£
5
3
5
6
3
2
2
3
1
1
9
40
(6)
F
6
8
3
4
2
6
1
2
2
0
12
46
(7)
Gross
inventory
accumula-
tion (+)
2
;
2
0
1
2
0
0
3
0
1
12
(8)
Exports to
foreign
countries
5
6
3
0
2
4
1
0
2
o-
0
23
(9)
Government
purchases
1
3
1
1
1
2
0
0
1
0
8
18
(10)
Gross
private
capital
formation
3
4
3
2
3
1
0
0
2
0
0
18
(11)
Households
14
17
5
4
9
8
0
2
12
0
1
72
(12)
Total Gross
Output
64
59
40
39
40
46
8
13
32
5
85
431
•o
o
'Sales 10 indUMmsarld M.U
'Purchases from industries
lop of Ihc table from the industry lisied in c.n-ti row HI the left of Ihe I.ible
I [he lefl of [he [able by Ihc industry listed at Ihe [op of each column
' From Miernyk, Wm. H., Input-Output Analysis, Random House (5th printing 1967).
23
-------
entire nation and even specific agencies,
such as a hospital.
The preparation and use of input-
output models are essentially the same
as for any econometric model. Some
simple alternatives can be analyzed by
paper and pencil studies.
Mathematical Programming
In a situation to which mathematical
programming applies, the following fac-
tors are assumed to be identifiable:
activities—processes or services which
must be carried out to accomplish de-
sired results,
resources—materials, consumables or
processing capacity which is available
in limited or constrained amounts,
outputs—the results of the activities;
these are usually implicit in the levels
of activities,
a utility measure—which indicates the
overall value of producing the out-
puts,
coefficients—factors or parameters
which measure how much of each re-
source is used for one unit of each
activity, and
weights—which indicate the addition
to the utility measure for a unit in-
crease in each output.
In our earlier terminology, the levels
chosen for the activities are the control-
lable variables. The maximum amounts
of each resource, the parameters, and
the weights are the uncontrolled vari-
ables. The parameters are usually de-
termined by the technological charac-
teristics of the processes, the weights by
economic factors and the resource con-
straints by previous capital expenditures
or resource limitations. The relationship
between outputs (and weights) and util-
ity is the objective function [22].
As an example of mathematical pro-
gramming from the public sector, the
activities might be the application of
controls on pollution. The more con-
trols that are introduced the higher the
level of the activity. The resources used
are funds, materials and space con-
straints which limit the extent to which
controls can be introduced. The outputs
24
are the reductions in pollutants. The
utility is the benefits of reduced pollu-
tion; better health, etc. Utility might be
estimated by assigning weights to reduc-
tions in pollutants which gives an over-
all estimate of the value of the re-
duction. For example, it might be more
important to reduce sulfur dioxide than
particulates. The utility function then
might contain weights such that sulfur
dioxide reductions were weighted by a
higher number than particulates.
For every unit of control introduced
a certain amount of each of the re-
sources is used. The coefficients indicate
the extent of this usage. If the utility
and resource relationships are all linear
(that is, there are no economies of scale,
no diminishing returns or other such ef-
fects) then the situation can be repre-
sented by a linear programming model.
Optimizing solutions for such linear
cases can almost always be found.
Where one or more of the relationships
are not linear, then we have a non-linear
mathematical programming problem.
Optimizing solutions can not always be
found for these. However, stating a
problem in the form of a non-linear
mathematical programming model may
be useful in suggesting the nature of the
optimum or indeed in finding one by
some special means.
Mathematical programming models
are highly structured, unlike simulation,
and are generally applicable only in well
defined cases where resources are allo-
cated to pre-defined programs or activi-
ties.
With linear situations, computer pro-
grams already exist which find the op-
timum. The analyst merely has to
choose the proper computer software,
introduce the data which represents his
model and submit the program to the
computer. There may be the usual diffi-
culties in getting the data in the right
form. But the use of linear programming
is generally simpler than for other
models.
For nonlinear situations a few spe-
cialized optimizing programs exist. If
the analyst can use these he can usually
-------
expedite the development of the opti-
mizing process. Solutions to nonlinear
problems, however, use large amounts
of computer time and, therefore, are
not always justified.
A good introduction to linear pro-
gramming is reference [22].
Decision Trees
Decision trees are a simple form of
simulation which is structured by ag-
gregating future activities into major de-
cisions and their consequences [6]. The
model represents only three basic vari-
ables : (1) the probability of each of the
possible consequences of decisions,
(2) the cost and (3) the benefit, usually
measured in dollars of each possible
consequence. The purpose of a "tree" is
to estimate the expected or probable
value of taking each of several alterna-
tives at intermediate decision points. A
tree can incorporate estimates of the
immediate and future costs that will
arise because of the decision and of the
consequences of future decisions.
A decision tree may be looked at as
an overall model of the possible conse-
quences of a decision. Other more de-
tailed models would be used to obtain
the estimates of the probabilities, the
costs and the possible benefits from
each of the alternatives. Figure 8 shows
a typical decision tree, describing a sim-
ple and more detailed model of the pos-
sible alternatives and consequences of a
pollution control or education program.
The main mathematical process used
in the decision is Bayesian statistics. Ini-
tially subjective estimates are made of
the probabilities of various conse-
quences. Then the Bayesian statistical
method is used to get more refined esti-
mates of the probability of the combina-
tions or sequences of activities. This
gives the net estimate of benefit by
computing the probable total benefit
minus the probable total cost of each
alternative.
One of the main uses of this analysis
is to help determine the value of addi-
tional information about a situation. In
order to do this it is necessary to have
some estimate of the probable outcome
an information gathering effort, e.g., a
major survey. This combined with the
basic decision tree information, allows
an estimate of the probable change in
the overall outcomes, if the information
were to be collected. Since it is usually
easy to estimate the cost of the infor-
mation collection, it is possible to weigh
this against the probable change in the
benefits to determine if the information
collection effort is worthwhile.
The main assumptions in use of deci-
sion trees is that the future can be sum-
marized by a sequence of activities
followed by decisions and that the al-
ternative consequences of each decision
can be identified. It also assumes that
the required data can be estimated.
Construction of the tree is extremely
straightforward. It involves simply
drawing the tree on the basis of infor-
mation available about the alternative
sequences of events that are likely to
take place in the future. The sequences
of events can be derived from either
the results of another modeling effort or
on subjective estimates of the decision
maker and staff.
In some cases data about the proba-
bility and costs of each activity is avail-
able from other studies. Often in a de-
cision tree analysis, the estimates are
made by the subjective input of the
staff, experts, and the decision maker.
Various techniques have been developed
to elicit from decision-makers estimates
of the probability of alternative events
occurring in such a way as to obtain fair
and unbiased estimates.
The computations for a tree can usu-
ally be done by pencil and paper al-
though computer programs might help
in a very complicated tree.
A decision tree analysis might be a
good model to use both at the begin-
ning and at the end of a more exhaus-
tive analysis. At the beginning it can
help pinpoint the decisions that need to
be made, their probable consequences
and to determine whether the overall
analysis effort has any value. At the end
it is a useful device for summarizing the
25
-------
results of detailed studies to get again
a picture of the overall cost-benefits
from the decision.
III. HOW MODELS ARE
CREATED AND TESTED
In order to clarify the nature of mod-
els and of the process of modeling,
this section presents a review of the
steps which an analyst may go through
to create and test a model, and then to
use it to help the decision maker. All of
the steps which can occur will be men-
tioned, but not all of them are required
in any one case. In some cases the
tested model exists and its use can start
almost immediately. (For application of
the process to specific problems refer to
the literature cited at the end of this
chapter and to the use of models de-
scribed in the other chapters.)
Recognizing the Need for a Model
We cannot give a rule for recognizing
the need for a model in any given situa-
tion. Up to this point in our discussion
we have asked the reader to assume
that a special and important class of de-
cision-making aids, termed models, has
been shown to be of value in making
decisions of substance. We are the first
to recognize that this assumption is not
always true. There are many specific
problems for which models as presented
in this volume do not provide useful in-
puts. We do feel, however, that decision
makers and their staffs must be in a po-
sition to determine if and how a deci-
sion problem can be resolved more ef-
fectively by the analytical power of a
model. As part of the attack on any
such problem, there should be a con-
scious choice to investigate or to not
investigate the suitability of a model.
This chapter, and the descriptions in the
succeeding chapters of how models
have been of value, is directed towards
improving the quality of this conscious
choice. Decision makers and their staffs
must rely on their previous experiences,
and on professional contacts, reading
and training to determine those situa-
tions for which models and related
methodology are applicable.
26
Suppose that the decision maker be-
comes convinced that a model could be
helpful. What happens next?
Analysis often begins as a result of a
specific management directive. When
the problem-formulation phase is ini-
tiated through management's actions,
the assignment may be vague or quite
specific; if it is specific it may be right
or wrong. The analyst might be told to
"see if we can reduce the cost of operat-
ing our vehicles" or he might be spe-
cifically told that "we need another ve-
hicle, prepare a justification for it." The
second directive might actually be
wrong, since a detailed study could
show that better scheduling and routing
rules would increase production as
much as adding a vehicle and would do
so more cheaply. When the analyst re-
ceives very specific directives, he is un-
der some organizational pressure to
carry them out. However, he should be
R«9,.».te Value ». t (1000) '•"'" 2
,). 4[IOOO)-200«'-?0
( ) Probt-b.l.ly of C«ije.c»_o«nc.«.
[ ] Cost °-f Alternative
FIGURE 8—Decision Tree Examples
-------
Realistic
Key Decision Being Ar\alyz.ed
( ) Consequence. Points
Probable. Future. Decisi'on Points
Nat
Benefit
CDollar
Va.lue.o-f
Reduced
Pollution)
-200
12.00
-ZOO
ooo
£00
000
( )
Conseq.uer.ce
FIGURE 8— Continued
27
-------
aware that doing this may result in a
suboptimal solution. If preliminary anal-
ysis indicates that this is the case, the
analyst should be sure the decision
maker is willing to forego the chance of
a better solution.
It is important to keep in mind that
the first time a model is used within an
organization is quite different from sub-
sequent uses. The first time usually in-
volves a1 large investment; subsequent
uses are less costly. The first time there
may be unresolved questions about the
validity of the model; its output should
be taken only as guides. Each use of the
model should improve its validity and
acceptability so that eventually its out-
put may be taken as a decision to be
modified occasionally. Obviously the
more complex the situation, the longer
before the model becomes fully accept-
able (and in many policy situations this
may never occur).
Let us look at the steps involved in
the first-time use of a model. Fig. 9 in-
dicates how the process of selecting a
method of analysis might proceed.
Problem Definition
The process starts by defining the
problem: a complex and creative ac-
tivity. It involves determining the
boundaries, at least tentatively, of areas
of concern. It requires the definition of
the following:
• the decision; specified by identify-
ing those factors or variables which
the decision maker can control; the
controllable variables.
• measure (s) of performance by
which the value of the decision is
to be judged.
• an objective function to relate cer-
tain output variables to the mea-
sure of performance; it tells how
to estimate the relative value of the
outcome of any decision.
Choice o] Analysis Method
After the problem is defined, the an-
alyst asks, "Does any standard model fit
the problem?" If one of the standard
models does fit, the appropriate solution
can be found very efficiently since pro-
cedures for solving most standard mod-
x" Formulate ^~"x
f profclerr ^^
^(preliminary data )
V^^analysisJ^^X
^~~L
^\
^ ^\
,/ Does ^x^^
^^ any standard ^x. yes
^x. problem? s^
(.Analyst 'a choicel ^v^/""'^
* *
Use
intuition Enumerate
to irake alternatives
decision
,
sO
Run
to select
best
alternative
* 4 T
Create c=Jnot Create an analytic
model the problem
Identify
alternatives
1
Select
best alternative
Figure 9. A process for selecting a decision- aiding method.
Set up problem
in model form
(which implies
choosing a range
of alternatives)
1
Solve model
(usually to
get optiirurr)
I
Confirm solution
TJ
<^ solution ^x.
^^ acceptable? < J
| DECISION
1
I
1
I
i
I
I
' 1
1
I |
I
1
I
1
no
28
FIGURE 9—A process for selecting a decision-aiding method.
-------
els are known. In this case, the right-
hand sequence of steps in Fig. 9 is fol-
lowed:
(1) The problem is set up in the
standard form.
(2) Data are gathered to provide the
inputs for the model. Specific
parameter values are estimated,
sometimes using statistical tech-
niques.
(3) Any necessary adjustments are
made in the model to account
for the particular situation.
This process is even easier if there is a
case where the model has been applied
to a similar situation. This reduces the
work in Steps 1 and 3. One purpose of
this book is to make the reader aware of
standard and special, but well-developed
models.
From the decision maker point of
view, it is a critical step to determine
whether there is a standard model or
not. If there is, the cost of the modeling
effort is relatively low and it is worth
assigning analytic staff to carry the mod-
eling process forward (at least until
good cost estimates can be made). If
not, the development of a model should,
perhaps, be explored with others who
have similar problems before making
any expensive commitment.
The model is solved by deducing
which is the best of the range of possi-
ble decision variables, using the optimiz-
ing or search processes associated with
the standard model. Jn a complete op-
erations research study, the solution de-
rived through the model would be con-
firmed by field tests, where possible,
and this solution, if it is acceptable to
management, is implemented.
If none of the standard models fit the
situation in question (which is a com-
mon occurrence), then the analyst has
the following alternatives.
He can try to create a suitable mathe-
matical optimizing model. This may in-
volve applied mathematics, and in many
cases, behavioral research. Such analysis
is a high-risk alternative; a suitable
model may not be created within the
time frame available for decision mak-
ing. However, if a model can be cre-
ted, then the steps on the right side of
Fig. 9 apply. If not, one of the other
alternatives must be chosen.
When no standard model fits, the an-
alyst may choose to use simulation. A
special simulation model, which is a
predictor, must be designed. The first
step here would be to determine if there
is a model already developed that
represents a similar situation. If so,
adapting it may be the most effective
approach. Simulation models are, in
general, fairly costly and require a ma-
jor commitment. Computer simulation
languages have been developed which
aid in reducing the cost. To use the
simulation, the alternative solutions are
identified, and the simulation model is
used to test for the best alternative.
When found, the alternative may be
confirmed by field tests.
If the analyst decides not to use a
simulation model, two approaches re-
main, direct experimental and intuition.
In the former, alternative courses of ac-
tion are identified and the best is se-
lected by direct experimentation in the
real world. Finally, if none of these ap-
proaches are used, the analyst and the
decision maker can resort to intuition.
The Basic Steps in Model Design
Figure 10 is a flow chart of the ma-
jor steps that could be taken in the de-
sign of a model (or a major adaptation
of an existing model) [4]. We describe
these steps in general terms in that an
understanding of the process by the
decision maker will facilitate greatly
his ability to interact with model de-
velopers.
Notice that at a number of points in
the process may return to a previous
step. This illustrates one of the im-
portant characteristics of successful
modeling: the earlier steps are always
subject to revision as additional informa-
tion is obtained. For example, a review
of data often causes some reformulation
of the problem; especially, as is often
the case, some data are unobtainable.
Actual runs of the model almost always
suggest new alternatives, and therefore,
a return to alternative definition.
29
-------
Analyze data requirements
and available sources
of information
Formulate models
of subsystems
Combine subsystem
models into a model
Gather data and
estimate parameters
If required, program
and debug computer
model (or choose
existing software)
To earlier
steps in
process
Analyze results and'
present to
management |
*
I Field tests 1
_ _
( Decision
\
Implement I
results i
FIGURE 10—Steps In Designing And Using A Model
Model building is as much an art as
it is a science. One of the difficulties in
using a flow diagram to represent the
model building process is that the proc-
ess looks more scientific than it really
is. The flowchart in Fig. 10 is only a
guide and should not be interpreted as
a method that automatically produces
the creative leaps required to translate
a complicated, real world system into
a more compact and manipulatable
model.
Model Specification
Specification is the most critical step
in developing a model of a system. An
30
analyst's success in accomplishing other
research objectives depends on correct
formulation.
The first step is to specify the objec-
tives to be achieved through the analy-
sis. These objectives will generally be
stated by management after they recog-
nize that some aspect of the system is
not functioning to their satisfaction. The
problem, as management sees it, is
likely to be defined vaguely (from the
analyst's point of view), and the objec-
tives stated in qualitative terms. It is the
analyst's job to translate these qualita-
tive objectives into operational terms
that can be related to output variables.
-------
For an optimizing model this will in-
clude the creation of an objective func-
tion. Usually the analyst will create this
function by assigning weights to each
output parameter or result according to
its importance to management.
Along with specifying the output var-
iables and an objective function, the
analyst tries to identify relevant vari-
ables in the system; that is, variables
that effect the outputs. He then sepa-
rates the relevant variables into two
classes; those having values that can be
controlled by the decision maker and
those which cannot. The analyst's goal
will be to choose the levels of the con-
trollable variables with the aid of the
model, in a manner that optimizes as
nearly as possible the stated objective
function. The distinction between con-
trollable and uncontrollable variables is
not always clear. Depending on the
scope of the study, variables are some-
times treated as uncontrollable, although
the decision maker has (or has poten-
tially) some control over them. The be-
havior of people in generating trash is
uncontrollable in the short run and is
so considered in sanitation truck sched-
uling studies. But this behavior is con-
trollable by educational programs or in-
centives.
Constraints are uncontrollable con-
stants, e.g. upper limits on resources
available. (We have treated problem
definition and model specification as if
there were a clear-cut sequence in which
the analysis occurs: the steps are really
intertwined.)
Knowledge of existing models and of
theories is an important source of guid-
ance for problem formulation. (Philo-
sophically, is it even possible to describe
any problem situation precisely without
some model in mind?) For example,
most analysts who are faced with an al-
location problem use the ideas of the
standard model called linear program-
ming to initially organize the variable
relationships, constraints, and system
objectives in their minds. This thought
process influences the way the problem
will be formulated, even when the ac-
tual situation does not satisfy linear-
programming assumptions.
When the analyst has set the specifi-
cation, he begins the task of model con-
struction. Model construction usually
begins by the identification of subsys-
tems and variables in the subsystems.
General rules cannot be given for seg-
menting a large problem into subsys-
tems; this is almost entirely dependent
upon the structure of the system being
analyzed. Subsystems should be as in-
dependent of each other as is possible.
The size of a subsystem necessary to
meet this requirement depends on the
amount of interaction between the var-
iables in the total system.
The extent to which observation and
previous experience assist in the under-
standing of the subsystems varies. An
analyst with experience in office proce-
dures will have little trouble formulating
subsystem models about operations of a
specific office. However, even an ex-
perienced welfare analyst could have
trouble formulating relationships that
predict the effect of a change in welfare
qualification rules. One reason for this
is that such predictions require an un-
derstanding of recipient behavior, and
less is known about representing be-
havioral processes than about represent-
ing information and office processes.
Perhaps the most important point
about model building is that the an-
alyst should be intimate with the situa-
tion and its theoretical basis, either from
previous experience or by intensive
study. To successfully model a pollution
situation, say, it is necessary to un-
derstand chemistry, thermodynamics,
fluid flows, supply-demand-price theo-
ries, etc. To simulate the behavior in
a particular welfare situation, it is neces-
sary to understand what is known about
relevant psychological and sociological
theories of behavior, as well as to know
how the social services are provided.
Analysis of Data Requirements and
A variability of Sources
In the model specification step all
parameters and variables that effect the
measures of performance were identi-
fied. Now the analyst determines what
data are needed.
31
-------
For modeling, data are needed to:
• estimate values of constants and
parameters,
• provide starting values for all var-
iables,
• provide data to which outputs can
be compared for validation; his-
torical values of key variables.
To ensure that this data will be available
sources of data are located and their
adequacy is evaluated.
Creation of the Model
Even though the model is of a stand-
ard type or one that has been developed
elsewhere, the analyst may still have to
adapt it to the particular situation. This
may be a major effort in manpower
and time, although conceptually less
difficult than designing a model de novo.
It is an effort that can consume several
man-months for a simple case, like the
vehicle replacement problem, or dozens
of man-years, in policy or major alloca-
tion cases, like the natural gas regula-
tion or pollution problems.
As just discussed, various types of
data are needed to test, operate and vali-
date the model. A critical step, and
often the most costly step, is the mun-
dane process of getting the data. The
model serves as a guide to what data are
required: this is one of the advantages
of having a model. The activities re-
quired are:
• Negotiate with sources of data to
obtain it; in public applications,
the data are often in the files of
many different agencies. Privacy or
confidentiality considerations may
make data acquisition difficult.
• Obtain the data from the sources;
this presents two kinds of prob-
lems: (1) the economics of ex-
tracting data and (2) the political
problem of gaining the coopera-
tion of an agency to use its data. In
regard to the first problem, if the
data are not already in machine-
readable form (cards or tape) it
may not be worth the effort to use
a model that requires the data. In
some cases estimates of parameters
and initial values can be made
32
with small samples of non-machine
readable data.
• Edit the data and performing sta-
tistical operations to estimate
parameters or to forecast future
values of variables. (This can
involve major computational and
data processing efforts).
Computation: Programming and
Debugging
Since a model consists of a set of
variables and their logical and mathe-
matical relationships, a computer may
be appropriate for analyzing alternative
solutions. If this is not the case, then
hand computational procedures, tables
and other aids may be all that is re-
quired. Generally, programs for stand-
ard models are already available in
pretested software, i. e. available com-
puter programs. A model adapted from
someone else's work probably exists in
programmed form, but may need adap-
tation. If neither of these are the case,
then the analyst must prepare the cor-
responding computer program. Some-
times an aid to the preparation of new
models is available in the form of an
analyst-oriented, computer language.
There are several such languages which
are quite helpful in reducing the time
and cost required to formulate, pre-
pare, test and debug models, analysts
should be aware of these.
Model Verification and Validation
Further steps in model development
include verification and validation. The
former is concerned with determining
whether the statement of the problem,
e.g. the computer program, represents
the desired model under all anticipated
conditions. This might include using
the model with input data which cor-
respond to known output measures.
The validation step seeks to establish
how close the model mirrors reality. In
a few cases the analyst can compare
the model's output measures against
historical results or the results of a field
experiment.
Model Use
At this point we have a tested model
program and data. If the model is an
-------
optimizing form, then it is now ready
for use: the data are input and the pro-
gram run to produce the outputs. Most
such programs not only produce the
optimum values of the decisions vari-
ables, but also sensitivity information.
This might include an indication of the
costs of deviating from the optimum,
and the benefits that might be derived
by relaxing constraints, that is by chang-
ing factors originally assumed to be
"uncontrollable."
If the model is only a predictive
model, then one more step is needed:
it is necessary to decide how it will be
used to search for the best decision.
The search process may be:
• try several alternatives, or
• design a simulated "experiment" to
try alternatives in a controlled way,
which insures trying a wide range
of them, or
• try a number of alternatives at
random, or
• use a formal search process in
which the next alternative to try is
computed so as to lead to a higher
utility.
Analysis and Presentation of Results
The results of a model are seldom
completely consistent with preconcep-
tions of the outcome. The study should
provide new insights into the interrela-
tionships between the components of
the system. There have been cases
where insights into new alternatives,
derived while designing and preparing
to use the model, were the most valu-
able results of the process. Therefore,
it is critical that the presentation of the
results to management are in a form
that maximizes this insight. Ideally, the
decision maker will be involved through-
out the process and would have both
contributed to and gained from these
insights.
Since it is unlikely that the analyst
has been able to make a perfect trans-
lation of the objectives into a model,
the decision maker is wise to generate
his own alternatives for analysis. The
analyst can improve the objective func-
tion by interacting directly with man-
agement concerning the relative value
of the alternative solutions.
Implementation
Any analysis should be looked at
from three points of view. First, it
should provide specific operational
recommendations which can be imple-
mented. Second, it should provide de-
cision makers with additional knowledge
and understanding of their organization
and environment. This knowledge may
uncover important, but currently un-
recognized, problems that require
further analysis. Third, the results of
any study should be used to improve
the model and the experience of the
analyst.
Documentation
Documentation is a vital part of the
process of developing and implementing
a model. Documentation serves as the
basis for communication between the
various people who must be involved in
the modeling effort if it is to be suc-
cessful. Such communication paths must
be created between the decision maker
and the analyst, and between the analyst
and other personnel affected by the
study.
In some cases there is also communi-
cation from the analyst to the profes-
sion in general (i.e., through journal
articles, professional meetings, and so
forth) so that others may improve prac-
tices as a result of individual experience.
One thing that must be documented
is the definition of the problem. This
includes :
• a description of the organization in
which the problem exists.
• a statement of the decision that is
to be made and the range of
alternatives possible (to the extent
that they are presently recognized).
• a list of the constraints and guide-
lines considered to be outside the
problem area, which form the set
of assumptions under which the
analysis is being done.
• the model specification,
• a complete statement of the basic
nature of the processes in the sys-
tem.
33
-------
The documentation should also in-
clude the results of the analyses, recom-
mendations and some statement on how
the model should be revalidated and
updated based on the results of imple-
menting the decision maker's choice of
solution.
IV. PROBLEMS IN USING
MODELS
The purpose of this section is to bring
together a discussion of the problems
that can arise in attempting to use a
model.
Defining Measures oj Effectiveness
It would seem that a decision maker
should know what he is striving for and
how to measure progress towards his
goals. It turns out, however, that, when
an effort is made to define specific mea-
sures of progress, difficulties arise.
Measures of progress are also called
"measures of effectiveness," "measures
of performance," "criteria," or "indi-
cators." An objective function is a rela-
tionship between certain observable and
measurable phenomena to compute a
single overall measure of effectiveness.
The kinds of difficulties that arise are
the following:
• Agreement cannot be reached on
what the measures of effectiveness
should be.
• Certain objectives cannot be quan-
tified.
• Quantifying measures can be
stated, but there is no feasible way
of making the measurements to
determine their value at any given
time.
• There is agreement on a set of
several measures but no way of
combining them to form a single
overall measure of effectiveness.
There are methods for handling multi-
ple criteria [9, 10, 32]. It is a difficult
problem, however, and it arises fre-
quently in government where most pro-
grams do have more than one goal.
To the extent that the problems just
mentioned are a reflection of the fact
that the participant decision makers
34
truly have different values, the solution
must lie outside of the modeling proc-
ess. To the extent that the problem is
one of communication and definition,
it is usually solved by meetings among
the relevant people in a situation con-
ducive to good communication and
exchange. To the extent that the prob-
lems are economic or technical, such as
that there is no feasible way of making
the measurements implied by the speci-
fied criteria, then either surrogate indi-
cators must be sought or else the mod-
eling effort given up. The use of
surrogate measures implies that the de-
cision maker is taking on faith a rela-
tionship between the desired measure
and the surrogate indicator.
Aggregation
In most cases the model, which is an
abstraction of the real world, does not
represent every person, event or activity
that could be relevant; rather it repre-
sents aggregations or groupings of these.
A critical problem in the design of a
model is to decide to what extent these
groupings should occur. If the aggrega-
tion is too great, then certain detailed
phenomena which can affect the pre-
dictions and decisions may be lost. If
the aggregation is too fine, however,
the model becomes unwieldy and un-
usable.
Data Acquisition
This is largely an economic problem.
A few models may call for data which
are inherently unobservable (this is par-
ticularly true for certain behavioral
phenomena). Most models have been
designed so that the data required to
establish parameters, coefficients, initial
values and so on can, in principle, be
observed and measured. The problem is
that the cost of making these measure-
ments may be so high so as to make the
modeling effort infeasible.
In some cases a modeling effort has
led to the recognition of the need for
an information system. The modeling
itself then must await the implemen-
tation of that system.
There are other problems related to
-------
the use of data, having to do with the
invasion of privacy or confidentiality.
Some data may not be available because
divulging them would either compro-
mise information about individuals or
about the organization and how it
operates. In the long run, organizational
data about most public organizations
can be made available. However, the
problem of individual privacy is still a
major one. Often models require only
statistical or aggregate data so that in-
dividuality can be eliminated at an early
stage of processing and so avoid the
privacy problem, [34].
Verification and Validation
The computer program which repre-
sents the model must be thoroughly
tested to insure that it does represent
the desired model. There are cases
known where a model has been used for
several years before certain errors have
been found which indicate that the
model has not been giving completely
correct results.
A more serious problem is in deter-
mining the validity of the model, [4]:
"Suppose, an analyst feels his
model is an accurate representa-
tion of a system and he presents
it to management for their use in
decision making. The latter then
asks, 'How do we know it is valid?
How do we know its predictions
will come true?' These questions
must be answered at some point in
every study.
How can we be sure that the pre-
dictions made by any model will
be correct or at least will be better
than the prediction made by some
other method (e.g., by judgment)?
Ultimately this becomes a question
of the credibility of the model.
Therefore, we must examine what
evidence is required by a manager
before he will utilize a model as
an aid in his decision making.
Mathematical models have an ad-
vantage in this regard over simula-
tion models. If, for example, a
situation can be shown to fit the
assumptions of a linear program-
ming model, then the manager has
the support of evidence that shows
that linear programming models
have proven effective in other
(albeit different) situations. The
only possible evidence of validity
for a simulation model that has
been developed specifically for a
situation is that the model has made
satisfactory predictions in the past.
If this is the first time the model is
being used, such evidence is not
available. This difficulty is most
severe with a simulation model of
a nonexistent system, for the ana-
lyst cannot even test it using his-
torical data."
Recognizing that it is never possible
to completely validate a decision-aiding
model, since there are never real data
about the alternatives not implemented,
we suggest that the validity of the
mode] should be determined by the
application of the following steps:
(1) The analyst assures himself that
the model performs the way he
intends it to, using test data, and
if available, real historical data.
(2) Reasonableness is checked by:
(a) showing that key subsystem
models predict their part of
the world well (using his-
torical data).
(b) showing that the param-
eters have reasonable
values.
(c) having people who are
knowledgeable about the
situation (preferably in-
cluding the decision maker)
review the model in detail
and agree to its structure
and parameters.
(3) The decision maker has an
opportunity to explore the use
of the model to become familiar
with its predictions and to ex-
amine the interactions it implies.
At this point the analyst and
decision maker may be able to
agree as to what is a close
enough fit between model out-
put and actual data.
(4) The model is used to aid deci-
sions. Careful records are kept
of its predictions and of actual
results. (This may involve a
time span of years, so that the
evaluation procedure has to be
setup carefully.)
35
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Cost and Personnel Requirements
The use of a model can be very ex-
pensive, particularly the first time. A
typical modeling effort in a non-trivial
situation can easily consume two or
three staff years, plus thousands of
dollars of computing time and require
one or more years of calendar time.
This is especially true if the model is
designed for a particular application,
but can be equally true when the model
is of a standard type or is one built by
Others.
Often the personnel required for
these efforts is time of staff already on
board and, although it displaces other
analytic projects (a significant oppor-
tunity cost), it does not show up as a
specific budget item. The computing
time required to test and run a model,
however, usually is a very specific item
and therefore gains more attention that
it deserves. Models can consume thou-
sands or tens of thousands of dollars of
computer time if the work is not care-
fully controlled.
Although a modeling effort may be
easily justified by the savings and in-
creases in effectiveness gained through
better decisions, it is a difficult invest-
ment to justify in advance. Thus the
decision maker must allocate funds for
the initial model development effort
somewhat on the basis of his judgment
and faith in the lead analyst.
Setting Up the Model
One of the more difficult modeling
processes is to translate the real world
into the model. This problem arises
when the decision maker wants to de-
fine an alternative which does not exist
and wishes to analyze this alternative
via the model. The decision maker
defines the alternative in terms of such
factors as policies, techniques to be
used, and personnel assignments. These
must be translated into specific model
parameters. This step is a creative proc-
ess on the part of the analyst which
must be understood fully by the de-
cision maker when he interprets the re-
sults of the model.
Interpreting Results
The outputs of a model must be
interpreted into plans for action. Most
decision makers wisely recognize the
model outputs as a guide and not as
gospel. Nevertheless, having invested a
great deal of effort in a model and
having observed its very precise (but
not necessarily valid) outputs, the
model results may weigh heavily in the
decision making. Therefore, it is im-
portant to understand the effect of the
choice of the model on the decision
process. Since every model is an ab-
straction and emphasizes certain aspects
of the real world and not others, differ-
ent models will have different influ-
ences. The decision maker should con-
sider this when interpreting the results
of the model. The decision maker must
fully understand the modeling process
so that he can either change the model
to reflect his views or interpret the
results appropriately.
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York, Ronald, 1968, pp. 251-264.
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Manager's Guide to Operations Research,
New York, Wiley, 1964, or for more
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Hall, 1967.
12. Steele, J. L., The Use of Econometric
Models by Federal Regulatory Agencies,
Heath, Lexington, 1971, pp. 31-33.
13. Forrester, J. Urban Dynamics, Cam-
bridge, Mass., MIT Press, 1969.
14. Thompson, S. P., Calculus Made Easy,
Macmillan, London, 1946.
15. Moroney, M. J., Facts from Figures,
England, Penguin (A234).
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(Vol. I), Applied Statistics (Vol. II),
Penguin (X5, X6) 1968.
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Quantitative Approaches to Management,
New York, McGraw-Hill, 1971 (revised
ed.), Chap. 14.
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Digest, 1965, p. 39.
19. Mirasol, N., "A Queuing Approach to
Logistics Systems," Operations Research,
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Methuen Mono., New York, Wiley, 1961.
21. Brown, R. G., Statistical Forecasting for
Inventory Control, New York, McGraw-
Hill, 1959.
22. Gass, S., An Illustrated Guide to Linear
Programming, New York, McGraw-Hill,
1970.
23. Kogiku, K. C., An Introduction to
Macroeconomic Models, New York, Mc-
Graw-Hill, 1968.
24. Samuelson, P. A., ed., "Mathematics in
Economics," Review of Economics and
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ductory Analysis, New York, McGraw-
Hill, 1967.
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Comm. Docket No. AR61-1, (1963) p. 6.
27. Duesenberry, J. S., et al., The Brookings
Quarterly Econometric Model of the
U.S., Rand McNally, 1965.
28. Liebenberg, M., et. al., A Quarterly
Econometric Model of the U.S., Survey
of Current Business, 1966, pp. 13-39.
29. Amstutz, A. E., Computer Simulation of
Competitive Market Response, Cam-
bridge, MIT Press, 1967.
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New York, Universe, 1972.
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D326-0, 1967.
32. Courtney, J. F., et al., "A Goal Pro-
gramming Approach to Urban-Suburban
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Programming Model for Academic Re-
source Allocation" Management Science,
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vacy and the Computer: An Annotated
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37
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Chapter 2
Models and Policy Making
By
Peter W. House
Gene R. Tyndall
I. INTRODUCTION 41
Purpose 41
Scope . 41
II. POLICY MAKING DEFINED . 42
Levels and Scope of Policy Making 43
Scope of Problems 45
III. POLICY-ORIENTED MODELS 47
IV. NEEDS OF POLICY MAKERS 49
Interviews and Questionnaires 49
Questions About the Policy Maker . . 49
Questions on the Policy-Making Process 50
Questions on the Use of Models in Policy Making 51
V. OPPORTUNITIES FOR MODELERS AND POLICYMAKERS 51
Challenges to Modelers 52
Challenges to Policy Makers 55
VI. CONCLUSION 55
REFERENCES . 56
APPENDIX—AN EXAMPLE: THE STRATEGIC ENVIRONMENTAL
ASSESSMENT SYSTEM (SEAS) 56
Scope of SEAS 56
Residuals 58
Effects 58
Reactions 58
Evaluators 58
Expected Uses of SEAS 59
39
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-------
Models and Policy Making
I. INTRODUCTION
Throughout the chapters of this book,
especially within the Primer section,
there are implied assertions that models
are "natural" aids for decision makers
at all levels of management. Yet, there
is more than sufficient evidence to sub-
stantiate the impression that, regardless
of their objectives, the use of models by
high-level decision or policy makers in
the public sector is quite limited. In
fact, in our view, the gap between the
potential development of strategic
models and policy maker needs and
uses seems to be, in some areas, widen-
ing.
Purpose
In this chapter we describe this phe-
nomenon—largely from the point of
view of the policy maker—and attempt
to clarify some of the misconceptions
and related issues. Insofar as the litera-
ture contains previous work and posi-
tions on this issue, we acknowledge
those who have contributed in the past.
However, we feel that by and large the
modeling profession, as is the case in
varying levels of degree in other pro-
fessions, has been somewhat reluctant
to recognize and criticize itself for these
kind of shortcomings. It is our thesis
that model developers, model users and
decision makers must collectively seek
an improved process of development
and eventual use of models for policy
or strategic purposes. We must learn
from the past and overcome the reasons
which have led to over-criticism and
a reluctance to use models to assist
directly in policy making.
Scope
A principle of effective writing is
that one should orient his message
toward a specific audience. The reason
for this rule is obvious, as the back-
ground and needs of the intended audi-
ence constrain and define what can be
read and absorbed in a final product.
There is some question as to whether
a similar match is sought with the same
rigor in the modeling community. In
the early days of model building, the
specialists in social science were only
accidentally the ones who were inter-
ested in empirical model design. Because
of this and other reasons more closely
related to the existing Gestalt of the
mathematical community, modeling
grew with an emphasis more on tech-
nique than on analysis. To a large
extent, this remains as a problem.
In the following pages we begin by
defining what we mean by the policy
maker and policy making (in modeling
terms what we hope are the "users").
We recognize the difficulties in sepa-
rating policy making from decision
making; policy from action; manage-
ment actions from staff recommenda-
tions, etc. However, from the point of
view of the policy maker, this difficulty
may be academic. In fact, this issue
may well be the fundamental basis for
the problem we define and describe
throughout this chapter.
Next, we discuss policy-oriented (or
strategic) models—what they purport
to be, what they are not, and what in
our view they ought to be. Further, we
approach the "needs" of policy makers,
attempting to structure a process
wherein these problems may be mini-
mized or even eliminated.
Finally, we conclude with a discus-
sion of opportunities for model builders
and policy makers because we believe
though the challenge is great the payoff
is substantial. Policies and policy-level
41
-------
decisions have been made largely on
the basis of intuition, staff judgments
and default. If the addition of the use
of models can really improve the proc-
ess, then the opportunities should be
identified, discussed and acted upon
without delay by all who seek to ad-
vance the profession and to improve
public policy.
Also included as an Appendix to this
chapter is a relatively lengthy descrip-
tion of the Strategic Environmental
Assessment System currently being de-
veloped within the Environmental Pro-
tection Agency. This discussion is meant
to exemplify some of the many ways
strategic models can be designed to be
of more direct use of the policy level.
We feel it important to emphasize at
the outset that, by the modeling pro-
fession, some of the views expressed in
this chapter may be interpreted as al-
most "ascientific" in the sense that we
attempt to describe a policy need. As
the chapter indicates, such a description
of policy making and the opportunities
for models to assist in the process does
not follow the standard approach of
defining the problem, testing alterna-
tives, etc. In fact, the process is prob-
ably more subjective and qualitative
than scientists would hope. The signif-
icant point is that policy-level problems
do not always lend themselves to scien-
tific analysis—much less to definition.
Thus, the means by which they can be
addressed are not always as clear as
the kinds of decision problems we find
addressed in the literature and "solved"
by models. This is not meant to imply
that it is therefore impossible to con-
struct models for assisting policy mak-
ing but, rather, that a new perspective
is necessary in order to modify the
process by which models are developed,
tested, validated and applied in order
for them to be helpful to the policy
maker.
II. POLICY MAKING DEFINED
Within the scope of this Guide, the
term "policy making" is restricted to
the public sector. At this level of de-
scription, the policy maker will be
42
recognized as the person or group of
persons (e.g., his immediate staff) who
make the principal decisions which
guide the public sector. Within the in-
stitutional form, these persons are
elected (or appointed and confirmed)
by a constituency whose desires they
presumably (and normally) serve to
operationalize and, in fact, they are
responsible to the constituency for their
actions.
To accomplish this purpose, these
policy makers operate with a staff which
is normally divided along functional
lines and is specialized in carrying out
specific portions of the policy pro-
gram. Figure 1 illustrates in simplified
fashion the paradigm of the policy
maker. It also points out one of the
anomalies of the departmental system
which helps explain some of the diffi-
culties involved in modeling for policy
uses. Although one description of the
policy maker's role in this nation is
that of a translator for implementing
the public will, the existence and roles
of the media and professional societies
(as spokesman for the public) define a
direct link which often bypasses the
policy level. It is the existence of this
"shunt route" which lies at the root of
one of the basic problems of modeling
for policy makers; namely the profes-
sional requirement to satisfy not only
the needs of the policy maker, but also
the demands of the professional com-
munity. Because policy makers change
as a function of elections and one's pro-
fessional career is predicated on peer-
group status, it is usually the case that
the modeling community (and staff for
that matter) often tends to be more
loyal to the latter than to the former.
As a result of the nature of policy
and the peculiar characteristic of de-
partmentalization described above, it
is particularly difficult to define "policy
making" for the purposes of advocating
the use of models for assisting in the
process. It is possible, however, to gen-
erally bound the process by describing
policy making in terms of levels and
scope.
-------
Public
(Media and
Professional
Societies)
Policy Level
Policy Guidelines
Departments
FIGURE 1—Policy and the Organizational Structure
Levels and Scope of Policy Making
It is important to acknowledge the
obvious differences in levels wherein
public policy is made and to illustrate
the differences in scope of problems. In
recognizing these differences we men-
tion the levels of policy making and
point out the similarities in process such
that the principles suggested in this
chapter can apply to all policy making
that fits our description. It should also
be recognized that such a discussion is,
of necessity, oversimplified. However,
since we are not specifying particular
policy problems or case studies in this
chapter, generalizations should suffice
for illustrations.
Our hypothesis then is that policy
making can be defined as those actions
(or considerations) taken by elected
officials, or their immediate staffs, at all
levels of government; and that the proc-
ess of policy making at this highest level
is differentiated from that at the staff,
or even program level, due to the scope
of problems, issues and necessary de-
cisions that must be made on behalf of
society. The following descriptions of
levels serve to illustrate this idea.
At the Federal level, the President,
his immediate cabinet, the White House
staffs, the heads of Executive Depart-
ments, the sub-heads, and Office Di-
rectors are all policy makers but with
very differing problems, needs for in-
formation, analytical requirements, and
so on. Then too, each Administration
differs in its centralization/decentrali-
zation of policy making and conse-
quently each "job" varies in its au-
thority and responsibilities.
The making of Federal policy is an
interesting process and one that has
been well discussed in the literature.
For purposes of illustration, we de-
scribe below a common problem—
urban policy making—and "trace" it
through each level of government in
order to describe the differences in
scope and ramifications. Certain aspects
of urban policy have been, as one of
the chapters in this book discussed,
amenable to the use of models.
The Federal government does, in a
sense, have a macro-urban policy, al-
though the quality and comprehensive-
ness of the policy is, and should be,
continually criticized. At the highest
level, the President reports to Congress
periodically on the status of the na-
43
-------
tional urban policy [1]. Essentially, the
policy problem at the Federal level is
what programs to pursue and in which
form to pursue them [2]. The emphasis
on the new Federalism with revenue
sharing, Federal reorganization, and
decentralization of decision making,
represents a type of national urban
policy. Yet, the policy decision to pur-
sue such courses of action rests on an
evaluation of urban programs and their
cost-effectiveness. Urban renewal, trans-
portation, education, housing, anti-
poverty, and pollution control are ex-
amples of such programs. Such a policy
is normally affected by incremental, yet
critically important, decisions on pro-
grams. In addition, national economic
and employment policies have ramifica-
tions for urban policy. An interesting
discussion of these matters can also be
found in [3].
The important point is that, at the
Federal level, policy makers decide on
programs designed to meet certain ob-
jectives. In so doing, they select from
alternative choices and make tradeoffs
among options. The process is not ob-
vious, but the results are observable.
For example, one need only analyze
the President's budget messages to de-
tect the results of such policy delibera-
tions.
There are, of course, different scopes
of national urban policy making among
Federal officials. Executive Depart-
ments, for example, recommend overall
macrourban policy while implementing
only that related to their area of re-
sponsibility. Nevertheless, policy choices
are made in a continuing manner in
Washington which determine what pro-
grams are to be funded (and which are
to be eliminated or reduced) at the Fed-
eral level for meeting urban objectives.
The significant aspect of the Federal
policy process is that sub-levels below
the President exist which have implica-
tions for scope as discussed below;
however, the essential principle is that
policy making implies a choice (or
choices) among or between alternative
program options or, at a slightly lower
level, a choice of tactical options within
a program.
44
At the State level a Governor, sur-
rounded by key department heads and
advisors, results in a policy making
process not too different from that in
Washington except for the obvious
fewer number of people and smaller
budget involved. As with Congress,
States have legislative bodies which also
make policy in varying degrees and with
varying interfaces with the executive
branch.
With respect to urban policy, the
States have a role similar to Washing-
ton, except that the problem also in-
volves choices which seek to maximize
the effect on urban objectives by com-
plementing Federal programs with a
particular set of programs at the State
level. Thus, one important policy issue
is what set of urban programs should
the State employ to achieve the maxi-
mum effect given the Federal programs
and how should these programs be
administered.
This is not to imply that the States
have only to complement Federal urban
programs. On the contrary, urban prob-
lems are of key importance to many
States and their forward, progressive
policies have often led Washington. An
interesting urban policy issue at the
State level is what programs to pursue,
given its own peculiar set of tax bases,
urban-rural population splits, growth
trends, income variance, environmental
goals, institutional arrangements, and
the like. Although the nature of urban
policy indeed varies from State to State,
the process is characterized by many
similarities.
At the metropolitan level we gen-
erally find Councils of Governments
(COG) with elected or appointed policy
makers normally attempting to act, in
the absence of metropolitan govern-
ment, in a coordinated fashion to
achieve whatever mutual goals are
identified. COGs are not, in themselves,
elected governments. There is signif-
icant variance in COG structures and
policy roles throughout the nation, but
fundamentally the policy making leve
represents a coordinative approach to
metropolitan-wide problems such as
-------
transportation, housing, crime, environ-
ment, etc.
COG's are almost universally sup-
ported by Federal policy, consequently
urban policy issues are viewed in much
the same context, albeit at a more
micro-level. The fundamental role of
COG's is to establish community goals
and actions in a coordinative manner,
seeking local elected-official support and
participation. Thus the metropolitan
policy maker responsibility is perhaps
characterized more by the need for com-
prehensive planning than the other
levels. It is not surprising, then, that
most urban models have been developed
for metropolitan problems. Models,
however, have not been particularly in-
fluential on metropolitan policy, which
helps to substantiate the essential thesis
of this chapter. A good illustration of
this problem at the metropolitan level
is contained in [4].
At the local level, whether it be a
county with a chief executive or com-
missioners, or a city with a mayor or
council, the level of policy making is
fundamentally that of micro-analysis
and "firing line" actions. The process,
however, is generally the same as that
above in that the policy maker relies on
a key immediate staff for recommenda-
tions and, to the extent he can, makes
policy on the basis of intuition, ability
to make tradeoffs or by default.
Urban policy-making at the lowest
level of government, consistent with the
"firing line" analogy above, is charac-
terized by tactical issues, although bud-
getary problems can be of strategic
nature. For example, the choice of
budget amounts for programs (e.g.,
streets, fire protection, education, etc.),
represents, whether consciously or not,
a strategic set of priority decisions
which reflect urban policy. The fact that
the budgeting process is accomplished
more and more often in the political
arena is illustrative of the public reali-
zation that financial allocations do help
translate policy into action. Yet all too
often policy makers (in this case local
elected officials) are not fully prepared
to respond to the public in this new
open fashion.
It is this characteristic that can be
found throughout the policy-making
process, regardless of the level under
study; namely, the consistent need to
decide on a course of action (or, sig-
nificantly, to take no policy action)
without sufficient information or time
to consider all the ramifications of the
possible decisions. It is also this char-
acteristic that makes policy making in
the public sector related to, although
not equivalent to, management decision-
making in industry, and we attempt to
describe this analogy below.
Scope of Problems
Concomitant with the highest level of
policy making is a set of problems
which is often ignored by model build-
ers, or even political scientists and
public administrators, except in a theo-
retical sense. Yet political figures make
critical decisions on directions of
courses of actions which involve huge
investments of funds and time. The
breadth of these issues is often over-
looked because of the nature of the
political process, but positions are taken
and policies are made anyway.
For illustrative and comparative pur-
poses, consider briefly one of the uses
of models in industry. The overall ob-
jective of any industrial concern is to
maximize profit. (We ignore for pur-
poses of this discussion more sophisti-
cated measures of commercial effec-
tiveness such as return on investment,
market share, etc.) This desire is shared
by the president of the company, by the
board of directors who elect him, and
by the stockholders who elect them.
Provided they are receiving what they
consider their fair share, it is also shared
by the labor force. This means that it
is possible to state an overall goal or an
"objective function" which is generally
consistent for all parts of the concern.
Further, this goal is part of the ethos
of the country and is legitimized in the
law.
Of course, this goal cannot be sought
after exclusively, nor can it be sufficient
to represent the total business affairs.
The side conditions set by other in-
45
-------
dustries, supply and demand conditions,
and customer opinion serve to temper
it. And attitudes, productivity, and
many intangibles affect it. Even so, the
overriding goal of industry is relatively
explicit and the measures of effective-
ness are fairly well understood.
Consider the socio-political area for
contrast. Regardless of what may be
said of business-economic objectives,
there is no question that they are more
defined and accepted than the possible
goals available to the political decision
maker. The personal goal of the presi-
dent of a corporation, in oversimplified
terms, is to remain the president. He
generally does this by making a profit
and by maximizing the growth of his
company, over both the long and short
run.
An elected (or appointed) official
also has the personal goal of remaining
in office, but it is less clear what he must
do to achieve this. To remain in office
he must balance his goal of staying in
office with the values and desires of his
constituency. Goals of the constituency
are often diverse and at times contra-
dictory; yet they are the group from
which all his power legally derives.
Moreover, the prospective elected
official, to be elected into office, must
play adversary politics and thus con-
tinually attempt to shift the objectives
of his constituency and convince them
that he can maximize the new goals. If
the two goals (that of the official in
office and of his constituency) are per-
ceived to be close to equal, then he
will likely be re-elected to office. If the
contender can enlargen the gap, then
it may be enough to force the incum-
bent out of office. It is recognized that
this analysis is sensitive to time and is
more valid the closer it is to election
time. It is also likely to be sensitive to
the size of the constituency; the
strength of the relationship being in-
versely related to size.
Certainly it would be a misstatement
to assert that all policy models should
be aimed at maximizing the vote-getting
potential of the politician. However, by
conceptualizing the politician's duty as
46
satisfying a constituency, rather than by
a more readily definable discipline or
functional standard (such as efficiency,
or cost-benefit, etc.), it may help
modify the model design from rigidity
in the area of normative solutions, and
may begin to structure designs which
are broader in scope though admittedly,
at present, less quantifiable in nature.
This oversimplified yet illustrative
analogy enables one to describe the
scope of problems with which the
elected policy maker is concerned. The
key variable—values and desires of the
constituency—must be the continual
basis for public policy analysis.
There is another perspective by which
the policy problem can be analyzed.
Most models have been developed to
solve problems of a physical nature.
The related necessary attention to detail
in solving such problems has been one
criterion for the use of computers, to
free "man" from mechanical, or rou-
tinized detail, so that he may turn his
attention to questions of "why". These
problem-solving techniques are opera-
tional in design-optimizations, least-cost
solutions, queing service, etc.; i.e., find-
ing best solutions to "tactical" problems
created by the selection of a set of
policies by a higher authority. Figure 2
illustrates the problem scope in such a
context. Analytical support at the
policy-choice level is necessarily macro
in its attention to detail, providing
strategic-type assistance in "direction"
rather than in administration. Support
to the programs themselves, even though
it may be "policy" in nature, should be
in more detail at the intermediate level
of Program Policy Decisions, and in as
much detail as possible for Program
Management Problems. In fact, this
analysis could be carried deeper and
could show, for example, that models
that are large, complex simulations are
often so engrossed in micro-level detail
they are no longer solving problems,
but rather are self-generating work.
Many functional models are of this
type.
Policy making, then, varies by level
and by problem scope. Decisions on
-------
(LEVEL OF DETAIL UNDER SCRUTINY)
MACRO-LEVEL (STRATEGIC)
PROGRAM
MANAGEMENT
PROBLEMS
'INTERMEDIATE-LEVEL
PROGRAM \ PROGRAM
B \ C
POLICY
DECISIONS
POLICY
DECISIONS
PROGRAM \ PROGRAM
MANAGEMENT \ MANAGEMENT
PROBLEMS 1 PROBLEMS
1ICRO-LEVEL
(TACTICAL)
FIGURE 2—Scope of Policy Problems
public policy, however, are made con-
tinually without regard to such ana-
lytical structure. To the extent models
can be helpful to the process, and we
believe they can given certain condi-
tions, such analytical tools should be
developed and applied as an integral
part of the process.
III. POLICY-ORIENTED MODELS
Just what is a policy model? If one
were to attend a number of the profes-
sional meetings held each year or read
the articles written by practitioners of
the modeling art, it would become ap-
parent that almost all feel that their
creations are "policy" models. In fact,
the great majority of the models pre-
sented in this book were claimed at one
time or another to be of this type.
From one point of view, many of these
models are probably related to policy
decisions inasmuch as they do have an
input into an overall policy scheme.
To leave "policy" at this vague point,
however, equates it to the term "de-
cision".
Logically all models can be handled
as a subset of decision models, which
is the approach described throughout
the other chapters. Further, the metho-
47
-------
dologies used to address policy ques-
tions can be viewed as synonomous
with those used for any others. It is the
contention of this chapter that this logic
set is the principal reason for the dearth
of models in this area. Although the
techniques may indeed be similar or
analogous, the problems themselves are
so unique that many analysts who pro-
pose to build "policy models" appear to
fall short of the goal. Therefore, the
problem can be said to be one not of
technique necessarily, but of content.
It is possible that one may find that,
having understood the problems, he
might wish to develop or expand tech-
niques, but such steps are presently only
conjecture. What is worse is that, con-
sistent with our analogy of the busi-
nessman above, the models purported to
be of policy scope are being used, if
at all, to assist in the optimization of
the administration of a program or a
policy after it has been decided to
implement it.
Most decisions to fund model de-
velopment (or model application) in
the governmental sector are made by
people who make, or help make, policy.
Consequently, it pays for those who
wish to build models to profess an
ability and willingness for making
models useful to such people.
An Assistant Secretary of Transpor-
tation once stated this problem in quite
a lucid fashion [5], His essential point
was that systems analysis, with its "bag"
of models, causes policy makers con-
siderable frustration in that analysts
constantly demand time to develop,
complete and test a variety of models
before policy choices should be made.
Yet policy decisions arise and must
often be made immediately. Utility of
models is rarely the principal goal of
the analysts.
In reality, researchers do not interact
with the policy maker himself, and only
to some limited extent with his staff or
with a particular department. Their
goals and desires may not agree with
those of the policy level, and the re-
sulting lack of specificity relegates
models to art forms which merely guess
48
at what is "really needed" by the client.
A typical process is that once the con-
tract or work statement is approved, the
"client" is no longer the policy maker
but one of the staff assigned to monitor
the effort. The staff monitor may indeed
be quite competent technically, but the
policy maker loses interest if his own
needs are omitted. This process, having
been repeated time and time again in
government, has helped cause staffs to
become cynical and to seriously ques-
tion the utility of all models.
For purposes of the policy-model
designer, the most important basic goals
of the elected official would seem to be
the following: first, to satisfy the needs,
interests and goals of his constituency;
second, to satisfy his own personal
needs in terms of pursuing the pro-
grams and ideals which motivate his
political life, and; third, to be able to
select, from a full range of possible
policy decisions, those which are most
effective in meeting the above two
needs.
Within this context, the ultimate
policy-making model might, for in-
stance, allow the policy maker to pro-
ject the effectiveness of various policy
alternatives based upon their ability to
achieve both his personal goals and
their potential effects upon societal
values and thus public opinion. The
official who understands which of the
issues are really the most relevant and
which should be given the greatest
weight will maximize his vote-getting
potential. And, the official who can
weigh beforehand various policy al-
ternatives in terms of their efficacy to-
ward achieving societal goals will be
able to make more effective decisions,
and be able to judge their developing
impact more accurately in terms of his
original goals.
In short, a policy model should assist
the policy maker in making policy
choices more effectively according to a
certain set of clearly identifiable goals.
This helps to explain why so many of
the planning models available today are
unsatisfactory at the policy level. Such
models have often taken several years
-------
to develop and are likely to be irrele-
vant to the contemporary goals of the
politician and his constituency.
Based on the above considerations,
the research direction should be to-
wards discovering the basic aspirations
and strategies of the currently elected
officials. This suggests, possibly, a
greater emphasis on voting behavior,
political structure, and personalized goal
orientations than are contained in most
present models. It may also signify the
need for more explicit statements in
policy models of the overall societal
implications of possible policies. An
example of this point is given in [6].
IV. NEEDS OF POLICY MAKERS
One of the basic problems associated
with policy modeling is the difficulty in
developing a clear definition of user
needs, agreed upon by both the model
builder and the policy maker. Generally
speaking, there appears to be little inter-
action between the policy maker and the
model builder during the initial and
design periods of the model. To the
contrary, there is often a feeling on the
part of the model builder that he under-
stands the problem, and certainly has
mastered the analytical technique to be
used; consequently, there follows
typically much discussion in the way
of briefing or educating the policy
maker as to what is "good" for him.
Seldom, however, are there any meet-
ings in which the focus is inverted and
the designer himself is educated. Little
wonder, therefore, that the potential
users of these models often feel alien-
ated toward them in that the resulting
products are not really tailored to their
needs.
Interviews and Questionnaires
One technique for establishing such
an inverted dialogue, and one with
which we are currently pursuing within
the Environmental Protection Agency,
involves the use of questionnaires in a
highly personalized and ongoing inter-
viewing process. The purpose here is to
design a strategic policy assessment
system (described in the Appendix of
this Chapter) which is tailored to the
strategic-type needs of the agency ad-
ministrators. Our hope is that the policy
makers will be able to utilize our
modeling skills to push the state-of-the-
art in the directions of their needs,
where such directions might be con-
trary to our instincts and training.
To begin this process (which we
expect to be a lengthy one), the ques-
tionnaire discussed below was con-
structed. In many instances the ap-
proach is quite naive, but it was useful
in bounding the discussion. We repeat
most of the questions here and, rather
than report the outcome of our meet-
ings (which are of internal use), we
discuss the rationale behind the queries
and what we are learning in a general
sense from the process.
Questions About the Policy Maker
1. Have you had any training or edu-
cation in the use of a computer? If
yes, what type?
2. What is your personal opinion of
the use (or misuse) of computers in
policy situations?
3. Have you ever had an experience
where you made a decision with the
assistance of a model? If so, what do
you feel should have been improved in
the process?
4. Do you have any analytical
training or education? What kind and
at what level? From what disciplinary
point of view? (i.e., engineering, social
science, natural science, etc.). Do you
apply this skill in typical policy situa-
tions?
The overall purpose of these initial
questions is to identify the frame of
reference of a policy maker who would
be using the model results. Too often,
models have little reference to the
vocabulary and training of the potential
user, particularly if he is to be a policy
maker. We recall that several years ago,
for example, a study done of the liberal
arts, legal, and social science profes-
sions noted that usually only economists
were really trained to interpret graphics.
Consequently, the presentation of in-
49
-------
formation in the form of histograms
and graphs added little illumination to
the results and, in fact, it was suggested
that they added a degree of confusion.
Furthermore, we have experienced an
era in which we tried to do something
about the real need for large masses of
data for decision making purposes.
Computer packages were developed
which provided manipulative capabili-
ties such as statistical routines and
canned analytical algorithms. These
packages, however, were generally well
beyond the capability of most policy
makers. Thus, the policy maker was
informed that information was kept in
some standard form and that he was
able to carry out all sorts of sophisti-
cated statistical operations on it. His
training, however, might not actually go
beyond high school algebra. To compli-
cate matters, most policy makers have
not experienced first-hand an interactive
man-machine system. They therefore
have no idea what is expected of them
or what to expect of the system in such
a context.
These points serve to illustrate rea-
sons why the literature and the industry
is filled with so-called "management
information systems" which most policy
makers avoid. To the extent that the
policy maker in question has no ana-
lytical training, suggesting to him that
he personally use a computer or model
may be ego-threatening. Secondly, if
he has no computer training or under-
standing, he is apt to expect to be able
to do a great deal more or a great deal
less with the operation that is rea-
sonably feasible. If, on the other hand,
he does possess some degree of training,
education, and/or experience is the use
of computers in management, an oppor-
tunity exists for meaningful dialogue on
the capabilities and limitations of
models with respect to his real prob-
lems.
In short, an understanding of the
background and training of the policy
maker may tell the model designer
what kind of assumptions he can make
in terms of input and output to the
model system. It will also tell him
50
how much work he will have to do to
preprocess data (or outputs) for the
policy maker's use. In fact, given the
demanding schedule of most policy
makers, it is unrealistic to assume that
he will have the time to devote to a
significant re-education along the line
of his analytical or technological capa-
bilities.
Questions on the Policy-Making
Process
1. In the context of your role in
this organization, how do you best
characterize your responsibilities in
policy making terms?
2. How do you usually make a policy
decision? Do you utilize a staff of
advisors, a few principal ones, or decide
mostly on your own?
3. How would you like to see policy
making done ideally? Why?
4. How and in what form do you
prefer to receive policy oriented infor-
mation—by memo? By report? By
problem statements with alternatives?
Why?
It appears from reading the pre-
ambles to many so-called policy models,
or the documentation on same, that few
model builders have a clear understand-
ing of how policy is really made. In
fact, it may be the case that nobody
really understands well this very com-
plex process. On the other hand, it is
imperative that the model builder under-
stand not how decision making is done
in some abstract fashion, but how the
particular policy maker that he is in-
terested in building a model for con-
ceives of and carries out his policy
making duties and the specific require-
ments and resources of the policy
maker's role. Likely, this very complex
and individualistic process is little
understood by the policy maker simply
because he carries it out almost in-
tuitively.
The use of computer models, how-
ever, requires something more than
pure intuition—although just knowing
what the policy maker means by "in-
tuition" is in itself useful. Neverthe-
less, the process must be reduced to
-------
explicit form if the model is to have
utility. Interestingly enough, discussion
of this set of questions will probably
provide the greatest education for many
model builders who presume to under-
stand the policy level.
Questions on the Use of Models in
Policy Making
1. Models (or systems) can be con-
ceived of as answer-generating devices
which can be used by policy makers to
help solve complex problems. They
can also be conceived of as no more
than another advisor who is consulted
on specific types of questions and whose
advice is weighted by the policy maker
with that of others. Do you feel com-
fortable with either of these statements?
One more than the other? Why?
2. If a "true" policy model were
successfully built, how would you want
to use it? For periodic reports of future
forecasts? For predicting the impact of
past decisions? For frequent use in
assisting in day-to-day policy decision
making? What kinds of outputs would
you prefer—charts? graphs? numbers?
memos? others?
3. Would you prefer to interact di-
rectly with such a model or delegate
its use to your immediate staff for their
use in formulating policy advice? Why?
4. It is asserted that modern decision-
making should take full advantage of
sophisticated information systems and
hardware. Such a viewpoint suggests
either (a) a specially designed "deci-
sion room" with full information dis-
plays; and/or (b) immediate access.
What are your views?
5. Do you face any policy questions
on a somewhat continuing basis which
a specific policy model might be able
to assist in answering?
6. What kinds of questions might
other high-level administrators face that
are different from those you men-
tioned? How about the regional ad-
ministrators?
7. Would you prefer a model which
would provide quick summaries of real-
world data, or would you prefer a sys-
tem that enables you to project the
probable impact of various policy
choices over time?
The above set of questions is aimed
at trying to understand, before any real
modeling interaction occurs, what the
policy maker would anticipate getting
out of a model and how he might ex-
pect to use it if he would get a model
designed to meet his own needs.
Listening to the policy makers who
are having models designed and built
for them can be a rather disheartening
exercise for model developers. The ex-
pectations of policy makers usually far
outstrip the current technical state of
the art. Early specification of these
expectations can help the model builder
to know whether he is being expected to
push the state of the art of modeling
significantly to gather new data, or
whether the policy problems can be
simplified and handled with available
tools. In either case, this understanding
will help pinpoint his own work in
terms of the time, manpower, and
resources available.
Further, and most importantly, these
questions are aimed at exactly how
the policy maker perceives using the
models when done. There are obvious
but important options for use which
ought to be discussed, if only in a gen-
eral sense, at the outset. Some of these
are as follows:
a. use in a "situation room", with
continual use for policy purposes:
b. use intermittently for "status of
the system" reports;
c. use personally, by interacting with
a terminal or video display unit:
d. use by policy and support staffs;
and
e. combinations of these.
V. OPPORTUNITIES FOR
MODELERS AND POLICY
MAKERS
Thus far we have described the
policy-making process, policy-oriented
models, and one approach to the deter-
mination of the needs of policy makers,
in largely a critical context. In this sec-
tion we attempt to structure in a gen-
51
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eral sense the kinds of challenges we
envision the modeling community and
the policy makers must address in order
to take advantage of the significant
opportunities for improvements in
public-policy making that effective
computer models can provide. A de-
tailed and quite interesting discussion
of "meeting the challenge" is contained
in [6].
Challenges to Modelers
There are several schools of thoughts
as to what types of models, not only in
form but in content, would be of most
use to the policy maker. As with all
problems, at various levels of abstrac-
tion various alternatives are relevant.
For instance, if a specific public issue
reaches significant proportions it will
rise to the policy level and, even though
in greater detail than generally handled
at this level, may require precise inputs
and rigorous handling. Perversely, the
detail and data requirements of such
models, although potentially of great
use to the policy maker, generally pre-
clude their application. Problems of this
sort often encompass a time constant
which coincides only by accident with
the time constant of the scientific com-
munity manipulating the models.
More to the point, there seems to be
a class of problems which the policy
maker deals with all the time, and to
which the modeling community has
only recently begun to address itself.
The policy maker, like the biblical
Solomon, continually must adjudicate
between departments with competing
needs for scarce resources. He will
tend to prefer those policies which
appear to be most effective in pursuing
his goals and in satisfying his con-
stituency and, at the same time, mini-
mize the negative feedback from those
parts of the system which he has been
forced to de-emphasize. Such models
are the type that trade off various policy
choices among comprehensive alterna-
tives. In fact, such tradeoffs have to be
accomplished within the boundaries
not only of relating all the parts of his
interest area to each other, but also of
52
relating them through time, so that a
short-run decision which maximizes an
immediate gain does not turn out to be
suboptimal in the long run. Conse-
quently, what appears to be called for
is a model which is at a gross or aggre-
gated level of detail, allows manipula-
tion of a large number of alternative
choices, is sensitive to the time dimen-
sion, and is relatively easy and quick to
load, run, and interpret the output in
policy terms.
If it is true that the policy maker
really could make use of such models,
why is it that they have not generally
been built or applied? A perusal of the
literature provides three general answers
to this question: (1) theories available
to build such models, particularly those
of the social/political institutions, are
barely hypotheses; (2) the specific
functions constructed which purport to
represent the system under considera-
tion are open to question; and (3) the
data are either unavailable or in the
wrong forms.
One of the largest single issues sub-
sumed in the above is that the proper
method of validating policy models is
unknown. Since such models may claim
completeness, or a comprehensive base,
the only test that apparently can be
done is to see whether they will repli-
cate one time period. However, if it is
truly a comprehensive model, it will
only do this on a probabilistic basis.
Consequently, the lack of precision gen-
erally found in many partial models
leaves the analyst with no rigorous
method of validation. Since large scale
forecasting models can often be used to
generate a series of possible alternative
futures, which may or may not be likel)
depending upon the assumptions mad(
as the model cycles through time, th<
range of outputs would have to evalu
ated on a "most likely" basis rather thai
on one which was deterministic.
What this means to modelers may b
that since we continue to apply partia
models despite the fact that perfec
validation of such models is impossibl
given all the time and detail representec
should we avoid developing policy moc
-------
els for the very same reason? As For-
rester discussed in [6], policies made in
the framework of complex systems (e.g.,
urban areas, national governments, the
environment) are subject to such inter-
active behavior in the systems that un-
expected and counter-intuitive results
may well be the rule rather than the
exception. With this phenomenon in
mind, how can we rationalize complex
partial models in the absence of com-
prehensive policy-making processes? It
is clear that more attempts must be
made to model systems and that lack of
validation cannot by itself be allowed
to obviate policy models. On the other
hand, this statement should not be mis-
taken for license. Some test of reason-
ableness will have to be made and the
standards of scientific integrity kept
high. In short, the plea is made for
further experimentation and limited use
as an alternative to the presently fash-
ionable ostracism. The significant prin-
ciple should be that specification of
goals for the system should be explicit
and objective [8].
The question of unavailable data is
interesting. Probably little frustrates the
policy maker who supports a large or-
ganization more than to be told that
there are not enough data available to
answer his questions. This reply, in
fairness to both sides, is probably both
right and wrong. From the point of
view of the researcher or analyst, the
policy maker has a habit of changing
his mind as to what information he
wants and thus changing his long-range
information needs. The time frame is
often such that just as the research
community begins to gear up and handle
questions of one type, the policy maker,
having made his mind up in that area, is
anxious to move on to other questions.
This means that the scientifically-trained
analyst is eternally frustrated as he
attempts to get the ever-finer detailed
information. This is particularly true
since, again, his judges are his peers
and not necessarily the policy maker.
Nevertheless, it does the policy maker
little good to be told that in two years
a finished model can give him an an-
swer, when he needs an answer today
[5]. From the point of view of the
policy maker, his responsibility is to his
goals and to those of his constituency.
The issues and questions that need
answers are not necessarily those that
are amenable to the scientific method.
Issues and needs change more rapidly
than do systems for data collection.
Pressures are such that answers must
be given, and policy choices made,
whether or not enough data are avail-
able.
Thus the challenges to modelers are
substantial. If we really want policy
makers to use our tools for improving
public policy, then it appears the stand-
ards must be modified, as should the
ways of going about developing models
and communicating and sharing them
with policy makers. And the process
should be opened to more involvement
on the part of policy makers (and to
the public too, for that matter).
But who constitutes the modeling
community? In the first place, it is a
misnomer to label model builders a
"community". If such a community
existed, there would be little function to
this book. In truth, when modelers from
various disciplines assemble, their inter-
action problems are similar to those of
getting any multi-disciplinary team to
work together. The journals they read,
the training they have, the vocabulary
(not only that of the particular disci-
pline, but also that of the mathematics
and computer languages) are all differ-
ent. Most ad hoc groups gathered to-
gether to support the policy level spend
an inordinate amount of time in just
communication problems among them-
selves, not to mention the substantial
difficulties they encounter interfacing
with the policy level.
In our view there is a need for a
group of policy-oriented scientists to
support the policy maker. These people
would have the responsibility for making
available, to the policy maker, timely
information on demand which will help
him make his policy decisions. The in-
formation would be the best available
at a particular point in time and the
53
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specific requirements of the policy
maker may or may not engender future
research projects from the general R&D
staff. Models would be a basic founda-
tion of such a support group. Of course,
we recognize that since the data and
structure of such models are still in their
infancy, advice to the policy maker as
a result of using general purpose models
will have to be of a probabilistic nature,
extent that they have educated them-
selves. The subsequent fear of the new
and unknown is a serious impediment
to change.
There does not yet appear to be any
group which would be dedicated to sup-
porting the policy maker in environ-
mental issues, as a full-time vocation.
To further illustrate this void, visualize
the following typology:
Basic
Research
Physical & Natural
Transfer
Agent
Planning
Operations
Research
or
Popularity
Transfer
Process
Output
giving him some confidence level as to
how good or reliable the estimates are.
Nonetheless, such timely advice could
be of great value to policy level prob-
lems.
For an example of such analytical
support capability to the policy level,
let us again focus on one area—the
environment. Conceptually, a policy
maker in any area could be supported
in essentially the same fashion.
It is implicitly assumed that there
must be comprehensive and long-run
planning of the environment if policy
is to be promulgated which will actually
result in both cleaning up and preserv-
ing the environment. In practice, how-
ever, the day-to-day implementation of
policy often does not accommodate such
concerns. This feature is obviously not a
function of capriciousness of the ad-
visors, but often of the fact that these
people are also constrained by training
and by attempting to satisfy their pro-
fessional community. For instance,
perusal of college catalogues shows that,
for those who majored in the areas of
law, social science, business, public ad-
ministration and liberal arts more than
a decade ago, few had any training in
analytical methods. This means that a
large portion of our policy leaders and
their advisors are conversant with mod-
ern decision-making tools only to the
54
In order to facilitate the transference
of a select number of research findings,
the portions of society concerned with
production support a group called "en-
gineers". The engineers are accepted by
not only the producers but by the basic
researchers, thus engineers develop their
own professional ethic. Because this
group of professionals is supported by
the producers, the objectives of the
engineers reflect the needs of this group.
The engineer prides himself on being a
problem-solver. He seldom looks at
problems from the perspective of how
objectives can be accomplished [8].
The policy maker in society really
needs this same sort of support. Unfor-
tunately, many who would otherwise
fulfill this function find it too risky, in
a professional sense, to become tainted
with "merely" implementing somebody
else's research. Those who made the
transfer between basic social research
and the political arena have sometimes
been labeled "popularizers", especially
by the basic scientist who does not see
the translation of his jargon to more
generally readable form as being useful
in the sense of advancing the state-of-
the-art.
Another group, who are more readily
identifiable, have attempted to fill the
gap. These are the planners. Their pro-
fession has grown up as complementary
-------
in that they have tended to define areas
of interest in line with political and ad-
ministrative jurisdictions. Unfortunately
for the policy makers, these people are
not usually available for day-to-day
support, nor do they usually possess the
skills necessary to handle the analytical
chores required by comprehensive, long-
range policy making. Thus this gap is
being rapidly filled by still another
contingency—the operations researcher
or management scientist.
The purpose of this sorte through the
search for a legitimized policy scientist
in the environmental field, (or environ-
mental analyst), is to suggest that only
when such a profession is implemented
will the policy maker have the impetus
to take the future into consideration.
The environmental analyst will have this
long-range viewpoint because of his
training, and his logic will be reinforced
by his peers. The policy maker will have
the confidence (rightly or otherwise) to
meld these factors into his policies,
since his advisors will do it for him,
attest to the soundness of the practice,
and communicate it well to the policy
maker. It is not, in short, logical to as-
sume that the policy maker will change
his habit pattern to a less certain
strategy. Therefore, the change will
have to come from his advisors, who
concomitantly will have to receive sup-
port and encouragement, either from
other social scientists or from their
own peer groups.
Therein lies the challenge to mod-
elers.
Challenges to Policy Makers
This treatise would not be complete
if it omitted a discussion of the ways
in which policy makers can make bet-
ter use of analytical support to their
policy process. This is not to say that
models should be used regardless of
whether or not they are of immediate
value to the process, but rather that the
policy maker has a responsibility to
ensure that public policy-making is as
rational as possible and takes into ac-
count the full ramifications of policy
decisions—both in the short and long
What this means in terms of the de-
velopment and use of models is that
policy makers should insist on being
involved in the process. Most effective
model builders would be elated to have
policy-level scrutiny and input to their
design process because it will greatly
enhance the utility of the models.
Furthermore, policy makers should
take the time to stay generally abreast
of the field. Seminars, literature and
staff briefings are important inputs to a
continuing analytical capability. An in-
timate knowledge of the responsibilities
of the job coupled with a general un-
derstanding of analytical tools can pro-
duce a credible and rational frame-
work for not only making policy
decisions but also guiding research,
studies, and other developmental efforts
before projects or issues become crises
or failures. It is recognized that time is
critical to a policy maker; however, the
value of effective and relevant seminars
has been proven to be significant.
Finally, policy makers should be in-
novative and willing to experiment with
new tools. Just as modelers have a re-
sponsibility to develop tools for policy
makers, management should be recep-
tive to new approaches. This is an ex-
tension of the interviewing dialogue,
directly to the use of new tools, their
critique, and feedback toward their
improvement. Improved public policy
will only evolve from a better under-
standing of policy needs, impacts and
implications.
VI. CONCLUSION
In this chapter we have discussed the
general problems associated with the
use of models at the policy level of
government. In the context of this
Guide, this chapter hopefully provides
some insight into the gap which exists
between models and the policy maker,
and attempts to clarify the policy-
making process as differentiated from
program decision-making and lower
levels of problem-solving.
Model building for policy use con-
tinues to be largely an art, with only
slight characteristics of science a part of
55
-------
the process. Policy making, on the other
hand, is continually subjected to pres-
sures for systematic approaches and
analyses—often by the very people who
design models. Unless this gap is closed
and a better common understanding
and appreciation evolves, the many
models described in the chapters of this
Guide—the majority of which have
seldom, if ever, been used by the level
of policy maker we are concerned with
—may represent the ultimate achieve-
ment of models in the policy-making
process.
References
[1] Report on National Growth 1972, Presi-
dent's Report to Congress, 1972.
[2] Moynihan, Daniel P. (ed.), Toward a
National Urban Policy, Basic Books,
Inc., 1970.
[3] Perloff, A. and H. Wingo, Issues in Ur-
ban Economics, Resources for the
Future, Inc., 1969.
[4] Levin, M. R. and Abend, N. A., Bureau-
crats in Collision: Case Studies in
Transportation Planning, The MIT
Press, 1971 (especially p. 241).
[5] Remarks by Paul W. Cherington, Assistant
Secretary of Transportation for Policy
and International Affairs, before the
Transportation Research Forum, Octo-
ber, 1969.
[6] Forrester, Jay, Urban Dynamics, The MIT
Press, 1969.
[7] Brewer, Garry D., The Politician, the
Bureaucrat and the Consultant: A Cri-
tique of Urban Problem Solving, to be
published in Spring 1973 by Basic
Books, New York.
[8] Hoos, Ida R., "Systems Techniques for
Managing Society: A Critique," Public
Administration Review, March/April
1973, No. 2.
Appendix
AN EXAMPLE: THE
STRATEGIC ENVIRONMENTAL
ASSESSMENT SYSTEM (SEAS)
To this point in the chapter there has
been little suggestion of potential reme-
dies for our list of inadequacies of
policy models. The above questionnaire
represents one possible step in the direc-
tion of change, an attempt to begin to
serve the policy level. SEAS, as a
model (or system), has the scope nec-
essary to span the total environment
and, ineed, takes into consideration
numerous factors whose operation af-
fects the policies and success of EPA
but over which the Agency may have
little, if any, control. This description
of SEAS should be considered an ex-
ample of a policy model under devel-
opment. It is not meant to be an impli-
cation that there are no other such
models, but rather, since the authors
are involved, the process is designed to
alleviate common and typical problems
associated with past efforts of this type.
Scope of SEAS
The SEAS system will utilize pre-
existing demographic, economic, tech-
56
nological projections to forecast envi-
ronmental conditions both on a national
scale and for the ten standard Federal
regions. Inputs will be specified at the
national or regional level, and outputs
will be expressed in terms of national
or regional indicators and assessments.
There are obvious conceptual prob-
lems in developing aggregate indicator
assessments from information that has
its major impact at the local level, such
as air and water pollution. There are
also policy difficulties in attempting to
develop solutions to pollution problems
with national (i.e., not spatially specific)
policies. In spite of these difficulties,
nationally aggregated assessments must
be made for the sake of policy makers
such as the EPA Administrator, Con-
gress, the Executive and others con-
cerned with environmental progress
over time and in relation to other na-
tional concerns.
SEAS will evolve to be a comprehen-
sive system capable of forecasting po-
tential future environmental pollution
problems and evaluating the response
of the environment to such factors as
changing goals, policies, standards, and
resource constraints.
-------
Figure 3 illustrates a generalized
schematic of the overall SEAS system.
The system is designed with flexibility
to allow evolutionary development with
continual improvement over time. The
basic core system depicted contains
eight components interconnected by a
series of functional relationships. The
eight components are: Change Agents
(Inputs), Processes, Stocks, Residuals,
Effects, Reactions, Evaluators, and Out-
put. A general definition of each of
these follows:
Change Agents (Inputs)
Population, economic, technologic, or
other eventful potentials whose change
in magnitude, direction, appearance or
disappearance may pose significant con-
sequences for environmental manage-
ment. Population inputs may include
changes in total growth, patterns of dis-
tribution, social and economic composi-
tions, and value orientations. Economic
inputs may include changes in total
growth, patterns of distribution, ac-
tivity mix, social responsibility, work
ethic, and multinational orientation.
Technologic inputs may include pollu-
tion abatement technology changes, im-
proved recycling technology, etc.
Processes
Major activities of an ecological,
socio-economic system which respond
to the Change Agents. Processes are
divided into five sub-modules: extrac-
tion, production, distribution, consump-
tion, and disposal. Each of these has a
human and non-human component. The
human components are those processes
which are initiated, sustained, or pur-
posefully affected by man while the non-
human components are those processes
which will "naturally" occur without
human intervention.
Extraction—involves obtaining raw
materials for utilization in the produc-
tion process. Raw materials may result
from mining natural resources, restora-
tion, reclamation, recycling, resource
recovery, decomposition, etc.;
Production—is defined as a synthesis
of raw materials, intermediate products,
energy (labor) and capital to yield a
potentially consumable product;
Distribution—involves those activities
associated with overcoming spatial sep-
aration;
Consumption—defines activities
which result in the utilization of the
output of the other processes; and
Disposal—defines the collection, stor-
age, transportation, absorption and dis-
sipation of waste materials that are not
completely utilized by the other proc-
esses.
Stocks
The supply of natural or man-pro-
duced resources which are effectively
available for use by the processes. Tan-
gible quantities can be sorted into three
arbitrary categories—depleted, fixed,
and variable.
Depleted Stocks—those stocks which
FIGURE 3—SEAS Schematic
57
-------
are renewed at a rate so slow as to be
considered negligible, i.e., coal, oil.
Fixed Stocks—stocks which have a
continuous supply, the process of re-
newal is not affected by man; and the
quantity or quality of the resource may
be diminished in local areas, i.e., water,
air, etc.
Variable Stocks—the rate of renewal
of these stocks depends on the physical
environment and magnitude of the
propagating or producing stock or
process, i.e., agriculture, forestry, etc.
Residuals
Emissions (air), effluents (water)
wastes (solid), laydown (pesticides)
and releases (radionuclides) that result
before controls (gross residuals) or
enter the environment (net residuals)
after abatement or recycling.
Effects
Residual levels in the different media
impact upon the socio-political, eco-
nomic, and environmental systems. The
magnitude and characteristics of this
impact will depend upon the deleterious
or beneficial qualities of the residuals,
the distribution or concentration of the
population at risk and the type and
sensitivity of the physical environment.
These impacts will be considered in the
effects modules of the SEAS system.
Reactions
Certain changes in socio-political,
economic, and environmental systems
occur in response to exposure to re-
siduals as well as actions taken to
counteract their impacts. For example,
provision of health care facilities may
increase, or populations and industries
induced to migrate.
Evaluators
Techniques which apply to the analy-
sis of the changes in the Stocks, Re-
siduals, Effects and Reaction Sectors.
Stocks—measurement of the effective
growth and decay rates, levels and
usage rates of the stocks by the different
processes and residuals.
Residuals—measurements of levels
58
and/or rates of increase (decrease) of
residuals on a regional and national
level as well as a comparison of previ-
ous years' levels and rates of change.
Effects-Reactions—analysis of the se-
verity, duration, and dispersion of the
effects on the socio-political, economic,
and environmental systems and their
subsequent reactions.
Output—The output of SEAS will be
designed and formatted to provide quick
summary options for policy assistance
and more detailed outputs for investiga-
tive purposes. The output will include
graphical displays and formatted statis-
tics by region and a national summary.
This brief overview of the model
should serve as an introduction to the
SEAS concept. It is certainly not suffi-
ciently detailed to satisfy the require-
ments of a systems analyst, but such
documentation is available. For illustra-
tive purposes we use the design to dis-
cuss its potential use within the Agency.
Because the System is only recently
operative, it will be best to discuss it in
generalities.
The first important aspect is the scope
of the model. The system will attempt
to look at all pollution media at the
same level of aggregation or analysis.
This is a design decision meant to enable
the policy levels of the Agency to con-
sider comprehensive decisions, across
the Assistant Administrators' responsi-
bilities and lines of authority. SEAS is
also to be used, hopefully, to assist the
Assistant Administrator for Research
and Development to focus on areas of
research where information is sparse
and where his experience tells him that
such information has priority. This
means that the level of detail will likely
not be satisfactory to some individual
users in given functional areas and al-
most certainly not adequate for the pur-
poses of the scientist-analyst. On the
other hand, because the policy maker
does not normally get involved in pro-
grammatic task level details, the tools
used to support him probably should not
be at this specificity either.
In addition to the scope of the model
in terms of the responsibilities of EPA,
-------
the system is sufficiently broad in scope
to generate possible alternative futures
that might occur without taking any
special actions. In the next section we
describe the context in which SEAS is
planned to be used in accordance with
the scope discussed above.
Expected Uses of SEAS
We realize that this description of
SEAS is limited; however, it is ade-
quate for the purposes of this paper.
There are two specific types of efforts
to make the SEAS system most useful
to the Agency. In the first place the
actual output itself is being designed in
close conjunction with the policy level.
It will not consist merely of a series of
tabular printouts, but will be formatted
so that the analysis is consistent, the
graphics and tabular information of the
type preferred by the users, and in a
form with which they are comfortable.
The second output design stage in-
volves emphasis on the type of informa-
tion that will be generated. SEAS, as a
forecasting system, is highly complex
and will be able to generate a great
variety of information. It is certain that
the potential amount of data which
could be reported will be huge and, if
one were to attempt to report it all after
each iteration of analysis, or even a
large part of it, the volume may well
preclude its use. Therefore, it has been
decided that the output will likely be in
summary form, in relation to selected
scenarios. The scenarios will be carefully
defined, again with the help of the
policy level, to present possible alterna-
tive futures in a form and in the kind
of detail that will assist in policy mak-
ing.
After developing projections based on
selected scenarios, SEAS will report
on the future state of the environment.
The technical staff will, with the help
of other experts, make judgments as
to which of the alternatives are most
likely and then use the other estimates
to statistically calculate the probability
of the result. Finally, the range of out-
Impact of Alternatives
Reactions
Effects
Pollution Levels Distribution
National — Regional
HI,-.,- ..(Mi..
IK.II,, oil..
Projected Scenarios
Executive Summary
>> ulliillo ..-I
I,, , ,MI, Ml
STATE OF THE
ENVIRONMENT REPORT
,,11.1)1,, 0,1
I I
Mitllii itlloir
.•11.1,1(1 ,.H"I
ul>ll> Ml »,
.11 I 0,1 .Mil
II, l,l,ll> I,l4
.,1.11 ! l.lll M.
oil I, , I O..I
II I,H| I'll
Illllll l.lll II,
II Ml.ll ool
II, ,.,1,11, 1,4
.1,1- lol ,
oil I u, I
.Hi l.i
I, Ml ..... 1,1
ill ..... 1.11, I >
111 loll .,.,,1
J [_
lllOltll Ollllll
,.„!,. nil, .,,1
>il>, iMf ,»!«
..rfl Jl,, oil.,,
MM* .1 ( III I
oil, , Im.ll
,, ,.lk.ll,l 0,1
FIGURE 4—State of Environment Report
Ml.. m'.Ni I
trill kill I
olloll., „ 1,1
4l.i ., ,11 > I
1,11, loll I ,,l
..Hull. j.. .1
•I., o.l.ll.
Mil loll ,,,,1
, II, M 1,11
,11,. ,.,l,lli I
l.lll loll ,,,,il
..lloll., o.l.l-
M l,lli I
59
-------
puts will be presented in terms of "best"
and "worst" cases according to the
particular interests of the policy makers.
Figure 4 illustrates schematically the
contents of the "State of the Environ-
ment", an annual (or periodic) product
of forecasting and analysis of the type
described above.
In summary, we have presented SEAS
as a system which is to be a tool for
use at the policy level of EPA. Its scope
accommodates the interests at this level
and as such is being designed so as to
provide maximum flexibility. The care
with which the results of its use can be
presented and the attention being paid
to making sure that the potential users
understood the assumptions in the sys-
tem, should help mitigate against, on
the one hand, unwarranted expectations
of the potential of the system, and fear
or derision of its real worth on the
other. Finally, its policy uses are ex-
pected to be broad in scope and, by de-
signing for maximum flexibility, hope-
fully diverse in nature. The ultimate
tests will come when it is fully devel-
oped and used.
60
-------
Chapter 3
Models in Air Pollution
By
Nozer D. Singpurwalla
SUMMARY 63
I. AIR POLLUTION: GENERAL DESCRIPTION OF THE PROBLEM 64
A. General Description of the Air Pollution Problem 64
B. The Notation of Averaging Time and Maximum Concentration 66
C. Decision Processes in Air Pollution 68
D. Mathematical Models in Air Pollution 69
E. Relationships Between Models and Decisions 73
II. DISCUSSION OF SPECIFIC MODELS USED IN AIR POLLUTION 76
A. Stochastic Models 77
1. Models for the Distribution of Pollutant Concentrations 79
2. Regression Models in Air Pollution Analysis 82
3. Models for Predicting Maximum Concentrations 86
4. Time Series Analysis Models ... 88
B. Deterministic Models 94
1. Diffusion Models . 95
2. Optimization Models 99
REFERENCES 101
61
-------
-------
Models in Air Pollution
SUMMARY
In this chapter we will discuss some
of the mathematical models that can
be used to obtain answers to the quan-
titative questions which arise in air
pollution problems. The mathematical
models discussed here have proven to
be of some value in analyzing specific
air pollution decision problems. More
important, however, by using these
models we are now able to examine
these problems more systematically and
evaluate proposed policies in more de-
tail.
Since the models that are discussed in
this chapter may be too technical for
some readers, we have presented our
material in two sections. In section I we
have given a non-technical discussion
of the nature and the use of mathe-
matical models useful in air pollution
problems. In section II we have given a
more detailed and technical outline of
these models.
In section LA we present a general
description of the air pollution problem.
We state with a minimum amount of
detail, the causes of air pollution in
both urban and rural areas, and the ill
effects of air pollution to man, animals,
plants, and property. We also discuss
here the setting of air quality standards
and their interpretation.
In section I.B we introduce and dis-
cuss the important notion of "averaging
times" and "maximum concentration"
and point out the relevance of these
concepts to the air quality standards. In
the interest of brevity and clarity of
presentation, this section is written more
informally, using mathematical notation.
In sections I.C and I.D, we discuss
the various decision processes in air
pollution and outline the various mathe-
matical models that can be used in air
pollution, respectively. We characterize
the models by the functions which they
can perform and by the methodology
employed to develop them.
In section I.E we discuss the relation-
ships between the models presented in
section I.D and the decision processes
presented in section I.C. We discuss
these relationships by using hypothetical
problems faced by various levels of
decision makers and how they would
use the models to solve their problems.
We also illustrate the interrelationships
between the various models and decision
processes by general diagrams. Readers
who are mainly interested in the use of
mathematical models and the decision
processes for which they can be used
will find section I.E a convenient place
to stop. Clearly, those readers who wish
to gain more insight into these models,
their basis and their underlying assump-
tions are advised to proceed to section
II.
Section II is divided into two sub-
sections. In II.A we discuss stochastic
models such as regression, time series
analysis and the extreme value theory
models. In II.B we discuss deterministic
models such as the diffusion models and
optimization models. Wherever feasible.
we illustrate the use of these models by
alluding to actual applications for which
models have been used. We also discuss
the basic assumptions underlying these
models, and point out the limitations
and the scope of these models.
In summary, this chapter on air pollu-
tion models is not intended to be all
inclusive and exhaustive. Rather, it is
written with the objective of being as
complete as necessary in order to con-
vey a basic understanding of those air
pollution decision problems for which
models can be of assistance.
63
-------
AIR POLLUTION
Models Discussed in Chapter
Summary Table
Model/Decision Area
General Type
Important Characteristics
Air Pollution Standard
Evaluation, Monitoring
Control
Air Pollution Standard
Evaluation, Monitoring
Control
Prediction of Pollutant
Concentrations,
Identification of
Significant Factors
Causing Pollution, and
Economic Analyses of
Air Pollution
Prediction and Fore-
casting of Pollutant
Concentrations,
Identification of Trends
Prediction of Pollutant
Concentrations at
Different Points in an
Area
Optimization of
Resources, Planning
Strategies, Making
Decisions
Probability Distribution
of Pollutant Concentration
Probability Distribution of
Maximum Concentrations
Regression Model
Time Series
Analysis Models
Diffusion Models
Linear Programming
Nonlinear Programming
Uses data to obtain a prob-
ability distribution of pol-
lutant concentrations. This
distribution can be' used to
find out how often a pro-
posed standard will be vio-
lated
This distribution can be used
to find out how often a pro-
posed standard for maxi-
mum concentrations will be
violated
Based on data we can evalu-
ate what factors cause pol-
lution. We can also predict
concentration levels based
on specified values of the
significant factors
Using historical data we can
forecast individual values of
future pollutant concentra-
tions. We can detect trends
in pollution levels
Using some data on wind
velocity, wind direction, and
other meteorological param-
eters, concentrations at vari-
ous points in space can be
predicted
Gives us a strategy for
optimum allocation of
limited resources such as
fuels, monitoring equipment,
etc. to minimize the control
effectiveness of an air pollu-
tion program
I. AIR POLLUTION:
GENERAL DESCRIPTION OF
THE PROBLEM
A. General Description of the
Air Pollution Problem
To a decision maker concerned with
environmental problems, the subject of
air pollution is of interest for com-
pelling reasons. While many aspects of
this subject are political and emotional,
some of the major questions are quan-
titative and indeed mathematical. Air
pollution comes from many sources,
varies widely from place to place, and
64
time to time and affects many individ-
uals differently.
The automobile problem involves
problems of traffic flow, and the varied
performance of vehicles of similar or
disparate models. Atmospheric condi-
tions add major variability to a problem
already characterized by variation.
Clearly, the building and testing of
mathematical models has to be a feature
of any attempt to become cognizant of
the problem as a whole.
Whenever combustion occurs, air is
polluted. Man pollutes his atmosphere
by burning fuels to produce energy, by
-------
waste incineration, by discharges of gas
and aerosol by-products from chemical
processing, manufacture, construction
and demolition. As the rate of fuel
combustion has increased over the
years, the emission of pollutants into
the atmosphere has also increased.
Though the problem of atmospheric
pollution is world-wide, it is primarily
a problem of municipalities where pol-
lutants are concentrated in relatively
small geographical areas that are so
densely populated. The geography of a
certain area plays an important role in
the generation of an air pollution epi-
sode for that area. The temperate zone
(latitudes 30°-60°) experiences more
variability in weather than either the
polar regions or the equator. Cold air
masses are formed at the poles and hot
air masses in the tropics. Variations in
these air masses combined with the
rotation and the roughness of the earth's
surface cause large pieces of these air
masses to break off and move through
the temperate zone. The transition re-
gions between masses of cold and warm
air are called "fronts." An "inversion"
is said to be formed when there is a
layer of warm air above one of colder
air. In such a situation, in the absence
of wind, pollutants entered into the
atmosphere will not be dispersed, creat-
ing a situation of concern. Understand-
ably, air quality is strongly dependent
upon weather. Superimposed on the
influences of large weather systems are
the complications introduced by cities
themselves. Any urban complex exerts
a notable effect on its own climatology.
The many structures rising to different
heights and arranged in different pat-
terns, the properties of the materials
used in these structures and the pave-
ments that surround them all play a
role in creating a localized atmospheric
system.
Air pollutants offend and harm man,
animals, plants and property in various
ways. One offense is odor, an effect that
can be sensed if pollutant concentration
exceeds the odor threshold for a few
seconds. Another effect is surface dam-
age. For instance, sulfur dioxide, an
acid pollutant, damages the surfaces of
man's upper respiratory tract, plant
leaves, buildings and metals. A third
effect is the toxicity created by pollut-
ants that enter the lungs and dissolve
in the blood and body tissues; carbon
monoxide and lead are such pollutants.
Usually surfaces and internal tissues
require a pollutant exposure of an hour
or more before much damage is caused.
Carcinogenic pollutants may cause can-
cer from a lifetime of accumulated ex-
posure.
The setting of air quality standards is
a major step toward controlling wide-
spread pollutants. The major purpose of
air quality standards is to prevent the
occurrence of adverse effects such as
those described above.
The concentration of an air pollutant
is a measure for expressing the degree
of pollution. The concentration is ex-
pressed in either parts per million (ppm)
or micrograms per cubic meter (ug/m3).
In the United States, the Federal govern-
ment sets national minimum air quality
standards for pollutants; however, the
states may set more stringent standards
if they wish. In these standards, allow-
able levels of air pollution are expressed
in terms of the concentration of a spe-
cific pollutant and the duration of ex-
posure to that pollutant.
Table 1, abstracted from the "Office
of Air Programs Publication No. AP-
89" shows the effect of various pollut-
ants as a function of the duration of the
exposure. For example, an exposure to
sulfur dioxide for a period of 4 days
impairs one's general health, whereas
an exposure of sulfur dioxide for a
period of one year or more would
damage vegetation, corrode materials
and of course impair one's health. At
the other extreme, an exposure to oxi-
dant of one second or more may cause
eye irritation. It is apparent from this
table that in order to relate pollutant
effects to pollutant concentrations, the
concentrations should be analyzed as a
function of exposure duration.
The mathematical models useful in
air pollution analysis refer to pollutant
concentrations and the duration of ex-
65
-------
Table 1. Relationship Between Air Pollutant Exposure and Effects
Approximate
exposure
duration
Effect
1 sec Sensation
Odor
Taste
Eye irritation
1 hr Student athlete per-
formance impaired
Visibility reduced
8 hrs Judgment impaired
Heart patients stressed
Vegetation damaged
1 day Health impaired
Soiling
4 days Health impaired
1 yr Health impaired
Vegetation damaged
Corrosion
Soiling
Pollutant
Carbon
Oxidant
Particulate
matter
Sulfur
oxides
posure, depending on what the model
is attempting to do. It is this aspect of
the problem that makes mathematical
models for air pollution quite involved.
Before we proceed any further, we
would like to point out to the reader
that the mathematical models used by
decision makers or by other analysts
dealing with air pollution problems are
quite involved and complicated. For
example, it is well recognized that diffu-
sion models useful to both decision
makers and other analysts are derived
from the complex phenomenon of heat
transfer and turbulent flow, and are
represented by lengthy and complicated
equations.
To be able to discuss and motivate
the use of these models in any satis-
factory and convincing manner, it is
imperative that we introduce some
mathematical formalization into our
discussion. What follows is with this
spirit in mind, though we have at-
tempted to minimize the mathematical
details to a point of absolute necessity.
We urge the interested reader to plow
through some of these fine details which
are presented in a style and manner
palatable to a non-technical reader.
To be able to discuss the mathe-
66
matical models presented here it is
necessary that we acquaint the reader
with some notions fundamental to air
pollution. This is the notion of an aver-
aging time and maximum concentration.
A discussion of these notions also
familiarizes the reader with the manner
in which air pollution data is collected.
B. The Notation of Averaging Time
and Maximum Concentration
In an effort to relate air pollutant
concentrations to the duration of ex-
posure, the notion of an averaging time
is introduced. Under the Continuous
Air Monitoring Program (CAMP) of
the Environmental Protection Agency,
pollutant concentrations are punched
into a tape every five minutes. Let t1;
tz, . . . , tki. . . , <,, denote the instants
of time, spaced five minutes apart, at
which concentrations of a certain pol-
lutant, say x, ,xt , . . . , xt are recorded
' J V V ' 1K
on a tape. Thus xt; denotes the concen-
tration (in parts per million or micro-
grams per cubic meter) of a pollutant
observed at time tt.
Larsen [1] refers to the xt. as values
of the concentration for a five minute
averaging time. Values of the concen-
-------
(ration cq for a ten minute averaging
time are obtained as
a, =-
•, a, = •
Similarly, values of the concentration
for averaging times of fifteen minutes,
say ft are obtained as
xtl + Xt2 + xt,
£» I f 3 r.
Pi — 3» P2 =
Similarly, one can obtain values of
the concentration for averaging times
of twenty minutes, one hour, one day,
one month, etc.
To be more general, we consider
values of the concentration for averag-
ing times of 5k minutes where k is any
number, an integer. Thus, averages of
length k are
hour average concentration of carbon
monoxide recommended by New York
State's community air quality objectives
is 30 ppm, whereas in the U.S.S.R., it is
1 ppm for a 24 hour averaging time.
According to CAMP an 8 hour averag-
ing time would correspond to k = 8 X
12 = 96, since one hour would cor-
respond to k = 12. Thus if the maxi-
mum of averages of length 96 for
carbon monoxide exceeds 30 ppm,
there would be a violation of the New
York State standard.
As mentioned before, the maximum
pollutant concentration is of main con-
cern to those involved with the control
of air quality. As a matter of fact, most
of the analysis of the CAMP data deals
with the maximum concentrations.
Table 3 abstracted from Larsen [2]
shows the observed maximum concen-
tration of pollutants in some U. S. cities
for various averaging times.
For example, the observed maximum
. +x
t
%+l
% + 2
For purposes of evaluating air qual-
ity, it is important to know the behavior
of the maximum average pollutant con-
centration since it is the maximum con-
centration lasting for a certain duration
of time that causes concern. Let i)k n
denote
-+xtn).
concentration of carbon monoxide for
Chicago for an averaging time of 8
hours is 35 ppm, a clear violation of
the New York standard given in Table
2, whereas for Los Angeles it is 28 ppm,
below the New York standard.
The models for predicting maximum
-+xtk), . . . , k-1(xtn_
k+i
-+xtn}.
The above expression states than i)k n is
the maximum of the averages of length
k, from a total of n observations.
The following table (Table 2), ab-
stracted from Larsen [2] shows the
maximum average concentration for
certain pollutants adopted as an air
quality standard by several states in the
U.S.A. and West Germany and the
U.S.S.R. It is clear from this table that
air pollutant concentration standards
are stated in terms of the various aver-
aging times, and it is of interest to know
the chances that the maximum concen-
tration exceeds the specified standards.
For example, the maximum eight-
concentrations as a function of averag-
ing times using extreme value theory
and time series analysis which will be
discussed later rely heavily on the con-
cepts laid out here.
The main objective of this section
was to introduce the decision maker
to the most important variable for his
decision making; namely, the standard
for pollutants. This standard being ex-
pressed in terms of the maximum con-
centration and an averaging time.
This section, which is a bit technical
in nature, has been presented prior to
the following section which deals with
decision making in air pollution, be-
67
-------
Table 2. Air Quality Standards
Pollutant
Gases
carbon monoxide
nitrogen oxides
oxidant
sulfur dioxide
Suspended Particulates
lead
total
Concentration and Averaging Time for Selected Standards
California
30 ppm
8hr
0.25 ppm
Ihr
0.15 ppm
Ihr
0.3 ppm
8hr
Colorado
0.1 ppm
Ihr
0.1 ppm
Ihr
0.1 ppm
24 hr
New York
30 ppm
8hr
0.15 ppm
Ihr
0.4 ppm
Ihr
100 Mg/m3
lyr
West
Germany
0.5 ppm
Ihr
0.2 ppm
Ihr
USSR
1 ppm
24 hr
0.06 ppm
24 hr
0.06 ppm
24 hr
0.7 jug/m3
24 hr
150/ig/m3
24 hr
Other
5 ppm
8hr
0.02 ppm
8hr
cause in this section we establish a
vehicle for discussing the decision mak-
ing processes. Had we reversed our
order of presentation we would not
have been able to pinpoint the problems
effectively.
C. Decision Processes in Air
Pollution
This section and the one which fol-
lows essentially capture the essence of
decision making problems in air pollu-
tion and the role of mathematical
models which assist a decision maker.
Since the models that are used here are
of a highly technical nature, what we
have done in this section of Part I and
the others which follow is to give a non-
technical discussion of the nature and
the use of these models. Part II of this
report outlines these models in a greater
technical detail and could be pursued by
anyone interested in investigating these
models in greater depth.
Decision-makers involved with an
analysis of air pollution are faced with
making decisions which can be broadly
classified under the following categories:
• Those involving the setting of air
pollution (quality) standards.
• Those involving the monitoring of
air pollution concentrations in
order to adhere to the specified
standards.
• Those involving the control of air
pollutant emissions from different
68
point and areas sources in a man-
ner which enables the air pollution
standards to be met and at the
same time does not hinder the
general economic welfare and the
day io day needs of the inhabitants
of a particular area.
The above decision processes are
quantitative in nature, since they in-
volve air pollution standards which are
maximum concentrations for specified
durations. Mathematical models to help
one execute these decisions effectively
have been developed. Though some of
the models will be specifically applicable
to one of the above decision processes,
there are some models which can be
used for more than one of the above
decision processes.
Before presenting a discussion on the
role of mathematical models in air pol-
lution analysis, some more details on
the decision processes outlined above
are next discussed.
The setting of air quality standards
is a problem well debated by those in-
volved in air pollution studies. The
major purpose of air quality standards
is to prevent the occurrence of adverse
effects such as those described in Sec-
tion A.
Once an air quality standard has
been set, the next task is to monitor the
standard. The question of how often
will the standard be violated, is a vio-
lation a genuine one or is it due to sta-
-------
tistical fluctuations, etc. will be of in-
terest to the decision-maker. The de-
cision-maker will also need techniques
which can predict the violation of a
standard, and based on this prediction
take preventive measures. The decision-
maker will also need to know the re-
liability of his predictions so that he
may not raise false alarms too often.
Since pollutants are emitted into the
atmosphere through various sources,
the decision-maker will often be faced
with the problem of deciding which
sources of emissions should be con-
trolled. For example, in any urban
area, emissions from automobiles, in-
dustrial chimneys, individual heating
units, power plants, etc. are common.
In order to adhere to a specified stand-
ard the decision-maker may want to
reduce the emission from automobiles
by requiring them not to pass through
certain areas, or by requiring that power
plants shift to low sulfur fuels, or by
requiring that individual heating units
be closed down. Each of these actions
affects the economic well-being and the
personal comforts of the citizens in this
area. Once again there are conflicting
objectives under which a decision-
maker is required to act and mathe-
matical models could be useful tools for
such decision problems.
These decision problems presented in
the above paragraph can be better con-
veyed by the following examples:
The mayor of a large city must de-
cide whether to approve a proposed
major addition to an electric power
generating station. If this addition is
approved, the residents of this area
would be assured their growing demand
for electric power at a fair economic
cost. However, approval of the addition
ivould lead to a further worsening of the
:ity's air quality. Should this addition be
approved?
The governor of a State must decide
vhether to pass legislation that would
nlace stringent limits on the sulfur con-
ent of fuels burned in the State. If
>assed, this will lead to a definite im-
>rovement in the State's air quality
but the consumers would have to pay
more due to the use of the more ex-
pensive low sulfur. Should this legisla-
tion be passed?
Each of the above decision problem
(or problems) is faced presently or has
been faced by public officials. More-
over, they are representative of a host
of similar problems that public officials
are increasingly being asked to con-
front, namely, "Should government
(State or Federal) adopt a specific,
proposed program to improve air
quality?" With each, there is the addi-
tional question, "What should the air
quality be?"
Due to the complex nature of these
problems, an individual finds it difficult
to decide which, if any of a series of
proposed air pollution control programs
to support. One cannot claim that
mathematical models can provide a
solution to any of the current air pol-
lution problems, but using these models
one may be able to examine proposed
policies in more detail than is currently
done.
D. Mathematical Models in Air
Pollution
As discussed before, the decision
processes in air pollution problems
being quantitative in nature, mathe-
matical models play an important role.
The variables to be controlled or pre-
dicted are the concentrations of the
various pollutants for specified averag-
ing times. It is to be emphasized that
mathematical models are abstractions of
reality and have to be used with cau-
tion. Before using these models one has
to ascertain that the basic assumptions
underlying these models are adhered to,
and realize that the conclusions ob-
tained from these models have to be
judiciously exercised. In summary,
mathematical models are merely an aid,
albeit a strong one, in the general de-
cision-making process.
The models that are discussed here
can be characterized by the functions
which they perform. As far as air pol-
lution problems are concerned, this
69
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functional characterization leads to two
broad categories:
1) Those models that are used for
the purpose of predicting or fore-
casting air pollutant concentra-
tions. The models (to be dis-
cussed later) which fall under
this category are:
a) Models for the distribution of
pollutant concentrations
b) Extreme value theory models
c) Diffusion models
d) Regression models, and
e) Time series analysis models
2) Those models that are used for
controlling or monitoring air pol-
lutant concentrations, and those
models that are useful in under-
standing the physical phenomena
which influence pollutant concen-
trations. The models which fall in
this category are
a) Diffusion models
b) Regression models
c) Optimization models, such as
linear and nonlinear pro-
gramming models
Clearly, there are some models which
can serve either one or both of the
above two functions.
The mathematical models useful for
air pollution can also be categorized by
the methodology or the scientific
thought employed to develop them.
Once again this type of characterization
leads to two classes:
1) Stochastic Models—These models
have a probabilistic structure im-
posed upon them. The models
which fall under this category are
a) Models for the distribution of
pollutant concentrations
b) Extreme value theory models
c) Regression models
d) Time series analysis models
A chief consequence of these models
is that results and conclusions obtained
through these models are probabilistic
statements. This is, the conclusions are
true only a specified percent of the
time. Such models have been well
accepted in several branches of scien-
tific and management endeavors. Until
recently, except for regression models,
72
such models have not been significantly
used in air pollution problems. Of late
their use in air pollution problems has
been increasing and such models appear
to have a great potential for future
work.
2) Deterministic Models—A deter-
ministic model is one which does
not have a probabilistic structure
imposed on it. The models which
fall under this category are
a) Diffusion models
b) Optimization models
The dispersion and the diffusion
models have been well discussed in the
literature, and are based upon idealiza-
tions of the physics of air transport and
fluid flow. Most of the dispersion type
models include meteorological variables
and are useful as predictive models.
Since these models involve a good deal
of idealizations of the physical proc-
esses, a great deal of care should be
exercised in making decisions based on
such models.
Most of the optimization models used
in air pollution problems are deter-
ministic in nature. Functionally they
fall under the category of models for
control of air pollutant emissions,
though they have also been used for
problems involving the allocation of
funds for air pollution control pro-
grams. The optimization models are of
use to management for making broad
based decisions and are extremely use-
ful and practical. Despite these ad-
vantages, there seems to be a dearth of
the use of such models in air pollution
analysis and management problems.
Once again, of late their use in air pol-
lution problems has been increasing
and it is likely that such models will be
used more and more once their capa-
bilities are discovered.
This section is concluded by empha-
sizing the following points.
1. For air pollution prediction
monitoring and control problems
mathematical models serve a;
valuable aids which have to b(
used judiciously.
2. The air pollution phenomenon i
extremely complex; it is a func
-------
tion of the meteorology, clima-
tology, the demography and the
urbanization of a certain area.
What is more, some of these
variables interact with each other
and are also time dependent.
Mathematical models are ideali-
zations or simplifications of
reality and are developed under
specific assumptions. In using
these models one should ensure
that the assumptions are adhered
to and one should treat the re-
sults and conclusions from these
models with extreme care.
E. Relationships Between Models
and Decisions
Before going into the specific details
regarding the proposed models, it is
We will next consider several illus-
trations, each addressing itself to a
specific problem and then consider an
illustration wherein several of these
models could be used in the same prob-
lem.
1. A decision maker at the State or
the Federal level is interested in evalu-
ating or setting a standard for a certain
pollutant. Specifically he wishes to
know how often the observed concen-
tration will violate the standard under
question.
The decision maker will first collect
some data on the pollutant under ques-
tion and use the model for the dis-
tribution of the pollutant concentra-
tion. The following is a schematic of
the steps, chart i.
Input
Pollutant
Concentration
Data
Model for the Distribution
of
Pollutant Concentration
Output
Probability that the
proposed standard
is violated
worthwhile to point out how these
models relate to each other and how
they can aid a decision maker at the
State or the Federal level. This is possi-
ble since the models have been func-
tionally categorized as predictive and
forecasting or control and monitoring.
As far as a decision maker in the Fed-
eral or State government is concerned,
the control and monitoring type models
are of the greater interest to him. As
will be shown later, the prediction mod-
els could serve as inputs to the moni-
toring and control models. A decision
maker concerned with the setting of
pollutant standards will be most con-
cerned with predictive and forecasting
models. Of course, as pointed out be-
fore, the use of these models for specific
management type tasks is not clear cut.
3ne may wish to use some or all of
he above models based on his specific
need. As a rule, these models which
ire designed for more general use can
x adapted to one's situation depending
in the problem at hand. In view of
his it is important for a decision maker
o understand the use, the capabilities
ind the limitations of each of the mod-
:ls discussed here.
2. Suppose now, that this decision
maker is satisfied with the standard dis-
cussed in 1 above. However, he wishes
to test if the observed maximum con-
centration will violate this standard
too often. As discussed before, air
pollutant standards are often set for
maximum concentrations observed for
certain averaging times. Thus a ques-
tion that may arise is, "how often does
the observed maximum concentration
for a specified averaging time exceed a
given standard?"
The decision maker will now use in
addition to the model for the distribu-
tion of pollutant concentrations an
extreme value theory model. A sche-
matic of the steps involved appears at
the top of p. 74, chart ii.
3. It is conjectured that there are
several controllable factors which con-
tribute to the pollution of a certain
geographic area. Some of these may
be amount of industrial heating, the
amount of traffic flow, number of in-
dustrial plants which emit effluents into
the air, the quality of fuels used by
these plants, the population of an area,
etc. A decision maker wants to verify
this conjecture, with the ultimate aim
73
-------
11
Input
Pollutant
Concentration
Data
that by controlling those factors that
contribute the most to the pollution,
he can improve the air quality. In effect
the decision maker wishes to know
which factors contribute to the air pol-
lution and to what extent. He also
wishes to know by what amount can
the air pollution be reduced if he re-
duces the effect (the values) of these
factors.
For this problem the decision maker
could use a regression model, provided
that the assumptions for regression are
satisfied.
The following is a schematic of the
steps, chart iii.
Output
k Probability that
proposed standard
is violated by
maximum
concentration
4. Now suppose that the decision
maker discussed in 3 above would like
to make broad predictions or forecasts
of future pollution in his area based on
the increase (or the decrease) of the
values of his factors. For example, he
may know that the population in his
area is projected to grow by a certain
amount or that due to the construc-
tion of a public transportation system
in his area, there is going to be a de-
crease in the traffic. Based on these
projections he may wish to predict
the pollutant concentrations in his area.
The decision maker could use the
111
Input Data
Values of the factors
and the pollutant concentration
corresponding to these values
I
Model for the distribution
of pollutant concentrations
I
Are the assumptions
of the Regression Model
satisfied?
Yes
No
Use standard
Regression
Model
Use Amended
Regression
Model
Output
Significant Factors
74
-------
regression model discussed in 3 above 6. The city management council of
to accomplish this, chart iv. a metropolitan area is considering giv-
Input
Projections of
factors relevant
to study
h.
p
Regression
Model
developed in
3 above
b-
Output
Prediction of
future pollutant
concentrations
IV
5. Certain regulatory measures have
been instituted in a particular area, in
an effort to lower the level of, say
carbon monoxide concentrations. After
a certain period has lapsed, that is,
some time after these control measures
have been introduced, a decision maker
would like to ascertain if there is a
downward trend in pollutant concen-
trations. He would also like to deter-
mine if this trend is going to continue
into the future, assuming that there
are no anticipated changes in the fu-
ture which are going to increase the
concentration levels.
An appropriate model that can be
used here is a time series model. A
time series model has fewer assump-
tions in it than a regression model,
it is a model based on past data alone,
it can detect trends, both cyclical or
otherwise, and what is more, it can be
Input
Data on
Wind Velocities
Weather Conditions
Emission Rate
Other Variables (see Part H of Report)
ised for forecasting and predicting.
t is to be emphasized that a regression
nodel is developed for the purposes of
stimation and not for the purposes
•f predictions. However, with regres-
ion models one can perform predic-
ions in a limited fashion. A time series
lodel is designed purely for the pur-
oses of forecasting and predicting.
The following is a schematic of the
eps involved, chart v.
ing permission to a power company to
install a large generating plant in its
vicinity. The generating plant will have
a large stack (chimney) from which
pollutants will be emitted into the at-
mosphere. When the wind velocity is
low, these effluents could disperse
within the metropolitan area increasing
the amount of pollution in that area.
The downtown part of the metropoli-
tan area is densely populated and a
city planner would like to know the
ground level concentration due to efflu-
ents emitted by the stack The city plan-
ner has information about the wind
velocities, weather conditions, etc. An
appropriate model to use here is the
Gaussian plume diffusion model, or
other diffusion models, discussed in
Part II.
The following is a schematic of the
steps involved, chart vi.
Concentrations
at various points
in the area
vi
7. A decision maker is faced with
the problem of selecting air quality
standards which minimize for the so-
ciety the total cost of pollution. The
total cost of pollution is the cost of
pollution control. Problems of this
nature involve a complex decision mak-
ing process, a conclusion from which
has several consequences. Problems of
this nature involve several conflicting
objectives and are not direct and
Input
A large amount
of pollutant con-
centration data
fc
w
Time
Series
Analysis
Model
fc.
Output
• Trends
• Forecasts
75
-------
straightforward. Several factors, eco-
nomic, social and political have to be
considered in decisions of this type.
Models that can be used here are
the optimization models or the deci-
sion theory models. The following chart
abstracted from Drake, Keeney and
Morse [3] depicts the flow of steps
involved, chart vii.
The outputs from the chart below
can be used as inputs to an optimiza-
tion model.
In any decision making environment,
several of the models discussed here
may have to be simultaneously em-
ployed as indicated below, chart viii.
These models are mere aids to the gen-
eral decision making process, and the
outputs from these are not to be con-
sidered as all encompassing.
The arrows between the regression
models, the time series analysis models,
the extreme value theory models and
the diffusion models indicate that they
may have to interact with each other
to obtain consistent results. The dotted
boundary encloses the stochastic mod-
els.
II. DISCUSSION OF SPECIFIC
MODELS USED IN AIR
POLLUTION
In this section we outline some spe-
cific stochastic and deterministic mod-
vn
Inputs
Standard of living (e.g.,
demand for electric power)
Air pollution control
technology
Current air pollution pro-
grams and legislation
Pollution Problem
Air pollution
emissions
Air pollution
concentrations
Measurement
of air pollution
concentrations
Control
Proposed air
pollution control
legislation and
programs
Existing air pollution )
control legislation / -
and programs J
Availability of
government funds
Direct program costs
Priority of an air pollution control program!
relative to other government programs ("
Outputs
Adverse effects
on residents
Adverse effects
on the city's
economy
General model for evaluating air pollution control programs.
Note: the arrow symbol —» reads "influences."
Source; Drake, Keeney and Morse [3].
76
-------
Vlll
Decisions
els which have been used in air pollu-
tion analysis. We shall point out the
inputs and the outputs of these models,
the major assumptions underlying
these models and the nature of conclu-
sions from such models. For conven-
ience, we shall first discuss those mod-
els which have a probabilistic structure
an it, and then discuss the deterministic
models. How these models can be used
las been discussed above. In the in-
erest of exposing to the reader spe-
:ific developments in mathematical
nodels for air pollution, this section
s detailed and technical.
i. Stochastic Models
We first introduce the following no-
itions and conventions, which are nec-
ssary to discuss the mathematical mod-
Is that are mentioned here.
Let the concentration of a certain
ollutant, say sulfur-dioxide or carbon
lonoxide, etc., be denoted by X. From
aw on, X is a generic name given to
ic concentration of any pollutant. We
(all assume that X varies according to
me probabilistic law, one that we
auld like to know or determine. In
probability theory X is known as a ran-
dom variable.
Since X varies, it takes several values,
and let xlt x2, . . ., xn denote the various
values it takes. For example, xa, x2 . . .,
xn may be the observations from the
CAMP data discussed in I.B before. We
shall denote the particular values which
X takes by x; this is a convention
adopted in the interest of generality and
brevity. The probabilistic law according
to which X varies can be described by
the following statement:
Probability (X < x) = F(x).
F(x) is known as the distribution func-
tion of X, and it varies between 0 and
1. It can be shown that F(x) completely
describes the probabilistic behavior of
X.
If X can take all values in an interval
(finite or infinite), X is said to be a con-
tinuous random variable. We will as-
sume, that as far as air pollution prob-
lems are concerned, X is always a con-
tinuous random variable.
If X is a continuous random variable,
77
-------
it can be proved that there exists a func- The variance of X, denoted as
-------
1. Models for the Distribution of
Pollutant Concentrations
Models for the distribution of pollu-
tant concentrations are of fundamental
interest. It is these models which enable
us to introduce a specific probabilistic
structure for the stochastic models in-
troduced later. The determination of an
appropriate model for the distribution
of a pollutant concentration should be
construed as the first step in any statis-
tical analysis and decision-making pro-
cedure. Such models are very useful for
the setting of air quality standards. For
example, Larsen's [1] work on the log-
normal distribution falls in this category
of models.
The determination of the distribution
of a pollutant concentration is essen-
tially determining the functional form
of f(x) or F(x) discussed before. Thus,
we are interested in determining the
probabilistic law which explains the var-
iation of the concentration of a particu-
lar pollutant.
In order to be able to do this, we will
have to make several assumptions.
As assumed before, let x1; x,, x3, . . .,
xn be the values of the concentration
for a particular pollutant for some av-
eraging time, say t,.
Assumptions
i) We shall assume that the values
x1? X2, . . ., xn are statistically in-
dependent; that is, they are not
correlated.
ii) We shall assume that the n ob-
servations x,, x,, . . ., Xj, are taken
from some unknown distribution
F(x) which does not change in
time.
Discussion of the Assumptions
Recall, that in Section I.B we had de-
[Oted the successive values of the pol-
itant concentrations from the CAMP
ata by xtj, xt, . . ., x, , where tj
-------
statistics. The procedures that are most
commonly employed are:
i) Probability plotting procedures,
ii) Chi-squared goodness of fit test
procedures,
iii) Kolmogorov-Smirnov tests.
From a practical point of view, prob-
ability plotting procedures seem to be
the most expedient and simple. In this
procedure, either the observed data, or
simple transformations on it, such as
logarithms, are plotted against estimates
of the distribution function F(x) on spe-
cial paper, known as probability paper.
For X = xh a reasonable (unbiased)
estimator of F(x) is —l—-, where the
n + 1
Xj, refers to the ith smallest observation.
Probability paper for commonly used
distributions is commercially available,
and the acceptance of a hypothesized
distribution is usually based on the line-
arity of the aforementioned plot.
It is to be emphasized here that the
acceptance of a hypothesized distribu-
tion based on probability plotting proce-
dures is not to be treated as all conclu-
sive and final.
There is a lot of judgment involved
in entertaining a decision of the type
discussed here; namely, accepting a hy-
pothesized distribution as a reasonable
one to use. Firstly, the question of con-
cluding linearity may be a subjective
one despite the fact that there are sta-
tistical procedures for assisting this pro-
cedure. Secondly, the observed data may
be incorrectly observed, i.e., it may not
be reliable, or it may not be available in
a sufficiently large volume for an an-
alysis of this type. It is also possible
that the same set of data may be rea-
sonably well explained by two or more
conjectured (hypothesized) distribu-
tions. This is because the differences
between some of the well known dis-
tributions are dominant at the tails of
these distributions and the available
data may not cover the entire range of
the distribution. In such cases what may
be needed is more data which are
spaced to cover a large range of the dis-
tribution, together with technical opin-
ions of specialists who may be able to
conjecture the appropriateness of a dis-
tribution based on the physical proc-
esses which generate it.
Once a distribution for pollutant con-
centrations has been adopted, it must
be borne in mind that this is merely an
idealization of the distribution which
may be quite complicated.
a) The Lognormal Distribution
As mentioned before, this distribu-
tion has been widely used in an analysis
of air pollution data. Of course, there is
much debate as to whether this distribu-
tion is a reasonable one for all air pol-
lutants.
A continuous random variable X is
said to have a lognormal distribution if
f(x) =
1
V27TO-X
, 0 < X < 03
It is easy to verify that if Y = logeX,
then Y has a normal distribution with a
mean fj. and a variance o-2.
The probability density function of a
lognormal distribution is shown below.
It can be verified that the mean of thi
distribution is
and that its variance is
— 1).
From a practical point of view, ofte
in the analysis of air pollution data, or
needs to estimate the mean pollutai
concentration and the variance of tl
pollutant concentration for some po
lutant which is conjectured to have
lognormal distribution.
If KJ, x2, . . ., xn denotes the air pc
lutant concentration values discusst
80
-------
before, then an estimate of the mean
concentration is given as
n
A = 2los Xi/n>
1=1
and an estimate of the variance of the
concentrations is
The next question is to determine if
the data x1; x2, . . ., xn does have a log-
normal distribution. Probability plots
for the lognormal distribution can be
obtained by plotting the logarithms of
the observed data, namely, logexI;
Iogex2, . . ., logexn on normal probabil-
ity paper. Such a plot for some particu-
late data is shown in the accompanying
figure (Figure 1). Since the points are
not quite on a straight line, it is difficult
to conclude if this particulate data can
be described by a lognormal distribu-
tion. The lognormal distribution is dis-
cussed in good detail by Aitchison and
Brown [4]. Larsen [1] has concluded
that concentrations are approximately
lognormally distributed for all pollu-
tants, in all cities for all averaging
times. Based on this conclusion several
standards for relating air quality to av-
eraging times have been adopted.
b) The Gamma Distribution
This distribution for pollutant con-
centrations has been conjectured by
LOGARITHM OF CONCENTRATION OF PARTICULATEs (in ug/m ) .
FIGURE 1—Plot of logarithm of paniculate data (in pg/m3) on normal probability paper
81
-------
Barlow and Singpurwalla [5]. This con-
jecture is based on the observation that
air pollution data being highly skewed,
any skewed distribution may be a rea-
sonable one to consider.
The probability density function for
the gamma distribution is shown below.
i •-
f(x)
. 5--
Methods for estimating the parame-
ters of the gamma distribution are given
by Choi and Wette [6], Probability plots
for the gamma distribution can be ob-
tained by using the procedure suggested
by Wilk, Gnanadesikan and Huyett [7].
The procedure is rather involved to be
discussed here.
c) The Weibull Distribution
This distribution for pollutant con-
centrations has been conjectured by
Barlow [8]. Once again, this conjecture
is based on the skewness of the observed
data.
The plot of a typical Weibull dis-
tribution is shown below.
Estimators of the parameters £ and 8
of this distribution are obtained by us-
ing tables provided by Nancy Mann
(1967).
Probability plots for the Weibull dis-
tribution can be obtained by plotting
versus
log xx < log x2 <,...,< log x,,, where
xt < x, < x.,, . . ., < xn are the ordered
observed pollutant concentrations. Such
a. plot for the particulate data discussed
before is shown on the accompanying
figure (Figure 2).
2. Regression Models in Air Pollu-
tion Analysis
Because of the general applicability
of regression models to a wide variety
of situations, these models have been
often used in air pollution analysis. For
example, regression models have been
used to evaluate and forecast expendi-
tures due to air pollution abatement
strategies, to discuss the effects of the
various variables on air pollution, and a
host of other applications. More re-
cently, regression models are used to
construct what are known as "smog
diagrams" in an analysis of air pollu-
tion data. These will be discussed later.
Regression models have also been used
to evaluate certain health effects due to
pollutants in the atmosphere. It is to be
stated that regression models can be
used as diagnostic tools or as predic-
tive tools in air pollution analysis.
In view of the several applications of
regression models to problems in air
pollution we shall first review some as-
sumptions in regression models and es-
tablish some convention and notations
common to such models.
a) Conventions and Notation
Let Y,, Y2, . . ., Yk be known vari-
ables, X an observable random variable
and ft, ft, . . ., fik unknown parame-
ters. Then, the relationship
X=00 + ft Y! + ft Y2 +
is defined as the general linear model.
For example, X could be the observ
able concentrations of a certain polk
tant, and Y^ Y2, . . ., Yk may be ot
servable values of the variables such £
wind speed, average temperature, win
direction (in radians), average pre
sure, etc. which influence the concei
trations of a given pollutant.
Our objective is to obtain estimat
of the parameters ft,, ft, . . ., ft, so th
given some values of Y1; Y2, . . ., Y
the value of X can be predicted. (
course, a knowledge of /80, ft, . . ., ,
will also help us to assess the contrib
tion of the variable Yfl to X.
82
-------
FIGURE 2 — Weibull plot of paniculate data (in ug/ma~) on linear by linear scale
Let Yy, i = 1, 2, . . ., n denote the
fferent values which variable Y, j =
2, . . ., k takes. When the variables
j, j = 1, 2, . . ., k take values i = 1, 2,
. ., n, let X take a value X;.
That is, when we set Yj = Yu, Y2 =
,i, . . ., Yk = Ykl, we observe X = Xt.
Our data leads us to a following rep-
sentation of the model
= ft, + j8, Yn + p, Y2
+ - • •
= A, + A Y12 + /32 Y2
k Yk
k Yk2
For example, the first equation states
that when variable YL takes a value Yh,
and variable Y2 takes a value Y21, . . .,
and variable Yk takes a value Ykl, the
random variable X takes a value X,.
In regression theory, the X is referred
to as the dependent variable and the
Yj's, j = 1, 2, . . ., k as the independent
variables. In the illustration above we
have n sets of data, and it is necessary
thatn> k+ 1.
b) Principle of Least Squares
The principle of least squares, or re-
gression requires us to pick thoseA values
of the /Si's, namely #>, /§b . . ., /3k such
that
83
-------
is minimized, where
Xi = /30 + /3lYlu+/32Y2l+...+
0kYki, i=l,2, ...,n.
The above minimization procedure is
quite straightforward and can be rou-
tinely performed on a computer.
c) Variations in the Basic Model
The model presented in section (b)
is known as a linear model because it is
linear in the parameters /30, ft, . . ., /6k.
In view of this, any non-linearity in
the Yj, such as log Y3, or ^Y^ or sine
YJ, for any of all j would still retain
the basic character of the model as long
as there are no parameters which are
non-linear. For example, if it were con-
jectured the sulfur dioxide concentra-
tions Xj are linear functions of the
logarithm of the wind speed Y! and the
square root of the average temperature
Y2, then the model
would be still a linear model, since
a transformation Y! = loge Y\ and
Y2 = v Y2 would give us a linear model
X, = y80 + /8IY11 + /8sYM,
i= 1,2, .. ., n.
In several instances, a non-linear
model can be cast into the framework
of a linear model by simple transforma-
tions. For example, suppose that based
on some diffusion equations it is conjec-
tured that the carbon monoxide con-
centration X is related to the average
temperature as Y!
A logarithmic transformation leads us
to
- log K! = /30 + ft Yu,
again a linear model.
d) Step-wise Regression Procedure
The step-wise regression procedure is
so commonly used in practice, includ-
ing problems pertaining to air pollution
that it deserves special mention.
In practice, one rarely knows the
form of the model he should use. He
may consider a certain number of var-
iables to be the pertinent ones but he
may not be sure if all the variables that
he has considered are really relevant or
not. The model discussed in 2 (a) is one
that we may be willing to tentatively en-
tertain, or one which because of rea-
soning based upon the physical nature
of the problem at hand, we are willing
to adopt.
The step-wise regression procedure is
a procedure which allows us to systemat-
ically pick a variable from a given
number of variables, and include it in
the model or exclude it from the model
based upon the contribution of that
variable.
The step-wise regression procedure
first picks that variable whose contri-
bution to the model is the largest anc
then picks another variable from the
remaining ones to see if its contribu-
tion is significant. A nice feature of the
step-wise procedure is that it eliminate1,
from the model any variable which i
had previously included in the model i
the contribution of this variable i
minimized by the choice of subsequen
models.
Computer programs routinely pei
form the step-wise regression procedur
in a highly mechanized manner.
e) Prediction Intervals from Regre.
sion Models
A (1 — a)% prediction interval ca
be obtained for a new predicted value <
X, say x, for values of Yj, at Yj,, j =
2, . . ., K, and I ^ i.
We illustrate by considering a simp
linear regression model in two variabl
In the figure below, the data is in<
cated by crosses, the estimated li
based on least squares
X1 = j30+/3,Y11
is also shown, and the hyperbolic CUP
represent the (1 — a) % prediction
tervals. It can be verified that these
tervals are the narrowest within
range of the data, especially at the ci
ter and spread out as we move aw
towards the ends. It is for this reas
84
-------
that it is not advisable to make predic-
tions from regression lines for points
too far away from the range of the data.
The hyperbolic nature of the prediction
intervals is due to the assumption of
normality of the error.
of August, September and October for
the years (1962-1969) were used. The
6-9 A.M. three hour averages were
used for total hydrocarbon and nitrous
oxide concentrations. The maximum
hourly average concentration occurring
Estimated Line
Lower Prediction Interval
For example, if we wish to predict
the
X at
2 .
Yj = Yu, where
.A ., n, then X, is
X(l is the lower
X,^ is the upper
value of
YI, =£ Yu, i =
the predicted value.
prediction limit and
prediction limit.
The interpretation of the (1 — a) %
prediction limits is that the probability
that the random interval (Xw — X,,)
contains the true value X, is ( 1 — a) % .
f ) Applications of Regression Analy-
sis for Constructing Smog Dia-
grams
As mentioned before, regression an-
alysis has been widely used in air pollu-
ion problems. We illustrate here an ap-
plication of this technique to construct
vhat are kown as "smog diagrams." A
mog diagram is a pictorial depiction of
he mathematical relationship between
•xidants, hydrocarbons and nitrogen
ixides. These pollutants are responsible
or the smog in a particular area.
The results reported here are based
on that day at the downtown Los Ange-
les station was used for the total oxidant.
Using a step-wise regression proce-
dure the logarithm of the oxidants were
fitted by a quadratic model in hydro-
carbons (HC) and nitrogen oxide
(NOX).
The model is written as
X = log (oxidant) =
Yi
where Y1=log (NO^/17.5), Y2 = log
(HC/4.6), Y, = Y,a, Y4 = Y! Y,,
Y, = Y22, Y, = Y,2. Yr = Yt Y22 and
Yg^Yi2 Y22; 17.5 and 4.6 are con-
stants used for computational advan-
tages.
Results of the Regression
The step-wise regression procedure
eliminated all the variables except Yt
and Y2 to yield the following estimated
relationship:
or
log (oxidant) = 2.6 + .54 L
i a study conducted by Merz et al.
'] for the downtown Los Angeles air
onitoring station. Data for the months
+.15
Thus, estimators of the parameters /30,
fa and fa are 2.6, .54 and .15 respec-
tively.
85
-------
The following diagram depicts this
relationship; this diagram is called the
smog diagram.
situation typical with air pollution data.
These and other details are discussed in
the following sections.
100
Nitrogen
Oxide
Boundaries of data
oxidant line
. 5 X3(-/-/-/>
34 15
Hydrocarbons
"SMOG DIAGRAM"
As indicated by the dotted lines,
when the level of hydrocarbons is at
2.5 and the nitrogen oxide is at .5, the
total oxidant takes a value of 8. The
shaded area represents the region cov-
ered by the data, and predictions within
this region are the most reliable.
3. Models for Predicting Maximum
Concentrations
In Section I.B we had mentioned
that the maximum pollutant concentra-
tion ijk n of a particular pollutant is of
interest. We had also stated several
State and Federal standards for air
pollutant concentration for a specified
averaging time.
In an attempt to set standards, based
on maximum concentrations, which are
reasonable, or in an attempt to investi-
gate the reasonableness of a specified
standard, we resort to the use of ex-
treme value theory.
The application of extreme value
theory to air pollution problems is rela-
tively new. It was first advocated by
Singpurwalla [10] and then followed up
by Barlow [8]. Barlow and Singpurwalla
[5] have also indicated how the extreme
value theory can be used in problems
where the data may be correlated, a
86
a) A Statistical Model for Maximum
Concentrations
Reverting to the notation established
in Section I.B, let Xtl, Xt2, . . ., Xtn be
the values of the concentration for a
particular pollutant, for a five minute
averaging time.
Let us assume for now, the following:
i) the values Xtl, Xt2). . . ., Xtn are
statistically independent (i.e. no
correlated),
ii) the values Xtl, t2, . . . , Xtn ar<
taken from a fixed distribution F(x
which does not change.
iii) the distribution F(x) is either a log
normal, a Weibull, a gamma,
normal or an exponential distribi
tion.
Discussion of the Assumptions
As we have pointed out in Sectio
II.A.I, the assumptions (i) and (ii
may be difficult to realize in all tl
cases. Despite this difficulty, we coi
tinue with the discussion here, becaui
we can prove that the results obtains
by assuming independence serve as re
sonable bounds for similar results und
the non-independence case (Barlow ai
Singpurwalla [5]).
-------
Assumption (iii) is very general and
there should be no difficulty in realiz-
ing this assumption in practice. Of
course, several other distributions can
be included under assumption (iii) as
long as these distributions belong to
the domain of attraction of the limiting
law discussed later in this section. The
concept of the "domain of attraction"
of a limiting law is quite mathematical
and is omitted here; for more details on
this we refer the reader to Gnedenko
[11]-
As discussed before, we next form
averages of length k, and obtain i)kill as
Max {k-'(Xti
,k-HX,n_t+l
. + Xtk),
-+Xtn)}.
Since iyk n is a function of the ran-
dom variable X whose values are Xt ,
Xt2, • • •.. etc., T?k)1 is also a random
variable whose probabilistic behavior is
described by what is known as an ex-
treme value distribution, if assumptions
(i) and (ii) hold. If assumption (iii)
holds, then as n gets large, and if k is
moderate, i.e. if the averaging time is
moderate
exp -
vhere /3k u and ak n are parameters or
:onstants, known as normalizing con-
tants. The above result follows from
he extreme value theory (Fisher and
"ippett (1928)). We illustrate below a
tot of the extreme value distribution
Thus, using extreme value theory, we
in describe the random behavior of
e maximum concentration 7jk „ as a
nction of the data, n, and the averag-
g time 5k. We illustrate an application
this in the following problem.
b) Applications to Air Quality Data
Studies indicate that plants grown in
a particular area could be visibly dam-
aged if the 8-hour average • concentra-
tion of oxidant exceeded .03 ppm.
Thus, if the air management board de-
sired to prevent such damage they
might set the air quality standard at a
maximum value of 0.03 ppm for an
8-hour averaging time.
The question of how frequently the
above standard will be violated and
other related questions can be answered
by determining the probability that the
maximum concentration ijkll exceeds
some value X (say .03 ppm) for some
averaging time tft (say 8 hours). The
constants /3,; „ and akn are to be ob-
tained from air pollution data, and are
a function of the distribution function
F(x) discussed in assumption (iii). For
more details on this, the reader is re-
ferred to Singpurwalla [10], and Barlow
and Singpurwalla [5]. Bounds on /?kill
have been obtained by Barlow [8].
c) Extensions for the Case of De-
pendent Data
It was assumed in Section 3.a that
the values Xti, Xf2, . . . , Xt are in-
dependent. It was also mentioned that
X i
— 00 < X < 00,
the assumption of independence gave
us meaningful bounds for the distri-
bution function of the maximum under
the non-independence case. These re-
sults are highlighted in this section.
We shall now assume that the values
are dependent (or correlated) such
that the "autocorrelation function" is
always positive and it damps out. The
notion of an autocorrelation function
is discussed in Section 4.e to be pre-
sented later.
The results that are given here are
true under a much stronger notion of
dependence known as "association."
The concept of association is due to
Esary, Proschan and Walkup [12] and
is quite mathematical to outline here.
However, it is true that a necessary
87
-------
condition for association is that the
autocorrelation function be positive.
Barlow and Singpurwalla [5] prove
that if the data Xti, Xtz, . . . , Xtn is
associated, then
. . . , etc. is referred to as a time
series. We need to predict Zt+/, where t
denotes the present time, and I =1, 2,
. . . , denote the future points in time.
t is known as the "lead time" for which
It is easy to recognize the fact that
the right hand side of the above equa-
tion is the distribution function of the
maximum concentration under the
assumption of independence.
In words, the above result implies
that when the air pollution data is
correlated (which is often the case),
then the probability that the maximum
concentration of a specified pollutant
for some averaging time, say 5k, is less
than or equal to X, is greater than the
number obtained through the right hand
side expression.
Thus, the assumption of independ-
ence in extreme value theory, when the
data are associated (positively corre-
lated), gives us conservative results.
4. Time Series Analysis Models
Air pollution data being highly de-
pendent (correlated), time series
models for analyzing these data appear
to be the most appropriate. Whereas
regression models are used for diag-
nostic and perhaps for prediction pur-
poses, time series models are mainly
used for prediction purposes.
Time series models have been used
in air pollution analysis to predict either
future pollutant concentrations or
trends for various pollutant concen-
trations in several cities. Time series
nodels require a healthy amount of
previous data but no model assump-
tions, such as linear models, quadratic
models, etc. used in regression models.
We shall outline in this section the
various time series models that can be
used in an analysis of air pollution data
and indicate a specific example of its
use.
a) Statement of the Problem
Let Zt, Zt_1? Zt.2, . . . , be a set of
observations at equispaced time points
t, t-1, t-2, . . . . Z,, Zt.,, Zt_3,
the forecast is required, and if Zt(^)
denotes the forecast of Zw, the Zt(^)
is known as the forecast at origin t
for lead time t.
For example, Zt, Zw, Zt_2, . . . ,
could represent the concentrations of a
particular pollutant at times t, t — 1,
t — 2, . . . etc., where the t's could be
spaced 5 minutes apart. Thus the
CAMP data could be considered to be a
time series.
Loosely speaking a "stationary time
series" is one which is in equilibrium
about a constant mean, say p.. A "norr-
stationary" time series is one which is
not stationary. Typical examples of
non-stationary time series are stock
prices, uncontrolled processes and even
pollutant concentrations where no con-
trol policies exist.
We assume that the observations Zt.
Zt.n Zt_2, . . . , which are highly de-
pendent are generated by a series o
shocks At, AM, .... We furthei
assume that the At, At_1( . . . etc. art
independent random observations fron
a distribution which is normal with ;
mean zero and a variance o-2. The At
At_1( . . . , values are also known a
the "white noise" process.
This concept is perfectly general, an
difficult to dispute. Thus as far as th
assumptions in time series are cor
cerned, we need not worry much aboi
their violation, since they are quite get
eral. The assumptions stated here ai
more of a concept, an idealization, an
are thus not restrictive.
b) Some Stationary Time Seri
Models
i) The Autoregressive Model
These models are very useful
practice, including air pollution pro
lems.
Let us denote Zt — ^ by Zt, Zt_a —
by Zt_j and so on. What enables us
-------
do this is the stationary property which
assumes the existence of a fixed mean
Then, if fa, fa,
constants the model
are any
is known as an autoregressive process
of order p. In this process, we idealize
that the current value of the process
Zt is the sum of the p previous values
of the process, each multiplied by a
parameter fa, i = 1, 2, . . .p.
The first and the second order auto-
regressive processes are most com-
monly used in practice.
ii) The Moving Average Model
The process
d) The Notion of An Autocorrela-
tion Function
In order to identify a time series
model, the autocorrelation function is
used. Consider the pairs of values
(Zt, Zt+I) and (Zt, Zt+2) for all values
oft.
If we plot the pair (Zt, Zt+l) for all
values of t and if we observe the fol-
lowing plot, we conclude that the pair
(Zt, Zt+1) is negatively correlated.
t+1
is known as the moving average model
of order q.
iii) The Mixed Autoregressive-Moving
Average Model
In order to obtain parsimony, that is,
in order to explain a large class of
models with as few a number of param-
sters as is possible we introduce what is
cnown as the autoregressive, moving-
iverage process, abbreviated as the
\RMA(p,q) process. In this process
we have
In practice, both p and q are rarely
reater than two.
c) Non-Stationary Time Series
Models
To introduce non-stationary consid-
'ations in the model we consider the
th difference to the Zt values. That is if
e take the dth differences of our data,
e obtain an ARMA(p,q) model. If
= 0, the process reduces to an ARMA
•ocess.
The ARMA process is a very general
ocess which includes an ARMA(p,q)
ocess when d = 0, an AR(p) process
len p and d are zero, and an MA(q)
ocess when p and d are zero.
Now suppose that we plot the pair
(Zt, Zt+2) for all values of t, and if we
observe the following plot, we conclude
that the pair (Zt, Zt+2) is positively cor-
related.
"t+2
The covariance between Zt and Zt+k
is known as the "autocovariance" at
lag k. It is denoted by yk. When k = 0
the autocovariance reduces to the vari-
ance.
The "autocorrelation" at lag k is the
ratio of the autocovariance at lag k
to the variance; it is denoted by pk.
Thus
A plot of /SK versus k, for k = 0, 1,
2, ... is known as the "autocorrela-
tion function." Clearly, the autocorre-
lation function starts at plus or minus
89
-------
one and tails off as k increases. The
autocorrelation function gives us an
idea as to how the observations are
correlated with each other. That is, are
successive values dependent on each
other or not, and if they are dependent,
the nature of this dependence is im-
portant.
There are several practical considera-
tions to be taken into account for esti-
mating pk. We outline these below:
i) n should be at least 50
ii) K should not be larger than n/4
iii) it is enough to round off the esti-
mates of the autocorrelation
function to two decimals
In the accompanying figures we pre-
sent plots of two time series and their
autocorrelation functions. These plots
have been abstracted from Barlow and
Singpurwalla [5].
e) Forecasting Using Time Series
It was stated before that time series
models are mainly used for prediction
purposes. Specifically, we had stated
that given pollutant concentrations.
we would like to predict concentrations
at a future time period Zw, for I = 1,
2, .... We had also suggested that
the forecast of Zi+t, would be denoted
by Zt<7). The function Zt(7), t = l,
2, . . . , is known as the "forecast
function."
Once a series has been identified, and
its parameters estimated for which
there are algorithms available, there
are techniques available for predicting
future values. These techniques are
based on certain properties required of
the forecast function and have been
automated for computer implementa-
tion.
The assumption that the random
shocks At are normally distributee
allows us to obtain prediction intervals
on our forecasts.
June Isc 11 21 30 July u
1970 1
FIGURE 3—Oxidant Concentrations in ppm for Livermore, California June—August, 1970
90
-------
x
X y X
Illl
0 t-4 t-3 t-2 t-1 t
''L, — * — * F°
/ ^t*^*
(fer^ - LC
t+l t+Z t+3
We illustrate these ideas by the fol-
lowing diagram
Values
of
f) An Example Illustrating the Use
of Time Series Analysis to Air
Pollution Data
Merz et. al. [9] have performed a
time series analysis of the air monitor-
ing data from the downtown Los
Angeles station. This analysis revealed
the existence of certain trends. It was
concluded that hydrocarbon, total oxi-
dent and carbon monoxide are trending
downward. Nitric oxide is trending up-
wardl ^_,- Upper Prediction
Interval
Forecast Function
Lower Prediction
Interval
Time
Data Base and Method:
The concentration variables were
hydrocarbon, oxident carbon monoxide
and nitric oxide. The bi-weekly average
of the daily maximum hourly average
at the downtown Los Angeles station
were the data.
A time series analysis of the data
covering the period from 1955 to 1967
was made. Using this data a forecast
i 2
10 12 14
Lag In Days
16 18
20
22
26 28
SURE 4—Sample Autocorrelation Function for Oxidant Data From Livermore, California
June—August 1970
91
-------
was made for the periods covering
1968-1969. A comparison was then
made between the forecast and the
actual data.
A guiding principle in the choice of
models was parsimony; i.e. as few
parameters as is possible are used which
will still adequately describe the data.
If the forecast rises or falls we have
discovered a trend. In this analysis, the
random shocks are viewed as related
to a combination of variables including
meterological factors such as wind
speed, humidity, inversion layer, height
and light intensity.
Results
The results in this analysis for the
total oxident data are given in the
figures below abstracted from Merz
et al. [9].
The figures consist of two graphs.
i) a time series analysis and a fore-
cast based on data from 1955 to
1967 together with 1968 and
1969 data
ii) a time series analysis and fore-
cast based on data to the end of
1969
Data to 1968
forecast (1968-1967)
1968-1969 Data (Otetrv*
1956 1958 1960 1962 1964 1966
1968 1970
Bi-weekly averages (pphm) of the daily maximum hourly averages for total oxidant
downtown Los Angeles station, data to 1968. forecast to 1970, data for 1968. 1969.
40.0
30.0
20.0
10.0
'1955 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71
Years
Bi-weeJdy averages (pphm) of the daily maximum hourly averages for total oxidai
downtown Los Anyefa station, data to 1970, forecast to 1972.
92
-------
FIGURE 5—Carbon Monoxide Concentrations in ppm for Livermore, California June—August
1970
1 2
10
12
14
16 18
20
22
26
23
Lag in Days
'IGURE 6—Sample Autocorrelation Function for Carbon Monoxide Data from Livermore,
California June—August, 1970
93
-------
Comments:
The first analysis and forecast sug-
gested that there would be no change
in total oxidant from 1967 on. When
the 1968-1969 data were incorporated,
a downward trend was suggested. This
trend can be ascribed to control meas-
ures on the hydrocarbons. 1955-1967
data base: Model ARMA (0,1), with
d=l. 1955-1969 data base: Model
ARMA (0,1), with d=l. The model
identified here is a non-stationary
model, since d = 1.
B. Deterministic Models
As mentioned before, deterministic
models do not have a probabilistic
•CHICAGO AIR POLLUTIO*
SYSTEM ANALYSIS
PROGRAM
( ] 0- 200
EC2S3 zoo- goo
HH 900- 1000
|H 1000- 1900
•• BOO-tSOO
FIGURE 7—Sulfur Dioxide Emission from Residential Space Heating for 1968
94
-------
structure imposed on it. Prominent
among these are the diffusion models
proposed by meterologists working on
air pollution problems. The other class
of deterministic models used in air
pollution analysis are the optimization
models which will be briefly mentioned.
We shall first discuss a few diffusion
models.
1. Diffusion Models
Diffusion models serve to gain in-
sight into the relation between metero-
logical elements and air pollution. These
models may be likened to a transfer
function (a black box) where the in-
put consists of both the combination of
weather conditions and the total emis-
sion from sources of pollution, and the
output is the level of pollutant concen-
tration observed in time and space.
These models take into consideration
the nature of the sources, the levels of
concentration at the receptors, and the
atmospheric processes such as photo-
chemical action and eddy diffusions.
a) Historical Background
The pioneer in this work is Frenkiel
[13] who developed a mathematical
model for the city of Los Angeles.
Turner [14] laid the foundation for
daily operational models in his de-
velopment of the Nashville model. One
of the most extensive efforts in the
development of an urban air pollution
model for SO, is that of the Argonne
National Laboratory [15]. Pooler [16]
and Meade and Pasquill [17] have de-
vised models to provide monthly or
seasonal values of pollution concen-
trations.
b) The Gaussian Plume Equation
Model
Mathematical equations of urban air
pollution models describe the process
by which pollutants injected into the
atmosphere are diluted. The modified
Sutton equation, also known as the
"Gaussian Plume Equation" enjoys the
widest use. Figures 7 and 8 abstracted
from "An Urban Atmospheric Disper-
sion Model" [18] depict the dispersion
of pollutants emitted into the atmos-
phere. Figure 7 shows the distribution
over an area, where as Figure 8 shows
the propagation of effluents.
Consider an elevated point source as
illustrated by a stack shown below. The
coordinate system for this stack has its
origin at ground level, at the base of
the stack. The X-axis extends hori-
zontally in the mean wind direction.
The Y-axis is horizontal in the cross-
wind direction; the Z-axis is vertical.
. Plume Center
Effective Stack
Height h
95
-------
The "effective stack height" is the
height at which the plume center line
becomes horizontal—let this be denoted
byh.
Let
X(x,y,z;h) = pollutant concentration
at point x,y,z for an
effective stack height h,
/ig/m3.
Q = emission rate gms/sec.
u = mean wind speed,
meters/sec.
o-y,(rz = standard deviation of the
plume concentration dis-
tribution along Y and Z
axis respectively. (Note:
cry and
-------
Table 4. Key to Stability Categories
Surface Wind
Speed
(at 10 m)
m sec'1
< 2
2-3
3-5
5-6
> 6
Day
Night
Incoming Solar Radiation
Strong
A
A-B
B
C
C
Moderate
A-B
B
B-C
C-D
D
Slight
B
C
C
D
D
Thinly Over-
Low Cloud
E
D
D
D
£3/8
Cloud
F
E
D
D
The neutral class, D, should be assumed for overcast conditions during day or night.
' 10.
DISTANCE DOWNWIND, kn
100
IGURE 9—Horizontal dispersion coefficient as a function of downwind distance from the source,
97
-------
1,000
~i£S3H?a
1,!.^V~3
ttTntr:
i.'
^SSpji^p^pr'F'Fi ~ 1
1.0
0.1 I 10 100
DISTANCE DOWNWIND, Inn
FIGURE 1Q—Vertical dispersion coefficient as a function of downwind distance jrom the source.
and
Vs — stack gas exit velocity m/sec,
d = inside stack diameter m.
p = atmospheric pressure mb.
Ts = stack gas temperature °K.
Tn = air temperature °K.
c) The Box Model
This model is simpler than the model
previously discussed and is used only
as a preliminary tool for analysis.
98
Let
u = mean wind speed
V = volume of box
h = inversion height
£ = length of box
-------
Assumptions
a) The source emission rate S (mass/
unit time) of any pollutant of in-
terest, into the box is constant with
time.
b) There is instantaneous perfect mix-
ing within the box. Thus, the con-
centration C of any pollutant is uni-
form throughout the box at any
time.
c) The air pressure and temperature
are uniform and constant.
d) Reactions involving the pollutants
are ignored.
e) The wind blows only clean air into
the box at a rate Q = hLu. Dirty
air of pollutant concentration C,
leaves the box at the same rate Q.
Let C(t) = concentration of a pol-
lutant at time t. Then, a mass balance
for the pollutant in the box yields the
equation
dt
or
dc.-S-_.C_
dt ~~ V ~ T
where T = V/Q is the average resi-
dence time of a unit mass of the pol-
lutant in the box.
Let C0 — pollutant concentration at
Then, C(t) has the solution
C(t)=~(l
and Lim C(t) = — a steady state con-
t->oo ^
:entration.
Comments
The assumptions of the model are
lighly simplified.
• instantaneous mixing does not
occur and hence pollutant concen-
trations are not uniform.
• choice of the average wind velocity
is critical.
Example
Let h = 300 ft.
V=9.3X 1012cu. ft.
u= 5 m.p.h.
.'.L = (V/h)V2=i.76X 105ft.
/.Q = hLu = 1.39 X 1012 ft. 3/hr.
T = ~ = 6.7 hrs.
It is reasonable to assume that in
about one day (t «=< 4T) the pollutant
concentration will reach its steady state
value.
The S for SO2 is quoted as 396 tons/
day or 3.84 X 104 Ibs./hr.
_= =2.76X10-8 lbs./ft.3
or 4.45 X 10~4 grams/meter.
The air quality standard for SO2 is
0.5 ppm. or 1.43 X 10-3 grams/meter.
2. Optimization Models
The techniques of mathematical pro-
gramming of which linear and non-
linear programming are the most popu-
lar fall under the category of optimiza-
tion models. Recently, these models
have been successfully utilized in sev-
eral aspects of the decision making and
control aspects of air pollution man-
agement.
These models along with the implied
concepts of viewing complex systems in
terms of interrelated activities has
proved to be a major contribution to
the field of scientific decision making.
The versatility and adaptability of these
deceptively simple mathematical mod-
els appear to have no bounds. In view
of the above arguments it is natural that
these techniques have found use in air
pollution control and management prob-
lems.
Despite the proven success of such
models in several areas of decision mak-
ing, their use in air pollution control
and management problems appears to
be limited. One possible explanation for
this may be the fact that up until now
analysts involved with mathematical
models for air pollution have concen-
trated more along the lines of data
analysis and data management, or have
worked along the lines of diffusion and
meterological modeling. It is anticipated
99
-------
that once the problems of data analysis
and air pollution modeling have been
reasonably well solved, decision makers
will have to draw upon the optimization
models to solve a new generation of
problems that will surface. The discus-
sion which follows is written with a
view of exposing the decision maker to
the capabilities of optimization models
in the hope that he will stimulate and
encourage their widespread use, when-
ever feasible.
We shall illustrate below a few such
applications.
a) Application to Alternative Air
Pollution Abatement Policies
In selecting and enforcing air quality
standards it is the control authorities
responsibility to determine the level of
abatement which minimizes for society
the total cost of pollution. The total
cost of pollution is the cost of damage
due to pollution and the cost of pol-
lution control.
A fuel substitution model was de-
veloped by A. Teller [19] for estimating
the cost of satisfying air quality stand-
ards. In this model it is assumed that
there are two types of fuel. The ob-
jective is to find the minimum cost
combination of fuel A and B which
satisfies the air quality standard. There
are two constraints in the model; these
are
i) the combination of high and low
polluting fuels should have the
same caloric value as before the
substitution.
ii) the amount of pollution resulting
from this combination should be
less than some air quality stand-
ard.
The following notations are used.
A = originally used high pollut-
ing fuel.
B = substitution fuel—less pol-
luting.
T1a = no. of tons of A presently
used by source J.
Tjau = decision variable; no. of
tons of fuel A.
T.jbu = decision variable; no. of
tons of fuel B.
Cja(b) = cost/ ton of fuel A(B).
Kja(b) = BTU/ton of fuel A(B).
H] = no. of BTU's required by
source J.
Ejn(i» — emission/ton of fuel A(B)
from source J.
Sj = air quality standard at re-
ceptor I.
M1( = meterological parameter re-
lating emissions at source J
to air quality at receptor I.
X, = percent substitution of fuel
B for fuel A at source J.
The linear programming model is
Minimize (Cb Tb» + Cja Tjg")
1=1
subject to
Computer packages for solving the
above model are commercially avail-
able.
The objective is to minimize the total
cost of fuel for all sources subject to the
constraint that for each receptor the
sum of the reductions in pollution re-
sulting from each source's use of dif-
ferent fuel is at least as great as the
necessary reduction in air pollution con-
centration.
Assumptions
The above model has the following
assumptions inherent to it.
i) fuel substitution is the onlj
method of abatement.
ii) that there can be up to 100%
substitution of fuel B for fuel A
iii) all emissions result from com
bustion.
Any variations in the above assump
tions can be incorporated into th
models, though the structure of th
above model will slightly change.
The linear programming solution prc
vides much useful information beside
100
-------
obtaining values of the decision vari-
ables. This information is outlined in
detail by Teller [19].
b) The Energy Quality Model
The Energy Quality Model (EQM),
discussed in [20], is designed to deter-
mine the quantities of fuel, by fuel type,
to be supplied to each fuel district to a
specified set of demand regions under
given assumptions of air quality stand-
ards, the demand region's energy re-
quirements and their ability to utilize
the fuels and the fuel supply districts'
abilities to supply its fuel types.
The EQM is an optimization problem
which is designed to distribute fuels
from many sources (districts) such that
energy requirements of destinations (re-
gions) are met in a manner which mini-
mizes total national cost of obtaining
the fuels subject to specified air quality
restrictions on emissions and each des-
tination's ability to utilize the fuel types.
The problem discussed here is a
standard linear programming problem
except for the fact that it has a large
number of variables. Such large scale
problems can be solved by using what
is known as the Dantzig-Wolfe decom-
position algorithm, provided that certain
conditions are satisfied. Reference [20]
provides a detailed method of solving
the above stated problem.
References
[1] Larsen, R. I., "A New Mathematical
Model of Air Pollutant Concentration
Averaging Time and Frequency,"
Journal of Air Pollution Control Asso-
ciation, Vol. 9, pp. 24-30, 1969.
[2] Larsen, R. I., "Air Pollution From Motor
Vehicles," Annals of the New York
Academy of Sciences, 136(12), pp.
275-301, 1966.
[3] Drake, A. W., Kenney, R. L., Morse, P.
H., (Editors) Analysis of Public Sys-
tems, MIT Press, Cambridge, Massa-
chusetts, 1972.
[4] Aitchison, J. and Brown, J. A. C., The
Lognormal Distribution, Cambridge
University Press, 1963.
[5] Barlow, R. E. and Singpurwalla, N. D.,
"Averging Time and Maxima for De-
pendent Observations," to appear in
the Proceedings of the Symposium on
Statistical Aspects of Air Quality Data.
1972.
[6] Choi, S. C. and Wette, R., "Maximum
Likelihood Estimators of the Param-
eters of the Gamma Distribution and
Their Bias," Technometrics, Vol. II,
No. 4, pp. 683-690, 1969.
[7] Wilk, M . P., Gnanadesikan, R, and
Huyett, M. J., "Probability Plots for
the Gamma Distribution," Techno-
metrics, Vol. 4, pp. 1-20, 1962.
[8] Barlow, R. E., "Averaging Time and
Maxima for Air Pollution Concentra-
tions," Proceedings of the Sixth Berke-
ley Symposium on Mathematical
Statistics and Probability, Vol. VI, pp.
433-442, 1972.
[9] Merz, P. H., Painter, L. J., and Ryason,
P. R., "Acrometric Data Analysis—
Time Series Analysis and Forecast and
an Atmospheric Smog Diagram," At-
mospheric Environment, Vol. 6, pp.
319-342, 1972.
[10] Singpurwalla, N. D., "Extreme Values
from a Lognormal Law With Appli-
cations to Air Pollution Problems,"
Technometrics, Vol. 14, No. 3, pp.
703-711, 1972.
[11] Gnedenko, B. V., Sur la distribution
limite du terme maximum d'une series
aleatoire, Ann. Math., Vol. 44, No. 23,
1943.
[12] Esary, J. D., and F. Proschan, "A Re-
liability Bound for Systems of Main-
tained Interdependent Components,"
Journal of the American Statistical
Association, Vol. 65, pp. 329-338,
1970.
[13] Frenkiel, F. N., "Atmospheric Pollution
in Growing Communities," Smith-
sonian Report for 1956, pp. 269-299,
1956.
[14] Turner, D. B., "A Diffusion Model for
An Urban Area," Journal of Applied
Meteorology, Vol. 3, No. 1, pp. 85-91,
1964.
[15] Croke, E. J., Carson, J. E., Gatz, D. F.,
Moses, H. et. al., "Chicago Air Pol-
lution System Model, Third Quarterly
Progress Report," Argonne National
Laboratory, ANL/ES-CC-003, 1968.
[16] Pooler, F. Jr., "A Diffusion Model for
An Urban Area," Journal of Applied
Meteorlogy, Vol. 3, No. 1, pp. 85-91,
1964.
[17] Meade, P. J. and Pasquill, T., "A Study of
the Average Distribution of Pollution
Around Staythorpe," International
Journal of Air and Water Pollution,
Pergamon Press, Vol. 4, Nos. 3/4, pp.
199-211, 1961.
101
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[18] Roberts, J. J., Croke, E. J., and Kennedy, Scientific Computing Symposium on
A. S., "An Urban Atmospheric Dis- Water and Air Resource Management,
persion Model," Argonne National pp. 345-353, IBM, White Plains, New
Laboratory, Report ANL/ES-CC-005, York 1968
1969.
[19] Teller, A., "The Use of Linear Program- [20] "Technical Analysis of the Application
ming to Estimate the Cost of Some of the Dantzig-Wolfe Decomposition
Alternative Air Pollution Abatement Technique in the EPA Energy Quality
Policies," Proceedings of the IBM Model," MATHEMATICA, Inc., 1972.
102
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Chapter 4
Models in Water Resources
By
David H. Marks
SUMMARY . .105
I. WATER QUALITY . .. 107
A. Description of the Area 107
1. Problem Identification . 107
B. Models in the Aid of Water Quality Decision Making 110
1. Descriptive Models . Ill
2. Management Models . 114
C. The Delaware Estuary, An Example 119
D. Summary of Water Quality Models 121
II. WATER QUANTITY 122
A. Description of the Problem . . 122
1. Problem Identification . 122
2. Water Use . 123
3. Functional Groupings for Problem Solutions 125
B. Models in the Aid of Water Quantity Decision Making 125
1. Descriptive Models 125
2. Management Models 127
3. Case Study—Rio Colorado, Argentina . 129
4. Summary , , 133
REFERENCES . 133
103
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-------
Models in Water Resources
SUMMARY
This chapter deals with modeling in
the aid of decision making for the man-
agement of a vital resource: water. The
level of complexity and multiplicity of
the problems involved in allocating this
resource for its desired uses and in
limiting the overall impacts of those
uses upon the environment and society
is great. We find it convenient to cate-
gorize our discussion by considering the
two areas of water quality and water
quantity. Although there are interac-
tions between these two areas, the divi-
sion nevertheless helps to focus on two
different aspects of a similar problem:
optimal resource allocation in a public
sector problems where, unlike the pri-
vate sector, there is no complete pricing
mechanism to guide the decision or
express preferences. The focus on water
quality is pollution which we define as
waste inputs to water which preclude or
damage the employment of water for
other uses such as recreation, water
supply or wild life. Pollution loads are
produced both by the disposition of re-
siduals from process use (industrial and
municipal wastes), and as a by-product
of development and land use policies
(decreased quality of urban storm run-
off and increased sediment loads). Are
here better uses for the residuals, better
development policies than the present
mechanisms or is better quality justified
,o support other uses? As with any pub-
ic sector decision problem, the costs
ind benefits of any action to bring about
mprovement are not all directly meas-
irable in commensurate units or towards
he same interest groups. Thus the
ecision maker must find some formal
nechanism to help balance these diverse
factors in the choice of when, where,
how and how much should be invested
for water quality.
In water quantity, we are concerned
with the physical aspects of water and
its allocation to proper use. The avail-
ability of water is spread quite differ-
ently spatially and temporally than
where it is needed. Thus the decision
maker is concerned with designing in-
vestments and strategies for capturing
and transporting the resource in reliable
quantity. Occasionally the problem is
the control of excessive water as in
flooding. Decisions as to what these
uses should be and how much should be
allocated are again of great importance.
There are diverse interest groups with
different preferences and objectives;
costs and benefits are not in commen-
surate units and may fall differently on
the various segments of society. The
decision maker again must weigh and
balance these factors in making invest-
ment decisions.
The role of models in the study of
these decisions is pervasive. There are
many different aspects of the problem
where analysis using modeling is the
principal information input to the de-
cision process. In this chapter modeling
in water resources is discussed from the
perspective of the problems addressed
and where new developments can help
improve decision making.
Water Quality
The decision makers charged with
deciding how much, where and when
investment should be made and what
strategy should be used require infor-
mation about a variety of questions to
define and evaluate the options avail-
able. Models to aid in this process fall
105
-------
into two categories: descriptive and
management. Descriptive models show
the impact of changing pollutional pat-
terns. The most prevalent models of this
sort are those that show the response in
space and time of a water body to in-
puts of pollutants such as municipal
sewage or heated water. Normally the
response is measured in terms of some
physical parameter of the water body
such as its dissolved oxygen concentra-
tion or temperature. Less well developed
are models that translate these physical
parameters into estimates of damages or
benefits. Ecosystem modeling has re-
ceived attention in the past few years
but is still in its infancy. Models to
show economic, demographic and social
impacts on water quality changes and
thus estimate benefits and costs have
also been developed. Other processes
which produce pollutants such as storm
runoff have been modeled, as well as the
technologic components for controlling
pollution.
Management models are developed to
help choose from among alternative
control strategies those which best sat-
isfy given quality goals. Generally these
models focus on the decision to be made
by a regional authority for investment
in and implementation of a water qual-
ity management plan.
Water Quantity
Here the decision maker must decide
on how water is obtained, controlled
and transported and to what use it
should be put. Descriptive models help
to evaluate how much of the stochasti-
cally varying resource will be available
and how storage or other policy de-
cisions will operate to capture the re-
source and/or to reduce its flooding
impacts. Management models help to
investigate investment decisions in con-
trol, storage and transport, as well as
which allocation of funds to use by
selecting from the available options that
set which best satisfies objectives. Here
again these models must formally iden-
tify the multi-objective nature of the
problem and account for costs and
benefits by the appropriate objectives
in order to provide important informa-
tion to the decision process.
The water quality and quantity mod-
els discussed in this chapter are given
in the Summary Table.
WATER RESOURCES
Models Discussed in Chapter
Summary Table
Model/Decision Area
Water Quality
Pollution Impacts in
Water Bodies
Ecologic Modeling
Urbanized Storm Runoff
Modeling
Models of Treatment
Technology
Models of the Economic and
Social Impacts of Water
Pollution Control
Pollution Impacts on Ground
Water
106
General Type
Important Characteristics
Analytic Simulation
Statistics
Simulation
Simulation
Statistics
Simulation
Input-Output Analysis
Simulation Systems
Analysis Games
Statistics
Simulation
Shows impacts on physica
parameters of water bodies dm
to waste inputs (usual param
eters dissolved oxygen, nutrients
salinity and temperature)
Models address broad strateg
of organisms and specific tactic
Shows quality aspects of urba
runoff and allows both land us
and structural controls
Helps to design, size and cos
treatment facility
Attempts at defining econom
and demographic charges and t
aid in implementation
Temporal and spatial dispersic
of pollutants
-------
Model/Decision Area
Regional Waste Management
Optimal Taxing
Power Plant Siting
Watershed and Catchment
Models
Synthetic Rainfall and Stream
Flow Generation
Groundwater Modeling
Economic and Social
Impacts of Water Resource
Development
Regional Water Demand
Projections
Regional Water Supply
Analysis
Preference Analysis and
Implementation
Reservoir Management
nvestment Scheduling and
Sequencing
>ipe and Aqueduct Networks
Design
jauging Station Location
"echnology Design
General Type
Important Characteristics
Optimization
(linear, dynamic, integer
and geometric program-
ming)
Optimization (linear
and nonlinear program-
ming)
Optimization (linear
programming)
Simulation
Statistics
Simulation
Simulation
Systems Dynamics
Statistics
Input-output Modeling
Linear Programming
Game Theory and
Optimization
Statistics Simulation
Optimization
Optimization
Optimization
Simulation
Optimization
Simulation
Statistics
Optimization (dynamic
programming, geometric
programming)
Investment models for the fol-
lowing problems: Regional least
cost treatment, equitable cost
distribution, treatment plant
location, low flow augmentation,
in-stream aeration, bottom de-
posits, storm water
Tax schemes to support regional
investment
Regional supply models which
consider environmental stand-
ards
Shows the response in terms of
runoff to a rainfall intensity and
pattern
Generates long synthetic rain-
fall and stream flow data traces
which have similar statistical
properties as short observations.
Movement and availability of
ground water
Models for predicting economic,
demographic recreational effects
of projects
Estimates water requirements in
various use sectors and cate-
gories
Finds optimal supply investment
for a given demand
Regulating operation to provide
a stochastically varying resource
to varying competing demands.
Project scheduling under budget
constraints
Sizing and configuration analy-
sis
Gauging location to maximize
information
Optimal sizing and choice of
subsystems for treatment
I. WATER QUALITY
. Description of the Area
1. Problem Identification
In order to consider the variety of
lodels helpful in the decision processes
>r establishing the management of
rater quality, it is necessary to focus
n the factors that cause the problem,
hat type of decisions can be made to
sal with the problem and who will
lake them.
What Causes the Problem—Water
quality problems are caused by the use
of water as a disposal medium to the
extent that other uses of the resources
are impaired or foregone. We must view
the assimilative capacity of water to
receive and degrade wastes as a valu-
able but limited resource that must be
properly allocated just like any other
resource. Unfortunately, the traditional
private sector pricing mechanism which
expresses society's preferences for other
107
-------
types of resource use breaks down in
the case of a common, public resource
such as the ability of the environment to
assimilate wastes. The result has been
an overuse of the environmental re-
source leading to its deterioration with
little attempt to recover and reuse waste
material. A brief recounting of the type
of processes that create wastes which
eventually enter water and the other
water uses which waste disposal may
interfere with serves to highlight the
diverse, complex nature of the problem.
It is possible to differentiate between
two different ways that waste materials
enter water. This distinction is im-
portant for it helps to recognize those
waste sources that are more amenable
to direct control. The first way is
through water use. There are many
different water uses and most of these
uses return water to water bodies that
is diminished in quantity and quality.
Sometimes the addition of wastes to
water is deliberate in that the water is
being used as a transport mechanism to
take wastes away from the place where
they are generated. In other cases, the
water is being used for a particular
process and becomes contaminated by
materials it come in contact with. In
both of these cases, the source of the
waste and the point at which it enters
the water body is specific and identifi-
able. One can think of a variety of
control alternatives ranging from tech-
nological devices located "at the end of
the pipe", to process changes and other
policies which will either lessen water
use or change the wastes that enter the
stream. These are referred to as point
source wastes. Examples of point source
wastes are those from domestic usage,
industrial use and heated water dis-
charges from cooling usage.
Another type of waste enters water
bodies as the result of a combination of
the normal rainfall runoff process and
policies for the disposition of land and
air resources. These include the pollu-
tion of surface runoff to streams and to
groundwater from non-urban areas and
agricultural areas. Such sources are
non-point source problems and are
108
normally amenable only to changes in
policies and to process changes which
keep wastes away from the runoff
process. There is little large scale tech-
nology that is helpful. Sources include
storm water runoff to water bodies from
urban and agricultural areas.
The primary uses of water which have
a major quality concern are municipal,
industrial, cooling, recreation, aesthet-
ics, navigation, agriculture, and waste
disposal. It is clear that there is conflict
between these uses in that each require
a different level of quality and each
deteriorates quality through use in a
different manner. Certainly a legitimate
use for water is the disposal of wastes,
but it can be shown that this use in
excess precludes other uses. Thus waste
discharges to a water body only become
pollutants when they interfere with some
other desired use. If it is decided to use
a stream mainly for waste disposal and
no other use is desired except naviga-
tion, this would not in the technical
sense be pollution. However, such single
object use of water is generally deemed
socially unacceptable in the U.S. and
an attempt is made to handle more than
one use for a water body. Still, require-
ments to use the water for non-contact
recreation, industrial processes and cool-
ing may be far lower than using the
water for water contact recreation, fish
and wildlife and municipal water sup-
ply. Thus different levels of improvec
water use may be chosen.
What Decisions Can Be Made?
As with any scarce common resource
problem, the public sector must inter
vene to ensure that resource allocatioi
does reflect the objectives of society
This intervention can come in the forn
of laws that prohibit certain types o
activities that create pollution, requir
waste treatment and set environments
standards, or in economic incentive
such as taxes or subsidies which act a
price surrogates to cause the privat
sector to shift its resource use. It is clea
that to establish rational policies for th
limiting of such environmental deter
oration, a careful weighting of all tt
complex technical, economic and socii
-------
implications of waste management upon
the diverse and often conflicting objec-
tives of society is of the utmost im-
portance. For instance, every process
that develops goods and services for our
basic well-being, as well as the extra
trappings of an affluent society, requires
the use of limited resources and pro-
duces residuals which must be ac-
counted for in some manner. We must
consider how much of these residuals
will be tolerated in the environment
when the alternatives to reduce these
may mean serious economic costs in
resources, lost jobs or even the elimina-
tion of certain current development
activities. A simple law requiring pollu-
tion to stop does not take into account
the objectives and purposes of the proc-
esses that created the pollution in the
first place. Thus, the decision maker,
who must balance the answers to these
delicate questions, is faced with a very
complex, difficult and quite subjective
task. This chapter is devoted to the role
that analytical models have played and
can play in ordering policy decisions,
both by helping to quantify some of the
trade-offs between objectives for the
system and by providing better insight
into how the system operates. The ques-
tions the decision maker must face cen-
ter around two broad but interactive
issues. What quality is desired and what
is the best way to obtain it? These ques-
tions help to bring to the forefront the
prominent decision issues. It is clear
that there is no answer to one question
without actually investigating both
simultaneously. The quality desired is
very much a function of how much that
quality will cost, not only in direct
economic costs, but in terms of oppor-
tunities foregone for investment in other
worthy public sector activities such as
hospitals, roads, schools and parks. As
with any public sector problem, the
recipients of the benefits of the im-
jrovements are diffuse and, due to the
complexities of the system, we are not
capable of assessing directly the value
received. Thus, the question of how
;osts will be allocated and whether that
illocation is equitable often turns out
to be a more pertinent question than
what the total cost is. Further, since
the goal of the decision process is to
come up with a plan that will and can
be implementable, care must be taken
to see that the participants in the plan
understand and accept its objectives and
equity, and that the proper institutions
exist for running the plan and assessing
the costs.
The problem of establishing quality
standards is extremely difficult for it
requires the ability to predict the cause
and effect relationship between waste
discharges and water quality, not only in
terms of physical impacts on other
water uses, but on their social and
economic reverberations as well. This
has led to considerable use of models
to identify such cause and effect rela-
tionships and for evaluating control
alternatives.
The mam difficulty for the technical
investigations will be in defining the
quality that is desired. Without the
ability to assess preferences for water
quality and water uses for all users, we
must fall back on attempts to define
possible water uses and their cost im-
plications.
The difficulty in determining what
water use to choose falls into two sepa-
rate categories: determining a set of
physical parameters that show if a
certain water use is possible or not, and
determining whether a particular water
use is justifiable within a region in terms
of impacts on economic and social ob-
jectives. It is clear that the second task
is very difficult, including as it does
assumptions about social preference
and the linkage between water quality
and regional activity. However, it turns
out that the first problem, that of find-
ing physical parameters, is a major defi-
nitional problem with which the various
standard-setting agencies have to deal.
Because most organic material degrades
in natural water bodies by micro-
organisms which use dissolved oxygen
in the stream for the degradation proc-
ess, stream dissolved oxygen (D.O.) is
the most commonly used surrogate indi-
cator for overall water quality. How-
109
-------
ever, this by itself is not a good indicator
for all situations. For municipal water
supply, there is a concern for chemicals
and pathogenic organisms concentra-
tions. For cooling water the most im-
portant characteristic is the temperature.
Thus, choosing the desired water quality
indicator is an exercise in identifying
the important pollutants in the area and
how they reflect on water quality in the
water body. Also, concern for the types
of water use possible in the area and the
improvements necessary to bring about
that quality must be considered. The
key problem is to then balance the cost
of eliminating to some degree the waste
sources against the benefits of the re-
sulting quality increase. As quality in-
creases are often implicitly stated, this
balancing is a subjective process, as will
be shown in the discussion of the Dela-
ware Estuary model.
In general, the role of models in the
process is one of clarification, not
decision making. A variety of models
increases the decision maker's under-
standing of his options and the sensi-
tivity of his policy decisions.
Who Makes the Decision
The public sector nature of the prob-
lem requires the intervention of govern-
ment to order the many diverse interest
groups. The term decision maker, while
quite comforting to the analyst who
likes to think that one person assimi-
lates all the information and decides, in
fact is a euphemism for a very diffuse
decentralized coalition of pressure
groups and different levels of govern-
mental officials.
In the U.S., the major role of estab-
lishing water quality standards and
types of waste control that will meet
those standards fall to Federal, State
and regional organizations. The re-
gional management organization is a
recent attempt at problem oriented
institutions that have legal authority to
manage all aspects of the problem with-
out questions of state and local political
boundaries. An example is the Delaware
River Basin Commission which has
control over all water resources activi-
110
ties related to the Delaware River in
the states of New York, New Jersey,
Pennsylvania and Delaware. It repre-
sents a partnership of these states and
the federal government to implement
control strategies and quality plans.
Such innovative regional organization
will continue to provide major impetus
for quality control. Most management
modeling is done from the perspective
of the regional authority as the decision
maker.
The major lead on setting broad scale
policy questions and in generating
money for improvements has been the
federal government through the Envi-
ronmental Protection Agency. As a par-
ticipant, as well, in the regional organi-
zations it exerts a powerful influence.
The role of the States has been reduced
to that of participating in regional
schemes and otherwise implementing
national goals.
B. Models in the Aid of Water
Quality Decision Making
The models used in water quality
decisions are closely related to the types
of decisions being made which are in
turn influenced by the character and
nature of the problem. In most prob-
lems there are two types of models that
can be considered. One is a descriptive
model which explains the cause and
effect relationship between a particular
policy and the important parameters in
the system. Most simulation models fall
into this category. The important aspect
here is that the model is descriptive; it
shows the results of a given policy. The
second type of model is the management
model which is both descriptive and
prescriptive in that it shows cause and
effect and attempts to choose between
alternatives which best meet established
objectives and constraints. Most opti-
mization models are of this form. Both
types of models have their individual
defects. While optimization models can
choose between alternatives, structural
considerations limit one to very sim-
plastic representations of the underlying
cause and effect relationships. On the
other hand, while descriptive models
-------
can be made as detailed and as intricate
as necessary, they can consider only one
alternative at a time. Thus in most ap-
plications such methods are used in
consort; the management model sug-
gests areas of good design for further
consideration by the descriptive models.
1. Descriptive Models
Waste Input—Physical System Re-
sponse Models. From the earliest in-
vestigations in water quality the engi-
neers have built mathematical and
analog models to represent the response
of the physical system to waste inputs.
This allowed the investigation of the
response of the physical system when
new control plans or new waste inputs
were put into action. Prominent among
these models are dissolved oxygen mod-
els which show the biological response
of the water body to organic inputs;
temperature models which show the
temperature response to heated water
inputs; and salinity models which meas-
ure the amount of salinity intrusion in
estuaries as a function of the fresh water
flow in the estuary. We next discuss each
in turn.
The modeling of dissolved oxygen
has evolved from the earliest case of
an assumed one-dimensional, steady-
state stream effected only by carbona-
ceous wastes to the present state-of-the-
art which allows consideration of both
spacial and temporal considerations in
stream and tidal estuaries for both
9L 1 d
9c
-
ABx
at
(Qc) +
EA
carbonaceous and nitrogenous wastes.
An excellent reference is the Tracer
Report (104) which was prepared for
EPA as an assessment of the art in
estuarine modeling. Estuaries, which are
the sea-tidal portion of large rivers, are
of particular interest as they are usually
most heavily populated and industrial-
ized. Further, they are biologically im-
jortant because they are major habitat
jroduction areas. Finally, from the
hydrodynamic point of view, they rep-
resent complex analysis problems be-
cause of the interaction of the ocean
tides and the incoming fresh water
inflow from upstream. The Tracer Re-
port deals with three- and one-dimen-
sional temporal models of estuary
hydrodynamics, and includes the con-
sideration of dissolved oxygen effects
caused by carbonaceous and nitrogenous
wastes for the one-dimension, steady-
state, estuary case; the case most sus-
ceptible to large-scale solution. Solution
of the differential equation model used
to represent the process is accomplished
by analytical integration of the differen-
tial equations over time. For anything
but the most drastic simplifying assump-
tions, this proves to be very difficult.
From a large-scale, computational point
of view, a finite section approach is
more feasible. The estuary is divided
into a series of segments and it is as-
sumed that each section is completely
mixed. This in essence replaces the de-
rivatives in the steady-state equation
with difference approximations. A one-
dimensional, time-varying model for a
two-stage, Biochemical Oxygen Demand
—Dissolved Oxygen (BOD-DO) reac-
tion which translates organic inputs into
a distribution of organics in the estuary
(Equation Al), then translates those
organics into estuary dissolved oxygen
(Equation A2) would take the following
form:
A
-KrtL
(A 1)
f K.,(cs - c) - KrtL + P - R - B (A 2)
where L = a measure of the organic
material in the estuary due
to waste loadings
K., = reaeration coefficient
K(] = decay coefficient for the
reduction of stream or-
ganics by biologic action
P = photosynthetic oxygen in-
puts
R = losses in oxygen due to
biologic respiration
111
-------
B = losses in oxygen due to
decomposition of bottom
deposits
A = the cross-sectional area of
the estuary
Q = the freshwater inflow
E = dispersion coefficient (tidal
effect)
t = time coordinate
x = distance coordinate meas-
ured along the estuary
c = dissolved oxygen concen-
tration in the system
cs = dissolved oxygen concen-
tration at saturation
The inclusion of temporal variations of
this form are accomplished using a
difference method with the equations
being stepped through in time. Such a
method is described in Pence et. al. (79)
and is included in a model distributed
by the EPA (30).
For non-estuarine rivers, EPA has
also been instrumental in establishing
both steady state and time varying
models of dissolved oxygen behavior.
They have aided state agencies in the
implementation of two models devel-
oped for the Texas Water Plan which
are available in computer packages.
DOSAG-1 (101) is a steady state model
which includes both carbonaceous and
nitrogenous leads and may be operated
on to find stream D.O. response to
several different sets of input stream and
waste loading conditions. The model
will also calculate the amount of water
needed for flow augmentation to reach
a specified dissolved oxygen standard.
QUAL-1, a time varying non-steady
state model (Texas 100, 102) allows the
investigation of stream dissolved oxygen
on an hourly basis when input param-
eters are varied in that time scale. This
type of model is used to determine how
often and to what magnitude stream
conditions vary over time due to a given
control policy.
We next turn our attention to stream
temperature models. With electrical
energy production already being a major
withdrawal user of water and with antic-
ipated future demands, the question of
how heated discharges impact on re-
112
ceiving waters is one of great impor-
tance. Every new power generation site
must be carefully evaluated to show
how its discharge will be distributed,
not only for ecological protection, but
to insure that the plant's efficiency is
not impaired by the heating of its cool-
ing water. Extensive modeling has been
done for the problem of translating
heated discharges to stream, estuary and
coastal site water temperature profiles.
Examples can be found in the Tracer
Report (104) and in Stolzenbach, Adams
and Harlemen (95) of the state-of-the-
art in modeling such discharges. The
successful translation of these tempera-
ture increases to estimates of biological
change is still very much in its infancy
and is addressed in another section.
The last set of models within the
general framework of physical system
response models deals with salinity in-
trusion. This area is of interest in
estuarine waters because salinity in
water can destroy its use for most
municipal and industrial processes and
because it can mean rapid change for
biological communities. Salinity intru-
sion is most strongly retarded by the
magnitude of the fresh-water flow in
the river portion of the estuary. In sum-
mer and drought periods, the lessening
of this flow can mean serious increases
in salinity at points where fresh water
is normally derived for other purposes.
Models of this process are helpful in
planning for emergencies and for evalu-
ation of the effect of upstream water
diversions on downstream salinity. The
model developed by Thatcher and
Harleman (103) is an example of such
a model.
Ecologic Modeling. The term ecologic
modeling will be used to describe those
models which attempt to predict the
changes in ecologic communities due
to changes in wasje control policies. As
Holling (47) points out, the use o
mathematical modeling and in particu-
lar computer simulation in this area
has taken two main thrusts: one tha
concerns itself with the broad strategies
used by organisms and the other that i;
concerned about the specific tactics usec
-------
by organisms. The first leads to con-
sideration of ecosystem organization
and stability in terms of this evolution
of populations and of communities,
while "the second deals with analysis of
the mechanisms and underlying inter-
action between parts of ecological sys-
tems. These models are described in
detail in Pattern (79) and O'Neill et al.
(77). It should be noted however, that
the art is still not to the point where
direct ecologic evaluation of the benefits
(positive or negative) of a change in
water control policy for a specific area
can be made. However, the amount of
attention and excellent work being de-
voted in this area is very encouraging
for future developments.
Urbanized Storm Runoff Modeling.
As noted earlier, runoff from storms in
urbanized areas picks up waste material
as it is collected in storm sewer systems
and then discharged to receiving waters.
The problem of how to control such
pollutional loads is strongly amplified by
the fact that the waste flows occur only
a limited number of times during a year
and then have very large volumes in
short time spans. Developing treatment
for such infrequent high volume waste
flows is virtually impossible without
some consideration of storage and other
means of slowing down and spreading
out the loads. The most important
model developed in this area is called
the EPA Stormwater Model and it is
described in Lager, Pyatt and Shubinski
'60). For a detailed representation of an
urban catchment including population
estimates, configuration of the sewer
md storage system, time since last
>torm and a given design storm, the
nodel develops, not only the hydro-
,raphs of the volume of water moving
it any time and point through the sys-
em, but its quality as well. Initial in-
'estigation shows the water quality of
term runoff to be worst in the earliest
>art of the storm thus allowing a strat-
gy of treating and storing only that
lortion. This important model in effect
Hows the evaluation of proposed com-
ined storage and treatment facilities, as
fell as the pollutional impact of storm
water collection systems. It is routinely
used by consultants and local govern-
ments, as well as higher levels in the
decision making process involved in the
control and treatment of urban storm
drainage. Other models for clarifying
land use policy and water quality inter-
actions are discussed in Jameson (53).
Models of Treatment Technology.
The technology for treatment of munici-
pal waste discharges represents a variety
of different physical, chemical and bio-
logical components, which must be sized
and developed within a total systems
context. A major modeling effort by
EPA in developing a computer system
for sizing and evaluating waste treat-
ment systems has been developed by
Smith (93) and has proven very helpful
in estimating general treatment costs
and trying out design alternatives.
Models of the Economic and Social
Impacts of Water Pollution Control.
From the point of view of evaluation
of control alternatives to decide what
level of quality is desired, some evi-
dence of the benefits of such a policy
is necessary. We would like to know,
for instance, what impacts, plus or
minus, a river clean-up would have upon
jobs, economic activity, increased rec-
reation participation and other gross
indicators of social well-being. The his-
tory of modeling in such questions is
at best fragmentary and far behind our
ability to model the physical system
response. This is not surprising as the
physical system is much better defined
and understood. For the most part,
social system benefit estimates have
been based on intuitive models or simple
regression estimates. Recent work indi-
cates that analytic modeling can be
carried out in this sector. Use of re-
gional input-output tables specially con-
figured for calculating the economic
impacts of pollution control is shown by
Miernyk (75). Use of systems dynamics
to show the feedback interaction be-
tween water resource investment and
demographic and economic trends in a
region has been developed by Hamilton
et al. (42). Gates et al. (33) also used
systems dynamics to show political and
113
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institutional response to new water
quality legislation in California. At-
tempts by the EPA to develop simple
models to be used in simulated games
representing the decision to determine
preferences and strategies for reaching
implementation are reported by House
and Patterson (48). Such attempts are
very encouraging and point to a much
better understanding of the evaluation
of all the impacts of governmental re-
source development in the face of a
serious conflict in objectives.
Models of Pollution Impact on
Groundwater. Models to show the im-
pact on physical parameters due to pol-
lutional inputs have reached a fairly
high level of sophistication where both
temporal and spatial effects can be
noted. The article by Bradehoeft and
Finder (9) and Reddel and Sunda (82)
are examples of the computational and
theoretic state of the art in this area.
2. Management Models
Here we begin an investigation of
models which allow a selection between
alternatives according to specified ob-
jectives and constraints. Such models
are most often used in consort with the
descriptive models such as those de-
scribed in the previous section. The
reason for this is that the management
model must of necessity have a more
simplistic view of the cause and effect
relationships in the system, and the
descriptive models are helpful in check-
ing out in more detailed fashion the
system configurations suggested by the
management models. There are issues
introduced when considering manage-
ment models which have to this point
been rather subjectively hidden in the
discussion of the descriptive models.
This is the choice of objectives and the
measures of effectiveness for those ob-
jectives necessary for evaluation of a
solution. Optimization techniques usu-
ally require a one-dimensional objective
in order to be effective, while any
problem worth its analysis, particularly
in water quality management, has many
diverse and conflicting objectives. The
approach used in almost all of the man-
agement models to handle multi-objec-
114
lives is a surrogate approach which
allows the use of single objective opti-
mization techniques. One objective used
is national income (economic effi-
ciency). This is normally not measured
by net benefits since pollution control
benefits for this objective are difficult
to identify in economic terms except by
the cost of the control procedures. This
in most cases is represented in the ob-
jective function. Another important ob-
jective is society's desires for environ-
ment quality. This is represented in the
model by specified quality standard
constraints which must be met.
Another issue is the equity of the solu-
tion and its ease of administration.
This too is also handled as a constraint
but in a more subjective manner and is
discussed in detail later in this section.
Our discussion of the management
models is best focused by looking at
particular types of problems. One
major problem area, with many sub-
models and much research, is the range
of choice open in the investigation of
water quality in complex regional urban
settings. Another problem, usually con-
sidered quite independently, is the
energy expansion-environmental effects
problem faced in the location of new
electrical generation facilities. Manage-
ment models in optimal technology
design are also discussed.
Regional Waste Management Prob-
lems. In any complex urban setting the
combination of large population and in-
dustrial enterprise means that there
will be serious water quality problems
that require control because of impacts
on other water uses. The specific prob-
lems that contribute to this genera
deterioration of quality include: muni-
cipal waste discharges, industrial waste
discharges, urban storm drainage, tribu-
tary and upstream loading and bottorr
deposits from previous pollutional load-
ings. While we have outlined contro
schemes for most of the individua
pollutional sources, it is clear that th<
best alternatives, particularly in th<
case of runoff and other non-poin
sources of pollution, may well bi
through land use or other polic;
-------
changes that keep wastes out of water
in the first place. Also, when one begins
to look at the region as a whole, there
appears to be a reasonable basis for
looking for economies of scale in con-
trol through regional cooperation in
the areas of joint treatment facilities,
measures for increasing the assimilative
capacity of the water body and better
land use planning.
The region as a whole seems a good
way of defining an administrative unit
within which the costs of control can
be successfully allocated among the
people in the region. Thus, the problem
referred to as the regional management
problem is the problem of finding the
set of policies, technology and control
schemes that satisfies the regional de-
sires for environmental quality and
equitable implementation at least cost.
Ideally, such a model to sort through
all these alternatives would allow as
decision variables all possible control
and policy options. This in terms of
computational and conceptual problems
has not been possible. Modeling instead
las been directed towards the investiga-
ions of a set of sub-problems within
.he region to supply information about
he options available. These models
nclude the regional effluent control
nodel, the regional treatment facility
ocation problem, flow augmentation by
ipstream releases, instream aeration for
ncreasing the assimilative capacity of
he water body, urban storm water man-
.gement, nontreatment control alterna-
ives such as the removal of bottom
eposits and other problems. These
lodels are directed at developing a
sheme that would then have to be ad-
linistered by some form of regional
uthority and do not explicitly consider
le implementation problem. In another
eld of work, many investigators have
>oked for pricing schemes that would
low a decentralization of the imple-
lentation process. Through the imposi-
on of charges, polluters could be made
> adjust their waste loads to a more
>cially desirable alternative. The prob-
m comes in deciding what structure
and magnitude such pricing schemes
should take to be implementable.
The problem of regional effluent con-
trol was the first regional model
attempted and is directed towards find-
ing the set of effluent changes at mu-
nicipal and industrial sources necessary
to reach desired quality standards meas-
ured in terms of stream dissolved at
specific points along the water body.
Many authors have suggested models
for this problem which essentially take
the form of a mathematical program-
ming problem with linear constraints:
Minimize z = 2}f.j(
(A3)
Subject to
i = 1, . . . , m (A4)
0 < Xj <
j= 1, . .
n (A5)
where xf = the amount of waste to
be removed at source j
in pounds per day of
Biochemical Oxygen
Demand (decision
variable—unknown).
U, = the upper bound on
waste that can be re-
moved at source j in
pounds per day of Bio-
chemical Oxygen De-
mand (known).
fj(x,|) = the cost of removal of
Xj (known).
Ay (xs) = the quality response at
some point i in the
water body caused by a
waste loading of Xj at
source j, for a given set
of physical parameters
(known).
bj = the minimum desired
improvement in quality
at point i (known).
There are several important assump-
tions buried in this simple formulation
that should be discussed. Notice that
the objective (A3) calls for the mini-
mization of the cost to the region as a
whole without any notion of the allo-
cation of the cost. The choice of which
115
-------
sources will be reduced will be based
on a combination of strategic location
and efficient methods for treating
wastes, rather than on some notion of
how much damage is being caused by
the waste source. The formulation
stresses an overall efficiency objective
without taking into account distribu-
tional problems. Thus it would be
possible, and has in fact occurred in
several application studies, that large,
inefficient sources which have done
little to concentrate or reduce their
waste flows are required to make no
changes even though their damage is
great, because of the great cost involved
in redoing the whole plant. Meanwhile,
small, highly efficient sources where in-
vestment has already been made will be
called on to treat further, since wastes
are already concentrated. This calls for
some means to reallocate the efficiency
costs of the improvement either among
the polluters or among the beneficiaries,
and some regional institution to ad-
minister and collect that cost. Multi-
objectives in the model are achieved by
the specification of the desired quality
to be obtained. Notice that there is no
aspect of time in the formulation, that
the problem is viewed as steady state
under some conservative definition of
water body parameters, rather than re-
flecting the stochastic nature and un-
certainty of stream flow, waste flows
and physical parameters. Usually, the
stochastic effects are considered using
the time varying descriptive models
discussed in the previous section to
evaluate the treatment configuration
derived from management model
studies.
The decision variables Xj represent
the amount of present waste discharge
that will be removed and are specified
to always be non-negative. Thus, no
source is allowed to reduce its treat-
ment level and there can be no further
degradation of quality conditions.
Where present quality levels are high,
they will remain high. This would pre-
clude an attempt to bring in new in-
dustry to an area to make use of
assimilative capacity available above
116
that which it required. The concept of
new polluters at a future time and how
they would receive allocations is
another policy question that would have
to be considered.
Attempts at solving the problem are
aided by a linear assumption for the
constraints and by the form of fj(Xj),
which is assumed convex and approxi-
mated by linear segments. Sobel (94)
and later ReVelle et al., (85, 86)
Loucks et. al., (66) presented linear
programming solutions using linear
approximations of the convex cost func-
tions. Liebman and Lynn (61) pro-
posed a dynamic programming model
for the non-estuary case.
Attempts at bringing more equity to
the solution have also been attempted.
One such formulation is the "uniform
treatment" model which requires that
all polluters treat their waste loads to
the same percentage removal while
meeting required standards as before.
This model can be written as:
Minimize S
subject to:
j
(A6)
, m (A7)
P + l s if s > p.
'j \ (AS)
Xj=0 ifS
-------
and the other symbols are as previously
defined. Note that ^ = (1 — PJ)UJ for
each source.
This formulation presents no prob-
lems if no treatment facilities already
exist in which case the total waste dis-
charge f, from each source is ut. But
if some treatment already exists, a con-
straint such as Equation (A8) is needed.
That allows the choice of a uniform
treatment level below the existing treat-
ment if it is acceptable. While the
problem of solving Equations (A6)
through (A9) would appear quite diffi-
cult as there are discontinuities in the
constraint set, in fact optimal solution
is obtained by a simple iterative process
in which S is increased incrementally
until the goals are met.
This uniform model is essentially the
same as the efficiency model in Equa-
tions (A3) through (A5) but has an
added constraint, i.e., Eq. (A8) which
means that the regional treatment cost
for the uniform model must be at least
as great as that for the efficiency model.
The uniform model's "equity" feature
of allocating costs to users more fairly
yy requiring all users to provide treat-
ment to the same specified treatment
evel is the reason for this increase in
regional cost. However, closer examina-
ion of the features of the plan reveals
t has its faults. Requiring the same
sercentage of waste reduction ignores
he fact that the size of waste dis-
•harges and the costs associated with
xed improvements vary greatly from
ource to source. Thus a high degree of
emoval at a site of a small waste
ource contributes little to quality but
oes increase costs at that source. Simi-
trly, the use of a uniform treatment
:vel requires that all sources including
lose having no effect because of their
•cation must raise their treatment level
) obtain increased quality at a particu-
.r point. However, the model does have
te appeal that it is easy to administer
i the sense that each polluter is told
rectly the percentage of waste he
ust remove and no attention need be
given to cost allocation as it has to be
internalized.
A compromise between these two ex-
tremes has been suggested. It is the
zoned uniform model and requires that
sources be divided into zones which
reflect equivalent activity, location and/
or damages created and that uniform
treatment levels be found for each of
these zones so that a given quality goal
is reached for the region at least cost.
This model is formulated as:
Minimize Jfj(Xj)
subject to:
J > b, i=l, . . . ,m (A10)
Xjd-Pi) c
t-
JifSk>Pj
Xj =0
ifSk
-------
as the range of decision variables has
been increased from at source treat-
ment only to include the building of
piping systems, relocating waste dis-
charges and the allowance for siting
a few large-scale, regional-treatment
plants. Such an increase in decision
variables causes serious non-linearities
in the cost function and in predicting
the cause and effect relationships of
pollutional discharges into water bodies,
particularly when the shifting of a load
means a change in the hydrodynamic
flows in the stream. Though several
attempts have been made to deal with
this problem there have been severe
computational problems. Graves et al.,
(36) first studies a problem which
allowed only piping of the wastes to
areas of better quality, but did not in-
clude treatment as a variable. This
caused problems because it allows deg-
radation of areas of better quality in
order to improve areas of extremely
bad quality. It was in effect a redistri-
bution of wastes to make use of avail-
able assimilative capacity. In a later
work, which is available through the
EPA, Graves et al., (37) proposed
another model which allows both treat-
ment and piping to be decision varia-
bles. The objective function is to mini-
mize the cost of treatment plus the cost
of building transportation pipeline while
meeting requirements for improved
stream quality at specific points. The
regional treatment facility problem will
continue to be one of great modeling
interest due to recent legislative impetus
and apparent economies.
Flow augmentation is a control al-
ternative which attempts to increase the
assimilative capacity of the stream by
increasing the amount of dilution water
present during low flow periods. Such a
method is quite expensive as it involves
the allocation of upstream storage in
reservoirs to this use and is to be con-
sidered only after adequate waste treat-
ment has been applied. Grantham et
al., (34) in work sponsored by the
EPA, employ an economic description
of the value of low flow augmentation
by constructing an optimization model
118
of least cost effluent control which
shows how the cost of regional treat-
ment decreases with increased flow in
the system. Thus the effect of the flow
augmentation is developed not in the
objective function but in the constraint
coefficients which describe the cause
and effect relationship in the physical
system. Young and Gitto (111) report
on using modeling of flow releases to
control acid discharges in streams.
Another method for increasing the
assimilative capacity of water bodies is
to increase the oxygen supply by arti-
ficial aeration using large-scale me-
chanical equipment. This is an alterna-
tive only justifiable in extremely pol-
luted rivers where treatment related
schemes have been applied but cannot
provide enough improvement. Work in
this area to size and space the equip-
ment is presented in Tarassov et al.,
(98). The optimization technique used
is Pontryagin's Minimum Principle and
represents one of the few attempts at
applying control theory in this area.
Ortolano and Thomas (78) suggest
simple models for evaluating the re-
moval of bottom deposits.
As noted earlier, a major pollutiona
load to water bodies is urban storm
water. A descriptive model, the EPA
Storm Water Model, has previous!}
been discussed which for a given con
figuration of control, storage and pipin
facilities will show the magnitude anc
quality at any point in the system ir
response to a design storm (60). Th<
problem with a descriptive model, sue
as this, is that it is relatively expensiv
to do sensitivity analysis to compar
many alternative designs. Optimizatio
serves as a possibility for building
screening model that will suggest goo
alternatives for the simulation proces:
Kirshen and Marks (57) report on
linear programming model in whic
storage location, storage size, addition;
piping and treatment, location an
operation are decision variables. Tr
objective function is to minimize coi
struction and operation costs whi
meeting treatment and flooding coi
straints. They report good success
-------
developing meaningful design configu-
rations for further consideration using
the simulation model.
The previous models have all dealt
with the management of wastes in a
regional context from the viewpoint of
the technologic controls to be applied.
As suggested by Kneese and Bower
(58) another approach is to look for
pricing schemes, i.e. charges or taxes,
which will cause polluters to internalize
pollution costs and thus shift their ac-
tivities. The main advantage for such a
scheme is that it allows each waste
source to make its own optimal adjust-
ment rather than having a method ex-
ternally prescribed. This leads to a
degree of decentralization which allows
for more rational individual decisions.
Several researchers have investigated
the problem of finding a set of prices
for a region which would bring about
desired water quality levels. Haas (45),
Haimes (39) and Upton (106, 107)
discuss multilevel optimization tech-
niques for the problem which charac-
terize the different levels of decision
(the choice of quality levels, the setting
of prices, and the user response). The
main difficulty in such work is not in
the premise of such charge schemes,
but in their acceptance and implemen-
tation. There has been strong reaction
against pricing schemes in principle and
ittle attempt by the government to
develop a large-scale, computational
jxample to evaluate such a method.
It is clear that future population and
development pressures will cause even
itronger interactions between pollution,
he recovery of materials and the more
;areful use of resources. In this case,
mcing schemes for the resource system
.s a whole seems an area of important
uture modeling and consideration.
)orfman and Jacoby (25) examine
egional policy by identifying different
uterest groups within a region and
lowing how weighting their prefer-
nces develop different quality levels
nd public expenditures in a region.
'nergy Production and Thermal Pol-
ition. Recent models to consider new
atterns for the expansion of electrical
energy production have explicitly con-
sidered environmental standards as a
factor in site and technology choice.
Farrar et al., (29) report on a large
scale linear programming model to
investigate the supply for a given energy
demand pattern in a region at least cost
of construction and operation, while
meeting reliability and environmental
constraints. The environmental con-
straints are considered by evaluating
each site available in a region for the
types of generation and abatement
technology that might be located there
and still meet given temperature and air
pollution standards. Shiers and Marks
(92) report on a water pollution model
which develops this information for a
variety of different receiving water and
technology alternatives. The result is a
series of models which displays good
generation expansion schemes that meet
environmental standards and which can
be used to demonstrate the economic
impact of environmental standards on
the cost of energy production.
Technology Design. Management mod-
els have also been used to design the
technology systems for handling and
treating wastes. Evenson et al., (27)
reports on a dynamic programming
model of an industrial waste treatment
system and Liebman (62) shows a
heuristic algorithm for designing gravity
sewer systems. Dynatech (26) has de-
veloped models for optimally configur-
ing electric generation equipment.
C. The Delaware Estuary,
an Example
The first use of a regional manage-
ment planning model was by the Fed-
eral Water Quality Administration in a
1964-67 study of the Delaware Estu-
ary which runs through New Jersey,
Pennsylvania, and Delaware. The prob-
lem included 90 major waste sources,
approximately 24 quality constraints,
and piecewise linear approximations for
cost functions and was repeatedly
solved using linear programming pro-
cedures to evaluate a variety of differ-
ent assumptions about goals, stream
and economic parameters.
119
-------
In designing water quality improve-
ment programs for the Delaware Estu-
ary, the Federal Water Quality Admin-
istration generated several alternative
schemes to reach a range of quality
goals. As they could demonstrate that
the technical alternatives such as low
flow augmentation, piping, stream aera-
tion, and storm water control were
clearly dominated by selecting waste
treatment levels at each source for the
particular conditions on the Delaware,
the latter alternative was the only one
considered. No consideration was given
to taxing or incentive schemes or to
the possibility of regional treatment.
Six sets of alternative water quality
goals were chosen with the help of
citizen groups, conservationists, indus-
trialists, and governmental representa-
tives. Objective set I represented the
best that could technically be obtained
by requiring maximum waste reduction
from the 90 largest waste producers
using the estuary. At the other extreme,
objective set V represented the cost to
keep the conditions as they were at the
time. As can be seen in Table A.I, a
considerable expense is needed just to
maintain the status quo. The objective
sets II, HA, III, and IV represent
various possible alternatives in between.
The goals are noted in Table A. 1, along
with the cost to meet the goals under
different cost allocation assumptions and
with some estimates of benefits.
Costs, including capital costs and the
present value of operation and main-
tenance expenditures, were estimated to
obtain each quality objective set using
the least best, uniform, and zoned uni-
form treatment models. The quality to
be obtained from each objective set
included the valuation of visual,
esthetic, and public health benefits, as
well as the quantifying in dollars of
fisheries, recreation, and water supply.
These costs and benefits are presented
in Table A.I.
There are several important factors
to be noted about the costs. First, the
cost of maintaining present conditions
over the next 15 to 20 years is signif-
icant. Without action things will get
worse. In the lower quality ranges
(objectives II-IV), the difference be-
tween a least cost and uniform treat-
ment model is quite significant. To
reach higher quality levels, it must be
remembered that there are many waste
sources over which there is no readily
available control. Thus, to account for
these, more of the treatable wastes must
be removed. Since the cost of treatment
versus the percentage of waste at a
source removed is highly convex, costs
go up quickly. As well, there are rela-
tively few waste sources under con-
trol and meeting higher goals requires
that almost all be removed, thus giving
little difference between allocation
models.
For this particular region, an insti-
tution exists for the region specifically
designed and empowered to deal with
water resource problems, the Delaware
River Basin Commission (DRBC).
Such figures as those in Table A.I pro-
Table A.1
Capital and Present Value of Operation and Maintenance Costs in Millior
Dollars to Obtain Stated Objectives under Three Types of Management Model'.
(Dollar value of some of the benefits for each objective are given.)
Objective
Set
I
II
HA
III
IV
V
Least Cost
Model
695
442
387
291
238
140
Zoned Uniform
Model
695
493
430
326
256
140
Uniform
Model
695
509
439
383
319
140
Evaluation of
Some Benefits
($Million)
492
430
430
303
282
162
120
-------
vide excellent supplementary informa-
tion for such a decision-making plan-
ning body to use along with its basic
political, social and economic knowl-
edge of the region. The plan finally
chosen by the DRBC was a compro-
mise between two originally specified.
Objective set III was strongly cham-
pioned by industrial and governmental
interests who had a large economic
stake in the outcome. Objective set II
or I was the choice of the various con-
servation and civic groups. A compro-
mise, objective set IIA, was selected and
the DRBC is now involved in the prob-
lems of implementing, financing and
overseeing the implementation process.
D. Summary of Water Quality
Models
From the above discussions, we see
that both the major categories of de-
scriptive and management models are
used in a wide range of decision making
problems. A proper evaluation of the
impact of such models in the total
water quality decision framework must,
of course, lead to a conservative con-
clusion. Much needs to be accomplished
to bring the researcher, with his con-
cerns about model structure and data
and grinding out a solution, closer to
the decision maker who is constrained
by a diversity of forces which range
from budget to technological to spe-
cific environmental considerations. In
most cases, institutional progress has
been made and river basin authorities
have been set up within a legal frame-
work that makes implementation pos-
sible. But even a regional authority
must still decide how it will assess costs
and make large-scale decisions. More
attention must be paid to modeling of
.he implementation process and the
rolitical market place in which the vari-
aus objectives and interest groups nego-
iate solutions. The existing manage-
ment models have addressed problems
vhich, while computationally difficult,
vere in fact easy to conceptualize. The
'act that there has been difficulty in
mplementing results stems naturally
rom two problems. In some cases re-
searchers have addressed themselves to
problems that interested them, not the
people who had to make the decision.
In other cases, the modeling process
was seen by the analyst as synonymous
with the decision process. This is just
not possible for there is no way to
capture the complexity of the decision
process in a model and the analyst must
be content to provide information which
helps illuminate for the decision maker
the tradeoffs available in the decision
process.
It is clear from the consideration of
descriptive models that only a small
beginning has been obtained in the
vitally important questions of trans-
lating physical system responses to bio-
logic and ecologic responses in the sur-
rounding habitat and to economic,
social and demographic responses in
the surrounding region. These are very
difficult modeling questions, not only
because such processes are suspected
to be highly dynamic and non-linear,
but because there is great difficulty in
conceptualizing their structure.
An important trend is the realization
that descriptive models and optimiza-
tion models are not competitive model
structures but processes to be used
jointly to attack problems. Each can
provide information and guidance in
the area where the other is weakest.
More attention will be placed in the
future on applying these techniques to
modeling in systems not yet fully under-
stood such as ecologic and economic
systems. Also important is the consid-
eration of waste management and re-
source use as an integrated system.
Further investigation must be given to
land use-water quality interactions and
to policies that prevent pollution from
reaching receiving waters such as zon-
ing, better construction practices, etc.
Pricing schemes in resource use and
pollution control deserve much more
attention than they have received for
they provide a rational structure for
coordinating a whole series of inter-
active yet seemingly diffuse systems.
Thus, considering pricing schemes
really becomes an attempt to expand
121
-------
the system's boundaries to get at some
of the exogenous effects which are driv-
ing the system.
II. WATER QUANTITY
A. Description of the Problem
1. Problem Identification
The general problem of water re-
sources is the allocation of a resource
that is distributed in space and time in
the proper quantity and quality to a set
of often conflicting alternate uses. In
the previous section, we dealt with that
aspect of the problem that relates to
water quality and the way pollution
control may be evaluated in the context
of having water available in sufficient
quality to allow desired water uses. In
this section we deal with the quantity
aspects of water. This involves the
evaluation and decision processes neces-
sary to distribute water differently than
it is distributed now. In some cases the
problem of water quantity is that there
is too much on a particular place as in
the cases of flooding, drainage and
water logging or agricultural lands. In
other cases, it is supplying more water
at a particular location for a particular
use than is available there. Both cases
may involve the building and operation
of large capital intensive structures for
storage, transportation and treatment
to change the physical phenomena that
do occur. To arrive at the correct dis-
tribution of water among its various
uses is a problem in public decision
making for much the same reasons that
water pollution is a public problem.
The normal private market system,
based on private ownership and price
for exchange as a measure of prefer-
ence, breaks down in the face of public
resources such as water, particularly
when the scale of investment necessary
to reap the benefits of water develop-
ment is so large. In the absence of a
market mechanism, the decision process
must make allocations among various
water uses based on some form of
analysis which reflects the multiple ob-
jectives for its use and the preferences
for different ordering of objectives by
122
different interest groups. Consider a
reservoir built to store water for several
different purposes: recreation, water
supply, flood control, power generation
and flow releases for downstream uses,
such as agriculture or low flow aug-
mentation. Inflow to the reservoir is a
stochastic variable with high trends in
the spring and low trends in the late
summer and early autumn. For flood
control purposes, the reservoir is best
operated by leaving it empty so that it
has capacity to dampen flood peaks
should floods occur. For uses such as
irrigation, it is desirable to fill the
reservoir in the spring so that the water
can be released when it is needed in the
summer. For uses such as recreation
which depend on a full reservoir, it is
best to store water and to keep it stored.
Thus, there is a conflict in that alloca-
tion or operation of the system for one
use means less is available for another
use. It is in the following areas in which
the model builder can provide valuable
information: (1) establishing what is
expected to occur in the system due to
natural processes, (2) how control
alternatives and allocation to different
uses impact on these processes, (3)
what benefits are gained by a particular
use, and (4) what are the pertinent
tradeoffs between objectives.
The basic framework for the con-
sideration of the multi-objective aspects
of water allocation is presented by two
major works from the Harvard Water
Resources Program in the early 1960's
(see Maass et al., (68), and Marglin
(73)). They helped to demonstrate the
need for the consideration of objectives
other than the traditional efficiency 01
national income measures which hac
been and, in some cases, continue to b«
the single objectives for project evalua
tion. Other objectives for consideratioi
which vary from project to project alsc
include regional income, environmenta
quality, national defense and other pos
sibilities. The problems in considerin
multiobjectives is two-fold. First, sui
able measures of effectiveness must b
chosen for each objective that reflec
the major concern for it. Such measure
-------
need not necessarily be in commensu-
rate units: national income may be in
dollars, while environmental quality
may be measured in miles of scenic
river preserved. Second, accounting
systems must be set up which show the
impact of a particular project configu-
ration on the relevant objectives. This
results in a net benefit transformation
surface such as shown in two dimen-
sions in Figure 1, in which all feasible
solutions are ranked according to their
impact on the defined objectives and
the envelope of the surface represents a
superior set of feasible alternatives in
the Pareto sense. That is that every
point on the surface is feasible and
exhibits the property that any move
along the surface implies gain for one
objective only at the expense of loss for
another objective. Choice of the proper
place to be on the surface is a function
of the social welfare function of society
as shown in the hypothetical surface and
indifference curve intersection at point
A in Figure 1. The difficulty comes not
Dnly in developing what the net benefit
.ransformation surface looks like but
n determining what the shape of the
iocial welfare function looks like. It
s well demonstrated by Arrow (3)
hat such a gross measure of society's
tesires can not be found by aggregating
ndividual or interest group preferences
ven if they could be assessed. Thus,
ic role of the analyst becomes that of
bowing what the transformation sur-
ices between different objectives look
ke and perhaps hypothesizing the
references of different interest groups.
ere the role of models for the water
NET BENEFITS TO OBJECTIVE ONE
FIGURE 1—Multi-objective Analysis
resource decision process is so prevalent
throughout all phases of the investiga-
tion as to make it difficult to distinguish
model building in water resources from
water resources analysis itself. Models
are addressed to understanding and
describing the underlying processes that
transform rainfall into surface runoff
and groundwater, to determining what
are the effects of building control and
transportation technology, to predicting
the impact of water development on the
surrounding social, economic and politi-
cal environment, to decide on when and
what to build and the best way of oper-
ating a system. The next part of this
section deals with the different types of
water use, how allocation of quantities
to one use can conflict with other uses,
and to what system objectives each use
contributes. Then the various aspects of
water resource analysis are discussed by
functional form of the specialists who
deal with individual problems. In sec-
tion B the role that models play in de-
veloping information both from the
descriptive and management sense are
presented. Then a case study for the Rio
Colorado, Argentina, developed by the
MIT Water Resources group is briefly
presented to show what types of models
were used at the various decision levels
of the problem.
2. Water Use
Wolman (108) in his article "The
Metabolism of Cities" describes the uses
to which water is put to in the U.S.
These uses are indicative of the quan-
tities involved in present consumption
and of preferences in future consump-
tion. What is striking is the way the
uses are presently distributed and the
question of how future demands will be
met. Of the 4200 billion gallons of
water per day of precipitation that falls
each day in the U.S., about 40% is
utilized where it falls for the growth of
vegetation, forests and crops, while
another 30% evaporates directly from
the soil or returns to the atmosphere
through evaporation from vegetation.
Of the remaining 1200 billion gallons
available for other uses, about 800
billion gallons are reasonably available
123
-------
in terms of transportation, institutional
and quality problems. Major uses in-
clude:
a. Irrigation of Farm Lands. This
represents about the largest usage of
water in the order of about 140 billion
gallons per day in 1960. Since irriga-
tion implies supplying water where it is
not normally available, this means that
water from somewhere else must be
diverted to the irrigation area and away
from other potential uses. Further, the
use of water for most irrigation uses
depletes it both in quantity through
losses and in quality through the chlo-
rides and nutrients picked up in the irri-
gation process. Traditionally, the use of
water for irrigation has been seen as
having both strong national income and
regional development components,
while the return water implies an en-
vironmental problem. To this end, large
public investments have been made to
transport these large volumes of water
often over great distances so that irri-
gation can take place. The price of such
water, either actual or implied, is far
below the price charged for other uses.
b. Industrial Use. Industries with-
draw water for many purposes ranging
from process water to cooling water
and waste dilution flows. This use in
1960 in the U.S. was on the order of
60 billion gallons per day and the re-
turn flows are often diminished in
quality and quantity. Objectives here
are both national and regional income,
as well as a negative impact on en-
vironment.
c. Cooling Water for Steam Electric
Utilities. Electric power production
using steam driven turbines requires
tremendous volumes of cooling water
which are normally returned without
consumption but with increased heat
content. This use in the U.S. in 1960
was about 98 billion gallons per day.
Projected future cooling water needs as
electrical energy demands increase are
enormous. Relevant objectives include
national and regional income as well as
the environment.
d. Municipal Use. Municipal use of
water normally averages about 150
124
gallons per person per day for washing,
consumption and waste. While this
seems like a great deal of water, the
total usage of about 23 billion gallons
per day is only about 8% of the total
water usage. Here water is used for
development, and aesthetics and return
water causes environmental problems.
Other important water uses do not
necessarily require the withdrawal of
water from its natural source, but may
require additional flows to allow use to
take place there. These include naviga-
tion, water based recreation, aesthetics,
power production, support of fish and
wildlife, commercial fisheries and waste
disposal.
In a more subtle and less obvious
fashion, water can also be seen as a
necessary prerequisite and principa
focus for development of other activi-
ties. Water resource investment by gov-
ernment is often used by governments
not only to increase income for the na-
tion but to redistribute it among the
citizenry. Often projects such as TV/
have a strong regional developmen
focus. Allocation of water to variou:
uses have strong implications of ou
priorities for development and thi
necessary ingredients such as power an<
agricultural goods for that process
There are an enormous number of gov
ernmental agencies in the water re
sources business with the main cor
struction authority going to the U.S
Army Corps of Engineers (Defense'
the U.S. Bureau of Reclamation (Ii
terior), and the Soil Conservation Ser
ice (Agriculture). Each exists main
for different objectives, yet each buil(
multipurpose developments. Given tl
future stress caused by more and mo
demand for a fixed resource, it is cle,
that water will be reused more ef
ciently and that projects will serious
interact. Thus, careful attention must
brought to the allocation process. T
decisions to be made are either at
governmental level or, if private, wi
the approval of the government. In m<
cases, governmental units such as t
Corps of Engineers design and bu
their own works. In local governme
-------
often both the design and construction
is subcontracted.
3. Functional Groupings for Problem
Solutions
As is demonstrated by the complex
technical, social, political and economic
interactions in water resource develop-
ment, many different talents are neces-
sary in the analysis of water quantity
problems. Several fields of subinterest
can be identified and, of course, there is
major overlap in many areas. These
categories are discussed next.
The field of hydrology and hydro-
ogic engineering is concerned with the
understanding and analysis of the rain-
'all runoff relationship. Interest centers
about the statistical properties of rain-
all and flood events in order to predict
jnd simulate their occurrence, the mod-
:ling of catchment response to predict
he runoff quantities and timing for
•ainstorms and the design of structures
ind land use controls for controlling
oods and providing water for other
ises. A major subfield is ground water
lydrology which deals with questions
if water movement and availability
inderground. Because of the highly
tochastic nature of rainfall amounts
nd timing, there is a strong statistical
asis to this work. Further, urbaniza-
ion of catchments leads to changes in
ae quantity and quality of runoff. The
ubfield of urban water management
eals with the particular effects of
rbanization and development on water
;sources. Normally, the hydrologists
ork both in government and in private
ractice to predict ahead of time the
sks involved in building in a particular
•ea, the impact of new construction
id the control alternatives available
ir ameliorating present or future
•oblems.
Hydraulics and Hydraulic Engineer-
g deals with the mechanics of water
>w. Problems of interest are the move-
ent of water in channels and other
nduits, the structures necessary to
eate power or provide storage and the
icration of systems for multiple use.
The job category of Water Resource
anner or Water Resource Engineer
requires knowledge of the other two
areas plus integrating knowledge on the
evaluation of projects. This requires an
understanding of economics and insti-
tutions, as well as of the mathematics of
systems analysis for planning system
configurations. Often this function is
carried out as a team effort with differ-
ent disciplines handling different parts
of the job within the framework of the
decision information to be generated.
There are two distinct levels of ap-
proach which divide along the fields of
the descriptive and management models
described in the next section. The first
field requires the ability to model cause
and effect relationships of particular
actions. This area is simulation oriented
and relies heavily on regression, dy-
namic modeling and the computer to
predict system responses. The second
field implies the selection among alter-
natives of the best configuration. Mod-
eling at this level is both simulation and
optimization.
B. Models in the Aid of Water
Quantity Decision Making
As mentioned previously, the models
to be discussed impact at different levels
in the decision process from the broad-
est scale allocation problems to the
microscale of every day operation of a
system. A distinction will be made
between descriptive models which
attempt to show the cause and effect
relationship between a particular policy
and the important parameters of the
system, and management models which
attempt to choose among policies.
1. Descriptive Models
An important question in hydrology
is the simulation of rainfall-runoff
events, and modeling is used extensively
in this process. One important area is
computer modeling through simulation
of the actual physical phenomena in-
volved in the process. Crawford (21)
describes the Stanford Watershed
Model, and Harley (44) describes the
MIT Catchment Model. Each of these
represent large scale computer based
attempts at organizing the important
data for a catchment such as degree of
125
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imperviousness, amount of vegetation,
population and geographic conditions,
and predicting the timing and volume of
runoff at any point in the system for a
given storm. Such models are used
routinely in practice for several pur-
poses. First they can be used to simu-
late proposed control schemes and to
evaluate the level of flood security at a
site. They can also be used to predict
downstream effects due to changes in
the catchment. One of the most crucial
issues in development is the interaction
between changes in land use and water
resource characteristics. As the use of
land changes from a natural state to
one of more intensive structural and
economic activity, runoff and flooding
problems are accelerated and water
quality conditions are affected. What
makes the problem even more im-
portant is that land use planning rarely
takes this into account. The remedial
measures for control, once the land
development has taken place are costly
and difficult because of the dispersed
nature of the problem. The quality issue
is very important in urban catchments
where much of the street litter and air
pollution fallout are caught in storm
water drainage. The work of Lager
et al. (60) and of Chen (18) are di-
rected towards these models. All the
models are fairly heavily data depend-
ent but computationally able to repre-
sent reasonable sized catchment areas.
They are all simulation models in the
sense that a model of the physical sys-
tem is operated mathematically over
time in response to a given input event.
Another important issue in hydrology
is an attempt to gain statistical infor-
mation about the time spacing of storm
events and of the magnitude of river
flow quantities. The ability to statisti-
cally generate long time series of data
which have similar characteristics to
short available data records has been
one of the most important aspects of
the field. Fiering (31) summarizes the
theoretic basis for this synthetic gen-
eration of data which has become an
accepted part of the design and plan-
ning process. Other work in this area
126
include important papers by Mandel-
brot (71), (72), Tschannerl (105)
and the development of a great many
computer routines by the Hydrologic
Engineering Center (HEC) of the U.S.
Army Corps of Engineers (51). The
HEC is instrumental not only in com-
puter model development in hydro-
logic engineering problems, but also
serves as a major teaching and research
center for other government agencies
involved in this field. Examples of their
work include papers by Beard (5), (6),
and large scale computer packages for
a variety of hydrologic functions (19),
(20). Other areas which depend on the
knowledge of the statistical character of
rainfall and streamflow events are the
design of reservoirs for the collection
of water for use at a later time and to
prevent floods by dampening flood
peaks. The flood problem of course has
received considerable interest. Day (22)
has developed a model for the consid-
eration of investment in non-structura
flood control, while Bhavnagri (7) has
developed a stochastic model for flooc
proofing in a flood plain. Askew (4)
has considered the problem of the sta-
tistical aspects of critical droughts anc
many of the HEC programs, particu
larly Beard ( 5 ), deal with the statistica
definition of safe (guaranteed) yiek
from a reservoir.
Groundwater presents an importan
modeling area with much attention be
ing placed on attempting to analytically
or through simulation describe the spa
tial and temporal aspects of its move
ment and availability. Breitenbach (1C
describes many of the digital computin
aspects of such modeling. Freeze (32
has developed very complex models c
the physical processes in groundwate
which are very precise, but have eno
mous data and computational time n
quirements. Kleinecke (56) describi
the use of linear programming for tt
establishment of parameters for grouni
water systems. Thus, while we mo
often think of optimization as a to
for choosing among alternatives in i
economic environment, in dealing wi
physical systems, it may also be used
-------
identify important parameters of the
system. Finder (81) and Taylor (99)
are further examples of the role of
computer models and analysis in the
description of groundwater movement.
A most important aspect in the de-
velopment of water resource planning
is not only the estimates of cause and
effect relationships in the physical sys-
tem but in the surrounding social and
economic systems as well. It has long
been realized that new water resource
development can bring about important
changes in demographic variables, in-
come redistribution and other factors.
Because these aspects are much more
difficult to model they are only just
beginning to receive attention. On a
regional basis, Hamilton et al. (42) use
systems dynamics models to show the
demographic and economic aspects of
developments in the Susquehanna River
Basin, Lofting (64, 65) uses input-
output models of the economy to show
the value of water development in an
economic context. Such input-output
analysis was also used by Schaake (91)
in the estimates of regional demand for
ivater in the future. More detailed
studies of residential demand using sta-
istical modeling are reported by Howe
ind Lineweaver (49) and Hanke (43).
^adros (97) uses both statistics and
)ptimization to estimate recreational
emand for water resources projects.
iaissman (40) also uses optimization
o determine manpower needs for irri-
,ation developments in Mexico.
2. Management Models
The consideration of management
icdels which investigate and choose
mong a series of alternatives requires
le resolution of tradeoffs between
lodel reality and computational ability.
he trend in the past few years in this
;ld has been from very complex opti-
ization models, which could not be
lived for large scale cases, to relatively
mpler optimization models, called
reening models, which could suggest
lutions for large scale problems for
rther investigation. The philosophy to
evolved here is one of the conjunc-
re use of optimization and simulation
techniques in management models,
each technique having complementary
strengths and weaknesses.
The basic problem in water resource
planning is to decide on the optimal
timing and investment in capital struc-
tures and operation of a given system to
meet stated objectives. The attendant
problems in solving or even formulating
such a general management problem
are many fold and include the stochastic
nature of the system both in hydrologic
and economic terms, the difficulty in
identifying and dealing with multiple
objectives, and size and dimensionality.
We are thus led to a subdivision of
different models, each directed towards
an aspect of the general problems.
These models are used in the spirit of
supplying information and understand-
ing of the decision-makers problems,
not in optimally solving them.
We first consider the problem of
choosing between multi-objective proj-
ects. Here there are conflicting desires
by different interest groups for the out-
puts of the system, and difficulty in de-
veloping and comparing benefits to the
different objectives. Models directed
towards the problem include the fol-
lowing. Major (69) in a paper on the
North Atlantic Region Water Resources
Study of the U.S. Corps of Engineers
tells of the role systems analysis has
played in large scale plan formulation
for water supply. More theoretical
methods are suggested by Marglin (73)
and Major (70). Cohon and Marks
(16) present computational methods for
generating transformation surfaces be-
tween multiple objectives using linear
and integer programming and identify
both objective function and constraint
methods for representing the transfor-
mation surface. Haith (41) describes
models for assessing preferences for dif-
ferent objectives by different groups.
Rogers (89) uses game theory and
mathematical programming to show the
payoff matrix for project development
between two nations on an international
river when there is the possibility of
cooperation in planning.
Management models have a sig-
127
-------
nificant role in the actual operation of
individual components of the system.
In particular, reservoirs are often run
for different objectives such as power
generation, flood protection, water
supply, and recreation which require
different modes of operation. The im-
portant question here is how much
water should be stored and released in
the system when the inputs to the sys-
tem for the time period are stochastic.
Roefs (87) summarizes many of the
attempts at mathematically modeling
such problems. ReVelle (85, 86) in a
series of papers on reservoir operation
uses chance constrained linear pro-
gramming and a linear decision rule to
design operating policy for a reservoir.
Joeres et al. (54) consider the opera-
tion of an interconnected system using
both linear programming and a sto-
chastic simulation. Loucks (66) deals
with the concept of using Markov
models to determine optimal reservoir
operating rules, and Young presents a
dynamic programming model (109).
Bodin (8) and Butsch (15) have also
done work in this area. Several authors
have addressed the issue of using
mathematical programming in the de-
sign of multi-component systems.
Jacoby and Loucks (52) deal with
optimization/simulation interactions on
a large scale case study for the Dela-
ware system. Hendari (46) and Butcher
(13) also present programming models
for this type of investigation. The prob-
lem of optimally determining where
given water supply demands will be
served from is dealt with by deLucia
(23) using a linear programming model
for the North Atlantic region. Demand
estimates are derived from the earlier
described works by Schaake (91), and
the optimization problem was to match
up supply and demand while minimiz-
ing cost to the region. Another im-
portant issue in management models is
the issue of the time that investment
should be made. Such considerations
are brought about both by budget con-
straints which limit the resources c.vail-
able for construction in any one time
period and by the existence of benefits
128
for projects that change over time as a
result of exogenous market changes.
Because of the extra dimensionality
added by the inclusion of time, such
considerations are usually addressed in
separate models. The easiest considera-
tion is the capacity expansion model
which assumes that there is no inter-
action between projects and that de-
mands for services are increasing. The
numerous literature in this area, mostly
based on dynamic programming is
represented by Morin and Esogbue
(76), Scarato (90), and Butcher, (14).
In cases where there is more interde-
pendence, dynamic programming proves
more difficult and other types of pro-
gramming models are necessary. Young
(110) and Facet and Marks (28) both
use linear and integer programming
algorithms.
In the Facet model, both a schedul-
ing and sequencing model is presented
for highly interactive systems. A sched-
uling model allows the choice both of
project size and construction time as
decision variables. Such models are
severely limited by number of time
periods and decision variables if satis-
factory computational results are de
sired. A sequencing model assumes tha
a size has been chosen for each project
usually by a screening model plus simu
lation, and then uses integer program
ming to decide on an optimal sequeno
for the projects. While more restrictiv-
in formulation, computation is muc
easier and much less costly, thu
allowing more sensitivity analysis.
The design of the hydraulic systerr
for transporting water and for procesi
ing it for different uses have also bee
the subject of management model
Buras (11) is an example of the use (
optimization in the design of aquedu
size and pumping cost using dynam
programming in a tree type networ
Because there is no redundancy in t
system, the flow in any link is unique
known and even though costs are no
linear, the resulting optimization pro
lem is quite tractable. Local distrib
tion systems purposely have a gr«
deal of redundancy built into them
-------
allow for other system objectives such
as reliability. In this case the problem
becomes highly interactive because the
flow distribution in the system, instead
of being fixed, is a function of the
decision variables. This more difficult
problem has been the subject of a con-
siderable amount of study and work
such as de Neufville et al. (25), Kalley
(55), and Kohlhaus (59) are indicative
of management tools available for aid
in distribution system design. Huang
(50) reports on the use of optimization
in water treatment design.
Agricultural management of water
has received attention usually in the
context of the use of groundwater and
in the conjunctive use of ground and
surface water for the purpose of the
supply of the large volumes of water
necessary for agricultural uses. Rogers
and Smith (88) and deLucia (23) de-
scribe stochastic management models
"or the aid of agricultural decision mak-
ing. Aron and Scott (2) is an example
rf a large volume of literature dedi-
;ated to arriving at the optimal mix of
ground water and surface water use.
3urt (12) has dealt extensively with the
)ptimal development of groundwater to
neet expending needs for agricultural
ise.
Examples of other management mod-
Is developed include the work repre-
ented by Matalas (74) in the optimal
jcation of gauging stations for the
cquisition of data for the design of
'ater resources systems. Grayman and
.agleson (38) report on similar work
i the design of radar systems for
ithering information for the forecast-
g of storms.
3. Case Study—Rio Colorado, Ar-
•ntina.
This case study shows a typical water
source problem and the role that
odels can play in aiding decision-
iking for resource allocation for the
oblem. More detailed information
n be found in Grayman et al. (37).
ie Rio Colorado, shown in Figure 2,
es in the Andes Mountains as a re-
t of snow melt runoff and flows 550
les in an easterly direction to the
Atlantic without appreciable inflows
from precipitation. The average flow is
5000 cfs and it flows through a very
sparcely settled land (44,000 people
in 26,700 square miles). The main
purposes for management and develop-
ment of the river are irrigation and
power production, with flood control
and water supply also being relevant.
For these purposes, several major pur-
pose projects have been proposed by
Federal and Provincial groups includ-
ing diversions to the Rio Colorado from
the nearby Rio Negro and from the
Colorado to other basins. These are
shown schematically in Figure 3. The
models used to develop plans included
a deterministic linear programming
screening model, simulation models for
showing the response of the physical
system and of the demographic sector
to water resource investment in the
area and an integer programming se-
quencing model. The screening model
was of the form:
Maximize Net Benefits to Each Ob-
jective
Subject to Constraints on
Physical continuity
Technical possibilities
Policy Constraints
The means for handling the multi-
objective nature of the objective func-
tion included a weighting method which
involved choosing different weights for
the different objectives and a constraint
method where minimum requirements
were set for one objective while maxi-
mizing the other. The objective function
itself was assumed to be piecewise
linear, with a few integer variables re-
lated to whether certain large storage
projects should be built. The typical
size of such a model when developed
for three seasons and one yearly time
period (i.e., a deterministic assumption),
was on the order of 700 constraints and
700 variables.
An example of the type of informa-
tion that can be developed on multi-
objective decisions from such a model
is shown in Figure 4, which shows a
transformation surface between national
129
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FIGURE 2—Location oj the Rio Colorado, Aigentma
income and some measure of regional
equity. National income is measured as
net efficiency benefits in monetary units.
The choice of a metric for regional
equity poses more definitional problems.
Here a measure of the total deviation
from some equitable distribution is
chosen, with the efficient solution in
terms of national income having high
deviations in water allocation. As a
more equitable distribution is sought,
i.e. as there is a smaller deviation from
the equitable distribution, national in-
come decreases. The point H represents
a break point between export and non-
export from the basin, i.e. to gain equity
in water distribution, water must be
diverted from profitable national use,
which requires export from the region,
to uses within the region. The use of
such simple models make it possible to
do a great deal of sensitivity analysis
and suggest that a problem can be suc-
cessfully decomposed and that more
than one model can be useful in devel-
oping information.
130
Screening models such as these de
velop sets of configurations that appea
suitable for further investigation, pai
ticularly to capture the stochastic nt
ture of the system which was misse
by the deterministic screening mode
In this case two different simulatio
models were specified for this purpos<
One goal was to devise a simulatic
model that could, with very little inpi
data, provide insight into system b
havior. In areas such as the one und*
consideration, where little developme
has taken place, the availability of da
is often minimal. Thus, a detailed sim
lation model was built to explain phy
cal processes that were much too t
tailed for general purpose system sim
lation. Instead, such detailed simulatii
models are used to generate input de
and parameters for less deailed and th
more operable simulation models. T
model uses stochastic data generation
sequentially producing annual values
unregulated stream flow using a mu
variate Markov model. These anni
-------
nd:
S.lc 2 Z
Site 3
Region 2
Site 7
.... _ Import
Site 8 —- »
Site 9
Site 12
Region 4
^v
Reservoir
Power Plonf
Region 1
Site 5
Site 6
Site 7
Region 3
Site 9
Site 10
Site II
Sue 12
Site 13
Irrigotion
FIGURE 3—The River Basin and Development Alternatives
131
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••*
i.e
IJ_I _Zrr,oxl2.l0005
Nel Benefit Tronsformotion Curve
(Non-Inferior Set)
^ 436 400 3OO 200 100
Wall-Deviation in Water Allocation (m'/sec)
FIGURE 4—The Generated Net Benefit Transformation Curve
values are then disaggregated to pro-
duce seasonal, monthly or daily values
as required, while maintaining the in-
ternal means and covariances within
each year and between sites. The non-
physical system was also of concern
since the demographic effects of this
sort of water resource development is
vitally important in determining whether
to build it. The benefits of the projects
will only be reaped if people come to
this isolated region and work in agri-
culture and related industries. To this
132
extent a dynamic policy model based
systems dynamics was developed whi
showed the feedback relationships a
time delays involved in migration a
regional attractiveness.
The interactive use of these modt
plus additional data and benefit e
mates for input to the analysis proa
has brought about a series of alter:
live plans now under review by
government of Argentina. By outlin
alternatives and their impacts on i
ferent system objectives, the model
-------
proach has helped to start a construc-
tive planning dialogue between various
regional interest groups in Argentina
and, hopefully, the choice of a good
consensus plan acceptable to interest
groups—a necessity for successful im-
plementation.
4. Summary
In the previous sections, we have de-
scribed the modeling efforts in water
quantity. As with water quality, the
main emphasis in modeling has been
on the development of cause and effect
relationships for physical systems and
'or optimal management. The areas
where much more interest in modeling
is necessary is in understanding the role
af water and changes in its availability
.in the social and political system of a
river basin. First attempts at modeling
such phenomena have been mentioned,
but this type of work obviously needs
to be better understood. Another area
where more work is needed is in dealing
with the multi-objective nature of the
decision-making process. Better means
for assessing utility functions for inter-
est groups, for displaying alternatives
and for recognizing points at which
some agreement can be reached is im-
portant from the viewpoint of imple-
mentation. In terms of management
modeling, the most important future
developments will be in better modeling
the alternatives available for the control
of water resource impacts caused by
changes in land use and development
policies.
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137
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Chapter 5
Models in Solid Waste Management
By
Jon C. Liebman
SUMMARY 141
I. INTRODUCTION 141
Models of Policy Decisions 143
Models of Management Decisions . 143
II. USE OF MODELS IN SOLID WASTE MANAGEMENT 144
Models Relating to Waste Materials 144
Models Relating to Fixed Facilities 146
Models Relating to Vehicles . 149
Models Relating to Manpower 152
Models Relating to Entire Systems 153
Miscellaneous Models 154
I. EXAMPLES OF MODELS IN SOLID WASTE MANAGEMENT . 155
A Transfer Facility and Site Selection Model 155
A Collection System Simulation Model 157
The Jacksonville Study 160
l. USE OF OPTIMIZING AND SIMULATION MODELS 161
REFERENCES 162
139
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Models in Solid Waste Management
SUMMARY
The management of the urban solid
*'aste system is among the most com-
plex municipal or regional governmen-
al tasks, principally because of the wide
iiversity of the components of solid
vastes and the variety of systems in
:xistence. Modeling is therefore fre-
uently done on an ad hoc basis, and
he number of general models which
an be used in different situations is
elatively small.
In this chapter, we first discuss the
eneral nature of solid waste manage-
lent. Decisions are categorized as long-
ange policy decisions and management
ecisions; the focus of the chapter is
n the latter, primarily due to the pau-
ity of successful models dealing with
irge scale resource policy in the solid
aste area. We identify the two-stage
iture of management decisions, in-
jlving the specification of desired
rvice and the determination of solu-
MS which provide the service sped-
:d.
Models which deal with the compo-
mts of the solid waste system are
plored in detail. These include pre-
;tive models for waste generation.
itimization models for planning the
itallation of fixed facilities, models
aling with routing and scheduling of
; collection vehicles, and models
tich consider the scheduling of man-
wer. A subsequent section considers
uilative models of multiple compo-
tits or entire systems.
The final section of this chapter dis-
sses the detailed use of two solid
ste management models: an optimi-
ion model of transfer station site
jction, and a simulation model of an
entire solid waste collection system.
These two models have been applied
jointly in the city of Baltimore, and one
of them has also been used in a study
in Jacksonville, Fla. We describe their
use in these studies, and the kind of
information which they were able to
provide for decision-making.
I. INTRODUCTION
Solid waste management problems
are among the most diffuse of govern-
mental problems. Until quite recently,
no need has been perceived nor effort
made to view the solid waste system as
a single entity. The problems which are
now recognized cross political bound-
aries at all levels and, in many cases,
reach outside the traditional spheres of
governmental activity at any level.
There are a number of properties of
solid wastes which compound the diffi-
culties of decision-making and model-
ing. The first is that the term solid
waste encompasses an almost incredible
variety of materials. Ordinary house-
hold wastes, which in themselves con-
tain many different components, make
up only a small part of the problem
Bulky domestic wastes, such as refrig-
erators, bedsprings, etc., require a
different mode of handling. Still within
the area of municipal concern are such
diverse items as dead animals, demoli-
tion rubble, used Christmas trees, and
abandoned automobiles. Industrial waste
materials in various forms, some rela-
tively innocuous, others hazardous,
present yet a different set of difficulties.
In essence, solid waste is made up of all
materials which are unwanted and
which cannot be readily disposed of
into the gaseous or liquid waste systems.
141
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SOLID WASTE MANAGEMENT
Models Discussed in Chapter
Model/Decision Area
Waste:
Generation Prediction
Generation Prediction
Fixed Facilities:
Site Selection
Capacity Expansion
Facility Operation
Vehicles:
Vehicle Replacement
Single Vehicle Routing
Single Vehicle Routing
Multiple Vehicle Routing
Multiple Vehicle Routing
Manpower:
Crew Assignment
Route Scheduling
Overall System:
System Operation
Summary Table
General Type
Forecasting
Input-output
Integer programming
Optimizing: integer or
dynamic programming,
heuristic
Queueing
Integer linear program-
ming
Travelling salesman,
truck dispatching
Chinese postman
Heuristic
Simulation (random walk)
Non-linear programming
heuristic
Linear programming
Simulation
Important Characteristics
Uses historical data to forecast
amount of waste generated
Permits examination of im-
pact of changes in one sector
on waste stream in other
rectors
Selects sites for facilities frorr
among specified alternatives
considers costs of transporta
tion, construction, and opera
tion
Usually neglects changes ii
land value, interest rates
Analysis number of loadin;
docks, size of storage facilities
Selects vehicles to be replace!
Requires specific collectio
points
Treats collection as contini
ous along streets
Simultaneously districts
large area into truckloads an
routes individual vehicles
Determines routes randoml
user selects best route foun
Sequences vacation, time o
and overtime
Minimizes overtime and pen;
ties for late or early servic
Permits exploration of effec
of policy and equipme
change
Most solid waste problems have been
dealt with in local areas near the source
of the wastes. This is, in part, true be-
cause of the very nature of solids—they
don't go anywhere. Liquid and gaseous
wastes move by the force of gravity,
winds, diffusion; they have an effect on
people at some distance from their
source and, as a result, bring about
142
more centralized, regional activity aimi
at the mitigation or elimination of t
damage they cause. Solids simply
where they are discarded. Historical
concerted action has been taken wh
solid wastes have been viewed as cai
ing community or regional problen
thus, garbage collection was undertak
as a governmental activity out of cc
-------
cern for public health and aesthetic de-
terioration of neighborhoods, while the
unseen accumulation of waste material
from an industry has often been left as
a problem to be handled by the indi-
vidual firm. Society has regularly taken
the position that unwanted materials
should be removed only as far as nec-
essary to get them out of the way. This
accounts for the burgeoning of auto-
mobile graveyards, which was permitted
until they were perceived as a blight
upon the landscape, interfering with the
public welfare.
This local nature of the problem has
naturally led to a wide variety of local
solutions. Each individual producer of
waste, each firm, each municipality has
developed its own method of handling
its own particular problems. There has
been little motivation, either economic
or political, to work together for com-
mon solutions. As a result, there are
.vide differences in the methods of deal-
ng with solid wastes, even between
;imilar municipalities. There are two
mportant effects of these local differ-
:nces. First, large existing capital in-
•estments in fixed facilities in each
Dcality make the development of re-
gnal solutions, which would be advan-
ageous if starting from scratch, fre-
uently uneconomical. Second, models
nd techniques which are useful in
nproving the situation in one locality
lay be quite useless in another place
scause of the differences within the
cisting systems.
A related difficulty which hampers
odeling efforts is the sparseness of
;able data. It has become quite clear
recent years that large amounts of
ita are available. But each unit in-
>lved in some aspect of solid waste
ndling gathers its data somewhat
ferently. Bookkeeping techniques are
ferent. Collection vehicles, even
jugh they may be individually
ighed, collect different components of
id waste in different cities, so that it
difficult to develop a true picture of
makeup of waste streams. Labor
ictices, particularly methods of pay-
nt, vary so greatly as to make it
virtually impossible to generalize on
labor costs from one place to another.
It should be clear from the above
paragraphs that there is no unified view
of the solid waste system. There is no
single plan of attack; there are no
prescriptions for a planning and de-
cision-making process. Thus, to discuss
decision-making in solid waste manage-
ment automatically means a fractionated
approach which looks at various aspects
of the overall problem, always seeking,
of course, to integrate into larger and
larger assemblages.
Models of Policy Decisions. It is con-
venient at the outset to recognize two
distinct kinds of decisions. One, which
will be discussed only briefly in this
chapter, might be termed the long-range,
large-scale policy decision. Included in
this class are decisions relating to na-
tional resource management policy: e.g.,
the extent to which recycling and recla-
mation should play a part in solutions
of solid waste problems, and the meth-
ods to be used to encourage and imple-
ment such policies. Modeling efforts in
this area have rarely been attempted.
The most promising approach is in the
use of modified input-output models.
The usual economic input-output
model provides information concerning
the impact of a change in the output of
one sector of the economy on all other
sectors. Such a table may be modified
to include waste flows as well as money
flows. In this form, it provides an esti-
mate of the impact of changes in waste
policy on the economy. The results,
however, must be used with care, since
an implicit assumption of the table is
that industries continue to use raw
materials in the same proportions (i.e.,
constant technology).
Models of Management Decisions.
The decisions with which the remainder
of this chapter deals might best be
termed "management" decisions. They
are more commonly encountered on
local, regional, and occasionally state
levels and they are most frequently con-
cerned with the planning and operation
of facilities and equipment within an
existing institutional and policy frame-
143
-------
work. This implies that, for the most
part, we take as given the generation of
solid waste in its current or projected
varieties and quantities, and consider
only the system used for collecting,
transporting, storing, treating, and dis-
posing of this waste. Separation for
recycling, and other methods of reclaim-
ing useful materials, may be included
within this system and considered on
an operational, rather than policy, level.
Within this context, it is helpful to
view the decision-making process as a
two-stage one, though in fact the two
stages usually are carried out jointly.
One stage is to specify the kind of
service desired, while the other involves
determining methods for obtaining that
service at least cost. Clearly the cost
influences the decisions regarding serv-
ice quality. In fact, if quantitative
measures of benefit could be associated
with the parameters of service quality,
the separation of decisions would not be
necessary and it would be possible to
optimize the entire system for maximum
net benefits. Unfortunately, this is not
the case and the decision maker usually
finds himself in the position of explor-
ing the costs of obtaining various levels
of service, and finally selecting the
desired level subjectively.
Service quality decisions, whose
values cannot readily be quantified, in-
clude frequency of pick-up, location of
pick-up (whether backyard or curbside),
kinds of waste which will be picked up,
and whether or not separation by the
user will be required. These, and similar
qualitative questions, are not normally
explored by optimization models but
various descriptive and predictive mod-
els can be used to estimate the costs
involved with changing service quality.
Cost minimization questions include
number and type of facilities (landfills,
incinerators, transfer stations), and their
location. Size and type of collection
vehicles, and routing of these vehicles,
as well as number of men in the crew,
also must be decided. This list can be
extended, of course, to most of the
detailed decisions involved in the com-
144
plete design of any collection and dis-
posal system.
A solid waste system consists of four
components: (1) the waste itself, (2) the
fixed facilities used for transfer, treat-
ment and disposal, (3) the vehicles used
for transporting the waste, and (4) the
men who operate the system. In the fol-
lowing sections, models of each of these
components are discussed. Most of these
models are optimizing models with an
objective of minimum cost. The prin-
cipal exception is in models of waste
generation, which are merely predictive.
In a sense, optimizing models of waste
production depend on the developmen
of control variables not yet in existence
and are related to the policy decisior
models discussed in the preceding sec
tion.
Following the subsections on model:
of system components is a discussioi
of models of entire systems. Here thi
emphasis shifts from optimization t<
description and prediction, simply be
cause entire solid waste systems ar
generally too complex for optimizatioi
techniques.
II. USE OF MODELS IN SOLID
WASTE MANAGEMENT
Models Relating to Waste Material
Of particular importance to any analys
of a solid waste system is the ability
predict amounts of waste which will I
generated. Depending upon the partic
lar problem being analyzed, waste ge
eration models may be very high
aggregated, predicting amounts for lar
areas (as, for example, in a study
future disposal facility needs), or th
may be very detailed, providing infc
mation on a block-by-block basis (
would be needed in a detailed vehi<
routing study). Similarly, the tirr
horizon over which prediction is neec
also depends upon the purpose of
study. Waste generation models 5
rarely needed independent of soi
other model which uses waste gene
tion as an input.
The simplest solid waste general
model is of the form (Rao, et al. [43
-------
where S^ is the amount of waste gen-
erated in the ith time period in the jth
section of the planning region, ajjk is
the number of waste generating entities
of type k in the ith time period in the
jth section of the planning region, and
Rk is the unit generation of waste by the
kth type of entity. Generating entities
may be defined quite crudely (i.e. resi-
dential, commercial, and industrial), or
they may be much more finely divided.
This model assumes that the waste
generation rate of any type of generat-
ing entity remains constant over time,
the generation multipliers Rk being
determined by observation of an exist-
ing system. A somewhat more complex
model permits assumptions about chang-
ing rates of generation, and takes the
general form :
where Rik is the unit generation rate of
the kth entity type in the ith time period.
Obviously, obtaining data for such a
model is much more difficult.
The shortcomings of models such as
the above are obvious. They assume
that historical data contain all the rele-
vant information, and as a result, per-
mit little analysis of proposed changes
in waste generation systems.
Some efforts have been made to
model waste generation, including more
detailed information about types of
wastes generated, by the 'use of regional
input-output models. The data require-
ments for such models are enormous
and data collection constitutes a major
project in itself. The advantage of input-
output models is that they permit ex-
amination of the impact of a change in
operation of one economic sector of
he model on solid waste generation
hroughout the entire system. As sug-
gested earlier, their shortcoming is that
hey do not consider technology changes
nside an industry as the result of
;hanges in other portions of the system.
-or example, the introduction of a ma-
or paper recycling industry which pur-
chases waste paper might cause other
industries (or households) to shift in the
direction of more waste paper produc-
tion; the input-output model assumes a
constant rate of waste paper production
per unit of output of the industry.
Two other important shortcomings of
all waste generation models should be
mentioned. The first is that there is some
degree of dependence in every such
model on projections of population
over the time horizon; recent history
demonstrates clearly that the art of
population projection, despite significant
advances, has a long way to go. When
one adds to this the large effects of
technology change on amounts and
types of solid waste, one must conclude
that any projection for other than short
time periods must make large allow-
ances for error.
A second, somewhat unsettling factor
is that we do not completely understand
solid waste generation, even in the pre-
sumably simple household waste system.
This is nowhere more clearly demon-
strated than in the statistical study by
Quon, Tanaka, and Charnes [41]. In
this project, household generation rates
were studied before and after a shift
from once-per-week to twice-per-week
collection. Control areas, in which a
shift was not made, were also used.
The study demonstrated that there was
a very significant increase in the rate of
generation after the change and that this
increased rate persisted, even a year
later. The implication for a system
manager considering the costs of a
change in collection frequency is some-
what frightening. One is also tempted
to wonder what other apparently re-
motely related factors have large effects
on generation rates.
This is not intended to imply that
predictions of waste generation rates
are quite as unreliable as predictions of
heights of women's hemlines; but neither
are they as cut-and-dried as predictions
of the time of tomorrow's sunrise.
Waste generation projections are re-
quired for many management decisions
and modeling is as rational an approach
as we currently have available. There is
145
-------
a clear need for substantial additional
study in this area.
Papers in the bibliography which deal
with waste generation models are
Golueke [18], Golueke and McGauhey
[19 and 20], Morse and Roth [37], and
Quon, Tanaka, and Charnes [41].
Models Relating to Fixed Facilities.
There is a number of problems related
to fixed facilities which are amenable
to investigation by means of models.
Two of these which frequently are
solved by very similar models are the
selection of types of facilities to use for
treatment (facility selection problems),
and the selection of locations at which
to install these facilities (site selection
problems). The ability to consider these
two problems with similar models, and
even simultaneously within the same
model, stems from the fact that two
different types (or sizes) of facility
which might be installed at the same
site can simply be considered as two
different sites, with different associated
costs, and thus treated within a general
site selection model. In addition to
facility and site selection, models may
also be used to explore problems of
capacity expansion over time and to
investigate possible operating rules for
the existing facilities.
Models of site selection problems
have a long history, dating back to work
by Alfred Weber [59]. The fundamental
premise of all such models is that
facility location depends on finding the
optimal balance between costs of build-
ing and operating facilities and the costs
of transporting material to and/or from
these facilities. Some of the early work
in site selection assumes that only one
(or, in some cases, a fixed number
greater than one) facility is to be built
and that the cost of constructing and
operating the facility is the same wher-
ever it is placed. In this case the site
selection problem is simply to deter-
mine the location(s) at which to build,
such that transport costs are minimum.
A particularly simple solution for
the site selection problem is available
in the (rather unrealistic) case of linear
costs of facility capacity and linear
146
transportation costs. That is, the model
assumes that it costs Dj dollars for each
ton of waste which passes through an
incinerator at site j, and Tt1 dollars for
each ton of waste to be shipped from
source (collection area) i to site j. Given
a set of potential sites for facilities, and
a set of sources (collection areas) of
known amounts of waste, the model is:
Minimize:
Subject to:
for each source i
where X^ is the amount of waste
shipped from collection area i to site j,
and aj is the amount of waste generated
at collection area i. The objective func-
tion is simply the total cost, including
both transportation and facility costs,
and the constraints require that the total
amount of waste generated in each
collection area be collected. This prob-
lem is a simple linear program. One
may also add upper limits on the
capacity of the facility to be constructed
at site j, in the form
S Xij < bj for each site j
i
The problem may be solved by use of
the standard Hitchcock transportation
method, which is even more efficient
than linear programming. The solution
provides the amount of waste shipped
to each potential site (and, thus, the
capacity required for each facility), and
allocates the waste from each source to
the appropriate facilities. Facilities
which receive no waste are, of course,
not built. A similar approach may also
be used to include intermediate facilities
such as transfer stations where waste is
transferred from small collection ve-
hicles to larger long-haul vehicles foi
transport to a distant treatment 01
disposal facility; the resulting model is
in the form of a transshipment problerr
which may also be solved by a well
known technique.
The principal difficulty with thess
-------
models is that they neglect the initial
cost of establishing a facility. Because
of this usually rather large cost, the
unit costs for a facility decrease with its
size, and it becomes more attractive to
construct fewer, larger facilities. Thus,
models of the above type normally
overestimate the optimal number of
facilities.
There is in existence a number of site
and/ or facility selection models which
overcome this difficulty. By including a
0-1 variable which indicates whether
a facility is constructed or not, they are
able to consider the fixed costs directly.
However, they become mixed integer
programming problems and are there-
fore much more difficult to solve.
The general mathematical form of
such models is :
Minimize:
S S (T,,
i i
Subject to:
V X =
D^Xj,. + 2 FjYj
1
for each source i
Yi - £ xij ^ ° for each site j
where Yt is equal to 1 if a facility is
built at site j and zero otherwise, Fi is
the fixed cost of constructing such a
facility, and the other variables are as
previously defined. The objective func-
tion now includes the fixed cost of a
facility which is paid only if Y, — 1
(that is, the facility is constructed). The
second constraint requires that if a
facility is built, the amount flowing into
it may not exceed its capacity, while if
it is not built there may be no flow
into it.
A very similar model may be used to
select among various kinds of facilities
or various capacities of the same kind
3f facility at the same site. For example,
suppose that a 500 ton capacity in-
;inerator, an 800 ton capacity incinera-
or, or a 1500 ton capacity incinerator
nay be built at a particular site. The
hree facilities are treated as though
hey were at three different sites, and
he model used is identical to that
shown above. However, in order to
prevent a solution which constructs
more than one of the facilities, a con-
straint must be added. If the three
different facilities are represented by
j = 2, 6, and 9, the new constraint is
Y2 + Y6 + Y0 < 1
which prohibits building more than one
of them. Similar constraints can be used
to prevent any particular combination
of facilities which, for any reason, is
considered impossible or undesirable.
In some cases, these more complex
integer programming models are not
necessary in order to obtain an optimal
solution. If the number of potential
sites or facilities is small, it is possible
to find the solution by enumeration.
Suppose, for example, there are only
four possible sites under consideration
for the location of incinerators. The
optimal solution may have only one
facility, or it may have two, or three,
or all four. There are four possible
solutions with one facility, six possible
solutions with two facilities, four pos-
sible solutions with three facilities, and
one solution with four facilities, for a
total 15 possible solutions. For each of
these possible configurations, the fixed
cost of the facilities is known and it is
only necessary to allocate waste sources
to the facilities in such a way as to
minimize cost. This problem is again
in the form of a standard Hitchcock
transportation problem and can be
solved with comparative ease. Thus,
the overall optimum is found by solving
15 transportation problems, one for
each of the possible configurations, and
selecting the configuration which has
the minimum sum of fixed costs plus
transportation costs. As the number of
potential sites increases, the number of
configurations increases exponentially
(for n potential sites, the number of
configurations is 2"-l), so that the
enumerative approach cannot be used
for large problems. For example, with
five potential sites the number of con-
figurations is 31, with 10 potential sites
the number of configurations is 1023.
with 20 potential sites the number of
147
-------
configurations is 1,048,575, and with
50 potential sites the number of con-
figurations is approximately 1015.
A particularly important approach to
the solution of site selection models is
based on a heuristic fixed-charge algo-
rithm by Walker (57). The method is
designed to handle any linear program-
ming problem in which there is an
initial fixed charge for any variable
which becomes non-zero, as well as a
linear charge as the variable increases
in value. The solution technique is a
modification of the simplex method for
solving linear programming problems,
which does not guarantee global opti-
mality. However, computational expe-
rience with the Walker algorithm has
demonstrated that it almost always does
find the optimum solution, and when it
fails it still comes quite close in most
cases. The Walker algorithm has been
incorporated into a solid waste facility
location model by Roy F. Weston, Inc.,
and further extended by Argonne Na-
tional Laboratory's Center for Environ-
mental Studies. The code will solve
problems with in excess of 100 waste
sources and 50 facility sites with ease.
It also includes a number of optional
features which are particularly appro-
priate for solid waste problems.
A major criticism of site selection
models is that they generally consider
only transportation costs and the cost
of constructing and operating the facili-
ties. Site selection, particularly for un-
desirable facilities, actually involves
many considerations which can be put
into economic terms only with great
difficulty if at all. Thus, it is often
claimed that site selection models are
essentially useless because they can
shed no light on these nonquantifiable
factors. This attitude is contrary to the
philosophy that the purpose of models
is to provide useful information to
decision-makers. The useful information
provided need not be complete answers
but must be in a form which can be
integrated into the decision-maker's in-
tuitive understanding of the entire prob-
lem. In the case of site selection this
use of models is particularly easy. AI-
MS
most every site selection model con-
siders only a discrete set of potential
sites which have been identified by the
user. Thus, any sites which are felt to
be infeasible regardless of the econo-
mies they offer can be excluded from
the problem at the outset. After the
problem solution has been obtained, it
is still possible to exclude a questionable
site and re-solve the problem, thus
obtaining a second-best solution (from
the standpoint of cost). The difference
in cost between the two solutions pro-
vides the decision-maker with a measure
of the savings which may be obtained
by using the questionable site or, alter-
nately, of the cost incurred by avoiding
it. The final weighting of the unquanti-
fiable factors in such problems rightly
belongs in the political sphere; but the
availability of this cost information
provides the political decision-making
body with an additional and valuable
tool for reaching its decisions.
In one important sense, site selection
models represent a very short-sighted
view of the overall problem. These
models are solved at some particular
time when a need for additional facili-
ties is perceived to be sufficiently great
as to justify the facilities and they
presuppose a decision as to the total
amount of additional capacity which is
required. In a broader sense, the prob-
lem is really one of determining well in
advance when new facilities will be
needed and how much capacity should
be provided at each point in time over
some planning horizon. This problem,
known as the capacity expansion prob-
lem, can also be explored by means of
models.
The objective in a capacity expansion
problem is to determine optimal size of
plants to be constructed (or of additions
to existing plants) and the times at which
construction is to be undertaken so as
to minimize the present value of al
future costs. Various assumptions ma)
be made as to the length of the tim<
horizon and time may be treated eithe,
as a continuous variable or as a discrett
variable. It is, of course, assumed tha
-------
amount of waste generated is known as
a function of time.
Capacity expansion models are gen-
erally quite complex and very much
specialized to a particular set of assump-
tions. This specialization, plus the diffi-
culty of obtaining satisfactory data on
costs and projected waste generation
rates, has hampered widespread use of
capacity expansion models in the solid
waste field. An additional difficulty is
caused by the fact that land costs (and
thus, facility costs) change in an urban
area as it grows so that the cost of an
additional unit of capacity (particularly
with respect to landfills) is different at
different time periods. Most capacity
expansion models do not take this
factor into consideration adequately.
A particularly extensive model which
includes both initial site selection and
capacity expansion has been presented
by Esmaili [16]. The model uses an
elaborate objective function which in-
cludes both capital and operating costs
of facilities, haul costs, and a discount
factor for facilities which are not used
for the total period of their useful life.
The solution technique proposed ap-
pears to be an orderly enumeration of
possible configurations for each time
period with consideration being given
to a particular configuration only if it
yields an improvement over the best
configuration found so far.
One other application of models to
problems involving facilities is worthy
of note. Once a facility is in existence,
there are likely to be operating policy
questions which require investigation.
^or example, is it more economical to
lave a very small number of loading
jocks at an incinerator, thus requiring
/chicles to wait for some period of time
Before unloading, or to have more un-
oading facilities in order to reduce the
vaiting time? Similarly, is it more eco-
lomical to have a large storage area
ind operate a treatment facility around
he clock, or to have a smaller storage
icility and operate the treatment facility
nly during normal working hours?
Models for exploring optimal policies of
lis sort generally fall into the area of
queueing theory and one study of the
application of such models to solid
waste facilities has been made (Stern
[51]). As in the case of capacity expan-
sion problems, these models tend to be
rather complex and somewhat special-
ized.
Papers in the bibliography which deal
with facility models are: Anderson and
Nigam [3]; Clark and Helms [9]; Es-
maili [16]; Helms and Clark [22]; Lieb-
man [27] [28]; Marks and Liebman
[32] [33] [34]; Nigam [38]; ReVelle,
Marks, and Liebman [44]; Rossman
[46]; Schultz [48]; Skelly [50]; Stern
[51]; Walker [57]; Weber [59]; and
Wolfe and Zinn [60].
Models Relating to Vehicles. Model-
ing may be applied to several different
aspects of the waste transport system.
The most common applications of mod-
els in this area relate to the routing
and scheduling of collection (and occa-
sionally long-haul) vehicles. However,
models have also been developed which
may be used in scheduling collection in
different areas, and in selecting replace-
ment vehicles and scheduling mainte-
nance.
A vehicle replacement model (Clark
and Helms [10]) assumes the existence
of a particular fleet of vehicles and
known operating and amortization costs
for each vehicle type within the fleet.
The model selects the number of each
type of vehicle to purchase, given the
total number of vehicles to be replaced.
The number purchased is not necessarily
the same as the number retired, since
vehicles of different sizes may be added
to the fleet. Although the problem is an
integer programming problem, since
number of vehicles must be integer,
reasonably satisfactory (but not neces-
sarily optimal) solutions may be ob-
tained by using linear programming to
obtain a solution and rounding to near-
est integers. An extension of the model
is possible to permit determining how
many vehicles to replace (and which
ones), providing operation and mainte-
nance cost data are available for each
vehicle (or, at least, for each age-group
within a vehicle type).
149
-------
The overall problem of collection ve-
hicle routing has received a great
amount of attention, perhaps because it
is closely related to so many other
routing problems (school buses, milk
delivery, parcel delivery, mail delivery,
etc.). The entire problem requires divid-
ing the collection region into individual
areas, each of which generates one
truck-load of waste, and then routing a
vehicle from a depot to its area, through
the area, and back to the depot. Ideally,
the division into truck-load areas (called
districting) and the routing of individual
trucks should be accomplished simul-
taneously since the two are interde-
pendent. In many modeling efforts,
however, the two steps are examined
by independent models.
The objective in routing and district-
ing is to provide the required level of
service (collection from each waste
generator at specified intervals, usually
on specified days) with minimum cost.
Cost generally consists of two separate
items: depreciation of the vehicle, which
is a function of distance traveled, speed,
and load; and labor cost, which is a
function of time. Most models ignore
the effect of speed and load on vehicle
depreciation, thus making cost a func-
tion of distance traveled and time.
Early attempts at modeling collection
routing took the form of the classic
"traveling salesman" problem. In its
original form, the traveling salesman
problem requires a minimum distance
solution which starts at a specified point,
visits a number of points which require
service (in any order), and returns to
the original point. To obtain an exact
optimal solution to the collection vehicle
routing problem in this form would
require treating each individual waste
source (household) as a point which
must be visited and even then the solu-
tion might propose turning around in
the middle of a block, which is gener-
ally unacceptable. More frequently,
traveling salesman models are used by
aggregating individual sources into
larger units (say, a block face, or a
street segment) which are then treated
as points requiring service. Solution
150
methods for determining optimal routes
for traveling salesman problems are
generally unwieldy for problems with
more than about 50 points. A number
of rather good heuristic approaches do
exist, however. There have been some
attempts to extend the traveling sales-
man approach to obtain routes for more
than one "salesman" when all must
start and finish at the same depot, but
each point need be visited by only one
salesman. This is the equivalent of in-
corporating the districting and routing
problems into one model. This approach
was pioneered by Dantzig and Ramser
[13], and the problem formulation has
become known as the Truck Dispatch-
ing problem. A more advanced algo-
rithm based on the Dantzig and Ramser
method was proposed by Clarke and
Wright [11], and is used in modified
form in the IBM Vehicle Scheduling
Program which is available for System/
360 computers. Although the algorithm
is intended for cases with a compara-
tively small number of points requiring
service, it has been used successfully to
determine good (but not necessarily
optimal) routings for large municipal
areas.
In recent years, some progress has
been made through modeling the collec-
tion routing problem in the form of the
so-called "Chinese Postman's prob-
lem." The assumption in this model is
that service is required along all of the
streets in a network, rather than at
specific points. Thus, the single truck
routing problem attempts to find a route
through the street network which tra-
verses every street at least once, anc
minimizes the total distance traveled. I
should be clear that a lower bound or
total distance is the sum of the length:
of all of the streets since that would b<
the distance traveled if no streets wen
traversed more than once. Leonharc
Euler, in 1736, showed that it is pos
sible to traverse each street exactly onci
if and only if the number of street
incident upon each intersection is ever
The intuitive basis for this proof is tha
for every entry into a particular intei
section there must be an untraverse
-------
exit; thus, each time the vehicle enters
and leaves the intersection it utilizes
exactly two streets. If the number of
streets touching the intersection is odd,
there will be one remaining untraversed
street after the last exit from the inter-
section and re-entering the intersection
using this street leaves no untraversed
street on which to depart. From this it
is easy to see that if one wishes to make
a complete tour through a network
traversing every street at least once, it
will be necessary to retrace at least one
street from each intersection which has
odd degree (degree refers to the number
of streets incident upon the intersec-
tion). But if the retraced street leads to
an intersection which was of even de-
gree, the retracing effectively makes
that intersection odd. The only way to
prevent a retracing from making an
even intersection odd is for the retrac-
ing to go between two intersections
which are odd. It may be that several
streets must be retraced to get from
one odd intersection to another; this
retraced path both enters and exists
'rom intervening even intersections,
hus leaving them even, as shown in
7igure 1. Any tour which traverses all
streets in a network at least once will
•etrace paths between pairs of odd
ntersections; since the objective is the
ninimization of total distance, it is
lecessary to "pair up" the odd inter-
ections so that the sum of these paths
onnecting pairs be minimum. A par-
icularly elegant solution method de-
[CURE 1—A hypothetical street network,
owing retracings necessary in order to con-
'uct a tour which traverses all streets at
1st once. Circles indicate intersections of
'd degree; dashed lines show retracings
'lich make the degree of every intersection
en.
veloped by Edmonds [14] may be used
to find the optimum pairs.
Once the streets to be retraced have
been selected, there are many different
tours through the network which re-
trace only those streets and the con-
struction of such a tour is a compara-
tively easy task. Other objectives (such
as minimizing left turns) can be con-
sidered by the router who constructs
the tours.
The problem of routing multiple
vehicles (i.e. districting simultaneously
with routing) has not been optimally
solved. A good but complicated heu-
ristic for the "multiple postman's prob-
lem" is given in Edmonds and Johnson
[15] but this approach has not been
tested in practice.
It should be noted that a simple heu-
ristic solution for the problem can be
obtained by treating the entire collec-
tion area as if it could be collected by a
single vehicle. Once the retraced streets
for this fictitious vehicle have been
determined, it is possible to draw dis-
tract boundary lines which pass through
intersections in such a way as to keep
an even number of streets incident on
the intersection on each side of the
boundary. Thus, a complete tour is still
possible within each district without
retracing any more streets than the fic-
titious single vehicle would retrace.
Such an approach, however, neglects
the additional retracings which each
vehicle will have to make in traveling
between its collection district and the
depot. A heuristic using this method
and considering these added retracings
is given by Male [30].
The routing problem may also be
modeled by a simulator (Bodner, Cas-
sell and Andros [7]). In such a model,
the vehicle begins at an intersection
and randomly selects a street on which
to collect. Information on the amount
of waste collected on that street and
the time required may be provided as
input data or generated randomly from
an assumed statistical distribution; in
any case, the amount is added to the
truck's load and the time interval is
added to elapsed time. When the truck
151
-------
reaches the next intersection it again
randomly selects a street on which to
proceed. Whenever the truck reaches
an intersection where there are no re-
maining uncollected streets, a search is
made for the nearest uncollected street
and the vehicle proceeds to this point
(retracing) and then begins collecting
again. When the truck reaches capacity
it returns to the depot. When the
elapsed time reaches that of a normal
workday, overtime is charged. A route
constructed in this manner is not likely
to be particularly good; however, the
computer time required to run the
model is quite short, so it is possible to
make a large number of runs and select
the best route generated. An improve-
ment in this method might be obtained
if the search for nearest uncollected
street were converted to a search for
the nearest odd intersection with an
uncollected street, since paths between
odd intersections will ultimately be con-
structed anyway. The simulator can also
be modified to adhere to additional
rules which are felt to provide better
routes, such as avoiding left turns.
Some criticism has been leveled at
attempts to determine optimum vehicle
routes (Shuster and Schur [49]). The
basis for the criticism is principally
three ideas: the data requirements for
such models are prohibitive; there are
too many properties of a "good" route
which are not reflected in a mathe-
matical model; and a man, following a
good set of routing rules, can do an
excellent job of routing without the use
of a complicated model. There is a
good deal of validity in these claims,
particularly with respect to earlier mod-
els which completely determined a
route and left no flexibility for the
manager. However, the Chinese post-
man model determines only the streets
to be retraced for minimum retracing
distance, leaving the manager a great
deal of choice in how the tour is
actually to be constructed. In effect, as
is the case in facility models, the model
and the computer are used to do what
the manager is poorest at (minimizing
distance), while the manager is free to
152
use the excellent rules provided by
Shuster and Schur on the resulting net-
work. Though it is true that data re-
quirements are great if exact optimal
solutions are desired, such things as
travel time for deadheading can be
approximated rather readily so that the
computer codes can be executed with
little more data than the manager al-
ready has available. In addition, it is
important to note that the trend toward
large municipal data bases such as the
DIME file of the Bureau of Census
will make all the data required for
elaborate routing models readily avail-
able and make it possible to construct
new routes at frequent intervals.
It should be noted that the independ-
ence of routing and site selection
models is purely artificial. The selection
of vehicle routes is clearly dependent
upon facility locations; facility loca-
tions, however, cannot be truly opti-
mized without regard for the routes
which will be generated. Ideally, what is
required is a location-routing model
which seeks to optimize both simultane-
ously. In practice, however, routing is
usually a comparatively short-term
decision, while the location of facilities
is considered at infrequent intervals anc
for much longer time periods. Thus
the use of two independent model;
probably does not invalidate either.
Papers in the bibliography which dis
cuss vehicle models are: Altman
Bhagat, and Bodin [2]; Andros [4]
Beltrami and Bodin [5]; Bodnei
Cassell, and Andros [7]; Brown [8
Clark and Wright [11]; Coyle am
Martin [12]; Dantzig and Ramser [13
Edmonds [14]; Edmonds and Johnso
[15]; Fuertes, Hudson, and Marks [17
Liebling [26]; Liebman [27] [28]; Lo
[29]; Male [30]; Marks, Cohon, Moon
and Strieker [31]; Marks and Liebma
[32]; Marks and Strieker [35]; Mart
and Rothwell [36]; Owen [39]; Rothge
[47]; Shuster and Schur [49]; Strick
[52]; Wathne [58]; and Wyskida ai
Gupta [61].
Models Relating to Manpower. T
most pressing problem in the area
manpower is the scheduling of t
-------
workload so that it is equitably dis-
tributed among the workers and so that
the right number of workers is em-
ployed. There are three fundamental
steps involved in scheduling. First, it
is necessary to determine just what con-
stitutes a day's workload. How many
dwelling units (or tons) can a vehicle
and its crew collect in an hour? How
does crew-size relate to this figure?
What is the trade-off between dead-
heading time and amount to be col-
lected? Modeling yields little informa-
tion in this area; though some work has
been done on the problem, much re-
mains to be determined before models
can be used to solve the rest of the
questions. Second, the vehicle routes
must be balanced so that each crew
comes close to the pre-determined fair
workload. Heuristic routing models for
the multi-truck problem usually include
some effort to balance workload but,
again, there is more work needed to
obtain satisfactory solutions. Third,
crews must be assigned to daily routes,
and scheduled so that vacation periods,
days off, and overtime (if any) are
equitably distributed and arranged in
satisfactory sequences. This problem
las, until recently, received little atten-
ion; but several new papers (Altman
;t al. [l],-Bodin [6]) have developed a
•ather complex non-linear programming
md heuristic algorithm for scheduling
>f this sort. Another model (Tanaka
md Quon [53]) takes as its objective
he short-run scheduling of routes using
ivailable manpower so as to minimize
he sum of overtime costs and penalty
osts associated with late or early serv-
:e. To date these models have not been
ufficiently tested in practice to deter-
line their utility.
Models Relating to Entire Systems.
'he obvious difficulty with most of the
lodels discussed in earlier sections is
lat they do not consider the entire
)lid waste system of a municipality.
hus, the interplay between waste gen-
•ation, routing of trucks, location and
•pe of facility, and scheduling of man-
jwer is not explicitly considered. Most
the models discussed have been
optimizing models; the problem is that
any complete solid waste system is too
complex to be fitted into the form of an
optimization model. Thus, although
models of entire systems do exist, they
are usually simulation (prediction)
models rather than optimization models,
permitting the exploration of particular
policies and system configurations, but
not allowing direct optimization except
by trial and error.
Attempts have been made to build
simulation models of waste collection
and disposal which are general enough
to be used in any city. In general, these
models have been only marginally suc-
cessful. Each municipal system has its
own quirks and idiosyncrasies, and it is
extremely difficult for the modeler to
imagine all such individual characteris-
tics and allow for them in his model.
Thus, although efforts should be (and
will be) continued toward a general
model, it is to be anticipated that the
best simulation models of overall sys-
tems will be tailor-made for the specific
system for which their use is intended
for some time to come.
System simulators may be con-
structed at almost any level of detail
which is desired, depending on the
specific uses for which the models are
intended. For example, some models
simulate flow of material into and out
of facilities; others include simulation
of the movement of individual vehicles,
while the most detailed might (at least
in theory) simulate generation of waste
material at individual households and
its detailed movement through the sys-
tem. Generally this most detailed level
is not required for the decisions in
which the model is intended to assist.
Most system simulators include con-
sideration of the stochastic element of
the system, a factor which is not nor-
mally included in the optimization
models discussed above. In optimal
routing models, for example, average
vehicle speed is usually used to measure
the cost of travel over a particular
street. In simulation models, a mathe-
matical or empirical distribution of
truck speeds may be provided to the
153
-------
model, and values for speed may then
be selected randomly from this distri-
bution whenever they are needed. Thus,
multiple runs of a simulator provide
different answers just as multiple days
of operation of the real system yield
different results.
The most common output from a
system simulation is a value for total
cost of operation of the system. How-
ever, depending on the level of detail
built into the model, almost any in-
formation which could be obtained
from observation of the actual system
can also be obtained from the simu-
lator. Number of overtime hours
worked, number of trips to the incin-
erator, time of day of collection at
specific points, size of queues at trans-
fer stations, and other measures of
quality of service can all be obtained.
Again, depending on their level of
detail, system models may be used for
evaluating and comparing changes in
collection frequency, changes in routing
assignments and policies, new locations
of disposal and treatment facilities, po-
tential locations of transfer facilities,
or almost any other change in opera-
tion of a system. Such explorations
cannot be made in a vacuum, however;
the data requirements for simulators
are usually quite extensive. Particularly
when using a simulation model for
evaluating a new component of the
system, it is often difficult to obtain
necessary information on the perform-
ance of the component, It should be
kept in mind that simulation models are
best used for exploring the interrela-
tionships in a large system of a number
of individual components when the
behavior of the individual components
is well understood. Thus, for example, a
study of the need for and effect of
transfer stations in a system which does
not have such stations cannot be effec-
tive unless data are available concern-
ing the performance of the long-haul
vehicles which will be used in conjunc-
tion with the stations. Frequently, data
of this sort must be obtained from other
systems which already have the com-
ponents being considered.
154
Papers in the bibliography which deal
with overall systems models are: Hel-
ferich, Hoffner, and Gee [21]; Quon,
Charnes, and Wersan [40]; Quon,
Tanaka, and Wersan [42]; Rao,
Richardson, and Wismer [43]; and
Truitt, Liebman, and Kruse [54] [55].
Miscellaneous Models. Two other
kinds of models which have application
to solid waste management are not
readily classified in the framework used
above.
The technique of gaming has been
used in a number of areas for the pur-
pose of training decision-makers in an
environment which simulates the man-
agement of an actual system without
incurring the high costs associated with
management mistakes. An important
gaming model is APEX, an air pollu-
tion game. The success of these models
demonstrates their usefulness and simi-
lar models could certainly be beneficial
in the solid waste management field.
Wahi and Peterson [56] have developed
a game which uses a computer in an
interactive mode. The player (or play-
ers) is faced with a particular situation
in which some decision must be made
and has at his disposal various com-
puter programs for determining shortest
paths between points, optimal allocation
of waste sources to existing facilities,
etc. The player is introduced to the
decision situation gradually, in such a
way that his confidence in the use of
the computer as an aid is built with
experience, Klee [24] has also describee
a solid waste management game, de-
veloped by the Office of Solid Waste
Management of the U.S. Environ
mental Protection Agency.
The management of a solid wast<
system involves balancing of multipl<
goals, as suggested early in this chapter
The minimization of cost to provide ;
required level of service is only one par
of the process; the more difficult por
tion is the determination of the desirei
quality of service and the determinatioi
of whether an increase in some aspect
of service quality are worth the assc
ciated increased cost and decrease
level of other aspects of service quality
-------
The use of decision models as an aid in
the weighting of various quality and
cost goals so that alternative systems
can be evaluated has not been widely
explored; Klee [23] [25] has presented
the pioneering work in the application
of multiple goal techniques to solid
waste management.
III. EXAMPLES OF MODELS IN
SOLID WASTE MANAGEMENT
A casual perusal of the references at
the end of this chapter will reveal that
fully 75 percent of the listed papers
bear dates of 1970 or later. This is not
due to any attempt on the part of the
author to weed out earlier papers which
may have been outdated; on the con-
trary, the bibliography represents a
nearly exhaustive list of all the model-
ing work which has been done with
solid waste systems in mind, with the
exception of a few reports covering a
specific problem in a specific place. It
is simply the case that attempts to bring
modeling methodologies to bear on
solid waste problems are quite recent.
For this reason, it is not possible to
cite in the following sections many
examples of the application of general
models to solve real-world problems. In
most cases, the models have not yet
been applied; in those few cases where
models have been applied, either the
results have not yet been implemented,
or there is insufficient information to
udge the final outcome. The selection
af the two models discussed in detail
selow was motivated by the fact that
joth have been used in somewhat hypo-
hetical studies in the same city (Balti-
nore) and one has been used in an
ictual study in Jacksonville. These re-
ated uses of the models permit com-
>arison and a discussion of how simu-
ation and optimization may be used in
onjunction.
A Transfer Facility and Site Selection
iodel (Marks and Liebman [32] [33]
34]). Marks has developed an opti-
lizing model which determines appro-
riate locations for transfer facilities
rhen sources of waste and disposal
sites are known. The model minimizes
the capital and operating costs of the
transfer stations plus the transport costs.
Transport costs are taken to begin with
the trip from collection area to transfer
facility or disposal facility; costs of
actual collection are not included.
The collection area is divided into a
set of K collection tracts (representing,
ideally, individual truckloads), with an
amount of waste Sk generated at tract k.
There is a known set J of disposal
points and the capacity of disposal point
j is Dr A set of proposed intermediate
(transfer) facility sites has been sug-
gested. Potential transfer facility i has a
fixed charge Fs, a capacity Qi; and a
unit processing cost Vi per ton of waste.
The mathematical statement of the
model is:
Minimize: £ Fiyi + S] £ bklxkl
(1)
i ) k J
Subject to :2X i + 2*ki = Sk
J i
for each tract k (2)
for each transfer site i (3)
2 xkl - Q,y, < o
k
for each transfer site i (4)
S7 _1_ V w , < D
zkj i Jj wij — -^1
fe i
for each disposal facility j (5)
where:
bhi-
dk =
for each transfer site i (6)
cost of 'transporting a unit
(ton) of waste from tract k to
transfer facility i. including
processing cost at facility i
(V,)
cost of transporting a unit
(ton) of waste from transfer
facility i to disposal facility j
cost of transporting a unit
(ton) of waste from tract k to
disposal facility j
amount of waste transported
155
-------
from transfer facility i to dis-
posal facility j
xkl = amount of waste transported
from tract k to transfer facility
i
y{ = 1 if the ith transfer facility is
constructed, and zero other-
wise
zk1 = amount of waste transported
from tract k to disposal facility
The objective function (1) requires
the minimization of the fixed costs
associated with those transfer facilities
which are constructed (first term) plus
transport costs from collection tracts to
transfer facilities and processing costs
at transfer facilities (second term) plus
transport costs from transfer facilities to
disposal facilities (third term) plus
transport costs from collection tracts to
disposal facilities (last term). Equation
(2) requires that the amount of waste
taken from each collection tract be
equal to the amount generated there;
while equation (3) requires that the
amount into a transfer facility be equal
to the amount out. Equation (4) speci-
fies that if a transfer facility is not built
(yt = 0) it can handle no waste, while
if it is built (yt = 1 ) it can handle no
more than its capacity. Inequality (5)
prohibits shipping to any disposal fa-
cility an amount greater than its ca-
pacity, while constraint (6) requires
that a potential transfer facility can
only be built or not-built, and cannot
be partially built, (It should be noted
that the original model, described in the
referenced papers, did not explicitly
include flow directly from collection
tract to disposal facility, but permitted
it by the artificiality of constructing a
'"dummy" transfer facility with zero
cost) .
Because the model is a mixed-integer
linear programming problem, the solu-
tion method proposed is a form of
branch-and-bound, using a network
flow algorithm for solving the individual
branch problems. Cases with 40 col-
lection areas, 7 potential transfer fa-
cilities, and 2 disposal sites were solved
156
on an IBM 7094 computer in approxi-
mately 45 seconds.
Additional constraints may be placed
in the model without significantly affect-
ing the solution technique. The two
most important of these are (a) a
budget constraint, which limits either
the amount of capital costs incurred in
construction of facilities or the number
of facilities to be constructed, and (b)
a mutual exclusivity constraint, which
prohibits the construction of more than
one (or any other number) of a speci-
fied subset of facilities. This latter con-
straint permits the consideration of
several different sizes of facilities at the
same point, or the choice of no more
than one site in a particular neighbor-
hood.
This model has been applied in a
study of the collection system in the
northwest quarter of the city of Balti-
more. The data used were derived from
those collected for the simulation model
of Truitt et al. [55] discussed below.
The area studied is predominantly resi-
dential, with collection being made
twice per week.
The first run of the model was essen-
tially a verification trial to insure tha
the data had been abstracted withou
error and represented the collection
area reasonably well. No transfer sta-
tions were permitted and the mode
was simply used to calculate week!}
collection costs. The result gave a cos
of $16,600 per week while the actua
system cost is estimated to be approxi
mately 4 percent higher. This differ
ence was considered to be relative!1,
insignificant, thus indicating that th
data were accurate.
The model was then used to explor
the potential savings associated wit
transfer stations. Four sites within th
collection area and two outside the are
(between the area and the disposal site
were selected as the most likely loci
tions for a transfer station and th
construction and operation costs fc
stations of various capacities were est
mated. Several runs were made, eac
with transfer stations of a differei
capacity. The results indicated that wi
-------
an optimally located 600 ton/day ca-
pacity station, costs were reduced by
approximately $700 per week while
with a 900 ton/day capacity station the
reduction was approximately $900 per
week. Stations larger than 900 tons/day
had smaller reductions in total cost,
though even a 1500 ton station showed
a reduction of about $700 per week.
Also of interest was the fact that the
optimal site for a station was the same
for capacities of 900, 1200, and 1500
tons per day but different for a capacity
of 600 tons per day. Additional runs
were made for three times per week
collection and for increases in waste
generation rate ranging from 10 per-
cent to 60 percent; all showed the same
stability in selecting the identical site
alternative.
It was considered to be of particular
importance to determine the possible
effects of errors in estimating costs or
other data. Thus, a number of runs
were made in which facility costs,
transport costs, collection rates, etc.
were varied; these also demonstrated
remarkable stability. Transfer stations
remained (marginally) economical until
he facility fixed cost almost doubled:
and the same site was chosen with al-
nost all combinations of data.
A Collection System Simulation
Model (Truitt et al. [54] [55]). The
ystem simulator constructed by Truitt
is a doctoral dissertation had as its
ntent the demonstration of the feasi-
lility of utilizing simulation to compare
.Iternative policies of operation within
single city. It was also intended that
ie simulator itself should be sufficiently
eneral to permit its use for the above
tirpose in more than one city; that is,
exibility should be built into the pro-
ram so that differences between cities
ould be conveniently encompassed.
olicy parameters which are variable
ithin the model for purposes of com-
arison include: location of a single
ansfer station (if it exists), location
a single disposal site, collection fre-
.lency, collection vehicle size, pay
ale and overtime pay policy and
;hicle use and amortization charges.
Other variables which can be changed
indirectly include household density
and waste generation rate (varied by
changing the data base provided on
waste generation), season of the year
(varied by changing waste generation
rates), crew size (varied by changing
the vehicle collection rate data).
Two preliminary simulation models
were constructed prior to the develop-
ment of the third and final model.
These two models were used to assist
in constructing specific portions of the
final model and will not be discussed
here.
A single run of the system simulator
calculates the result of collection ac-
tivity by a number of collection trucks
in an urban area for one week, Monday
through Saturday. The area may be
composed of many subareas of different
population densities. A transfer station
may be present in the area, located at a
specified point. In this case, the model
also simulates the operation of waiting
lines at the transfer station and of the
long haul tractors and trailers used for
transporting the waste from the transfer
station to the disposal site. The disposal
site is also located at a specified point.
The output from the simulator lists
the cost for the week of the operation
of collection vehicles, transfer station,
and tractor trailers. These costs include
amortization, operation and labor. The
total tonnage collected is also provided.
In addition, mileage traveled by collec-
tion vehicles while collecting and while
traveling to and from collection areas
is provided, as is total mileage traveled
by long-haul vehicles. Amounts of over-
time generated and average hours in
the workday are printed, as are other
miscellaneous items such as the time
distribution of the lengths of transfer
station queues.
The input data for the simulator may
be divided into two sections: geo-
graphic data and field performance
data. Geographic data for the collection
area are generated by dividing the en-
tire area up into small tracts such as
census tracts, each with a population of
less than about 6000 people. For each
157
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such tract, the geographic coordinates
of the centroid are provided as well as
the total number of households in the
tract and the population density in
households per acre. In addition, travel
distance from the disposal site or trans-
fer station to the tract must be pro-
vided, unless the user is satisfied with
calculation of the distance based on
geographic coordinates. Household
waste generation rates for each level of
population density must also be deter-
mined. Geographic data for the transfer
station (if any) and the disposal site
simply consist of the coordinates of the
locations of each.
Field performance and cost data pro-
vided to the simulator include values
used for the calculation of amortized
cost of the transfer facility, hourly
charge for tractor trailer and collection
vehicle operation, drivers' and laborers'
daily pay rate and overtime rate, ca-
pacity of collection vehicle and long-
haul vehicle, minimum weights to be
accumulated in each of these vehicles
before they are permitted to empty, and
various miscellaneous values which
must be used in calculating vehicle and
facility performance.
The simulator calculates speed of the
long-haul vehicles, collection speeds of
the compactor-collection vehicles, and
transit speeds of the compactor-collec-
tion vehicles by selecting randomly
from frequency histograms provided
for each of these values. Thus, the
speeds of these vehicles must be ob-
served in actual operation and the re-
quired histograms constructed. Several
different histograms for collection
speeds are required, one for each of
several different population densities.
The simulator permits the inclusion
of an auxiliary compaction unit at the
transfer station to compact the waste
additionally as it is loaded into the
long-haul vehicles. If such a unit is in-
cluded, data must be provided concern-
ing its cost and the anticipated density
of the output waste.
As the simulator begins a day's oper-
ations, it sends the required number of
collection vehicles into the field to
158
assigned task areas. It calculates the
time and distance traveled by each
truck to reach its task area, then cal-
culates the collection time and distance
traveled until the truck is full. The
portion of the task area which is
complete is recorded and the truck is
then sent back to the transfer station
or disposal site. Time and distance are
again calculated and the time required
for processing the truck at the transfer
station is also calculated, including time
waiting in a queue if one exists. The
simulator continues in this manner until
each assigned task area is complete,
including calculation of overtime if it is
required. The behavior of long-haul
vehicles is determined in similar fashion.
At the end of the week's operation,
costs and other output data are cal-
culated and printed and the run is
terminated.
It is important to note that detailed
routing for each truck is not included
in this model. Times and distances
traveled during collection are based on
histograms of average collection rates;
times and distances traveled from col-
lection area to disposal site are based on
distances from the centroids of collec-
tion areas to the location of the dis-
posal facility and on histograms of
travel speeds.
The entire simulator, including data,
consists of approximately 3500 Fortran
cards. The simulator has been run or
an IBM 7094 in core memory and has
been adapted for use on an IBM 1130
The maximum population which ma}
be simulated on the IBM 7094 i«.
approximately 300,000 people; a singli
run (one week's operation) of such at
area on that machine requires less thai
one minute of computer time.
The completed model was tested am
its uses explored using the City o
Baltimore as an example. Althoug
extensive data gathering (involvin
approximately two man-months and th
cooperation of many vehicle operator
foremen, and city officials) was undei
taken, it must be kept in mind that th
purpose of the study was to demoi
strate the utility of the model, not
-------
determine specific answers for Balti-
more. Thus, some data (for example,
travel speeds of long-haul vehicles,
which are not currently used in Balti-
more) were extrapolated from other
cities rather than making short test-runs
in BaKimore.
The first runs of the model were
made as proof runs to determine how
closely the model duplicated existing
conditions in the northwest quarter of
the city. Two such runs were made;
each resulted in total costs within 2
percent of the actual system costs, with
all other output falling within a similar
distance from observed values. This
close agreement is not as remarkable as
it might seem since, after all, the under -
ying data for the model are simply sta-
istical measures of the performance of
.he actual system. It does demonstrate,
aowever, that the simplifications in-
lerent in aggregating household units
nto larger tracts and measuring col-
ection speeds for only a few different
lousehold densities do not significantly
tffect the validity of the model.
The model was next used to investi-
,ate the effects on cost and other sys-
em parameters of increasing collection
requency from twice per week to three
imes per week. To make runs simulat-
ig this collection frequency, it was
ecessary to adjust the frequency histo-
rams of collection rates to reflect the
jduced amount of waste at each eol-
ation. Since Baltimore has no areas in
hich collection is made three times
;r week, no data were available for
le construction of these adjusted histo-
•ams. However, in the existing, twice-
;r-week collection system, collections
e made when there have been three
iys since last collection and when
ere have been four days since last
illection, and data were available on
llection rates for these two condi-
>ns. In a three-times-per-week collec-
m system, collections are made
vice) when there have been two days
ice last collection and (once) when
;re have been three days since last
lection. Data for the latter condition
re simply taken, unadjusted, from
existing data; while histograms for the
condition of two elapsed days since last
collection were extrapolated. In any
real study, it would be advisable to
actually perform three-times-per-week
collection in a few areas of different
population densities and gather valid
data for collection rates. It should also
be noted that no allowance was made
for the possibility of increased waste
generation due to the increased fre-
quency.
The results of these trials indicated
that in order to collect three times per
week, the number of collection vehicles
operated within the area would need to
be increased from 29 to 36. Amorti-
zation, maintenance, and operation (ex-
cluding labor) of these additional 7
trucks caused an increase in cost per
ton collected of $0.58 while additional
labor cost in the entire system amounted
to $0.38 per ton. Thus, total cost in-
creased from $10.68 per ton to $11.64
per ton, or about 9 percent.
There is, however, a possible addi-
tional cost which is not directly indi-
cated by the model. If collection is
performed twice per week, then on each
of Monday, Tuesday, and Wednesday
one is collecting four days' waste accu-
mulation from one-third of the area or
the equivalent of 1.33 days' accumula-
tion over the entire area. If collection is
performed three times per week, then
on each of Monday and Tuesday one
is collecting three days' waste accumu-
lation from one-half of the area, or the
equivalent of 1.5 days' accumulation
over the entire area. Thus, the peak
daily loads on transfer stations and
disposal facilities increase by nearly
30 percent. There is, of course, an
assumption that waste generation rates
are the same on every day of the week.
In actual practice (and in the data
used by the model), this is not true;
nonetheless, there is likely to be some
increase in peak loads which might well
require increased capital investment or
increased overtime costs in the opera-
tion of facilities. Since the model does
not include costs of operation of dis-
posal facilities, and since there was no
159
-------
transfer station included in these runs,
a direct indication of these costs was
not provided; however, the model did
show that peak daily loads at the dis-
posal site increased from 297 tons per
day to 341 tons per day, or approxi-
mately 15 percent.
Additional runs of the model were
used to explore the potential savings
associated with the installation of a
transfer station within the collection
area. Data on construction and opera-
tion costs of a transfer station were
obtained from other cities, as were data
on the speeds and costs of long-haul
vehicles. A potential site for the loca-
tion of a transfer station was selected
and the coordinates of this site were
provided to the model. In the first runs,
the existing location of the incinerator
(approximately 8 miles from the cen-
troid of the collection area) was used.
The results showed that for both two-
and three-times-per-week collection,
costs with and without the transfer sta-
tion were approximately equal. The
number of collection vehicles required
with twice-per-week collection was re-
duced from 29 to 24; with three-times-
per-week collection it was reduced from
36 to 30. However, the resulting reduc-
tion in collection cost was equalled by
the cost of amortization and operation
of the transfer station and the amorti-
zation, operation and labor costs of
the three tractors and six to eight trail-
ers required to haul to the disposal site.
Because of the lack of an indication
of economies associated with a transfer
station, the model was further exercised
by relocating the disposal site both
closer to and further from the collec-
tion area. It was found that, for twice-
per-week collection, the cost per ton
varied with distance from the collection
area approximately according to the
following linear equations:
a) Without transfer station:
Cost/ton = $9.00 + $0,20/mile
b) With transfer station:
Cost/ton = $10.30 + $0.03/mile
The intersection of these two lines is at
approximately 8 miles; thus, for dis-
160
tances between collection area and dis-
posal site of under 8 miles a transfer
station in the collection area is uneco-
nomical while for greater distances the
transfer station rapidly develops sig-
nificant savings. For three-times-per-
week similar linear equations were
found; their fixed costs were higher and
their slopes were approximately the
same as those shown above, and their
intersection point was also at a distance
of approximately 8 miles. These results
cannot, of course, be used to develop
any, general conclusions about transfer
stations; they are valid only for the
particular area studied and the specific
configuration of vehicles and other
equipment which was assumed.
It is also possible to use the model
to investigate the advantages of includ-
ing a compaction unit in the transfer
station. This is done by increasing the
capital cost of the transfer station by
the cost of the compaction unit anc
increasing the density of the waste in
the long haul vehicle. Several runs were
made using the model with a compac-
tion unit designed to increase density ir
the long-haul trailers from about 45(
pounds per cubic yard to about 80{
pounds per cubic yard; the results indi
cated that savings associated with sue
a unit are not linear with transpor
distance and that rather large transpot
distances (in excess of about 15 miles
are necessary in order for the compac
tion unit to demonstrate any significar
savings over the transfer station alont
The Jacksonville Study (Reynold:
Smith, and Hills, Inc. [45]). A con
plete solid waste systems study ws
performed in 1970 in the City of Jac
sonville, Florida by the engineerir
firm of Reynolds, Smith, and Hills. Tl
need for this study was made apparei
by the 1968 consolidation of Jackso
ville and the surrounding Duv
County, resulting in a patchwork <
different solid waste systems. The enti
study was unusually comprehensrv
encompassing a complete fiscal ai
management review as well as recoi
mendations for the immediate futu
and for long-range policy. It is beyo1
-------
the scope of this chapter to discuss the
entire study; attention is devoted herein
to some uses of modelling in the de-
cision process.
The Truitt simulator described above
was adapted for use in a portion of the
study. Since the consultants had avail-
able an IBM 1130 computer, the model
was first converted to this machine and
tested using the original Baltimore data.
Modifications were then made to the
model to permit consideration of either
a 4-day or a 6-day workweek, since
both of these were possibilities for the
city. A great deal of difficulty was ex-
perienced by the consultants in making
these and other minor modifications.
the conclusion that the backup site was
also economically feasible. Simulation
of the use of a new disposal site without
transfer station indicated that if the cur-
rent disposal site were abandoned and
the new one used, the required number
of trucks would increase to 36 and the
collection cost would increase to $14.78
per ton.
Because the consultants felt that a
six-day workweek might prove to be
more economical, several simulation
runs were made using various com-
binations of workweek length, transfer
stations, and disposal site. The results
of these runs are summarized in the
following table:
Collection
Frequency
2/week
2/week
2/week
2/week
3 /week
3 /week
Workweek
Length
4 days
4 days
6 days
6 days
6 days
6 days
Transfer
Station
No
Yes
No
Yes
No
Yes
Number of
Trucks
33
27
22
18
29
26
Total Cost
($/ton)
13.46
11.90
12.58
12.01
16.46
15.35
This emphasizes the problem associated
with the construction of a general pur-
sose simulator intended for use in many
different cities under many different
sperating policies. Following this re-
structuring and extensive data collec-
ion, the model was used first to simu-
ate current municipal operation of 33
rucks collecting twice weekly in a
-day workweek. Cost of operation was
ound to be $13.46 per ton, which cor-
elated closely with actual figures.
This model was then used to explore
arious comparatively short-run alter-
atives which were under consideration
ar the city. For example, the use of a
•ansfer facility at an abandoned in-
inerator site was found to reduce the
jquired number of vehicles to 27 but
> produce significant delays in queue-
ig at the transfer station resulting in a
rge amount of overtime. Addition of
;veral more unloading bays in the
ansfer station reduced the overall cost
i $11.90 per ton. A simulation using a
ickup transfer station site about 1.5
iles further away from the collection
ea produced similar results leading to
These results, coupled with other por-
tions of the study, led to the recom-
mendation that a collection frequency
of twice per week in a six-day work-
week should be used, if possible. Two
additional runs of the simulator ex-
plored the feasibility of a proposed new
regional landfill and a proposed new
regional incinerator.
A facility location optimizing model
(Skelly [50]), similar to that of Marks
but including location of disposal facili-
ties as variables, was also used in this
study. The model was used principally
to explore long range (to 1990) re-
gional configurations of the entire sys-
tem, and showed that the most eco-
nomical arrangement consisted of two
regional landfills with seven transfer
stations.
IV. USE OF OPTIMIZING AND
SIMULATION MODELS
The studies discussed above demon-
strate that models are not generally
sufficient to provide final answers to any
management problem. Their greatest
161
-------
benefit may well be to assist decision
makers in developing intuition and
understanding the general behavior of a
system. Thus, no single run of any
model can be made to determine a
solution; rather, many runs using dif-
ferent assumptions should be made.
Simulation models and optimizing
models are inherently different. Opti-
mization, because the solution technique
requires particularly simple mathemati-
cal relationships, is usually done on a
skeletal model which includes only the
major components of the system and
reflects only the major interrelation-
ships between these components. Simu-
lation can be done with a model con-
taining much more detail but requires
much more computer time and much
more data. Further, simulation can only
explore the consequences of a particular
action or configuration, while a single
run of an optimization model deter-
mines the appropriate configuration. As
a result, perhaps the best use of the two
kinds of models would be in series,
applying optimization models to screen
large numbers of alternatives and select
a few which appear best, and then using
simulation to explore in greater detail
the consequences of these few alterna-
tives. It is unfortunate that in the
Jacksonville study the Truitt simulator
was inadequate to handle the regional
system which was explored by the
Skelly model.
An additional consideration in the
use of simulation is the current lack of
general purpose simulators. This places
each local area in the position of having
to build its own simulator from scratch
or modify an existing program to fit
its own situation. Either of these is a
formidable task. It is likely that a care-
fully constructed simulator can be
modified as time goes on to reflect al
changes in a system so that a city which
made the initial investment required tc
build a simulator would always possess
an up-to-date program but no success-
ful efforts of this sort have yet beer
reported.
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of Solid Waste Disposal Problems,'
Public Works, 98, September 1967.
61. Wyskida, R. M. and J. N. D. Gupta, "7
Routing Problem in City Solid Wast
Collection," presented at the 39th Na
tional Meeting of the Operations Re
search Society of America, 1971.
164
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Chapter 6
Models in Urban Development
By
James C. Ohls and Peter Hutchinson
(with contributions by)
T. R. Lakshmanan and Philip D. Patterson
SUMMARY 167
I. INTRODUCTION 167
I. SOME GENERAL THEMES IN URBAN MODELING 169
Large Number of Variables 169
Large Number of Policy Parameters . 169
Variables and Parameters Highly Intercorrelated . . . 170
Long Time Horizon 170
Data Limitations 170
Objectives of Urban Models 171
Simplifying Techniques . . 172
Evaluation Criteria 172
. MAJOR REVIEWS OF URBAN DEVELOPMENT MODELS 173
Introduction . 173
Twelve Selected Surveys 174
European Surveys 179
. SELECTED URBAN DEVELOPMENT MODELS 179
Partial Analytic Models 181
NBER Model—The Residential Sector 181
The Market Potential Model—The Retail Sector 184
Comprehensive Analytical Models 185
The Lowry Model . 185
The Urban Dynamics Model 190
Simulation-Gaming Models 193
CLUG—Community Land Use Game 193
RIVER BASIN MODEL 193
APEX—Air Pollution Exercise 195
CONCLUDING COMMENTS 196
REFERENCES 198
165
-------
-------
Models In Urban Development
SUMMARY
Public officials at both the local and
Federal levels must make important
decisions affecting urban structure and
urban growth. Zoning, urban renewal,
poverty programs, transportation plan-
ning, and housing programs are just
a few of the many areas of public
policy which are influenced by and
have effects on urban spatial location.
Because of the great complexity of
urban systems, modeling may have
^reat potential as an aid to formulating
md analyzing public programs in these
jnd other urban policy areas.
A substantial number of models of
irban structure have been developed,
ind they vary considerably with regard
o general approach and to specific
etails. Urban models of necessity in-
olve simplification in order to make
lem manageable, and the ways in
^hich specific modelers have chosen to
ccomplish this simplification can best
e understood in relation to the ob-
:ctives which the various models have
een designed to accomplish.
The government funding for urban
lodels dealing with predicting the size
id distribution of land using activities
ithin a metropolitan area has been so
idespread over the past twenty years,
at a substantial literature has already
;en developed comparing the models
td assessing the value of efforts made
date. This body of literature has
ceived recent inputs from a number
researchers who are critical of the
st modeling efforts. However, the
tiding of urban models continues as
; model builders reduce their claims
d expand their methodologies.
This chapter provides an overview of
the general themes in urban modeling
and of the major urban modeling ef-
forts during the past two decades by
first reviewing some previous surveys of
urban models. Then several selected
urban development models are exam-
ined in some detail. The chapter con-
cludes with a discussion of recent cri-
tiques of urban development modeling
and a view of the policy role of urban
development models.
The summary table shows the urban
models dealt with in this chapter.
/. INTRODUCTION
Urban areas are highly complex
forms of economic and social organi-
zation. Almost by definition of the
term, a city involves large numbers of
people and large amounts of economic
resources, all located in close physical
proximity to one another and all en-
gaged in complex patterns of interac-
tion. Public sector decision making in
the urban context—if it is to be effec-
tive in accomplishing policy objectives
—must be characterized by as great an
understanding as possible of the com-
plex interactions between different ur-
ban variables. Urban policy makers
must be aware not only of the immedi-
ate effects of their decisions but of the
indirect effects as well. The urban
policy maker who authorizes the con-
struction of a new subway line, for in-
stance, must have as sound an under-
standing as possible not only of the
immediate effects of the line in speed-
ing travel for existing commuters, but
also of such indirect effects of the new
line as changed industrial location pat-
terns, changed job opportunities for
minority groups, changed tax revenues,
167
-------
APEX
URBAN DEVELOPMENT MODELS
Models Discussed in Chapter
Summary Table
Model
NBER
Retail
Market
Potential
Lowry and
PLUM
Urban
Dynamics
CLUG
RIVER
BASIN
General Type
Analytic,
Partial
Analytic,
Partial
Analytic,
Comprehensive
System
Dynamics,
Comprehensive
Simulation-
Gaming
Simulation-
Gaming
Important Characteristics
Combines empirical and theoretical approaches in a
dynamic model for housing.
Locates large retail trade centers using drawing power
for customers. Is intimately tied to a transportation model.
Industrial land use is input exogenously and housing and
retail locations are derived. Several levels of refinement
and sophistication.
Simulates growth or industry, residences, and population
within a fixed area over a very long time period (50-250
years) .
Players make locational decisions. Payoffs based on loca-
tion theory concepts for housing, retail and industry.
Players make locational and other decisions as economic,
social, and governmental decision makers. Computer
simulation of population movements and market opera-
tions for housing, retail and industry.
Simulation-
Gaming
Players make some of the locational decisions and com-
puter model simulates population movements, business
operations, and voting behavior for housing and industry,
and changed needs for other public
services, all of which may result from
his decision.
It is no accident, therefore, that ur-
ban model building has received a great
deal of attention in the past two dec-
ades. Modeling techniques, which allow
their user to analyze complex, simul-
taneous relationships, would appear to
be especially well-suited to dealing with
urban phenomena and indeed there has
been great interest recently in construct-
ing urban models and in using them
in policy analysis. Spurred both by in-
creased concern about urban problems
and by recent advances in modeling
techniques, researchers and policy ana-
lysts have constructed literally hundreds
of such models in the past two decades,
and many have been formally pub-
lished. They have sought to accomplish
a broad range of specific objectives,
from understanding the underlying de-
terminants of spatial location within the
city, to analyzing the causes of city
growth and decay, to predicting future
168
land uses in specific parts of urbar
areas. The models' developers have
come from a broad range of back
grounds in both the social and natura
sciences. This chapter will describi
some previous surveys of urban models
survey some of the most importan
advances which have been made ii
constructing urban models and sho\
how these models have been applied t
policy making.
The term "urban model" must b
denned with some care. Taken broadl;
it might well apply to a high propo
tion of all the models described m
only in this chapter but in this entii
report. Since the United States is
highly urbanized society, most polis
making in this country takes place
an urban environment. Hence, mat
of the models described in other cha
ters of the report are set in an urb;
context and deal with certain subse
tors of urban phenomena. For the pv
poses of this chapter, however, we sh
adopt a more narrow definition of i
-------
ban model. Specifically, we shall limit
our attention only to models which at-
tempt to describe land use—housing,
commercial and industrial—and urban
development processes within an entire
metropolitan area. Thus models of, for
instance, educational planning or crim-
inal justice which are not concerned
with urban development will not be
discussed. Not all of the models which
we shall consider deal in an equally
comprehensive way with all facets of
urban development. For reasons of
simplicity, certain subsectors of the
urban process are suppressed in some
of the models and emphasized in others.
//. SOME GENERAL THEMES IN
URBAN MODELING
A clear conception of the high de-
gree of complexity and interrelatedness
of activity in an urban area is crucially
important in understanding the form
in which various urban models have
been developed. In this section of the
paper we shall explicitly examine the
reasons for this complexity. Doing so
will allow us to better understand the
complexity itself, and it will also pro-
vide a convenient context for discuss-
ing certain elements of urban develop-
ment and urban policy making which
will be referred to in our later dis-
cussions of specific models. Four gen-
eral reasons for the great complexity
of urban systems will be discussed be-
low. They are (1) the large number
of relevant variables, (2) the large
number of policy parameters available
to the urban public decision maker,
(3) the fact that variables and param-
eters are highly intercorrelated, and
(4) the extremely long time horizon
'acing the urban decision maker.
Large Number of Variables
One of the reasons for the high de-
jree of complexity of urban phenomena
s the large number of relevant varia-
)les which must be included in any
•easonably complete discussion of ur-
ian development. Housing, commercial
ictivity, industrial activity, natural re-
sources, transportation, and public serv-
ices are just a few of the urban varia-
bles of interest to policy makers, and
these must be considered as they relate
to literally millions of people and thou-
sands of businesses.
Large Number of Policy Parameters
Another factor which contributes to
the complexity of the task facing the
urban model builder who seeks to con-
struct a model which is useful in policy
making is that, not only is there a large
number of key variables, but there are
also a large number of policy param-
eters and policy-making contexts in
which models may be useful.
At the local level, for instance, gov-
ernment officials make many different
kinds of decisions which impinge on
the urban development process. For
instance, zoning decisions determine
what kinds of economic activity will be
allowed to locate in various parts of the
urban area. Transportation planning—
both the choice between alternative
modes and the choice of specific loca-
tions, schedules, and prices within
modes—also provides wide scope for
local decision making. Poverty pro-
grams and programs aimed at aiding
disadvantaged minorities to obtain
greater economic opportunity also pro-
vide important policy questions for
local officials. Local decision makers
also deal with a broad range of local
housing programs including public
housing and the enforcement of build-
ing codes.
There is also a need for an under-
standing of the development process
and for the use of urban models at the
Federal level. Many of the local pro-
grams listed above, for instance, include
Federal participation and hence involve
Federal as well as local decision mak-
ers. Furthermore, there are many pro-
grams conducted principally at the
Federal level which seek to have an
impact largely in urban areas. Federal
housing subsidy programs are an ex-
ample of these. Another general policy
area where Federal policy makers must
be concerned with urban phenomena
169
-------
is the general revenue sharing program
which has recently been enacted. This
program was largely developed in re-
sponse to fiscal problems perceived by
governments in urban areas, and urban
models have been developed which at-
tempt to provide insight into the role
of local government finances in influ-
encing the urban development process.
Variables and Parameters Highly
Intercorrelated
Thus we have seen that urban sys-
tems are made complex by the existence
of both large numbers of key variables
and large numbers of policy parameters
in the urban context. A third element
in the complexity of the urban devel-
opment process is the fact that all of
the variables and policy parameters
are highly interconnected. Large num-
bers of variables and policy parameters
need not, in themselves, lead to a com-
plex system. If it were possible to sep-
arate them into largely separate sub-
sectors, the urban system could still be
modeled relatively simply. In fact,
however, all of the variables in the
system are highly related to one an-
other. For instance, a change in the
transportation system is likely to have
important impacts on housing and in-
dustrial location which in turn are
likely to affect the need for provision
of public services which in turn may
affect the ability of the government to
provide transportation services, etc. Or,
to take one more example, a public
housing program may affect the num-
ber of potential workers in a given part
of the city, which may influence in-
dustrial location, which may have an
impact on transportation planning,
which may have a further impact on
the location of poor people and on
public housing decisions, etc.
Long Time Horizon
Besides the large number of impor-
tant variables and parameters and their
interrelatedness, there is still one other
important factor which should be men-
tioned as contributing to the complexity
of the urban model builder's task. This
170
factor is the need for an extremely
long time horizon in making many ur-
ban policy decisions. This need arises
because of the extremely long-lived
nature of residential, industrial, and
other types of investment in cities. Most
structures last at least 50 years, and
some last for centuries. This means
that policy decisions made today will
have important and to some extent
irreversible impacts on development
processes for decades to come, and this
adds to the complexity of the model
builder's task because he must attempt
to construct a model which is relevant
in gaining insight into events happening
not only at the present time but many
years into the future.
Data Limitations
Summarizing, then, we have seen
that an important problem facing the
urban modeler is the complexity of the
relationships which he is attempting to
represent with his model. We shall see
below that many techniques used in
urban models can be best understood
as attempts to handle this problem of
complexity. Before discussing this, how-
ever, it will be useful to consider a
second general problem faced by the
urban model maker. This second prob-
lem is data limitations. Accurate in-
formation on many key variables in
the urban system are often simply not
available. For instance, except for de-
cennial years, very little information is
available concerning even such a basic
variable as the total population in a
given city. And even in decennial years
when the U, S. Census of Populatior
and Housing is undertaken, there ii
substantial evidence that the data col
lected is not highly reliable-—especially
in providing information about minority
groups. Similarly, detailed data con
cerning the nature of industrial activit
in a city is typically only available ii
the years when a U. S. Census of Man
ufacturing is conducted.
Furthermore, even when data is co
lected for a key variable in a city, it i
often not available in a usable torn
For instance, in many cities propert
-------
tax and deed transfer records provide
substantial amounts of data concern-
ing individual parcels of land. But this
data is often not assembled in such a
way as to provide systematic samples
which could be useful in research and
model building.
There are a number of important
reasons for the unavailability of data.
One of them is that most of the key
parameters for an urban model are
behavioral in nature. For instance, it
is crucial to have information about
such behavioral questions as what in-
fluences families' and firms' locational
decisions or what the demand for trips
on a new transport system will be. And
because these parameters are behavioral
rather than technological in nature,
their quantification is conceptually dif-
ficult and, in practice, imprecise.
Furthermore, in most cases data
gathering through experimentation is
prohibitively expensive. A natural sci-
entist attempting to model a chemical
reaction can gain data by repeatedly
undertaking and observing experiments
with the chemicals, but such a proce-
dure is clearly not possible with regard
lo gaining information about the re-
sults of a multimillion dollar transpor-
ation investment. For the most part
he urban modeler must rely on such
nformation as the accidents of history
Drovide him with. (As a qualification
o this, incidentally, it should be pointed
nit that there has been increased in-
erest in recent years in forms of social
;xperimentation. For instance, the U. S.
;overnment is currently undertaking
mportant experimental type programs
esting alternative forms of the nega-
ive income tax and alternative forms
if housing subsidies.)
Still another practical problem in as-
embling data which should be men-
oned results from the fact that there
re often many governmental jurisdic-
ons within an urban area, and these
ifferent jurisdictions are often not
snsistent in the way in which they
ather and present the data which they
jllect.
Objectives of Urban Models
We have seen, then, that both the
complexity of the urban system and
data limitations create difficulties for
urban modelers. In order to gain fur-
ther insight into the exact nature of
these difficulties and into the ways in
which model builders have sought to
overcome them, we must turn now to
a brief discussion of the various spe-
cific objectives of urban modelers. Of
course, the list of exact objectives is
as long as the list of urban models
themselves, but it is useful to distin-
guish four general kinds of objectives
which seem to characterize most of
the models which have been developed.
The four objectives which we shall
discuss are (1) prediction, (2) policy
analysis, (3) optimization, and (4)
gaining a better fundamental under-
standing of the nature of urban proc-
esses.
In principal, of course, a single model
could be developed which accomplished
all four of the above objectives. If one
could create a model which provided
a full representation of the urban de-
velopment process, it could be used for
prediction, it would contain within it
key policy parameters for policy analy-
sis, it would allow one to optimize any
given objective function, and it would
—by its basic structure—give insight
into the basic forces underlying ob-
served urban phenomena. Unfortu-
nately, for the reasons discussed above,
such an all-purpose model is probably
not feasible at the present time. Given
current limitations in modeling and
solution techniques, both the complex-
ity of urban phenomena and also prob-
lems concerning the available data make
it extremely difficult to construct one
single urban model which can com-
pletely satisfy all four of these objec-
tives. As a result of these difficulties,
therefore, the urban modeler is forced
to make compromises between the
various objectives and to adopt simpli-
fying techniques which will make his
task manageable, even at the price of
lost completeness. The simplifying
techniques chosen depend, of course,
171
-------
on the principal objectives which a
given model seeks to accomplish, and,
as an aid to understanding the indi-
vidual models to be discussed below,
it will be useful to examine a number
of general approaches which have been
used in attempting to simplify urban
models to the point where they can be
made manageable in the context of
present-day modeling techniques. Three
simplifying techniques will be consid-
ered: (1) aggregation, (2) supressing
certain sectors of activity in the model,
and (3) taking some sectors of ac-
tivity as exogenous.
Simplifying Techniques
One frequently-chosen simplifying
technique is aggregation. This can take
a number of forms. For example, many
models rely on what we shall call sec-
toral aggregation. Certain sectors of the
urban economy are simply aggregated
together. For instance all forms of in-
dustrial and commercial activity may
be treated as a single kind of activity.
Another form of aggregation may
be geographical aggregation. Instead of
treating each parcel of land or each
small area of a city as an individual
unit, modelers have often found it con-
venient to lump geographical subunits
together into larger groups. For in-
stance, all parcels of land in the urban
area may be divided into two groups,
those in the center city and those in
the suburbs. Or, in some cases, geo-
graphical distinctions may be ignored
entirely and land in the entire area may
be taken as spatially homogeneous.
A second general technique for sim-
plifying urban models is to entirely
suppress certain sectors of activity in
the model. For instance, in a model
concerned only with residential loca-
tion, the entire industrial sector may be
ignored. Or in a model concerned with
the economic interactions between
households and firms, the existence of
minority groups may be ignored.
Finally, a third technique for simpli-
fying models is to take some sectors
as exogenous. A model may, for in-
stance, include the spatial location of
172
firms but assume that the firms' loca-
tions are predetermined outside of the
context of the variables which are al-
lowed to vary in the model. Or, to take
another example, transportation prices
may be included in a model but their
magnitude and the location of alterna-
tive transport modes may be taken as
given and not allowed to vary.
So far, we have pointed out that
complete models of the entire complex-
ity of the urban development process
are very difficult to create given the
current state of the modeling art, and
we have discussed a number of tech-
niques used to simplify urban models
enough to make them manageable. We
shall now conclude these general re-
marks about urban modeling by at-
tempting to identify criteria by which
various urban models can be evaluated.
Evaluation Criteria
It is probably not appropriate to
judge models by their overall corre-
spondence to reality. Inevitably, any
model so evaluated will be found to
depart from reality in many ways. In-
deed the essence of modeling is ab-
stracting from some facets of reality
in order to focus attention on other
aspects. Hence more limited criteria
are necessary. In the following para-
graphs we shall identify four criteria
which can be useful in appraising anc
comparing urban models. These foui
criteria are (1) inclusion of key varia.
bles, (2) simplicity, (3) consistency
with theory, and (4) consistency wit!
data.
The first criterion is whether or no
the modeler has included all of tb
variables which are necessary to ac
complish the objectives of his mode
For instance a model which is to b
useful for making specific zoning dec
sions must include a good deal of gee
graphical detail. To engage in signif
cant geographical aggregation woul
defeat the model's purpose. On th
other hand, a model constructed
aid planning of financial aid to rt
cities by the Federal government mig
appropriately make use of a great de
-------
of geographical aggregation. Or, to take
another example of this criterion, a
model which was aimed at providing
a useful planning tool for local plan-
ners could perhaps take Federal hous-
ing policy as exogenous. But a model
which is to be used as a planning tool
by the Federal Department of Housing
and Urban Development must clearly
include Federal housing policy as a
variable policy parameter.
Simplicity provides a second cri-
terion with which to appraise urban
models. It is the very essence of model-
ing that it is often useful to focus at-
tention on key variables in a system
so that they can be understood ade-
quately, and, as emphasized in our
discussion of the first criterion above,
important variables certainly must be
included in a model. But it may often
be counterproductive to clutter a model
with a large number of variables which
are not crucial to the model's basic
purpose. Inclusion of these extraneous
variables may make the model so com-
plicated that the reader is unable to
gain any true understanding of the
basic relationships between the key
parameters in which he is interested.
A third criterion with which we shall
evaluate the models discussed below
is consistency with theory. Long tradi-
tions of research in a variety of dis-
ciplines including economics, political
science, and urban planning provide the
prospective urban model builder with
i variety of theoretical tools to help
lim with his task. In light of this, it
seems appropriate to examine the con-
sistency of models with theory. For
nstance, there is a rich theory in eco-
lomics which predicts that as the price
)f land goes up, all other things being
icld constant, families will react by
onsuming less land as part of their
lousing consumption. There is some
iresumption, therefore, that a model
/hich deals with these variables but
oes not include this relationship may
ot be an adequate representation of
eality. There may, of course, some-
mes be reasons for ignoring such a
nown theoretical relationship. For in-
stance, the modeler may have been
aware of the theory but may have de-
termined to his satisfaction that the
relationship was not sufficiently quan-
titatively important to warrant its in-
clusion in his model. But in appraising
urban models it is often useful to at
least investigate the degree to which
the model builder has taken account of
existing theory.
Finally, another criterion which can
be applied in evaluating urban models
is their consistency with data. To be
sure, data limitations such as those
discussed above may often make rig-
orous attempts to fit a model to data
impossible. And in any case, since all
models necessarily involve abstracting
from reality, perfect correspondence
between variables in the model and
real world data is not to be expected.
Nevertheless, it is reasonable and often
useful to ask whether or not the urban
model builder, in constructing his
model, has fully made use of whatever
empirical resources were available. For
a given model, at a given degree of ag-
gregation, as much consistency as possi-
ble with the available data would ap-
pear to be desirable.
This completes our general remarks
about urban modeling. We have dis-
cussed the basic variables which urban
models seek to include; we have con-
sidered a number of difficulties inher-
ent in urban model building; and we
have identified a number of partial
criteria with which urban models may
be evaluated.
///. MAJOR REVIEWS OF URBAN
DEVELOPMENT MODELS
Introduction
Many dollars have been spent an-
nually during the past two decades on
the design and testing of urban develop-
ment models. This relatively long his-
tory of modeling of urban growth and
change has generated a significant lit-
erature of reviews and surveys that this
chapter will not attempt to duplicate.
Instead, this section will describe some
of the past survey efforts so that the
173
-------
reader may gain an appreciation of the
scope of such activity and also so that
the reader will be informed as to trie
best sources for more detailed model
descriptions and comparisons.
Figure 1 shows a matrix consisting of
twelve rows (selected model surveys)
and 21 columns (selected urban de-
velopment models). An "X" in the
matrix indicates that the survey dealt
with the corresponding urban model.
The model surveys are listed in chron-
ological order, but it must be borne in
mind that the dates attached to the
models refer to dates on which pub-
lished material was available. These
model dates may actually have pre-
ceded or followed the actual imple-
mentation of the models.
Before briefly discussing each survey,
it might be useful to state the type of
impetus behind each survey: "pre-
model requirement" or "academic." Al-
most half of the surveys were required
as an initial step to a new (or con-
templated) urban modeling effort. The
Traffic Research Corporation survey
preceded the development of the EM-
PIRIC model in Boston. The Donald
Lamb effort was prepared for the South-
western Pennsylvania Regional Plan-
ning Commission prior to a model con-
struction effort there. Douglass Lee
prepared his survey for the Cornell
Aeronautical Laboratory and expanded
upon it to produce a dissertation. Thus
a joint commercial-academic product
was achieved. The National Bureau
of Standards conducted its survey on
behalf of the Model Cities office of the
Department of Housing and Urban
Development. The purpose was to de-
termine the applicability of decision-
making models for the Model Cities
programs at the city level. The Nagel-
berg and Little survey was conducted
as part of the Institute for the Future's
plan to develop an urban research
laboratory.
The other surveys were stimulated
mostly by academic forces. The May
issue of the American Institute of
Planners journal in 1965 was devoted
entirely to articles dealing with urban
development models. The journal pro-
vided this special issue for the educa-
tional benefit of its readers who are
professional planners concerned with
the urban development process. Ira
Lowry prepared his classic article for
original presentation at the June 1967
Conference on Urban Development
Models conducted by the Highway Re-
search Board. Britton Harris prepared
his paper for original presentation at
the Resources for the Future sponsored
Conference on Urban Economics in
1967.
The book by Kilbridge et al. evolved
out of the Urban Analysis Project
sponsored by the Harvard Graduate
School of Business during 1967-1969.
The paper by George Hemmens was
presented at a computer simulation
techniques seminar series at George
Washington University in 1970. The
book edited by David Sweet grew out
of a Models of Urban Structure Confer-
ence sponsored jointly by Battelle of
Columbus and Ohio State University.
The review article by Goldstein and
Moses appeared in the June 1973 vol-
ume of the Journal of Economic Lit-
erature. It is one of the few surveys
on urban models prepared by econo-
mists for economists.
The 12 surveys selected for brie
comment in this chapter are not ex-
haustive but they are representative o
the range of surveys made over th(
past decade. These twelve surveys an
described briefly in the following sec
tion and then reference is made t<
several European surveys that describ
urban development modeling abroad.
Twelve Selected Surveys
The Traffic Research Corporation
Survey
This survey conducted in 1963 ha
very few urban models to describ
since not many had been operated fc
specific geographic locations at thi
early date. Three of the four open
tional models listed by the TRC ai
found in the matrix in Figure 1. It
interesting to note that traces ^i the;
three models can be found in the EJc
174
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PIRIC model that eventually evolved
out of the TRC (now Peat, Marwick
and Mitchell) effort. The TRC survey
described five research-oriented tech-
niques and five conceptual techniques
in addition to the four operational ur-
ban development models. A brief evalu-
ation and critique followed a descrip-
tion of the fourteen land use forecasting
techniques contained in the survey.
The AlP Special Issue
In 1959, and again in 1965, the en-
tire May issue of the Journal of the
American Institute of Planners was de-
voted to urban models. The 1959 issue
appeared too early to describe any of
the urban models contained in the
matrix. The 1965 issue contained an
introduction and short glossary of terms
by Britton Harris, the guest editor of
the issue. In addition to articles by the
designers of seven of the models listed
in Figure 1, there was a future-oriented
article by Bill Garrison describing what
urban transportation planning models
might look like ten years later. The
major breakthrough expected by Garri-
son was in data handling and analysis.
Another excellent article in this AIP
issue was the one by Ira Lowry entitled
"A Short Course in Model Design."
In this concise review article, Lowry
discusses the uses of models (descrip-
tive, predictive and planning), levels of
aggregation, handling of time, con-
cepts of change (distinction between
stocks and flows), solution methods
(analytic, iterative, machine simulation,
and man-machine simulation), fitting
or calibrating the model (variables and
parameters), and testing the model
(sensitivity and performance). Since a
good portion of the literature with
respect to urban models has applica-
bility and relevance to other functional
areas of modeling, this article by Lowry
is a good example of a prototype arti-
cle that could be adapted to other fields
of modeling.
Donald Lamb Survey
Donald Lamb produced an informa-
tive review of existing land use models
as a preliminary step in the develop-
176
ment of a model for the Southwestern
Pennsylvania Regional Planning Com-
mission. His most telling criticism was
that none of the ten major models he
investigated were "concerned with the
validity of the projected change in the
regional level." That is, all of the mod-
els that he reviewed allocated growth
that had been forecast exogenously by
some technique or process independent
of the models themselves. This criti-
cism still applies to most urban develop-
ment models.
More carefully than in most reviews,
Lamb concentrated on answering the
question: "How does the model work?"
and "What does it mean analytically?"
Lamb defined his terms carefully, pre-
sented clear and helpful examples of
mathematical techniques (trend models
and logic models), and provided a
general framework for reviewing the
ten models in his survey. For each
model, Lamb provided a general de-
scription, presented its characteristics
(including equations) and data require-
ments and showed the operational se-
quence.
Douglass Lee Survey
The research report by Douglass
Lee (1968) entitled "Models and Tech-
niques for Urban Planning" brought
together some of the best description
material on urban models, synthesized
it, added to it, and thereby resulted in
the single most useful secondary source
of urban model information.
Lee discussed some of the dimensions
of modeling (comprehensiveness, dis-
aggregation, treatment of time, abstrac-
tion, and descriptive-behavioral-norma-
tive) that Britton Harris elaboratec
upon more thoroughly elsewhere (Har
ris, 1968). He summarized the para
digm developed by Ira Lowry (1967)
and abstracted the other urban mode
typologies developed by Steger (1965)
Traffic Research Corporation (1963)
Donald Lamb (1967) and Kilbridg
etal. (1968).
Lee also discussed the theories (sue
as the general equilibrium theory ani
the gravity model), methods (Simula
tion, social accounting, and econometri
-------
modeling), and techniques (such as
input-output, mathematical program-
ming and mathematics). As part of his
chapter on model construction, Lee
clarified the distinction among compo-
nents, variables (exogenous and endog-
enous) and relationships (functions
and parameters). This chapter con-
centrated heavily on the substantial
data demands of urban models and the
importance of model objectives.
The Lowry Paradigm and Survey
Ira Lowry developed an urban land
market paradigm that is a very useful
way of looking at how urban models
usually emphasized either the use to
which a piece of land is put or the
allocation of a particular activity to a
spatial location in the metropolitan
area. These two actions might appear
o be identical but Lowry showed the
subtle differences and used the para-
Jigm to characterize the seven urban
nodels he surveyed. This paper by
^owry is a classic in the field of urban
nodeling and can provide the reader
vith insights not easily gained in any
>ther way. The seven types of models
escribed by Lowry are (1) land use
CATS), (2) land use succession (land
ise over time-UNC model), (3) loca-
ion (EMPIRIC), (4) migration (lo-
ation over time-Polimetric), (5) hy-
rid (his own Lowry Model), (6)
larket demand (Penn-Jersey Model),
nd (7) market supply (the San Fran-
isco Model).
Harris Paper
Like Lee and Lowry, Harris presents
ore than a survey of urban models.
ather than dealing with the many
odel issues discussed by Lee or
opting some paradigm approach as
nployed by Lowry, Harris concen-
ited his attention on six fundamental
mensions of (urban) models:
1. Descriptive vs. Analytic
2. Holistic vs. Partial
3. Macro vs. Micro
4. Static vs. Dynamic
5. Deterministic vs. Probabilistic
6. Simultaneous vs. Sequential
He then went on to show how these
dimensions have been applied in the
case of retail location models, residen-
tial location, manufacturing location,
and the location of other types of land
uses (such as transportation facilities,
open space, office space, etc.). This
article by Harris is quoted often in the
urban modeling literature and his di-
mension scheme has been used in other
types of modeling as well.
Book by Kilbridge el. al.
This book devoted only three of its
eleven chapters to previously built ur-
ban models, and two of these three
were devoted almost exclusively to the
abstraction, verification, validation, and
application of the TOMM model. The
remaining chapters dealt with subjects
such as the role of models in urban
planning, population density concepts
and measures, and economic models for
housing analysis.
The opening chapter classified 20
well known models according to subject
(land use. population, transportation.
and economic activity), function (pro-
jection, allocation and deviation), the-
ory (behavioral, gravity, trend, and
input-output), and method (economet-
ric, mathematical programming and
simulation). This classification frame-
work is nice and neat but the simplifi-
cation necessary to categorize a com-
plete model according to such a rigid
structure has its pitfalls.
Hemmens Seminar Paper
In 1970, George Hemmens, who
edited the Highway Research Board's
special entitled "Urban Development
Models," made some observations about
the state of urban development model-
ing. To him, the models make land use
highly dependent upon accessibility (il-
lustrating the problem of making this
chapter independent of the chapter on
Transportation Models), deal with
highly integrated socio-economic group-
ings of households, and are based on
cross-sectional data (rather than time
series data). He feels that to a large
extent the meager use of and loss of
enthusiasm for some of these models
177
-------
is due to the fact that the formulation
of the urban development problem has
changed—away from planning metro-
politan areas or cohesive functional
units and toward solving problems peo-
ple have with housing, employment,
discrimination, etc. Hemmens thinks
the framework within which future
models are developed and used will
be more important than better data
and more sophisticated techniques.
National Bureau of Standards Survey
Some urban model surveys have been
performed for special types of users
and have employed specific and diffi-
cult-to-satisfy selection criteria. An ex-
ample of this type of survey is the
one prepared for the HUD Model Cit-
ies program by the Institute for Crea-
tive Studies and the Technical Analysis
Division of the National Bureau of
Standards. Using subjective "ideal
model" criteria of: comprehensiveness,
high disaggregation, short-run time
frame, analytic (i.e., behavioral), pre-
dictive, easy to use, and operational, it
is little wonder that the study found
no acceptable urban model. Yet the
study recommended the use of a model
(despite known deficiencies) for Model
Cities evaluation purposes because of
(1) the assistance it could provide in
the evaluation process, (2) the or-
ganization the model would bring to
data collection activities, and (3) the
educational role the model could play
with local citizens and officials.
For Model Cities purposes the study
concluded that the conventional urban
spatial models and urban input-output
models are less fruitful starting points
than the approaches suggested by urban
dynamics models, urban gaming models,
and aggregated impact models.
Nagelberg and Little Survey
This survey recognized three basic
types of urban models: computer simu-
lations, games, and gaming simulations.
For the nineteen models covered in this
survey, the authors attempted to con-
trast the models with respect to pur-
pose, uses, costs of development, major
assumptions, numbers and types of
178
parameters, computer requirements, etc.
For many of the models, inadequate
information makes it difficult to actu-
ally make cross-model comparisons. An
interesting effort was made to provide
a geneology of the urban simulation
models, but inaccuracies made the ef-
fort less than a full success.
Sweet Book
This edited work contains an inter-
esting survey article by Leslie King, the
1960 residential model description by
John Herbert and Benjamin Stevens,
the SEWRPC model description by
Kenneth Schlager, a description of a
land use allocation model applied to
Franklin County, Ohio by William
Habig. Other chapters of the book are
devoted to new concepts in urban-
structure models.
An appendix of this book shows the
results of a survey on computer utiliza-
tion and model development by metro-
politan planning agencies. A 40% re-
sponse from 226 agencies surveyec
yielded the finding that only 51 of the
91 responding agencies were using 01
planned to use computers. Only 26 o
these 51 agencies were currently usinj
urban development models (17 fo
transportation and 9 for land use). Onb
8 of these agencies originally develope<
the model they were using. Most of thi
respondents did advocate the develop
ment of additional urban models tha
would (1) provide better forecasts, (2) b
cheaper to run, and (3) quantify th
impacts of proposed land use change1.
They favored urban development moc
els that could use existing data files.
Goldstein and Moses Review Article
This recent economics-oriented su
vey of urban growth, land use, an
market process models is notewortl
for its fine treatment of the theoretic
models of Mills (1972) and Muth (1965
its comparison of the comparative st
tistics approach (Lowry, 1965) and t
dynamic approach (NBER, 1969) ai
its very comprehensive (438 items) 1
of references.
Goldstein and Moses review vario
theoretical models of urban process
-------
at greater length than is possible in this
chapter. The reader is referred to their
work.
To give a rough idea of the magni-
tude of previous efforts with regard to
urban modeling, the Regional Environ-
mental Systems Analysis Program at the
Oak Ridge National Laboratory has
collected 5000 abstracts of literature on
the development and use of "mathematic
models capable of simulating the eco-
nomic, demographic, societal, ecologi-
cal, and land-use responses of a geo-
graphical regional to alternative policy
decisions" (Myers, 1973).
European Surveys
Michael Batty (1970) from the Geog-
raphy Department at the University of
Reading has provided one of the best
reviews of land use modeling in Britain.
Most of the European models have
been derivatives of Lowry's Model of
Metropolis (1964). A. G. Wilson (1969)
of the Center for Environmental Studies
las added residential complexity to the
^owry scheme. Batty (1970b) himself
las applied a modified Lowry model to
he Nottinghamshire-Derbyshire subre-
>ion and to the Central Lancashire sub-
•egion (Batty, 1970c). These two plus
hree other applications of the modified
^owry are dealt with in some detail by
iatty in this excellent survey.
William Goldner (1971) at the Uni-
rersity of California at Berkeley re-
iewed the foreign applications of the
,owry model derivatives and contrasted
lese to the meager applications of the
,owry model in the U.S. Goldner dis-
usses the application by Cripps and
oote (1969) in Bedfore County, Eche-
ique et al. (1969) in Reading and
evenage, Music and Barber (1970) in
'ubljana, Yugoslavia, and the two ap-
ications by Batty mentioned above.
What is clear from both Batty and
oldner is that only the Lowry Model
srivatives, and to a lesser degree the
ikshmanan-Hansen model, of all the
.S. developed land use models, have
und much use abroad, and most of
is use has been in Britain.
IV. SELECTED URBAN
DEVELOPMENT MODELS
From the preceding review, it is ap-
parent that urban development models
were a growth industry particularly in
the 1960's. Quite a number of models
that vary in theme, policy scope, theo-
retical structure and empirical content
emerged in this era.
These urban development models
essentially allocate elements of urban
growth (firms, economic activities,
people) to geographical subunits of a
metropolis. However, they differ in the
criteria used for such allocations. Some
models are guided by past patterns of
development in the urban region; some
utilize microeconomic behavioral no-
tions of location; others formulate opti-
mization rules; still other models seem
to rely on what may be described as
intuitively attractive ad hoc proposi-
tions.
Some of the models describe only
one major sector of urban growth; for
example, the residential sector (Hansen
1959, Herbert and Stevens 1960, Don-
nelly, Chapin 1965, A. D. Little 1966,
NBER 1972) or the retail sector
(Lakshmanan and Hansen 1965, Berry
1965) or the industrial sector (Putman
1967, Goldberg 1967, Seidman 1969,
Rose 1967). Such models dealing with
one sector can be described as partial
models (Batty 1970a) that may form
components or submodels of general or
comprehensive models.
General or comprehensive models
deal with the broader range of urban
activities than one sector (Lowry 1964,
Hill 1965, Seidman 1964, Lakshmanan
1968, Forrester 1969).
Further, the models evidence a variety
of theoretical approaches. Some formu-
late other models using microeconomic
notions of decision making in the urban
land making (Herbert Stevens, NBER,
Chapin). Some build upon probabilistic
notions of interaction (Lakshmanan and
Hansen) or intervening opportunity
models (Lathrop and Hamburg, 1965).
Some use gaming-simulation approaches
(Feldt 1972, U.S. EPA 1972a and b).
179
-------
Others use optimizing models of loca-
tion (Schlager 1965).
In this chapter we present a selective
illustration of the dominant themes and
trends in urban development modeling.
We begin by recognizing at least two
broad groups of models.
One group of models representing the
highest level of abstraction is the set
of mathematical models that describe
urban development in analytical terms.
These analytical models use a variety
of mathematical models—sets of simul-
taneous equations, linear programming
formulations, differential equations and
so on. Most urban models are of this
analytical variety. We shall further
classify them into subgroups—partial
and general or comprehensive models.
Another broad class of models is
simulation-gaming. A simulation-gaming
model essentially is a game defining the
nature of interactions between players
assuming various decision roles and a
simulation model that analytically trans-
lates the consequences of the gaming
choices. Generally speaking, the players
set out certain decision roles guided by
a set of rules, and their output is trans-
lated in the simulation phase into con-
ditions that describe the outcomes at
the end of play of the game. These
conditions set the stage for the next
play. A number of these gaming-simula-
tion models have been built largely in
response to a perceived need for train-
ing and teaching. The educational ob-
jective of this class of models is, in fact,
their dominant objective.
From the above discussion we can
classify urban models as follows:
1. Analytical Models—partial
These are mathematical models
that deal with one sector of urban
development such as residential or
commercial.
2. Analytical Models—general or
comprehensive
These are mathematical models
that describe two or more sectors
of urban activities.
3. Simulation-Gaming Models.
Using this classification, Table 1
lists the models that are reviewed next
Table 1. Models by Class Discussed in This Chapter
Class of Model and Name
Brief Description
A. Analytical Models
Partial
Residential Sector (NBER Model)
Retail Sector (The Retail Market
Potential Model)
Comprehensive
Lowry Model and its derivatives
(TOMM, PLUM, Batty)
Urban Dynamics Model
B. Simulation-Gaming Models
Community Land Use Game
(CLUG)
RIVER BASIN MODEL
APEX
A dynamic economic model of the housing marke
An operational model of retail shopping activity.
A model that describes the location of iesidenc<
and nonbasic employment—several prototypes t
the Lowry Model development.
A model of long run growth processes.
Relatively simple table game—closely tied to ec
nomic location theory.
Players represent economic, social, and govei
mental decision makers. Uses the computer £
tensively to simulate migration, housing, empk
ment, transportation, shopping and time alloc
tion activities.
Players represent major political and industi
decision makers in an actual urban area (Li
sing, Michigan). Computer simulations of n
industrial growth, housing occupancy, votii
and pollution impacts.
180
-------
Partial Analytic Models
NBER Model—The Residential
Sector
Models of residential development
have attracted greater research than any
other type. From the early work of
Walter Hansen in Washington, D. C.
and that of Herbert and Stevens for
Philadelphia to the current efforts. A
number of residential development
models have been developed either as
partial or submodels of comprehensive
models. One of the more ambitious of
these models that incorporates some
features of the Herbert and Stevens
model is an ongoing effort at the Na-
tional Bureau of Economic Research
(Ingram, Kain and Ginn, 1972). The
NBER model is an ongoing effort devel-
oping various prototypes such as DE-
TROIT, PITTSBURGH I and II. Ex-
cept where explicitly noted, however,
the model described here will be the
one in the Ingram, et al. book (1972).
The National Bureau of Economic
Research model—more than any of the
other models surveyed in this chapter—
bcuses specifically on the housing mar-
cet and describes that market in con-
siderable detail. The location of employ-
ment in both local service and export
industries is taken as exogenous, and the
principal variables determined within
the model are the spatial distribution of
households throughout the urban area
and the types and prices of housing
which they consume. The model is a
short run dynamic simulation model
which starts with a given allocation of
households and housing units at a start-
ing period, takes demographic and in-
dustrial changes as exogenous, and
models the resulting changes in the loca-
tion and housing of families over time.
The model carefully distinguishes be-
tween the demand side and the supply
side of the housing market and portrays
the way in which both sides respond to
prices (see Figure 2). Hence, it will be
convenient to describe the model by
beginning with the demand side, then
discussing the supply side, and then
describing the process by which prices
are set.
In any given period, the model takes
as given the allocation of households to
housing which was made in the previous
period. The active participants on the
demand side of the model in the new
period, then, consist of those families
which move during the period either as
Start with last period's
families
Determine active participants
in housing market
Allocate families to types of
residences
\llocate families to available
inits
Start with last period's
housing stack
Determine changes in
existing units (depreciation,
conversion, maintenance,
etc. )
Determine new construction
Determine prices on the basis
of previous years' prices and
of current period interaction
of supply and demand sectors
FIGURE 2—National Bureau of Economic Research Model Processes
181
-------
a result of new household formation,
migration into the city, changes in stage
in life cycle or changes in employment.
These families are divided into different
family types on the basis of income,
family size, age of head, and place of
employment of head. The model must
allocate the families among 27 different
possible types of dwelling units and also
among the 44 different geographical
residence zones in the city. For instance,
one class of families consists of those
who have less than $10,000 of income,
which have 3 or 4 persons, and which
have a family head less than 30 years
old who works in a specific area. The
model must allocate families in this class
to housing types (e.g. single family-large
lot-high quality or duplex-row, or apart-
ment-small structure-low quality, etc.)
in different residential areas. This allo-
cation is done as a two-step process.
First the families are allocated to one
of the 27 housing types on the basis of
demand equations which are a function
of the prices of the different kinds of
housing. Then, having allocated the
families to specific housing types, the
model allocates the families to available
housing units of these types in different
parts of the city using a linear pro-
gramming algorithm which minimizes
the sum of families'' transport costs.
Thus the demand sector of the model
takes housing supply and prices as
given and allocates families on the basis
of prices and of family commuting
costs.
The supply side of the model is based
on the assumption of profit maximizing
behavior in the housing industry. There
are a number of basic decisions which
housing suppliers must make. They
must decide whether to build new build-
ings, whether to convert buildings from
one use to another, and how much
maintenance expenditure to devote to
existing buildings. These decisions are
made in the model on the basis of ex-
pected profitability. Essentially, the sup-
ply side of the model takes as given the
prices for different kinds of housing
units and the costs of alternative invest-
ment decisions—i.e., new buildings,
182
conversion of buildings, etc.—and then
selects investment projects which will
be profitable. This selection is done
subject to a number of constraints in-
cluding both zoning laws and also limits
in the amount of inputs available for
housing construction in any given time
period.
Thus both the demand side and the
supply side of the model use prices as
inputs in allocating families to housing
and in generating housing investment
decisions. The final step in describing
the structure of the model is therefore
to discuss how the prices themselves are
determined. Essentially, prices are cal-
culated using the "duals" from the
linear program which was used to allo-
cate families to different residential
zones. This is a somewhat sophisticated
technique and requires careful elabora-
tion. As was described above, the de-
mand sector of the model after it assignr
families to specific housing types, uses
linear programming techniques to allo-
cate the families to different residentia
zones in such a way as to minimizs
commuting costs. It is a feature of linea
programming techniques that they gen
erate a set of values, often callec
'duals," which—in the present case-
can be interpreted as indicating th
travel cost savings which would hav
resulted from having one additions
dwelling unit of each type in each res
dential zone. For instance, one of th
dual variables can be used to estima
the commuting cost savings which wou
have resulted in having—say—one exti
duplex-row type dwelling unit in
specific area. This, then, can be inte
preted as the amount of extra mont
which a family would have been willir
to pay for such a unit in that locatic
in addition to what it actually paid f
the dwelling unit that it was actua
assigned to. And these values, in tut
can be converted into a set of relati
single-period housing prices for differe
housing types in different locations. T
prices actually used as inputs in t
supply and demand parts of the mo<
are expected prices based on weigh
-------
averages of single-period prices for
previous periods.
This completes our basic description
of the structure of the model. The
model is basically a short run, dynamic
model. It computes the value of its
variables in a given period not on the
basis of a set of long term equilibrium
conditions but rather on the basis of the
variables' values in the previous period
and of simulated short run decision
making by demanders and suppliers in
the market.
While the creators of the model are
careful to point out that they have not
modeled a particular city, e.g. Detroit,
in any literal sense, the parameters of
many of the equations for the model—
particularly on the demand side—are
estimated using econometric analysis of
iata from the Detroit region. Detroit
lata is also used to generate initial
'alues for the variables in the model.
Appraisal
Rather than creating a tool for pre-
icting detailed land use patterns in
pecific geographical areas of the city,
ic authors of the NBER model are
lore concerned with creating a model
'hich will shed light on the underlying
ynamic forces shaping the structure of
le city and which will also be useful
i analyzing the effects of alternative
Dvernment policies, particularly those
feeling housing markets. They empha-
ze in their report, however, that their
:search is far from completed and that
ie present model is to be taken more as
progress report rather than as the
•esentation of a final version of work
lich achieves these objectives. Never-
eless, it may be of interest to discuss
eir progress so far, as represented by
2 current model, in light of the eval-
tory criteria outlined earlier in this
apter.
As we have noted before, the model
^resents an explicit attempt to incor-
rate more economic theory than that
ibodied in the typical empirical model
ille at the same time retaining more
)graphical disaggregation and more
•eful attention to calibration with
data than the theoretical models such as
those of Muth or Mills. Hence, we
shall examine the model with regard
both to its theoretical and empirical
content.
It is clear that the model does in fact
go far beyond most of the empirical
land use models with regard to the
degree to which it embodies theoretical
relationships. In particular, the explicit
modeling of market behavior and prices
on both the demand and supply sides of
the market is an interesting contribu-
tion. It should be pointed out, however,
that the necessity of keeping the model
computationally feasible has forced a
number of compromises with theoretical
consistency. For instance, as we have
described, the model represents families'
housing choice behavior as two distinct,
sequential steps: first the family chooses
a type of dwelling unit; then it chooses
a specific residential area. In theory and
fact, of course, these two decisions are
made simultaneously. Another example
of compromise with pure theory occurs
on the supply side of the model where
the algorithm which the model uses to
select profitable housing investments is
only an approximation to the theoreti-
cally-expected profit maximization be-
havior.
With regard to calibration with data,
the creators of the model have had
mixed success, also. Data limitations
have prevented serious attempts to sta-
tistically estimate the parameters of
many of the equations on the supply
side of the model. Substantially more
effort has been devoted to econometri-
cally estimating parameters of equations
on the demand side. But that there are
difficulties in this work is indicated by
the fact that many of the equations
which they estimate do not show a
statistically significant relationship be-
tween the amount of a given type of
housing demanded and its price.
It should also be pointed out that the
current version of the model leaves out
a number of key relationships which any
complete model of even residential loca-
tion must take into account. For in-
stance, as we have seen, all employment
183
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is taken as completely exogenous. Also
the effects of race and externalities be-
tween different types of residential land
use are not included in the model.
In summary, then, the model clearly
represents an interesting attempt to
combine some of the best features of
previous models, but—as its authors
themselves are careful to point out—in
its current version it is clearly not suffi-
ciently well-developed for use with any
degree of confidence in policy analysis.
The Market Potential Model—The
Retail Sector
The retail market potential model was
developed to describe the sales of each
of a set of large shopping centers in
Baltimore. This model is descended
from an earlier one (Lakshmanan, 1965)
and builds on the probabilistic notions
of shopping spatial interaction (Huff,
1962).
The model states that the size and
the number of retail establishments in
an area is a function of consumer
shopping expenditures accessible to that
area. The retail center in zone j attracts
consumer dollars (from consumers in
zone c):
• in direct proportion to the con-
sumer expenditures
• in direct proportion to its size
• in inverse proportion to distance to
consumers, and
• in inverse proportion to competi-
tion
The total sales at the shopping center
in zone j is the sum of all consumer
dollars attracted in this manner from
all zones where consumers live.
A simple econometric model relates
consumer expenditures for shopping
goods as a function of family income.
The use of this model and data on
zonal population and family income
generated the consumer shopping ex-
penditures by zone. The size of the
shopping center was measured by floor
space of the shopping center.
Appraisal
The market potential model was uti-
lized to generate annual sales of shop-
184
ping centers in the Baltimore Region.
Sales estimated by the model of a few
large shopping centers were within 5%
of the actual sales at these centers as
obtained from the sales tax records. A
more general assessment of the model
was carried out by using it to estimate
shopping trips from residential zones to
shopping centers and verifying these
against origin-destination survey data.
The model's ability to predict shopping
interactions in this fashion was note-
worthy.
The model was used to locate a se
of shopping centers in the future tha
balanced their profitability against th<
need to maximize consumer access tc
them.
The data required to develop and ap
ply this model are generally available ii
most transportation studies. The latte
generate data on population and famil
income by subarea. The factor the
describes the spatial attenuation of shof
ping interaction from a center can b
derived from the shopping trip distribi
tion data via a gravity model. In th
sense, this model can be implements
with the data available in transportatic
studies.
This model utilized probabilistic m
tions of consumer spatial behavii
rather than explicit notions of mark
processes. It is possible to view t
gravity type model as a shortcut way
capturing the outcome of the explii
market processes.
Another aspect of this model is t
rather simplistic representation of t
attractive power of a shopping cent'
Size is only one measure; the compc
tion and order of shopping goods a
their "image" to consumers are ot
dimensions of the attractiveness. S
of the shopping center may be, to so:
degree, correlated with these dim
sions, but there is definite ground
refinement here.
There are quite a few versions of
model that have been developed
Britain and elsewhere. McLoughlin,
and Foot (1966) used this model
estimate the impact of a large shopp
center on other shopping centers
-------
northwest England. These authors modi-
fied the variable that represents the
attractiveness of the shopping center
(size or floor space in the Baltimore
Model). They developed and used a
functional index complied from data
measuring the variety of retail stores in
each center.
Two other variations of the model
are documented for Oxford (Black,
1966) and Lewisham (Rhodes and
Whitaker, 1967). The major modifica-
tions in these applications were to the
attractiveness variable.
Comprehensive Analytical Models
The Lowry Model
In this section we shall present in
detail the model by Ira Lowry (1964).
Lowry's model is appropriate for our
discussion here because it illustrates a
number of important strengths and
weaknesses which characterize most of
the empirical land use models discussed
in the surveys reviewed in Section III of
his chapter. Although only Lowry's
model will be discussed in detail in this
section, various derivatives of this gen-
2ral type such as the Projective Land
Jse Model (PLUM) of the San Fran-
:isco region, will be mentioned briefly
n order to illustrate some recent de-
/elopments of this general area of urban
nodel building.
Lowry's model is calibrated to data
•ollected in the Pittsburgh metropolitan
rea. He divides the Pittsburgh metrop-
ilis into separate geographical districts
ach with an area of approximately one
quare mile. The model distinguishes
>etween two kinds of employers: export
idustries which produce goods and
srvices sold outside of the metropolitan
rea, and local service industries which
reduce goods and services consumed
>cally. The export sector is further
isaggregated into several major indus-
•ies, while the local service sector is
isaggregated into three different kinds
local service clusters depending on
te market area served by each kind of
uster (e.g. one category—"neighbor-
jod facilities"—needs only a relatively
nail number of customers to operate
efficiently, while the other categories—
"local facilities" and metropolitan facili-
ties"—need progressively greater mar-
ket sizes per cluster.
The model takes the location and
amounts of employment in the export
sector industries as exogenous and seeks
to allocate local service and residential
activity to each of the small districts in
the urban area. The procedure for do-
ing this is an iterative one and proceeds
as follows (see also Figure 3): As indi-
cated above, the model starts with the
exogenously-determined export industry
employment levels in each district. The
next step is to allocate export industry
workers from each of the districts to
residences. Essentially this is done using
what is referred to in the transportation
chapter of this book as a "gravity
model"—workers who are employed in
one region are allocated to residences
in other regions on the basis of the
accessibility (in Lowry's model, princi-
pally just distance) between the two dis-
tricts. The exact parameters of the allo-
cation formula are determined using
Pittsburgh data. For instance, if the data
showed that in the Pittsburgh region
approximately 15% of managerial
workers lived in districts which were
two miles distant from their place of
work, then the model would allocate
15% of such workers in any given dis-
trict to residences in districts two miles
away.
So far, then, we have seen how the
model makes an initial allocation of
export workers' residences. The next
step is to bring in the local service sec-
tor. This step begins by estimating the
market potential for each of the types
of local service industry in each of the
districts. This too is done with what is
essentially a gravity model. The number
of residents of district "i" who will shop
in district "j" is assumed to be an in-
verse function of the distance between
the two districts where, again, the
parameters of the function are deter-
mined by the available data. After this
is done, for each j, the total number of
shoppers coming to district j to shop
is computed by adding up the number
185
-------
Start with exogenously-given
export industry employment levels.
Use gravity model to allocate export
industry workers to residences.
Estimate levels of local service
sector demand.
Allocate local service industry
workers to residences.
2-estimate local service demand.
Check to see if last step
significantly changed local service
demand and to see if local
constraints are violated.
If so, iterate again
on allocation of local
service workers to
residences.
If not, solution
is complete.
FIGURE 3—Steps in Solving Lowry Model
coming from each district (including j
itself). Finally, in order to get total
market potential in district j, the num-
ber of shoppers just computed is added
to an estimate of the number of shop-
ping trips generated by people who
work in district j on the theory that
workers may make short trips from their
work place to purchase local services.
The market potential generated by
workers of a given type is simply taken
as proportional to the total numbers of
such workers in the region.
After market potential in each dis-
trict is estimated, local service employ-
ment is allocated to each district in pro-
portion to the market potential, except
that for each type of local service in-
dustry a minimum size constraint is
imposed. If the market potential in
given district is not at least as great a
the minimum size constraint, no low
service employment is created in tha
district, and shoppers are sent to nearb
districts. (This minimum size constrair
is necessary, of course, to simulat
economies of scale in some way—witi
out it there would be some fraction c
a major hospital, for. instance, in ever
small district.)
The allocation of local service err
ployment, then, adds more workers t
each district, and these are allocated t
residences in the various neighborin
districts on the basis of the same gravi
model used to allocate export sectc
workers to residences. The addition c
more workers and more residences
186
-------
the model however, changes the previ-
ously computed local service industry
market potential and hence requires
more local services in each district.
Therefore the model proceeds by iterat-
ing again on the previous procedure.
Specifically, new local service market
potentials are determined on the basis
of the initial allocation of local service
employment, and these market poten-
tials are used to create a new allocation
of local service employment, and a new
allocation of residences for local service
workers. This leads to yet a third esti-
mate of market potentials, and the
model thus proceeds iteratively until it
converges on a stable solution where
the computed values of market poten-
tials do not change significantly between
iterations.
Additional constraints are also put on
the model to ensure that the total
amount of activity allocated to a district
does not exceed the capacity of useable
and in the district. Specifically, the
model uses data from the Pittsburgh
area to determine the number of square
'eet of land needed per worker em-
ployed in each of the types of industry.
Then land is allocated to each industry
n each district on the basis of this data
tnd the remaining land is allocated to
•esidences as a residual. However, two
:onstraints are imposed in this process.
3ne is that total land used for export
md local service industries cannot ex-
eed total land available in a district,
nd the second is that the density of
esidences per square foot of land in a
istrict must be below a maximum value
st by the model on the basis of existing
jsidential densities in the Pittsburgh
3gion. If either of these constraints is
ot met in a district, some of its resi-
ential or local service activity is allo-
ited elsewhere.
As indicated earlier, there are quite
few prototypes of the Lowry model
3th in the U. S. and in the U. K. These
rototypes run the gamut from concep-
al modifications (Garin-Rigers, 1966)
rough experimental-conceptual (Cre-
ne, 1964; CREVE, 1965; Echinique,
)69) to operational-experimental-con-
ceptual versions (PLUM, Batty and
Ljubljana). Goldner (1971) has provided
an excellent survey of these. We shall
describe here only the PLUM model
which appears to be applied to a num-
ber of metropolitan areas.
The PLUM model follows Lowry's
basic approach in dividing up the urban
area into zones and estimating employ-
ment and transportation patterns in and
between zones, but it adds a number of
refinements. For instance, in computing
transportation times, more careful atten-
tion is given in the PLUM model to
estimating the impact of differences in
availability of transport systems between
different zones. The fact that trip times
may vary at different times of the day
with different amounts of congestion is
also brought into the model. Further-
more, the PLUM model devotes greater
attention to modeling acreage require-
ments for residential land rather than
simply taking residential densities as a
residual as Lowry does. Too, it allows
for the possibility that in different parts
of the city there may be different num-
bers of workers per household and also
different numbers of people per house-
hold. Somewhat more sophisticated
functional forms are used to replace
Lowry's gravity model specifications in
allocating workers to zones.
Appraisal
We have described the Lowry em-
pirical land use model in considerable
detail and we have shown how more
recent work in the area, as illustrated
by the PLUM model, builds upon the
Lowry approach while making substan-
tial refinements on how the approach is
actually carried out. We shall now dis-
cuss the strengths and weaknesses of the
Lowry model—and to some extent of
the general group of empirical land use
models—in light of the evaluatory cri-
teria developed in an earlier section. As
was pointed out, however, urban models
can best be evaluated in comparison with
the objectives which they seek to ac-
complish, and it may therefore be ap-
propriate to consider explicitly the ob-
jectives of this type of model. Of the
four objectives identified in our previous
187
-------
discussion, the two which these models
are most concerned with are prediction
and policy analysis. The designers of
these models have been specifically
interested in predicting land use pat-
terns, and the way in which models like
Lowry's can be applied in this way
is reasonably straightforward. For in-
stance, in the case of the Lowry model,
once an independent forecast of the
location of export industry employment
at some point in time is made, it is then
possible to use the model to predict
other types of land use. It is also reason-
ably straightforward to see how models
of this type can be used for policy
analysis. For instance—though Lowry
does not use it in this way in the cited
report—the model could be used to
investigate the possible effects of an
urban renewal project by constraining
the districts in the urban renewal area
to have the type of new land use pro-
posed for the project. It is also possible
to use some models of this type—though
not Lowry's—to analyze partial effects
of alternative transportation policies.
This can be done in models where the
gravity relationship which is used to
allocate residence places and work trips
is made to depend on both distance and
transportation costs. Given this specifi-
cation, the effects of changed transport
systems can be modeled as changes in
transport costs.
The two basic objectives of this kind
of model, then, are prediction and
policy analysis. Two other objectives—
optimization and understanding basic
structural relationships shaping the city
are less important in these models.
Consistency With Data
Turning now to an appraisal of these
models, one of our proposed criteria is
consistency with data, and on this cri-
terion models of this type appear to be
quite impressive. Given the planning
objectives of these models, it has been
necessary that they be fitted as closely
as possible to actual data, and the crea-
tors of these planning study models
have made careful efforts to use real
world data to a far greater extent than
188
the builders of most of the other models
which will be surveyed below. In some
cases literally millions of dollars have
been spent in gathering data and proc-
essing it in connection with the models.
It is worth pointing out, however, that
in spite of these efforts many data prob-
lems remain. One of the most important
of these difficulties is what has been
referred to as "cross-sectional bias"
(Brown, et al., 1972). Because of data
limitations mentioned in our earlier dis-
cussion of urban modeling, many of
these planning study models have found
it necessary to generate their own data
through surveys and sampling tech-
niques. This creates difficulties, how-
ever, because land use patterns at one
point in time may not adequately reflect
current market forces due to extremely
long adjustment lags in urban systems.
Densities of residential patterns, for
instance may be strongly influenced
by buildings created many decades pre-
viously, and hence, existing land use
patterns may not be entirely accurate
bases from which to extrapolate future
patterns.
Another problem concerning data
which empirical land use models face
is that, even with their major data col-
lection efforts, the accuracy of the call
bration of these models with data i;
often substantially hindered by the gen
eral problems in working with urbai
data which were discussed earlier. Thi:
creates an evaluation problem in that i
has proved to be extremely difficult t<
develop criteria with which to judge th
accuracy of the models. At the ver
minimum, of course, they should b
expected to generate results which hav
at least some resemblance to the cit
being modeled. And indeed they do. Bt
this minimum resemblance is alrno;
guaranteed by the structure of the moc
els—in the Lowry model, for instancf
by determining export industry emplo;
ment exogenously,^and, beyond th
minimum resemblance criterion, it
difficult to develop reasonable and usi
ful indices of the degree to which tr
models fit the real world.
In spite of these data problems, hov
-------
ever, it is clear that the empirical land
use models go further toward meeting
the consistency with data criterion than
do most of the other models to be sur-
veyed. However, when judged against
one of the other criteria identified previ-
ously—consistency with theory—the
empirical land use models do not com-
pare as favorably with other types of
urban models.
Consistency With Theory
One theoretical limitation of most of
the models of this type is that they do
not explicitly portray market processes
in urban land markets with any degree
of thoroughness. Land in different parts
of the metropolitan region has different
values depending on the relative desir-
ability of the alternative parts of the
region for various kinds of economic
activity. Presumably, potential land
users are influenced by these prices in
making their location decisions, and
indeed standard economic theory would
suggest that these prices play a key role
n the land allocation process. In many
)f the empirical land use models, how-
:ver, prices do not appear at all—as for
nstance in the Lowry model—or, if
hey do appear, they appear in a largely
uperficial way. It should be remem-
>ered, of course, that in terms of the
ibjectives of the creators of models of
lis type, suppression of market proc-
sses may be a reasonable procedure,
ince loss of detail in this area may
lake it feasible to have more detail in
ther respects—for instance in the geo-
raphical disaggregation which is these
models' principal objectives. Indeed, for
nme purposes, gravity type models like
le one Lowry uses can be looked upon
> a short-cut way of representing the
nal outcome of the market process,
id Lowry discusses this interpretation
his report. Nevertheless, failure to
irefully model market processes cer-
inly weakens the theoretical under-
nnings of these models.
Another criterion with which to judge
odels is that of whether given the pur-
ges of the models, they include the
iriables and relationships which are
intrinsically necessary in accomplishing
their objectives. The basic objective of
these models has been their use for
disaggregated local planning, and the
models have indeed been successful in
achieving a good deal of geographical
disaggregation. There is, however, at
least one respect in which they have
omitted a relationship which may be
intrinsically necessary for their planning
objectives. As noted above, many of
these models lack a careful attempt to
describe the locational decisions of ex-
port industries. Now, for the purposes
of planning on a relatively short-run
planning horizon—say for the next 5
years—this may be an entirely appro-
priate simplifying technique. However,
one objective of these models has been
their possible use as an aid in transpor-
tation investment planning. And this
creates some difficulty because trans-
portation investments—e.g. roads or
train tracks—are often extremely long-
lived. In considering the effects of such
investments it may not be appropriate
to take the location of export sector
activity as exogenous. This is especially
true since access to transportation may
well be a key factor in plant location
decisions. Therefore, empirical land use
models have often been criticized for the
fact that, even though some of them
have been intended to be used as an
aid in transportation planning, they
have concentrated mostly on the effects
of industrial location on transportation
needs while largely ignoring the feed-
back effects running from the trans-
portation system to the location of in-
dustrial activity.
Another characteristic of many of
these models which it may be appropri-
ate to mention here is that for the most
part they have ignored the existence of
different racial groups and of racial
segregation.
In summary, then, it can be said that
the empirical land use models can best
be understood if considered in light of
their principle objective—i.e. detailed
land use planning. The suppression of
certain variables and relationships in
these models and their limited use of
189
-------
theory have apparently been necessary
in order to make it feasible to attain the
geographical disaggregation and atten-
tion to data which their planning ob-
jective required. Nevertheless, even
taken on their own terms, a number of
criticisms of models of this type can be
made. In particular, their failure to
adequately consider the effects of plan-
ning decisions on export industry loca-
tion limits their usefulness. So too does
their failure to deal with racial discrim-
ination.
Since many of these models were
originally undertaken with the goal of
making them operational as planning
devices, perhaps the most reasonable
ultimate criterion on which to judge
them is whether or not they have proved
useful for this purpose. Here, too, how-
ever, the record is mixed. In some cases,
despite huge expenditures of time and
financial resources, the models have not
been made fully operational as planning
devices and have had to be abandoned
by specific planning projects. An ex-
ample of this, for instance, is the Penn-
Jersey study of the Philadelphia region
(Levin and Abend, 1971). In other
cases, however, some use has been made
of the models in planning applications.
For instance, the PLUM model de-
scribed above has been made opera-
tional, and so, too, have a number of
similar models designed for planning
applications in England. (For a descrip-
tion of these English applications, see
Goldner, 1971.) Of course, even in
these cases where models of this type
have been made operational, there is
no way to judge with any certainty
whether the final planning decisions
have been improved by the use of the
model. It is clear that no current model
of this type can be used mechanically
by itself for planning purposes—too
many variables have, of necessity, been
omitted. Some planners have found
them quite useful, however, in suggest-
ing general planning patterns and in
checking for overall consistency of
plans. Other users, on the other hand,
have felt that they have added relatively
little beyond that which could have been
190
accomplished by good planning judg-
ment. In any event, the overall record
of these models is a mixed one and it
seems safe to say that not all of the
hopes for such models which were held
in the early 1960's have in fact been
fulfilled.
The Urban Dynamics Model
The next model which we will con-
sider is the Urban Dynamics Model
developed by Forrester (1969). This
model attempts to explore questions of
long run urban growth and stagnation.
Forrester begins his model by identi-
fying three broad classes of potential
workers (managers, laborers, and the
underemployed), three broad classes of
housing (premium housing, worker
housing, and housing for the underem-
ployed), and three general types of
businesses (growing industries, mature
industries, and declining industries). A
public sector with taxes is also built into
the model. Changes in these variables—
as well as some additional, auxiliary
variables—are then modeled with an
interactive, non-linear, dynamic equa-
tion system which is meant to represen
the economy of a typical city. For in-
stance, the rate of migration of under
employed persons into the city depend:
in the model on an index of the attrac
tiveness of the city to such people which
in turn, depends on the availability o
housing and of new jobs. Or, to tab
another example, the amount of worke
housing in the system depends on th
amount of premium housing becomin
obsolete and on the rate of new cor
struction of worker housing. And thi
latter variable, in turn, is a function c
a number of other variables includin
the size of the worker population, tb
availability of land, and tax considers
tions.
Altogether, the model consists c
some 154 equations which model rel;
tionships of this sort between the var
ables. Forrester's model is a dynam
model which starts with a set of initi
conditions and simulates the behavior <
the system over time. In terms of t
span covered, Forrester is considerab
more ambitious than other urban mo
-------
els—he attempts to model changes in
cities over several hundred years.
On the basis of the relationship es-
tablished in his equations, as well as a
set of assumed parameters and initial
conditions, Forrester presents the results
of three sets of simulation runs of the
model. The first set of simulations deals
with the life cycle of cities. Within a
250 year time frame, the simulated city
grows slowly for the first 50 years, then
rapidly for the next several decades
until about the 100th year when popu-
ation, housing, and business are at a
ueak and all available land has been
consumed. From this point on the forces
hat generated the growth lead to rapid
decline until relative equilibrium and
stagnation are reached in year 175. This
jquilibrium remains stable throughout
he remainder of the run. Forrester
akes these results to be relatively rep-
•esentative of historical city growth
>rocesses. He further asserts that this
epresentativeness is a measure of the
•alidity of the assumptions and struc-
ure of the model.
The next series of studies which For-
ester presents is an analysis of the ef-
xts of various programs "to save the
ities" as they would operate given the
ssumptions of the model. Starting from
le equilibrium-stagnation point devel-
?ed in the first run, Forrester alters the
isumptions and parameters in the
lodel to represent in turn a job pro-
-arn, a training program, a financial
d program, and a low-income housing
mstruction program. The job program
is very little impact on the system. It
suits in slightly higher numbers of
w-income population and low-income
>using but lower numbers of working-
iss housing. Higher taxes and de-
sased new construction also results.
ic training program has similarly little
pact on the city. Its most dramatic
ect is that it transforms the city into
;onduit for training low-income pop-
itions. People from outside the city
: trained in the city and then return
the outside environment when they
d that job opportunities are limited
the rapid increase in people with
working class skills. The fiscal aid pro-
gram results in the city being more
attractive to low-income people, less at-
tractive to new housing and business
and consequently requiring a higher tax
rate. This counterintuitive result is
caused by the increasing demands
placed on the city as a result of the
shifts in population, housing, and busi-
ness. The low income housing program
has rather major effects which are detri-
mental to the city. The program leads
to an influx of underemployed workers
and rapid departure of working and
upper class populations as well as new
construction. Forrester concludes that
this series of policy simulation runs is
indicative of the counterintuitive nature
of the urban system.
As a final step, Forrester experi-
ments with other possible policy options
for improving the condition of the city,
including worker-housing construction,
premium-housing construction, new-
enterprise construction, declining-in-
dustry demolition, slum-housing demo-
lition and discouraging housing
construction (i.e., slum-housing demo-
lition and depression of worker-housing
construction). Of these seven alterna-
tives the results of running the model
are most unsuccessful for the city with
the housing construction programs and
most successful for the combined slum
demolition-new enterprise construction
program. To Forrester these results
confirm his theory that many city prob-
lems are the result of an economic im-
balance between housing and business
which cannot possibly be redressed
through housing programs.
As a result of these experiments
Forrester has developed a series of con-
clusions as to the behavioral charac-
teristics of complex systems as modeled
in Urban Dynamics. First, as suggested
earlier, he concludes that they are
counterintuitive. That is, they often
respond to policies in a way opposite to
that suggested by intuition or observa-
tion. Second, after performing addi-
tional tests on the model, he concludes
that the results are relatively insensitive
to changes in the parameters of the
191
-------
model. This suggests that the structure
of the model is of considerably more
importance than its assumed param-
eters or calibration. Third, he argues
that the experimental runs described
above suggest that the system is rela-
tively unresponsive to policy changes.
Fourth, Forrester notes that the system
as modeled is able to counteract and
compensate for externally applied policy
measures. Finally, he notes that the
results of the model indicate a tendency
toward low performance (eventual
stagnation) under a wide variety of
circumstances. While these five conclu-
sions do not provide a basis for opti-
mism they do, according to Forrester,
suggest an important new way for policy
makers to look at a system which they
are attempting to influence and con-
trol.
As was the case with previous models
discussed in this survey, it is useful to
consider the goals which Forrester's
work seeks to achieve before attempting
an evaluation of the model itself. Of
the four general objectives discussed at
the beginning of this chapter the Urban
Dynamics model seems most concerned
with improving our understanding of
the basic forces shaping urban areas.
Some qualifications concerning this
must be made, however, on the basis of
the general nature of the model. Many
of the relationships of the model are not
solely economic in nature. For instance,
Forrester attempts to include variables
concerning perception and attractive-
ness which are determined by both eco-
nomic and noneconomic forces. In
attempting to include relationships of
this type, Forrester has ignored ques-
tions of urban form or spatial location
in order to keep the model manageable.
The model clearly has a general and
"macro" orientation, and the relevant
policy issues with which this model
deals are more questions of direction
than detail. Except in the most general
sense this model does not seek to be
predictive, nor is optimization one of
its aims.
192
Appraisal
Given its goals, we may evaluate the
model in terms of the criteria we have
specified. First we shall consider the
extent to which crucial variables have
been included or excluded. As noted
earlier, the variables included may be
generally classified as those concerning
population, housing, and business.
Within these general categories For-
rester attempts to specify variables con-
cerned with the political, physical
social, psychological, and economic
nature of the city. Forrester's model is
a large one with a great number o
variables. However, its lack of specifu
attention to spatial location limits it
usefulness for analyzing some importan
urban phenomena such as suburbaniza
tion. The model also ignores the influ
ence of transportation technology am
technological change of all kinds. Wit
regard to our simplicity criterion, th
many equations in Forrester's mode
while making its operations somewh*
intriguing, do not lend themselves t
ready analysis. Those relationships c
effects which are really important t
the model's underlying theory ai
hidden in the complex form in whic
the model is presented.
Our third criterion is consistency wi
theory. Forrester makes no attempt
the Urban Dynamics model to use t
existing theory of urban developmer
He notes in his preface that in specif
ing the relationships of his model
consulted persons with practical e
perience in urban affairs and drew pri
cipally on their perceptions and expe
ences. The book contains virtually
references to existing theoretical Htei
ture in economics, political scient
urban planning or other professioi
disciplines.
Our final criterion involves
model's consistency with data. Forres
does not seek to use data in the spe
fication of his equations. He uses d;
analysis neither in fitting equations i
in testing generally for the existence
relationships. All the parameters in
model are made up on the basis of w
seemed intuitively plausible and of w
-------
generated apparently plausible simula-
tion results.
In summary, this discussion of the
Urban Dynamics model in terms of our
evaluation criteria leads to the conclu-
sion that while the model presents an
interesting view concerning the proc-
esses involved in city growth, its validity
is difficult to verify because it is not
carefully related to the current state of
empirical and theoretical knowledge.
The System Dynamics group at the
Massachusetts Institute of Technology
is applying the Urban Dynamics Model
to Lowell, Massachusetts with HUD
support (HUD Contract H2000-R).
Early indications are that Lowell may
be one of the places in the U. S. that
might conform to the pattern of growth
and decline forecasted by the Urban
Dynamics Model.
Simulation-Gaming Models
We turn now to a class of models
ivhich have generated a good deal of
nterest: urban simulation-gaming mod-
;ls. Various models of this type (En-
rirometrics, 1971) have been de-
veloped with different degrees of em-
>hasis placed on the gaming and
emulation components. These may vary
>oth in terms of relative importance to
ic overall model and in terms of their
nternal structures. In evaluating these
nodels we will distinguish between the
omponent parts, and discuss the irn-
ortance of each part to the overall
lodel.
CLUG—Community Land Use
fame
The first model of this type which
e will briefly describe is the Com-
lunity Land Use Game (CLUG)
iodel developed by Feldt (1972). The
LUG model is a manually-operated
ble game in which the gaming model
the dominant aspect of the exercise.
i CLUG the players develop a corn-
unity on a pre-existing grid system of
ads. Players in the game represent
dustrialists, businessmen, homebuild-
s and residents simultaneously. Money
ters the system from the sale of goods
industry to the outside. Money leaves
the system for the purchase of land, for
the construction of buildings, and for
the purchase, through taxes, of munici-
pal services. Players buy and sell land,
construct buildings, negotiate trade and
employment contracts and vote on pro-
posed extensions of municipal services.
The simulation part of the model oper-
ates to assess and reassess property and
to condemn buildings. The assessment
algorithm is based on the value of
nearby properties. The condemnation
procedure is stochastic and takes into
account the age of the buildings and
the players' renovation expenditures on
their properties.
The objectives of the CLUG model
are educational and emphasize the
forces that determine the process of
urban growth. Thus, the gaming model
is designed to deal with the important
factors that determine locational pat-
terns. The basic model is explicitly not
oriented toward objectives of predic-
tion, optimization or formulating public
policy, though the last of these has been
involved in the design of experiments to
supplement the basic game. Rather than
evaluate the manually operated CLUG
model, we will move on to a discussion
of a computer based derivative CITY-
RIVER BASIN MODEL.
RIVER BASIN MODEL
We turn now to two simulation-
gaming models, RIVER BASIN (U. S.
Environmental Protection Agency,
1972a and House and Patterson 1972)
and CITY MODEL (Envirometrics,
1971b) which are evolutionary develop-
ments that started with the CLUG con-
cept. The CITY MODEL was made
operational in 1970 and was based on
an extension of City I which, in turn,
was based on the CLUG format in-
volving expansion of the gaming com-
ponent and very extensive elaboration
of the simulation component. The
model requires 30-60 players and easy
access to computer facilities for opera-
tion of the simulation package. The
RIVER BASIN MODEL is an ex-
panded version of CITY MODEL with
193
-------
the addition of a water resources com-
ponent to both the simulation and gam-
ing phases. The description which fol-
lows will be for RIVER BASIN but
will apply in many respects to the CITY
MODEL as well.
The play of RIVER BASIN is
centered around the development of a
community in a geographical area
which is divided into a 25 x 25 unit
grid. Unlike CLUG, the grid lines in
RIVER BASIN do not automatically
represent roads. These lines are road
beds on which future construction may
take place at the discretion of the trans-
portation department of the government
in the game. The length of a grid side
is 2.5 miles. The players in the game
become decision makers in one or more
of three sectors: economic, social, and
governmental. Within each sector
further disaggregation of roles is de-
fined. Economic decision makers for
instance, control the construction and
operation of business activity; in four
broad groupings; basic industry (both
manufacturing and non-manufacturing),
service industry, residential develop-
ment, and agricultural activity. Within
each of these there is in turn further
disaggregation into specific economic
activities (11 types of manufacturing,
4 types of services, etc.). The social
sector decision makers represent and
make decisions for the population of
the area. The population is divided
into three classes which are differen-
tiated on the basis of income, educa-
tion, voting status, family size, and
worker status. The government sector
decision makers represent the main
political and bureaucratic decision mak-
ers in the system. There is an elected
mayor (chairman), and there are also
department heads concerned with tax
assessment, water supply, utilities,
municipal services (fire and police),
planning and zoning, schools, highways,
and public transit. The many players
within each sector must interact among
themselves and with players in the other
sectors in seeking to achieve their self
established objectives.
The gaming phase of a model run is
194
completed with the filling out of de-
cision forms by the players. These forms
are converted into input for the simula-
tion part of the model which is a highly
complex computer program. On the
basis of the gaming decisions made by
the players, this program then com-
putes new values for such key variables
in the model as population patterns,
water quality, employment patterns,
shopping patterns, use of transportation
routes, allocation of students to schools,
and the distribution of commercial ac-
tivity between areas of the city.
The model is more disaggregated
than in the case of CLUG and the
simulation component plays a major
role. In CLUG, players represent sev-
eral roles simultaneously, there are rela-
tively few numbers of roles, and there
is relatively little variety of choice in
decisions. In RIVER BASIN players
usually concentrate their efforts on one
or two roles, there are a wide variety o
roles, and the decision choices are ver)
diverse. Furthermore in the CLUC
model most of the calculations anc
decisions are made by the players them
selves. In contrast, in RIVER BASI>
all of the significant allocational deci
sions and computations are handled b;
the computer. It should be noted, how
ever, that substantial aggregation re
mains in the model. For example eac
population unit represents 500 peopk
and each economic activity represen
the average characteristics of firms in
general type of business activity. Th,
aggregation is necessary both to kee
the gaming phase manageable and als
to reduce computing costs in the simi
lation phase.
The RIVER BASIN MODEL wi
designed to achieve the education
objective discussed earlier and to ei
hance our understanding of the bas
forces which influence urban develo
ment. It is not concerned with issu
of prediction or optimization.
In evaluating the model we will co
sider the gaming component first. T
model includes a large number
variables that are generally consider
relevant to a systemic view of urb
-------
areas. It was developed, according to its
designers, from an analysis of the major
activities which take place in an urban
area and the gaming component was
designed to coincide with a general
model of urban activities. The fact that
the present formulation of the model
represents the latest step in a long series
:>f model development by the designing
jroup must be credited for some of
his inclusiveness.
The gaming phase of the model
ippears to be consistent with current
heory to the extent that current theory
iscusses the type and nature of the
oles involved in urban processes.
"urthermore, the game component of
le model, to the extent that it seeks to
nclude important aspects of the urban
ystem which have not been developed
ito theoretical models (e.g., the choice
etween recreation and politics, or cor-
aption in political and economic ac-
vity), plays a crucial role in reducing
le possible use of inconsistent or in-
alid theory in the simulation model.
/here good theory does not exist, inter-
;tions and decisions are gamed,
hereas when good theory does exist, it
often incorporated into the simula-
3n component of the model.
As an educational device the RIVER
Vith regard to the model's con-
ency with data, the designers sug-
t that the design and specification
the model itself was not initially di-
ly dependent on specific data.
srations of the model have, until
jntly, depended on hypothetical
•ting data.
APEX—Air Pollution Exercise
The final model which we will con-
sider in this general area of urban simu-
lation-gaming is the APEX model (U. S.
Environmental Protection Agency,
1972b). The APEX model, which was
first made operational in 1968—69, is a
successor to the METRO model and
the METROPOLIS model, all of which
were developed under the leadership of
Richard Duke at the University of
Michigan's Environmental Simulation
Laboratory. The historical roots of
APEX make it quite different from the
CLUG-RIVER BASIN type of models.
This model simulates the conditions of
the Lansing, Michigan area and the
roles that have been significant in the
development of that region. Unlike
RIVER BASIN, APEX is composed of
two operational components, a gaming
phase and a simulation phase.
The gaming sequence involves play-
ers in one of five general roles: poli-
ticians, planners, industrialists, com-
mercial developers, and air pollution
control officers. Within these sectors
there is additional differentiation be-
tween roles in the city and in the
surrounding county and between types
of industry and development. It is
noteworthy that households are not
included in the gamed component of
the model. Their inclusion in the simu-
lation component reflects the historical
development of the model. Whereas the
RIVER BASIN designers sought to
simulate the activities of the urban
system, the designers of APEX and its
predecessors have sought to model the
roles of the "principal" actors or de-
cision makers. This emphasis on iden-
tifiable decision makers has meant that
this model deals more with the environ-
mental context of given roles than with
the nature of the system per se.
The emphasis in the game com-
ponent on specific roles rather than
activities has meant that the simulation
component simulates some processes
that are gamed in RIVER BASIN. The
simulation component is comprised of
a number of interacting submodels
which (1) determine growth in export
195
-------
industry employment, (2) allocate local
service sector employment within the
different parts of the urban area, (3)
simulate voter response to bond and
tax propositions put before them, (4)
determine the results of political con-
tests between incumbents, as gamed,
and their simulated opponents, and (5)
determine the amount of air pollution
in the urban area.
Besides these main submodels there
are a series of major subroutines which
perform important model functions.
These include routines dealing with
capital plant, land value, prices, zoning,
taxes, entering firms, purchasing and
accounting, accessibility, non-white
population, and the news media.
The APEX model may be charac-
terized as somewhat more aggregated
than the RIVER BASIN MODEL. The
relative aggregation concerns the num-
ber of locations (29 analysis areas) into
which activities are allocated by the
simulation model (as compared to 625
in RIVER BASIN) and the number
of role types involved. The APEX
model has very detailed roles in the
government and business sectors but
leaves the household sector to the simu-
lation model.
The APEX model, like the others dis-
cussed in this section, was designed to
meet educational objectives and to im-
prove our understanding of the urban
development process. Specifically, the
current version of the APEX model
was designed to meet the needs of the
Air Pollution Control Institute and its
training program. The exercise is now a
part of the Institute's program to
develop administrators to take active
roles in air pollution control projects
in our urban areas. Thus, the educa-
tional objective of the model which was
explicit in its design is also explicit in
its use.
APEX is the last of the specific
simulation-gaming models which we
shall look at in detail. Before leaving
this general class of models, however, a
few general comments may be useful.
As distinct from some of the other
models we have considered, these simu-
196
lation-gaming models seek to represent
a systemic or holistic concept of urban
areas. As such they represent an im-
portant contribution to the study of
urban affairs. They are built on the
theory that some human interactions
cannot be modeled explicitly and mus
therefore be left to humans to perform
The simulation-gaming format allows
the designer to combine these un-mod
eled interactions with accepted theor
in the development of a more completi
model. We may learn more about thi
systems from these models and we ma;
also study the content of these humai
interactions. These factors give thes
models considerable potential for ex
perimentation.
V. CONCLUDING COMMENTS
This completes our survey of urba
modeling. There has been no attem
to survey all of the many urban mode
which have been created over the pa
two decades, but we have discussed
number of important models of diffe
ent types which are representative <
some of the major trends in urbi
model design and here indicated to t
reader that there is a large literatu
of surveys and evaluations. It may nc
be useful to conclude this chapter
taking a brief overall look at the degr
to which these models have been able
accomplish their objectives and at th
usefulness for policy makers.
In general, it would appear that si
stantial progress has been made
urban modeling in the past 20 ye
and that a great deal has been learr
in that time both about cities and abi
techniques for modeling them. Ne\
theless, it is clear that urban model
efforts have not been completely s
cessful in accomplishing all of tl
objectives. So far, for instance,
single model has fully succeeded
achieving both rigorous consiste
with theory and also close calibra
with the data from an individual c
The empirical land use models
haps go the farthest in the directior
close calibration with specific ur
-------
data. But they have often had to make
compromises with theory, and there
have been difficulties in making them
operational. The Forrester model and
some of the urban simulation-gaming
models suggest interesting hypotheses
about the dynamic relationships present
in an urban area, but they, too, have
not been fully coordinated both with all
of the existing theoretical literature and
also with detailed and accurate data.
We conclude this chapter by first
siting critics of planning models in
general and urban models in particular,
and then by offering our view of the
present, proper role of such models.
Lee in his article "Requiem for
^arge-Scale Models" in the Journal for
he American Institute for Planners,
'Lee, 1973) offers the following critical
issessment:
"The task in this paper is to evalu-
ate, in some detail, the funda-
mental flaws in attempts to con-
struct and use large models and
to examine the planning context
in which the models, like dino-
saurs, collapsed rather than
evolved. The conclusions can be
summarized in three points: (1)
In general, none of the goals held
out for large-scale models have
been achieved, and there is little
reason to expect anything differ-
ent in the future; (2) For each
objective offered as a reason for
building a model, there is either a
better way of achieving the objec-
tive (more information at less cost)
or a better objective (a more so-
cially useful question to ask); (3)
Methods for long-range planning
—whether they are called compre-
hensive planning, large-scale sys-
tems simulation, or something else
—need to change drastically if
planners expect to have any influ-
ence on the long run."
Lee directs criticism toward the cur-
it urban modeling efforts related to
rrester's Urban Dynamics model, the
JER model, and the Projective Land
e Model (PLUM). He sees little sign
success in either the past or current
>an modeling efforts.
3rewer (1973) has a more lengthy
critique that is based upon four types
of appraisal (theoretical, technical, ethi-
cal, and pragmatic). He deals thor-
oughly with the two community re-
newal program models (San Francisco
and Pittsburgh). His focus is on the
decision-making process in these two
complex urban settings and the attempts
to use large scale computer simulation
models for planning and development.
Brewer's book could benefit a public
official contemplating the construction
or use of a large scale computer model.
It provides the background and evalua-
tion criteria necessary to evaluate the
intended model-building process and
product.
In the light of these observations
about urban models, then, it may be of
interest to briefly consider their general
usefulness in policy making. With re-
gard to this question, there is a key
distinction to be made between the use
of models as a tool for policy making
on the one hand and as a replacement
for policy makers' judgment on the
other. It is clear from the above analy-
sis, that urban models are not now de-
veloped to the point where they can be
mechanically used as a substitute for a
policy maker's judgment in urban de-
cision making. We do not have a model
which will simply allow the public
official to "plug in the numbers" and
get back the correct decision with re-
gard to a housing or transportation or
zoning decision. None of the current
models can do this, because none of
them can fully capture the extreme
complexity of the urban public official's
decision-making environment.
Urban models can, however, be ex-
tremely useful as a tool or an aid to
urban policy making. They are not in-
tended to replace the urban policy
maker's judgment, but they can be
extremely useful in improving his judg-
ment. The empirical land use models,
for instance, can be a valuable aid in
helping the urban planner assemble and
manipulate a large amount of data
about urban land use in a systematic
and consistent way. And the Forrester
197
-------
and simulation-gaming models can help
alert the policy official to the complex
patterns of interrelationships in the
urban area and to the possibility of
counterintuitive results from his policy
decisions.
Thus urban models can be potentially
useful. But ultimately it is the policy
maker's task to use both the models
and his own judgment in attempting to
arrive to correct policy decisions. The
task of the urban model builder in the
future must be to continue to find ways
to integrate both theory and data into
models which will be of further use in
helping the policy maker with his job.
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ouse, Peter W. and Philip D. Patterson,
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uff, D. L., "Determination of Intraurban
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igram, G. F., J. F. Kain, and J. R. Ginn,
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kshmanan, T. R. and Walter G. Hansen,
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hrop, George T., John R. Hamburg, and
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Lee, Douglass, Models and Techniques for
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Lee, Douglass, "Requiem for Large-Scale
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Levin, Melvin R. and Norman A. Abend,
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Bureaucrats in Collision: Case Studies in
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Cambridge, Massachusetts, 1971.
Lowry, Ira, A Model of Metropolis RM-
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the National Bureau of Standards, U. S.
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1970
Putman, Stephen H., Industrial Location
Model (ININP), Technical Bulletin No. 5,
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1963.
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Shopping Demand," Journal of the Town
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1967.
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Barringer, "A Simulation Model for Re-
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Schlager, Kenneth J., "A Land Use Plan
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199
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200
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Chapter 7
Models in Transportation
By
Kenneth W. Webb
(with contributions by)
Frank L. Spielberg and Peter S. Loubal
SUMMARY 203
I. INTRODUCTION 204
Decision Making Agencies 206
General Types of Models 208
II. URBAN AREA TRANSPORTATION PLANNING 208
The Urban Transportation Problem 208
The Need for Urban Transportation Planning 209
Transportation Planning Techniques 209
Models for Urban Transportation Planning 210
Overview 210
Land Use Model . 211
Bay Area Transportation Land Use Model 213
EMPIRIC Land Use Model 213
Trip Generation Models 214
Zonal Interchange Model 215
Trip End Modal Split Models 216
Trip Interchange Modal Split Models 216
Network Assignment Models 217
Deficiencies of the Traditional Approach 217
Recent Developments and New Directions 218
II. INTER-URBAN TRANSPORTATION PLANNING 220
V. NATIONAL TRANSPORTATION PLANNING 222
A Transportation Assessment Model 223
Airport Investment Model 225
An Aircraft Route Effectiveness Model 226
Summary 227
REFERENCES 227
201
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Models in Transportation
SUMMARY
Since 1950 the use of scientific mod-
eling as an aid to transportation de-
cisions has developed to the point where
he total effort exceeds modeling use in
all other areas except the military. This
chapter contains descriptions of the
.ransportation decision-making prob-
ems and the models that have been
;mployed to solve them. Transportation
lecision making interrelates to prac-
ically all social and economic domains
>f local and national government. This
;auses the decision making to be par-
icularly difficult and the models to be
ather complex. A new freeway that is
a the proposal stage must be evaluated
ot only with regard to the effect on
raffle but also with regard to secondary
Tects on such matters as land develop-
lent relieving unemployment and so-
ial access. Negative effects such as
eighborhood disruption, pollution and
2sthetics must also receive attention.
uilding models that will assess this
rge number of characteristics is, to
iy the least, difficult. However, the
wards in terms of more accurate
anning judgments make the expense
id effort worthwhile.
Transportation decision making is in
insition, bringing about new facets
the modeling approaches. There is a
neral shift in governmental attention
fay from pure analysis of trips on
•planes and in automobiles, to analy-
of socio-economic effects on the chi-
ns who are riders or in the pathways.
tizen groups now have political power
prevent proposed highways and air-
rts because of infringements on their
hts. The recent change in the use of
,hway funds from strictly highway
construction to the use for mass transit
is another change in terms of techno-
logical approaches.
The variety of models that have been
developed and used on transportation
problems is quite extensive. They range
from multi-million dollar regional
studies to small models of alternative
designs for intersections in a city. The
models range over many facets of
transportation: school bus scheduling,
railroad scheduling, highway location,
airport design, maintenance of equip-
ment, crew scheduling, trash truck
routing are only a few examples.
This chapter presents the larger de-
cision problems and the related models.
It describes modeling approaches for
problems of a national or large local
area importance. Models of smaller
impact, such as intersection or traffic
signal system design are not problems in
the large and are not covered.
The first section of this chapter de-
scribes urban transportation planning
which is in a real state of transition.
The movement of citizens to cities and
the increasing attention to the variety
of needs of citizens is bringing an in-
creasing importance to the planning
function, which is for the most part
concerned with investments and their
effects.
The models here can be classified as
follows:
• Macro-Level—dealing with major
traffic corridors
• Messo-Level—generally dealing
with route location studies
• Micro-Level—generally design
planning such as intersections
At the macro-level, modeling is com-
posed of a set of submodels. First, a
203
-------
land use model is constructed to repre-
sent the land area in the region, the
uses of the land, and the transportation
network. Models are then developed
for generating trips that the citizens
and freight haulers might make, dis-
tributing these trips on the network,
and making choices of modes of travel
and the selection of the routes that each
trip maker might take. These models
are described in some detail in the
chapter to illustrate their complexity
and comprehensiveness.
The next section discusses a mega-
lopolis model developed to analyze the
transportation problems of the North-
east section of the United States. The
Federal government in the early 1960
period recognized that improvements in
this geographic area were necessary
because of the poor condition of the
railroads and the congestion of the
highways. New technology such as tube
trains and high speed surface trains
were tested on the model. It was also
found necessary to review investment
options and changes to public policy
which could be evaluated by the large
model. The Northeast Corridor Model
was actually composed of many sub-
models covering both freight and pas-
senger traffic. Demand was estimated
under several scenarios, followed by
mode and trip allocation to a network
model. Demand estimation was fol-
lowed by a model to assess the impact
of proposed networks incorporating the
innovations.
The third section of this chapter is
concerned with national transportation
planning. The Federal Department of
Transportation plans for movement of
goods and people on a national scale
and has a mission to disburse monies
to State and local governments for
investment in facilities. The planning
role is to determine the best disburse-
ment on a national basis to meet the
program needs and priorities. Addi-
tionally, the Department is responsible
for determining new legislation to meet
the new special needs.
In response to the evaluation needs
for disbursement of Federal monies to
204
the States and local governments, a
national model was developed which
assessed the highways, arterials, con-
nectors and local roads of the nation.
Seventy-four parameters such as acci-
dent rates, pollution, speeds, and
amount of traffic are input to the model.
This section describes the models usec
to evaluate this enormous amount of
data and made assessment of the bes
allocation of monies throughout the
nation. The national model results dc
not correlate well with the needs foi
investment as seen by the localities
This reflects the lack of conformity or
objectives between the Federal anc
local governments.
This section also describes a mode
used for the development of airports ii
the United States. Airports exemplif;
the complexities of public utility inves
ment. Federal bureaus regulate the ai
carrier industry while State and \oa
commissions make the airport capacit
decisions. The public demand for sen
ice is related to the capacity of th
system and the behavior of the carrier:
The model described relates the a
pacity and the cost allocation decisior
that must be made by the Federal go1
ernment.
At a more detailed level, the Feder
government has decision problems
evaluating airline operations for dete
minations on policies concerning far
and user charges, route awards, r
quests for service charges, mergers ai
intercarrier agreements, new termin
decisions, limits on airport operatic
and effects of new aircraft. A model
described which develops a method
approximate the mix of planes, rou
and schedules and terminal facilit
that will satisfy intercity passenger a
cargo demand at minimum social a
economic costs.
The following Summary Table li
the models that are described in t
chapter on transportation.
I. INTRODUCTION
It would be difficult to overstate
importance of transportation in shap
-------
TRANSPORTATION
Models Discussed in Chapter
Summary Table
Model/Decision Area
General Type
Urban Area
Land Use Model
Trend or Regression
Analysis
Trip Generation model Regression
Zonal Interchange
model
"rip End Modal Split
Vlodels
>ip Interchange
dodal Split Models
Network Assignment
rfodel
nter-Urban Transporta-
ion Planning
Northeast Corridor
.lodel
lational Transportation
'lanning
'ransportation Assess-
lent Model
.irport Investment
lodel
irport Route Effec-
veness Model
Gravity Model
Trend Analysis
Linear Regression
Moore Algorithm
Simulation and a variety
of Optimization tech-
niques
Ranking Analysis Cost
Benefit Analysis
Dynamic Programming
Gravity Model, Linear
Programming
Important Characteristics
The urban region is divided into zones
and employment and population and
determined for each
The frequency of origins or destinations
of trips in each zone is determined by
land use and socio-economic factors
Based on data from origin and destina-
tion surveys, the origins by zone are dis-
tributed by a model as destinations to
zones
The origin or destination statistics are
divided among modes according to the
factors of trip, trip maker and mode
The traffic between zones is allocated to
the available modes of transportation
according to factors of trip, trip maker
and mode
All trips are assigned to networks based
on minimal time or minimal cost to the
trip maker
A model for testing innovations in the
North East megalopolis for freight and
passenger systems
A national model to determine the best
disbursement of Federal funds to States
and localities
The model quantifies the benefits re-
ceived and the capacity required by vari-
ous airport user groups
This model is used to analyse the oper-
ational characteristics and management
characteristics of airlines and airports
3t just the overall commercial and
>cial patterns of the United States,
it the individual life style of each
tizen. The tremendous benefits of in-
•easingly faster and cheaper transpor-
tion were achieved by an essentially
lontaneous development of transporta-
:>n means—whether on waterways,
ilroads, highways or in the air. The
tendant problems of uncoordinated
owth and planning—railroad bank-
ptcies, decline of public transit—re-
lire solutions based on a more rational
iproach to both the industry's and
public's often conflicting concerns. In
addition, transportation decision-makers
are also being confronted with con-
comitant problems of pollution, ineffi-
cient land use, and energy shortages.
Resolution of the interrelated local,
State and Federal transportation prob-
lems requires an increasing reliance on
analysis, modeling and other proce-
dures for alternative evaluation and
selection.
Historically, transportation problems
were among the earliest to be studied
by the emerging modern management
205
-------
sciences, e.g. accessibility and facility
location—the Weber problem [76],
least-cost transportation connections—
the Hitchcock problem [59], shortest
paths through networks—the Moore
Algorithm [62]. These early efforts and
more recent developments now form a
valuable set of transportation decision-
making aids. These include the Urban
Planning Package of the Federal High-
way Administration [57] for highway
planning, and the multimodal UMTA
Transportation Planning System of the
Urban Mass Transportation Adminis-
tration [56], [73], [74] for private and
public transport planning.
The need for such aids grew out of
their incipient use in such major multi-
million dollar regional ground transpor-
tation studies as the Chicago Area
Transportation Study—CATS; Tri-State
Transportation Study—New York City;
Pittsburgh Area Transportation Study
—PATS; Penn-Jersey Transportation
Study—Philadelphia; and the Bay Area
Transportation Study—BATS. The
latter study was concerned with the
development of a regional ground trans-
portation plan for the nine county San
Francisco area. Large amounts of in-
formation were collected describing the
economic activities, population charac-
teristics, transportation facilities and
land use characteristics. Data sources
included public record, household inter-
views and private agency studies. The
data were input to a large regional
growth model which is described later
in this report.
Another example of the scope of
large transportation studies was a mod-
eling effort for the State of California.
The objective of this effort was to plan
a transportation complex for the long
range (50 years) to meet the needs of
the state for growth. The study team
examined all possible transportation
modes—tube trains, air cushion equip-
ment, sky buses, electric automobiles
and many others. The complex interre-
lated aspects of population, land use,
economy and technology with regional,
interurban and urban transportation
206
needs were examined using the set of
models depicted on Chart I.
Many models exist for special prob-
lems in local transportation, of much
smaller dimensions. For instance, the
problems of scheduling buses has pro-
duced computer models to bring more
efficiency to the operations [41], [35],
[36]. The experiments in Dial-a-Ride
bus systems were modeled for initial
testing of the system [39]. Models have
been developed for a multiude of design
problems for intersections, ramp en-
trances, traffic signal control systems,
school bus scheduling, etc. However,
these problems and their models will
not be discussed in this report because
they have little effect on overall plan-
ning for urban areas.
In the last half dozen years the trans-
portation decision processes have be-
come more concerned with the effects
of transportation systems on the users
and the people in the pathways. The
effects of noise, air pollution, disruption
of neighborhoods, hardship of being;
moved, effects on small business anc
even church memberships, and man)
other effects are being studied anc
modeled to a greater degree. (See [1]
[2], [3], [5] and [6]).
Decision Making Agencies
The decision making agencies in tb
field of transportation that have usec
models are numerous. Some of the mos
important are the following:
• City, County, and State depar
ments that have problems in th
structuring of road nets to serv
the needs of comprehensive plar
ning.
• Regional and inter-State plannin
bodies with decision making prot
lems of organizing highway an
road nets that serve the needs c
the larger-than-State areas fc
growth and control.
• Federal agencies that are respoi
sible for the disbursement of func
to states for the construction an
extension of networks to serve tl
needs of the country.
• Federal, State and local agencii
responsible for solving problems (
-------
THE CALIFORNIA TRANSPORTATION MODEL
OBJ & CONTROL
•PLANNING!-/)-* GOVT CONTROL "I
L__ _j \J L. —_ «-««.—.-— — J
w w w v T DA IUC O^ DT w w
» ™ » » IIW™ O i vi\ I« » T
TRANSPORTATION
SYSTEMS
CONTINGENCIES
EVAL
DATA
TRANSPORTATION
SIMULATION
, CALIF. N
/ SYSTEM j
V CHANGE •
V DATA X
TRANSPORTATlOl
DEMAND
TRANSPORTATION
DEMAND :,
9 ft
CHART I—The California Transportation Model
ource: Systems Technology Applied to Social and Community Problems, June 1969,
Committee on Labor and Public Welfare, United States Senate.
highway intersection design, traffic
control methods, parking needs
and other requirements of smaller
scale engineering.
Regulatory bodies such as the
Interstate Commerce Commission
(and some industry groups) that
fix rates that transportation sys-
tems are allowed to charge.
Federal, State, and sometimes local
agencies that regulate air traffic,
operations of airports and control
the flights.
Agencies at all levels of govern-
ment that regulate railroads and
shipping companies.
Transportation industries that make
decisions on proposed routes
207
-------
schedules, crew scheduling, facili-
ties, maintenance and many other
operational matters.
General Types of Models
As one can imagine, with the large
number of agencies involved in decision
making, we will find wide diversity in
transportation models. Generally these
fall into three main categories, although
there are exceptions.
(1) Transportation land use models,
which for an area under study, char-
acterizes the relationships among em-
ployment, housing, industry, and trans-
portation. The aims in these models are
to determine the transportation network
that promotes growth, employment and
other desirable characteristics. Trans-
portation land use models will be de-
scribed in detail in this chapter because
of their importance to large area de-
cision making.
(2) Linear programming, dynamic
programming and other non-probabi-
listic models are used generally to solve
decision problems where an optimum
result is needed and the problem can be
characterized by sets of equations. The
use of linear programming in the solu-
tion of least cost transportation routes
for goods going from several origins to
several destinations is classic in the
field. An application of dynamic pro-
gramming to determine a sequence of
airport investments will be described
in detail in this paper.
(3) Simulation has been used exten-
sively because it provides for the build
up of queues of autos, airplanes, trains,
passengers, school buses, public buses
and other objects in motion and being
serviced at points in the trip. The mod-
eling objective is usually to determine
the system that minimizes numbers in
quences or the time in queues. For
instance, the Long Island Railroad,
which has an unbeaten queuing history,
recently simulated its entire operation
to determine schedules, number of
equipments required, locations for new
facilities, and personnel needs. The
objective was to find the system that
minimized total trip times, waiting
times and random breakdowns. Simu-
208
lation and queuing theory models are
used for solving operational problems
for the most part. They will not be
treated here because their relative im-
pact on governmental decision making
is lower than deterministic models.
The sections which follow will pre-
sent only a few of the many models
used in governmental decision making.
Selections of transportation land use
models will be reviewed in detail be-
cause of their significance in local and
regional planning. Some of the repre-
sentative models used at the Federal
government level will also be reviewed
in detail as they have strong national
impact.
II. URBAN AREA
TRANSPORTATION PLANNING
The Urban Transportation Problem
The contrast between the excellent
service offered by the motor vehicle in
areas or during time periods when it
can be provided with adequate space
on the highways and sufficient parking,
and the situation encountered by most
drivers in metropolitan areas during the
rush hours is too well known to require
lengthy elaboration. Excessive use o
the private automobile can be charac-
terized by the following negative
factors.
Congestion—massive efforts of high
way engineers have not eliminatec
the frustration, time losses and cost
stemming from the incapability o
street and parking facilities to cop>
with ever-increasing peak demands.
Inefficient Land Use—the amount o
land needed to serve vehicles in inne
core areas has been increasing to
degree where the scarcity of Ian
available for the ultimate trip purpos
(employment, shopping, recreatioi
etc.) leads to sprawls that further tti
demand for street space. This causf
an upward spiraling of the problen
Air Pollution—other types of polh
tion are wasteful and unpleasan
Air pollution, mainly from mot(
vehicle exhaust, can become hazari
ous to health.
Excessive Consumption of Natur
-------
Resources—concern is growing that
some basic natural resources, e.g.,
fuel oil, will be depleted before
suitable substitutes can be found.
Negative Social Effects—excessive
motorization reduces the level of serv-
ice which can be provided by public
transit to those who cannot drive—
some 30 percent of the population
who are too young, old or infirm to
drive, and 20 percent of families who
have no car available. This reduces
their employment possibilities, di-
minishes their recreational opportuni-
ties and forces them to accept a low
level of personal mobility.
Mass transit is not just geared to
cope substantially more efficiently
with large demands for service than
the private car. A high rate of de-
mand is a prerequisite for achieving
good transit service profitably, or at
least a relatively low subsidy. The
post-war downward transit spiral
where decreasing patronage led to
increased fares and service reductions
followed by further drops in patron-
age has now been to a large degree
halted. The major question facing us
all is whether and how this process
can be reversed in a free-choice
society.
Will transit patronage consist of only
he non-drivers and those who have
ieen forced to abandon their cars by
npossible highway conditions, or can
substantial part of riders with rea-
Dnable access to transit be retaught to
se it? Is its main role to deal with
eak travel demands or can an accept-
nle level of utilization be achieved off-
eak? Does conventional transit tech-
Dlogy possess the capability to satisfy a
iajority of travellers, or do we have to
:velop novel systems to provide still
•eater speed, flexibility or comfort?
an a more efficient use of travel
odes be achieved by a pricing mecha-
sm?
Concurrently it must be recognized
it the private automobile has had
any positive social impacts and has
en overwhelmingly accepted by the
nerican public. Clearly it is not de-
able to undo the work of the past
'enty years. Rather the efforts in
nsportation planning must be directed
at recognizing the undesirable impacts
of auto usage and striving to develop
comprehensive multi-modal systems
which combine the best of all modes
while minimizing the adverse impacts.
The Need for Urban Transportation
Planning
A large proportion of the capital in-
vestment in any urban region is related
to transport facilities. Over the past
several decades, since 1948, the aggre-
gate highway expenditure in the United
States has been approximately $260
billion. These facilities are the means
toward the end of providing the resi-
dents of a region with accessibility be-
tween homes, jobs, services and the like.
Other means to the same end such as
vastly improved communication tech-
niques or rearrangement of land use
and land activity patterns could achieve
the same effect, but would likely result
in a different life style than that to
which we are accustomed.
For better or for worse, the majority
of U. S. citizens have made the implicit
decision to live in urban areas with a
relatively large spacial separation of
activities. Given this preference exten-
sive transport systems become a neces-
sity.
Transportation Planning Techniques
To provide a basis for rational de-
cisions in investments for urban area
transportation facilities the decision
makers must have estimates of the
probable results of a given investment
related to the current and anticipated
transport problems.
In an ideal situation the technician
would be able to provide decision mak-
ers with future state information com-
parable to current state data. Thus, it
could be determined if a given transport
investment reduced travel costs, pro-
vided the unemployed with better access
to jobs, resulted in an increased tax
base, reduced air pollution, provided
service to the handicapped, or re-
sponded to the host of expressed and
unexpressed desires of the regional
population and its component sub-
groups.
209
-------
Unfortunately, this ideal state has not
been achieved. The best that transpor-
tation planners have been able to do to
date is to develop somewhat crude fore-
casts of some elements of the overall
regional pattern. Such progress as has
been made has been achieved through
the use of models designed to represent
urban development and travel phe-
nomena.
Models for Urban Transportation
Planning
Models in general use in urban trans-
portation analysis have been focused
on forecasts of land development pat-
terns, the demand for travel among
subareas with a region, the mode of
travel and the choice of route. The
results of these techniques have per-
mitted evaluation of the usage of spe-
cific facilities with a view to required
size and/or economic feasibility.
A few more specific simulation mod-
els have been developed to investigate
vehicle movements on roadways, the
timing of traffic signals or power con-
sumption of rapid transit vehicles.
In general, models of urban trans-
portation have been scaled to the types
of issues to be addressed. Three broad
classes may be identified.
Macro-level—Dealing typically with
analysis of major travel corridors
only, this scale requires minimal de-
tail. Analysis at this scale is often
referred to as sketch planning.
Messo-level—Analysis in this group
are focused on specific facilities and
correspond to route location studies.
These models generally require a
large amount of data, but precision
need not be great.
Micro-level—These models treat
only a small portion of the transport
system such as a transit station or a
group of intersections, and are com-
parable to the final design stage in
construction planning. A large
amount of precise data is necessary
for accurate results.
Overview
Modeling techniques in one form or
another have been in use since the
210
beginning of major highway studies in
the early 1940's. Simple manual proce-
dures for forecasting travel and as-
signing trips to routes through a net-
work were applied in a systematic
fashion, although many judgmental de-
cisions were required.
Transportation modeling in its pres-
ent form began to develop in the mid-
19 50's with greater availability of large
scale computers. The predecessor agen-
cies of the U. S. Department of Trans-
portation as the primary sources of
funding for transportation planning
played a major role in the development
of the modeling techniques in current
use. In the early 1960's the Bureau of
Public Roads supported development
of computer programs and procedural
manuals for highway planning, while
the Department of Housing and Urban
Development funded development o
public transit planning models in the
period between 1965 and 1967.
While recognizing that the transpor
decisions of individual travelers encom
pass simultaneous evaluation of thi
need to travel, alternative destinations
alternative modes and alternative routes
the traditional planning models hav
been structured to treat each elemen
as an independent event. This structur
was adopted primarily for simplicity i
model development.
Five major types of models trad
tionally have been developed to repn
sent the events related to use of tran;
portation facilities. These are:
• Land use/land activity models
forecast urban development pa
terns,
• Trip generation models to foreca
the absolute number of trips,
• Trip distribution models to for
cast travel patterns,
• Mode-choice models to force;
the allocation of travel betwe
highway and transit and
• Route assignment models to e
amine probable paths of travel.
These have not been developed
specific formulations applicable to a
urban area; rather for each type thi
-------
has been one or more basic formulation
which required the fitting (calibration)
of parameters based on existing travel
in the specific urban area under study.
It has been this requirement which has
led to the large data collection costs
associated with transportation planning.
Chart II illustrates the typical sequence
in which the models have been used.
Chart III shows the history of the de-
velopment of the present models.
Land Use Model
It has long been recognized that the
demand for travel is a function of both
the transportation system and the pat-
tern of land use and land activity. An
area which is primarily residential will
produce trips from home to work,
school, shopping, etc., with a relation-
ship between the density of develop-
ment (number of people per unit area)
Land Use Model
The region is divided into zones and
by trend or regression analysis, the
population and employment are deter-
mined for each.
Trip Generation Model
The frequency of origins or
destinations of trips in each zone is
determined by land use and socio-
economic factors.
(either path, not both)
Trip End Modal Split Model
The origin or destination
statistics are divided between
nodes according to factors of
.rip, trip maker and mode.
Zonal Interchange Model
Based on data from origin and
destination surveys, the origins
by zone are distributed by a
model as destinations to zones.
Sonal Interchange Model
Jased on data from origin and
estination surveys, the origins
>y zone are distributed by a
tiodel as destinations to zones.
Trip Interchange Modal Split Model
The traffic between zones is
allocated to the available modes of
transportation according to factors
of trip, trip maker and mode.
Network Assignment Model
All trips are assigned to networks.
Some modeling efforts allowed
capacity constraints on assign-
ments which caused looping back
through modal split and zonal
interchange models.
CHART II—General Urban Area Transportation Planning Model
211
-------
1950
Manual
Analysis
1952
Network Analysis
Research
Uniform
Travel Growth
Models
Non-uniform
Travel Growth
Models " Fratar"
Trip Distribution
" odeling
1956
Shortest Path
Traffic Assignments
.Modeling ,
iS^ V
Trip End Mode
Choice Models
Trip Generation Using
Regression Analysis
1960
1964
1968
Trip Interchange Mode
Choice Models
Computer Software
for Highway Analysis
Disaggregate
Analysis
I
Computer Software for
Transit Analysis
Stochastic
Traffic
Assignment
Evaluation
Methodology
Direct
Demand Mo<
Interactive
Techniques
CHART III—Development of Transportation Models
and the number of trips. Similarly an
employment area will attract trips to
work.
On the other hand, it has also been
recognized that the development pat-
tern of a region is dependent, in part,
on the transport system. Constructii
of major facilities, such as freeways
rail lines, will open an area for develc
ment. Thus there is need for conside,
ble feedback between transportation a
land use planning.
212
-------
One approach to this problem has
been the development of models of
regional development patterns—land
use models—which incorporate as in-
dependent variables the existing land
use, the proposed transport system,
zoning policy, community service in-
frastructure, and the like. Not all com-
munities have used such models and not
all models have required computerized
application. Some areas have developed
their land use plan on the basis of exog-
eneously stated goals and then attempted
to design a transportation system which
would complement the land use. Other
areas have modeled the feedback be-
tween transport and land use, but with
simplistic techniques which can be ap-
plied manually.
Bay Area Transportation Land
Use Model
In general, a land use model deter-
mines for each zone in a region the
future population and employment dis-
tributions based on given estimates of
regional totals for employment and
sopulation. In addition, housing,
schools, and retail services may be fore-
cast.
In order to better understand the
vorkings of land use transportation
nodels, two of them will be described.
"he first is a model developed for the
Jay Area Transportation Study Com-
nission (BATSC) [15] which was con-
erned with the development of a re-
ional ground transportation plan for
le nine county area around San Fran-
isco as a function of the location of
asic industrial employment, location
population-serving employment and
ication of households. Eight industry
rpes are allocated to zones based on
:gression analysis of growth trends,
'.cessibility, slope of land, elevation,
ater frontage, rail lines, employment
msity, land use today, and current
are of county employment. The co-
icients of regression based on current
id past data are used for the 1990
riod.
The allocation of population-serving
iployment and households to zones
is based on estimates of probabilities
of trips to other zones using general
formulas for trip purposes. The trips
are of three types: home to work, home
to shopping and work to shopping.
Using this information and indus-
trial location, the model allocates popu-
lation to zones based on employment
in certain industries. The allocation of
population-serving population is a func-
tion of the allocation of industrial pop-
ulation and the related households. The
modeling is dependent on linear re-
gression to estimate parameters, but
also make use of deductive relationships
such as an assumed form which de-
scribes the probability of an individual
living less than time t from place of
employment.
As noted in the chapter on Urban
Models, land use models are quite com-
plex and require an extensive amount
of data (that chapter also critiques the
efficacy of such models). The major
outputs of a land use model—employ-
ment, population and households by
zones—estimated over the planning
horizon, are the inputs into the trip
generation models which calculate the
number of trips in and out of a zone.
EMPIRIC Land Use Model
Another transportation land use
model that uses somewhat different
techniques from the Bay Area model
is the EMPIRIC model designed for
the Washington Council of Govern-
ments [30]. The model consists of a
set of simultaneous linear equations
relating the changes which occur over
time in the distribution of population
and employment, within a region, to
the original distribution of such activity
in a given base year, to overall growth
in regional activity and to the effects
of exogenous planning policy and in-
vestment decisions. Activities are de-
fined in terms of district-level measures
of population, employment and land
use; planning policy measures are ex-
pressed in terms of changes in highway
and transit accessibilities, utilities,
service, zoning and open-space controls.
The linear equations relating the
213
-------
zone-by-zone shares of total regional
population and employment are for a
ten year period. They are then used
recursively for a total of thirty years.
The totals are developed outside of and
independently of the land use model.
The population is divided into age,
income, and size distributions, while
employment is divided into ten types.
The methods for developing the
model are to use linear regression on
data for 1960 and 1968. EMPIRIC is
composed of N linear equations in
2N + M terms, where N is the number
of variables of total value or change of
value and M is the number of policy
variables. In order to solve this by si-
multaneous equation solution methods,
some factors are reduced to 0 by judg-
ment which produces N equations in
N unknowns. The model is designed to
yield district-level forecasts of the re-
gional distribution of population and
employment for the years 1975, 1985,
and 1995, in a form suitable for use as
input to the Council of Government
comprehensive land-use, transportation,
community resources, public safety and
health planning activities. Each district/
time period forecast includes employ-
ment in the areas of industry, retail and
consumer service, Federal office, non-
government office, and others; and pop-
ulation by age, income and family size
distributions. Again, we note that these
projections are inputs into the next class
of models to be described, the trip
generation models.
Unlike many other aspects of trans-
portation modeling, no single recom-
mended approach to land use planning
has been accepted for use in all areas,
nor have Federal agencies funding these
studies suggested a recommended ap-
proach. Thus, a general land use model
formulation cannot be explicitly de-
scribed although many references are
available on several of the larger mod-
els.
Trip Generation Models
A trip generation model projects the
number of trips made to or from a
given area based on measures of ac-
214
tivity within the area such as per capita,
by household, by acre, by worker, by
dollar of retail sales, by square foot or
floor space or any other standard unit
of land use. In general, it is assumed
that the trip rates depend on the type
and amount of activity in a zone. Resi-
dential, commercial and industrial ac-
tivities yield different numbers of trips
in each zone.
A typical example of a trip genera-
tion model was developed for South-
eastern Wisconsin [15]. In this model,
trip destinations are estimated by re-
gression equations where the independ-
ent variables are total employment in
retail services, automobiles available,
total employment, and retail and service
acres.
There is a different linear expression
for each of the trip purposes of home to
work, home to shopping, home to other,
and nonhome based. In most cases these
equations have treated each subarea
(zone) as a data point. More recen
developments have been in the area o
disaggregate analysis which treats eacl
dwelling unit as a data point.
Chart IV outlines the independen
and dependent variables that are used ii
the Southeastern Wisconsin trip genera
tion model. The source for historic tri
description data is the highway surve
where the frequency, purpose, trip or
gin and trip destination statistics ar
collected. These surveys are a larj
component of the overall costs of tran:
portation models.
Another technique for trip gener;
tion developed in the early 1960's t
the Puget Sound Transportation Stuc
is called "cross-classification" analys.
Rather than using regression to dete
mine linear relationships, this techniqi
involves classifying each zone or dwe
ing unit according to its trip makii
related characteristics such as perso
per dwelling unit or employees p
dwelling unit. This may be a mu
dimensional stratification. The me
trip rate is then computed for ea
classification cell. In application zor
or dwelling units are multiplied by
appropriate cell mean trip rate to (
-------
Ajp = transit attractions in zone j of trip purpose p = 1,2,3,4
p = 1—home based work
p = 2—home based shop
p = 3—home based other
p = 4—nonhome based
j, = an + a12 (SE) - a13 (A) + a14 (E)
where (SE) is total employment on retail service land
(A) is automobiles available
(E) total employment
j, = a21 + a22 (RE)
where (RE) is retail employment on retail & service land
AJ3 = aai + a32 (SE) - ag3 (SA) + a.,4 (E) + a35 (RE)
where (SA) is retail and services acres
a42 (SE) - a43 (A)
(These are solved by regression on historic data)
CHART IV—Trip Generation Regression Equations
in a total trip estimate. The advantage
' this technique is the ability for analy-
5 at a disaggregate level and possibly
>r development and use of non-linear
lationships.
?nal Interchange Model
This model estimates trips between
jareas from input of trip endings,
her origins or destinations, in each
jarea. The input to the model for
:h zone is the number of origins or
itinations obtained by surveys or
3 generation analysis. The earliest
) distribution methods simply applied
istant trip rates to the survey results.
improvement in this technique was
Fratar model, which allowed each
e to have its own rate of trip gen-
ion. This has evolved into a model
d the "gravity model" which based
transfers on concepts of attractive-
s of a zone for trip ends and im-
ance between the originating and
ination zones.
'his model derives its name from its
formulation which is similar to New-
ton's gravitational equations. In brief,
the model states that the number of
trips between any two areas is directly
proportional to the amount of travel
activity in each and inversely propor-
tional to the difficulty of travel between
the areas. In actual practice this basic
concept is modified to reflect social
characteristics, travel paths by alterna-
tive modes, etc.
A typical gravity model is illustrated
by the following equation [16]:
= TiAjF(Dlj)Kli
11 j=n
2AjF(Dij)Ki,
]=i
where the factors of the equation are:
TJJ = trips produced in zone i
and attracted to zone j.
T! = trips produced in zone i.
Aj = trips attracted to zone j,
frequently a function of
floor space or acres of land.
215
-------
F(Dlj) = travel time or "friction fac-
tor" expressing spatial sep-
aration between the zones.
This is a monotonically de-
creasing function of travel
cost.
K,J = an adjustment (or calibra-
tion) factor to incorporate
social, economic, or other
factors. There can be more
than one adjustment factor.
In general, this formula is applied
for each (i, j) combination in an em-
pirical manner, adjusting factors to get
reasonable results.
A second type model that is in cur-
rent use is the "intervening opportunity
model." This takes the following form:
where,
P(V) =
: trips from zone i to zone j.
: number of trip origins at
zone i.
the probability that a trip
will end by the time V pos-
sible destinations are con-
sidered.
the trip destinations reached
before reaching zone j
where all zones are ordered
in order of increasing travel
time from i.
This formulation allows less proba-
bility of ending in zone j as the number
of intervening opportunities increases.
Trips are made by citizens to suit
their needs of the moment. They may
be in a hurry, desire comfort or pri-
vacy, or may desire many other aspects
of travel of a more subjective nature.
Often the traveler has a choice of
modes to suit his desires, such as rapid
transit, private car or a public bus. In
the planning process, one must deter-
mine the allocation of trips from zone
i to zone j among the available modes
considered in the planning exercise.
The models that determine the alloca-
tion are called modal split models [31].
Modal split models are generally either
"trip end" or "trip interchange." We
next discuss each in turn.
216
Trip End Modal Split Models
Trip end models allocate portions of
either trip origins or destinations to
alternate modes of travel based on
characteristics of the origin or destina-
tion. Trip end modal split models were
first designed for highway studies. The
Chicago Area Transportation Study
[17] first used this technique in 1955.
The method was to project subway trips
to 1980 based on 1956 rates, ther
project bus transit trips and finall)
project auto trips from zone i as £
residual. Input to this model is com
posed of four factors; subway rates
population projections, auto occupanc;
projections and quantity of autos pe
family. It is based on trip origins.
should be noted that the modal spl
model is made up of three submodel!
the central transit submodel, the loc;
transit submodel and the automobi
traffic submodel. Central transit is di
fined as trips ending in the Centr
Business District. Local transit is £
other.
Trip end modal split models ha1
become more complicated with the u
of increased numbers of factors. /
example of a more complicated ai
more sensitive and accurate model
a trip end modal split model called t
Southeastern Wisconsin Regional P!E
ning Model [15]. Tripmakers are ca
gorized into four kinds and trip
tractions are calculated by linear
gression on factors such as employme
automobiles, retail and service act
Trip characteristics are calculated bai
on friction factors, a function of do
to-door travel time. Transportation s
terns characteristics are differences
trip times. This model uses the outp
of the previously described Southeast
Wisconsin trip generation model as
puts.
Trip Interchange Modal Split Mod:
These models allocate the port'
of trip movement resulting from
distribution to the alternative trans
tation modes. The earliest and the n
simple is a procedure designed
Washington, D. C. in 1960 [31].
-------
concept is that the input to the model,
the total number of people moving
from zone i to zone j, are a market
that the modes compete for. In the
Washington model, the factors of travel
time cost, economic status of the trip
maker and relative travel service are
used for evaluation. Trip interchange
modal split models in other cities have
used other variables such as employ-
ment density, workers per household,
residential density, auto ownership,
length of trip, and time of day. Es-
sentially, in each case, the estimate of
he proportion of transit trips from zone
i to zone j is either based on linear
regression or nonlinear table look up.
ioth estimation methods depend on a
jreat deal of historical information.
The detailed data requirements for
;uch models are illustrated by the
iVashington, D. C. models need for the
'ollowing: the total interzonal trips for
vork and nonwork, travel times be-
ween zones by auto and public transit
iy purpose of trip, transit fare, waiting
'mes for transit and parking an auto,
uto parking costs, income levels of
ravelers, average auto occupancy, auto
rip costs between zones and by pur-
ose, and walking time for transit and
uto. An interesting feature of this
lodel was the use of diversion curves
•hich calculated, for example, the per-
:ntage of trips made by transit as a
jnction of travel time.
'etwork Assignment Models
The final step in the process of esti-
ating trips for a planning horizon is
assign the trips to the road and transit
:tworks. In the early transportation
anning efforts the assignment to the
:twork of a trip from zone i to a zone
ivas done by judgmental decisions as
the "most likely" route. However,
:hniques were developed in 1956 for
iding the minimum cost or minimum
rie path through a network [62]. On
5 assumption that people are all de-
ing the same thing, to make minimal
le or minimal cost routes, these ap-
aaches are now an accepted method
assignment of trips to a network. It
has also been used in an iterative man-
ner by altering trip times on links so
that all traffic does not get put on the
highest capacity links, or using "di-
version curves" which apportion trips
among shortest time and shortest dis-
tance paths.
A recent advance in route assign-
ment eliminates the concept of a single
path between two zones and assigns
trips on a probabilistic basis to all
routes within an envelope of feasible
paths.
Deficiencies of the Traditional
Approach
The transportation modeling process
as it has developed over the past twenty-
five years has served a purpose in that
it has laid a groundwork for systematic
analysis of urban problems and has, to
an extent, assisted policy makers in
making rational decisions. Unfavorable
public reaction which now attends many
transportation decisions indicates that
there are deficiencies both in the model-
ing process and in the way in which
model results are interpreted.
At the base of these deficiencies has
been the inability of planners and de-
cision makers to clearly formulate a
set of regional and subarea goals which
are compatible. Aside from general
platitudes such as maximum oppor-
tunity or freedom of mobility the plan-
ning profession has not been able to
formulate measures of desirable de-
velopment patterns which meet general
public approval. Thus, transportation
plans have been structured, for the most
part, to continue observed trends in
community development and lifestyle.
This basic formulation of regional
growth is reflected in the model results
in the form of ever increasing demands
for new highway facilities. When these
model forecasts are evaluated in re-
gional terms without consideration of
attendant subarea costs the results al-
most without question indicate the need
and desirability of massive highway
programs. While many highway im-
provements are clearly called for the
results of the modeling process has been
217
-------
to overstate the need and to avoid con-
sideration of alternatives which cannot
be readily simulated. The result has
been public dissatisfaction with trans-
portation plans and transportation plan-
ners.
More specific problems arise from
the basic model structure. The tradi-
tional chain of models treats each
travel decision—to make a trip; the
destination chosen; the mode used and
the route used—as an independent de-
cision. In actual fact a tripmaker con-
siders all facets simultaneously.
Trip generation models typically are
not sensitive to the supply of transport
services. According to the models
building new facilities such as a free-
way or rapid transit line will not, of
itself, result in more trips by the exist-
ing population. In fact, increased ac-
cessibility does result in more trips.
Trip distribution models have several
failings primarily due to the level of
aggregation. In few cases has the fore-
cast of travel patterns considered the
effect of transit in choice of a trip
destination. Only a few attempts have
been made to consider the character-
istics of individual trip makers.
Choice of mode—auto driver, auto
passenger, transit passenger—has been
the subject of much research over the
past decade. Models of mode choice
now can yield reasonable estimate of
usage for traditional transit systems, but
give little guidance on the potential for
the many new concept transit proposals
now under consideration. Similarly the
modes, requiring extensive data basis
and costly operation, provide little
guidance in transit system design.
A major failing has been in models
for system evaluation. Considerations
have been treated at a regional scale
with major attention on direct costs and
benefits—those items which are simu-
lated by the models. Little attention
has been given to economic and social
aspects of transport facilities, the im-
pact of neighborhoods disturbed by
facilities or the consequences of de-
velopment resulting from the facilities
and the attendant demands on other
aspects of community intrastructure.
218
Finally, the transport models have
not been constructed to consider equi-
librium situations. In fact, there is sig-
nificant feedback among all aspects of
the problem. Land use and transport
are intimately related. Highway con-
gestion impacts mode choice. Increased
parking demand is reflected in increased
travel cost. The cost and time involved
in applying the complex models, how-
ever, effectively precludes both cycling
of model application to equilibrium and
consideration of many alternative sys-
tems. It is perhaps this latter failing—
the inability to examine alternatives
within reasonable times and costs—
which has had the most significant
impact on the planning process.
Estimates based on the experience
of large scale urban studies indicate
that approximately 50 percent of the
cost is developed to data collection
and data processing with only 15 per-
cent devoted to evaluation. This is due
to the massive data requirements of the
current models. With this model struc-
ture planners have found that the cos
and time required to effectively trea
simple problems preclude analysis in ;
reasonable time frame. Thus, planner;
have not been able to provide timel;
response to the public or to politica
bodies such as city councils or the Con
gress. For truely effective planning, it i
imperative that response time and cos
be reduced so that analysis may b
provided to these public forums.
Recent Developments and New
Directions
Since the late 1960's most of the d<
ficiencies discussed above have bee
recognized by planning professiona
and research has been underway to d
velop techniques which consider tl
untreated aspects of planning, are mo
responsive to the political decision ma
ing process and may be applied mo
quickly and cheaply. We discuss a fe
of these next.
Multi-Modal Planning
Among the techniques now being i
lively pursued are those which \v
facilitate more accurate treatment
-------
systems containing non-highway ele-
ments. These multi-modal models per-
mit more effective treatment of both
traditional and new concept transporta-
tion facilities minimizing the highway
bias which has been engendered by the
availability of sophisticated highway
planning models without comparable
transit planning models. This new em-
phasis is illustrated by the UMTA
Transportation Planning Package now
available to and in use by local plan-
ning agencies providing a framework
for comprehensive transportation analy-
sis [73, 74].
Demand Estimates
The lack of interrelationship between
the several elements of the traditional
model chain is being attacked through
the development of "direct demand
models" [53]. This class of models,
which are still under development, at-
empt to simulate simultaneously all
aspects of the travel decision including
generation, distribution, mode choice,
md even route selection. In particular,
hese models attempt to overcome a
najor technical deficiency by relating
he demand for travel to the supply of
ransport services.
In addition the direct demand models,
is well as the newer versions of the
raditional models, place more emphasis
m disaggregate analysis. Rather than
reating large subgroups as a uniform
lass the disaggregate models recognize
lat each individual perceives transport
loices differently and, thus, makes dif-
;rent decisions. Only with such an
sproach, it is believed, can models
:curately simulate the totality of trans-
ort demands.
User-Oriented Planning Techniques
Other groups are devoting attention
> techniques which will permit cheaper
id more rapid consideration of al-
rnatives so that technical data can be
•oduced in a time scale commensurate
'th public and political demands.
lese efforts are focused on increasing
eed through use of less complex
alysis (sketch planning) [56] and
more effective utilization of the existing
techniques and large scale digital com-
puters (interactive planning) [58, 63,
68].
In sketch planning the premise is
that few major transport investment
decisions require absolute detail and
that, in fact, too much detail may ob-
scure the primary issues. By increasing
the scale of the problem the planner
requires less data and faces a less com-
plex situation so that many major trans-
port corridor alternatives and types of
transport facilities can be screened
quickly and cheaply leaving only a few
feasible alternatives requiring detailed
analysis.
Interactive planning reduces the time
scale for simulation so that in a few
hours a planner may evaluate a host of
alternatives keeping the results avail-
able for rapid evaluation and modifica-
tion. Thus the planner can profit from
experience to build upon prior findings
in developing new alternatives. This
technique offers great promise in effec-
tive utilization of human resources for
planning as opposed to mere data ma-
nipulation.
Data Sources
To reduce costs of planning increas-
ing emphasis is being placed on the use
of available data resources. Millions
of dollars have been spent in urban
area data collection over the past dec-
ade. This need not be repeated on a
periodic basis. Intragovernmental co-
operation of the use of census data and
other on-going programs combined with
statistically well designed subsampling
will enable models to be developed or
validated at considerably less cost.
Other Areas
Much attention is now being given to
new techniques to deal with urban travel
problems. These include better use of
existing street systems through demand
responsive traffic control system bus
priority lanes and the like. Models to
deal with this class of problem are now
under development. Other techniques
focus on the use of new concept, new
219
-------
technology concepts such as dual-mode
vehicles, dial-a-bus, personalized rapid
transit small vehicle systems, para-
transit, etc. To date no adequate meth-
odologies have been developed to model
these systems.
III. INTER-URBAN TRANSPORTA-
TION PLANNING
One of the most important models to
be developed in the field of transporta-
tion was the Northeast Corridor Trans-
portation model. The northeast mega-
lopolis is dependent on transportation
for movement of freight and passengers.
The megalopolis could not exist with-
out an efficient system of traffic flow.
It was recognized by the Federal gov-
ernment in the early 1960's that
improvements were necessary because
of the ill health of the railroads and the
congestion of the highways. MIT was
contracted to propose new innovative
technology such as tube transport, high
speed surface transport and other new
techniques. It was found necessary to
review investment planning and public
policy to determine the effects on the
corridor transportation. It was deter-
mined that it was imperative that as-
sessment be made of the future environ-
ment and the usefulness of new systems
and new policy in the environment. A
model was necessary for decision mak-
ing on the following type questions:
• The effectiveness to the Northeast
Corridor of proposed new and ad-
vanced technology, such as the
Metroliner service now in opera-
tion
• To determine the operational char-
acteristics and economic viability
of future transportation technol-
ogy
• To determine the changes in
transportation systems that will be
necessary to support projected
shifts in industry and population
• To determine the facilities that
will be necessary to support proj-
ected shifts in inter-modal han-
dling of freight and passengers
220
• To test the effects of public policies
on passenger and freight systems,
such as the development of AM-
TRAK
The complexities of these decision
problems led the Department of Com-
merce to consider modeling as the
method of arriving at answers. The
Northeast Corridor Model was the re-
sult [27], [28].
The objectives of the project were
to develop a framework of analysis of
transportation systems for general use
in transportation planning and to re-
duce the uncertainty in planning of
public investment and transportation
policy in the Northeast Corridor Re-
gion. The Region consists of those states
which have highly urbanized areas con-
nected or nearly connected to one an-
other along the eastern seaboard of the
United States. They are New Hamp-
shire, Massachusetts, Rhode Island.
Connecticut, New York, New Jersey,
Pennsylvania, Delaware, Maryland, Dis-
trict of Columbia and Virginia. Thi:
is roughly the Northeast megalopolis.
The states of the Northeast Corrido:
are some of the most highly urbanizec
in the United States. The majority o
the population is concentrated in th
cities which are manufacturing am
trade centers such as Boston and Ne\
York.
In the description of the Corrido
model which follows, the overall mode
is made up of nine submodels, as show
in Chart V. The workings of the sul
models will be described to illustra
the complexities of a model as va
as this.
The Corridor Model is designed
generate forecasts of the levels of ec
nomic activity in the States. These for
casts comprise "control totals" for mo
els which generate the forecasts
allocation of economic activity and po
ulation to a lower level of aggregatio
The flow from the Corridor Model to t
Inter-Regional Input-Output Model cc
sists of gross product by ten industr
sectors and the estimates of consun
tion. The flow also includes private nc
-------
Corridor
Model
Inter-Fegional
Input-Cutsut
Model
Regional
Freight
Model
Inter-Pep;ional
Allocation
Model
I
Passenger
Demand Model
Network Loading
Model
Analysis
of Impacts
Of Transportation
Model
CHART V—Northeast Corridor Model
'arm residential construction, gross
ixed nonresidential investment, pur-
:hases of goods and services of State,
acal and Federal governments. The
orecasts of gross product by industry
omprise the information necessary to
stablish the product for six subregions
'ithin the Corridor and the region out-
de of the Corridor, but within the
ates of the Corridor Project. The ex-
enditure flows provide the information
;cessary for the establishment of the
lal demands for the regions.
The Inter-Regional Input-Output
odel is an operational version of the
odel constructed by Wassily Leontief
id Alan Stout [29]. It disaggregates
e totals for each of the three regions,
irth, central and south into six smaller
jions with the Corridor, by the use
technological coefficients and param-
:rs which characterize interregional
mmodity flows, reflecting demand
d the quality of the transportation
.work. The outputs from the Inter-
gional Input-Output Model flow into
two other models. First, a model to
allocate population, employment and
income to approximately 100 subareas
of the Corridor. Second, a model which
generates the demand for freight trans-
portation services on the basis of the
predicted inter-regional commodity
flow.
The Inter-Regional Allocation Model
allocates population, employment and
income on the basis of a system of
equations which take explicit account
of the influence of changes in the over-
all transportation network. It thus pro-
vides the basis for forecasts of the
spatial pattern of regional economic
development as it is influenced by
transportation. Employment is pre-
dicted by industrial sector. Personal
income, wage differences, and the em-
ployment compositions are predicted
for the 100 subareas.
The forecasts from the Inter-Regional
Allocation Model are variables in the
model which predict passenger travel
demand. Passenger travel demand be-
221
-------
tween two areas is to a large extent
determined by the levels of economic
activity in the two areas, as well as the
characteristics of the transportation net-
work. The Inter-Regional Allocational
forecasts are used in the prediction of
freight demand among the 100 subareas
by using characteristics of the trans-
portation network.
The models as described were never
completed in the forms described but
were supplemented by approximation
methods and by other models. One
model in particular was of great sup-
plemental use, the Multi-Modal Trans-
portation Model System [77]. This
model is described in the following flow
chart.
When the demands for transporta-
tion services between origin and des-
tination pairs have been predicted, they
are allocated to routes within the net-
work using a computer simulation. In-
formation on predicted transportation
user costs per transportation unit and
predicted volumes of transportation us-
ing the network routes are converted
into measures of transportation users'
costs and benefits. Costs of the opera-
tors of the transportation system are
estimates, and a cost benefit analysis
of the direct effects of alternative trans-
portation systems is performed.
The complexities of each of the sub-
models of the Northeast Corridor proj-
ect may not be apparent in the brief
descriptions just made. The input-out-
put scenarios which are the basis for
testing alternative transportation sys-
tems are composed of many variable
estimates. The ranges of error of esti-
mate for the cost benefit analysis re-
sults are difficult to predict or even
to roughly estimate.
222
This was an iterative model when
the demand model initiated the estima
tion and supplied the mode operators
These operators made up service leve
without knowledge of what the con"
petitors are doing. The operators ot
serve the results from the last iteratio
of the results of their own and the
competitors' actions. This creates a ne1
demand and a new iteration. This c;
cling continues until the change froi
cycle to cycle becomes negligible. Tt
service characteristics of the modi
were altered in successive runs to allo
the modes a reasonable return on i
vestment and profit maximization.
IV. NATIONAL TRANSPORTA-
TION PLANNING
The Department of Transportatii
planning for transportation on a r
tional scale is generally in two decisi
making areas.
• Under existing legislation, to <
termine the disbursements of me
-------
ies to State and local governments
which best meet the investment
needs and program priorities. The
Federal government is committed
to provide increased flexibility in
Federal Aid programs, as con-
tained in the Federal Aid High-
way and Mass Transportation Act
of 1972.
• To determine new legislation to
propose to Congress to modify
the Federal role as planning un-
covers new and special problems.
The 1972 National Transportation
Report [11] is the first in a series of
reports of the state of transportation
in the Nation, and the plans of Federal,
State and local governments for im-
jroving the systems. As noted in the
972 Report, since 1957, 71% of the
'ederal monies have been spent on
lighways. Recent increases in use of
"ederal monies has been noted in ur-
lan mass transportation and aviation.
'he Federal government has been con-
erned mostly with developing high-
'ays, but now is getting increasingly
ivolved in local transportation. Only
jcently has the Federal Government
5ent anything on the railroads. In
idition, the Federal government is
jncerned in its comprehensive plan-
ng process with the depletion of the
lergy reserves of the nation. Trans-
lation consumes one fourth of the
lergy each year. Safety, air hijacking
d cargo security are also major con-
rns.
The States and local planning groups
ire asked to present their transporta-
n needs and the results are included
the 1972 Report. In the aggregate,
: States indicate a need for $670
ion for their needs of which 84%
'or highways. These requirements are
constrained by the reality of fund-
availability, energy availability, en-
jnmental degradation of alternative
d use priorities.
n order for the DOT to assess the
on's transportation needs, several
lels were used in preparing the 1972
lort, including the Airport Invest-
it Model [10] and a multi-mode
onal transportation model [12].
In addition to the National Transpor-
tation Report, the DOT is required to
provide a National Highway Needs Re-
port. This involves a field inventory in
each State of a representative sampling
of highways. These reports were pub-
lished in 1968 and 1970. The National
Transportation Report went beyond
this and did the following:
• Asked each State to develop and
report alternative capital improve-
ment programs subject to different
realistic Federal fund levels and
degrees of flexibility.
• Forecast travel and freight flow
by mode based on anticipated
growth rates of the economy, spe-
cial requirements such as defense
and the relationship between the
economy and traffic flow.
• Surveyed most transportation fa-
cilities and services largely by State
submissions, and performed eco-
nomic analyses to determine the
types of improvements likely to
be most profitable or of most value
to society.
• Surveyed the private sector and
other governmental agencies to ob-
tain estimates of future capital
investment requirements in these
sectors.
Another required planning effort re-
sults in the National Airport Systems
Plan and is directed at a ten year plan
for the development of the public air-
ports in the United States, to meet the
growth of aviation. These three reports
reflecting DOT planning efforts are re-
quired by existing legislation.
A Transportation Assessment Model
A planning model, TRANS [8], was
developed in response to the evaluation
needs for the National Transportation
Report and for assessing the disburse-
ments of Federal monies to the States,
TRANS is a national model which re-
quires as input the result from a mas-
sive national survey. This survey is
composed of 244,000 samplings of
highways, arterials, connectors and
local roads. Seventy-four parameters
are collected on each sampling, includ-
ing accident rates, pollution produced,
223
-------
average speeds, amount of traffic, travel
time, design characteristics, fatalities,
noise, aesthetic problems, etc. Stand-
ards are given to determine if a sam-
pling passes or fails on each of the
parameters. The model performs cost
benefit analyses on possible improve-
ments, measured in terms such as lives
saved or lost, and impact on the econ-
omy. The cost benefit ratios are then
ranked by State to gain a first approxi-
mation of the best use of Federal funds.
It also provides a method of evaluating
the proposals that come from each state
for extensions and improvements.
The TRANS model is an aggregative
systems. In the urban areas of over
50,000 population analysis is done by
individual highway units. Smaller urban
areas from 5,000 to 50,000 population
are grouped by State, while rural areas
are analyzed by the aggregate for the
whole State. A simplified flow diagram
for the TRANS model is shown in
Chart VI.
TRANS is really a large computer
analysis system following the steps in
Chart VI. The statistics on the 244,000
highway samples of 74 parameters are
fed into the subprogram that determines
the alternative remedies where systems
have failed standards. Based on related
socioeconomic data and the selected
remedial alternative for the highway,
travel demand is projected. The alterna-
tive highway is costed with regard to
renovation, new construction or ex-
tension. The cost savings to users is
determined by mileage savings. The
monies invested in the proposed alter-
natives are compared to the economic
and other benefits. Cost benefit ratios
are computed for each highway linli
and they are listed by ranking ordei
Transportation
System
Alternatives
Socio-Economic
Factors
Solution Set |
CHART VI—The TRANS Model
224
-------
for each State. The highest ranking
cost benefit ratios are the projects which
yield the most benefit for the proposed
investments.
The model results have not matched
the submittals from the States on their
highway needs, indicating a lack of
conformity between the two levels of
government with regard to objectives.
The objectives for most local areas are
not well defined and in some cases do
not exist.
TRANS has been used for policy
analysis as well. Some of the policy
results have been the following:
• If areas of one million population
or more staggered work travel
times uniformly over a 3 hour
morning and evening time periods,
this would bring about a 25%
reduction in required freeway
miles.
• In urban areas, an additional pay-
ment of $5,000 for each dislocated
family would reduce freeway miles
by 7% under existing funding
constraints.
• If the economic value of travel
time were to be doubled, it would
result in doubling the possible na-
tional arterial investment.
• If the cost per fatality were in-
creased by $100,000, urban invest-
ment levels would increase by 2%
and rural investment levels by 4%.
Airport Investment Model
In support of the planning effort of
he National Airport Systems Plan for
he development of the airports of the
Jnited States, an airport investment
nodel has been developed [10]. Air-
>orts exemplify the complex nature of
mblic utility investment and pricing
ecision making, which ranges across
istitutional, economic and operational
onsiderations. Federal bureaus regu-
ite the air carrier industry, while State
nd local commissions supported by
'ederal advice make the airport ca-
acity decisions. The public demand for
;rvice is related to the capacity of the
astern and the behavior of the carriers.
'emand for service is not uniformly
istributed over time in that intensive
utilization occurs for several hours of
the day and the demand is seasonal.
In the study about to be described,
capacity and cost allocation decisions
with respect to public airports are con-
sidered. A model is used to quantify
the benefits received and the capacity
required by various airport user groups.
User group demand elasticities are ap-
proximated by hypothesizing their re-
sponse to the costs and benefits of air-
port operating strategy alternatives.
From this, measures of effectiveness of
system improvement policies are ob-
tained. Approximate measures of sub-
sidization of peak users by off-peak
users and of general aviation by the
air carriers are also obtained. The model
and the study results were input to a
major transportation study [13] as a
basis for new legislation. The model
has not been used as yet for individual
airport decision problems.
In this model, passenger demand is
an input for a particular airport being
analyzed. Passenger demand is pro-
jected from 1970 to 1990 and in most
cases is assumed to be increasing. It
is also independent of the facilities
offered at the airport and the airline
schedules.
The problem addressed by the model
is to find the optimum sequence of air-
port investments in capacity to meet
the growing demand. There are two
ways for obtaining capacity increases:
• capital expenditures such as some
additional runways, more exten-
sive air control, construction of
new airports and development of a
separate short haul system, and
• non-capital alternatives include di-
version of general aviation to gen-
eral aviation airports and spread-
ing of peak activity into other time
periods.
Analysis of the capital expenditures
requires an assessment of the total cost
of usage of air carrier airports. Analysis
of the peak spreading in the non-capital
alternative requires assessment of de-
mand elasticities as related to the tim-
ing with subsequent inconvenience
costs.
225
-------
The model has two major parts:
• the calculation of total cost includ-
ing capacity cost, air carrier air-
craft delay cost, passenger delay
cost, general aviation delay cost
and general aviation passenger de-
lay cost. Capacity costs are re-
lated to the design of the airfield
and the ratio of air carrier opera-
tions to total operations, and
• a network analysis model of feasi-
ble expansion designs on a year
to year basis. There are a large
number of combinations of possi-
ble improvements of airports that
can be made on a year to year
basis. For instance a new runway
can be added in a certain year
and a new air control system the
following year. Or they can be
reversed, neither implemented or
only one of them. That results in
seven combinations for this small
problem. The model objectives is
to find a yearly sequence of im-
provements to the planning hori-
zon that minimizes the total cost.
The network analysis is done with
the dynamic programming technique.
Dynamic programming is a procedure
for selecting a sequence of decisions
which yield the best solution over a
time span. The optimal decision process
in this case is the sequence of invest-
ments in capacity to a planning horizon
of 1990. Each decision is the determina-
tion of the amount of capacity to add
to the airport each year. Each year has
a number of possible designs for the
airport associated with it. The design
possibilities for the nth year depend
on the design adopted for the (n-l)th
year, including no change from the
previous year.
An Aircraft Route Effectiveness
Model
The Federal government has require-
ments for models to aid in the evalua-
tion of airline operations in terms of
policies of fares and user charges, route
awards and requests for service changes,
mergers and intercarrier agreements,
new terminal decisions, limits on air-
port operations, effects of new aircraft,
and the impact of future growth. The
226
study and modeling effort about to be
described were aimed at developing a
method to approximate the mix of
planes, routes, schedules, and terminal
facilities that would satisfy intercity
passenger and cargo demand at mini-
mum social and economic costs [9].
The flowchart of the model is shown
in Chart VII. The heart of the system
is the network assignment module,
which assigns passengers, cargo and
aircraft to routes to minimize total
cost. Total cost is composed of airline
cost plus passenger and cargo time cost.
The output of this module is the daily
frequency of service required on each
route, along with the passenger (and
cargo) and aircraft assignments, and
a summary of the various costs associ-
ated with the solution.
The demand module estimates the
total daily passenger and cargo demand
for each city pair and determines the
share to be allocated to the air carrier
under study.
Demand
Module
I
Route
Module
Network
Assignment
Module
Timetable
Module
CHART VII—Aircraft Route
Effectiveness Model
-------
The route module selects the best
routes for a subsequent use by the net-
work assignment module. Demand,
geography, and route restrictions are
all considered.
The timetable module takes the daily
frequencies on each route and pro-
duces a non-optimal timetable, but one
that reduces carrier requirements as
much as possible.
The formulation used for the demand
module was a gravity model, described
earlier. Passenger traffic or demand be-
tween two points is hypothesized as
directly proportional to the product of
the masses of the populations and in-
versely proportional to the separation
between the points which is impedence
to travel. The friction factor is an ex-
ponential function of:
• terminal to terminal nonstop travel
time,
• ratio of actual expected travel time
to nonstop travel time,
• access time to and from terminal
to local origin or destination (in-
cluding average terminal process-
ing time),
• frequency of service, and
• fare.
The network assignment model is es-
ientially a decomposed linear program
hat assigns passengers and aircraft to
he routes on the basis of least total
:ost. The solution consists of the num-
>er of flights per day required to satisfy
he demand for each origin and des-
ination pair over specific routes.
This model was used in one instance
3 supply model results for a CAB
earing. The case was a prospective
merger of American and Western Air-
lines. The model results supported the
merger in terms of lower total costs and
the merger was approved.
Summary
In summary, the use of models in
making decisions on integrated national
transportation problems is in a be-
ginning phase. The models presented
above are designed for particular sub-
systems of the overall transportation
system. In reality the subsystems are in
competition with each other for both
freight and passengers. The existing
laws, rate structures, taxes and subsi-
dation appear to benefit one subsystem
more than another. Some subsystems
such as road networks are more con-
strained by local legislation and plan-
ning controls than are others. The ob-
jectives and priorities in local govern-
ment are diverse or non-existent, and
in many instances inconsistent with
national objectives.
These problems point to the need
for increased modeling effort on analyz-
ing the entire transportation system,
including railroads, shipping lines,
buses, trucks, passenger automobiles,
aircraft, etc. The required models for
such an analytical effort should allow
competition among the modes. With an
inter-mode competition model, policies
and fundings for a given mode can be
tested to see the effects on all modes.
The concept of a balanced transporta-
tion system of all modes could then be
studied for the purpose of changing
existing legislation and developing con-
sistent objectives and priorities appli-
cable at all levels of government.
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2] Massachusetts fnstitue of Technology,
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3] Wilbur Smith and Associates, "Mary-
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-------
[7] Highway Research Board, Press Kit,
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[35] Elias, S. E., A Mathematical Model jo
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51] Barton-Aschman Associates, Inc. and
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tion Simulation Model," November 3,
1972.
52] Brand, D. et. al., "Notes on a General
Framework for Transportation Analy-
ses," Proceedings of the ORSA-TSF
Urban Transportation Workshop,
August 1971, pp. 111-119.
3] Brand, D., "Transportation Demand
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4] Dial, R. B., "A Probabilistic Multipath
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viates Path Enumeration," Transporta-
tion Research, Vol. 5, 1971, pp. 83-
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5] Dial, R. B., "Demand Forecasting for
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Conference, Williamsburg, Virginia,
1972.
5] Dial, R. B., et. al., "A Procedure for
Long Range Transportation (Sketch)
Planning," International Conference
on Transportation Research, Surges,
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[57] Federal Highway Administration,
"Urban Transportation Planning—
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[58] Gur, Yehuda, "A Computer System for
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1972.
[59] Hitchcock, F. L., "The Distribution of a
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20,224-230 (1941).
[60] Loubal, Peter S., and Bernard Mendes,
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Model," Proceedings, Urban Traffic
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[61] Manheim, M. L., "Practical Implications
of Some Fundamental Properties of
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[62] Moore, E. F., "The Shortest Path
Through a Maze," Proc. Int. Symp.
on the Theory of Switching, Harvard
University, Cambridge, Massachusetts,
1-3, (1963).
[63] Peat, Marwick, Mitchell and Company,
"New Systems Requirements Analysis
Program," UMTA, Technical De-
velopment Plan, August 11, 1972.
[64] Peat, Marwick, Mitchell and Company,
"New Systems Requirements Analysis
Program," UMTA, General Func-
tional Specifications, Work Item 3:
Development of Interactive Sketch
Planning Techniques, December 29,
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[65] Pratt, R. H., "Demand Forecasting for
Short Range and Low Capital Inten-
tensive Options," UTDF Conference,
Williamsburg, Virginia, 1972.
[66] PRC/Systems Sciences Company, "New
Systems Requirements Analysis Pro-
gram," UMTA Executive Summary,
UMTA Transportation Planning Sys-
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[67] PRC/Systems Sciences Company and
A. M. Voorhees and Associates, "A
Manual Technique for Preliminary
Transit Feasibility Analysis," 1973.
[68] Rapp, Matthias H., "Man-Machine
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[69] Roberts, P., "Long Range Travel De-
mand Forecasting for Urban Trans-
portation Facilities," UTDF Confer-
ence, Williamsburg, Virginia, 1972.
[70] Ruiter, E., "Analytical Structures,"
UTDF Conference, Williamsburg, Vir-
ginia, 1972.
[71] Schneider, Norton, "Access and Land
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229
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way Research Record 293, 1969, pp. Analysis Program," UTPS Reference
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230
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Chapter 8
Models in Law Enforcement
and Criminal Justice
By
Saul I. Gass
SUMMARY 233
I. INTRODUCTION 235
The Criminal Justice System 235
Law Enforcement Decisions 238
Court Decisions 242
Corrections Decisions 242
II. LAW ENFORCEMENT MODELS 244
Models for Manpower Resource Allocation 244
Patrol Beat Design 251
Crime Prediction and Random Patrol 254
Simulation of the Police Emergency Response System 256
Perspective of Law Enforcement Models 261
II. COURT MODELS 262
Court Statistics 262
Court Planning and Operations 263
Court Simulation Models 266
V. CORRECTIONS SYSTEM MODELS 268
V. HOLISTIC APPROACHES TO ANALYSIS OF THE LE/CJ SYSTEM 269
REFERENCES 271
231
-------
-------
Models in Law Enforcement
and Criminal Justice
SUMMARY
Important and persistent decision-
making problems inherent in the ad-
ministrative and operational contexts of
this country's law enforcement and
criminal justice agencies are now being
resolved by the new methodologies of
modern scientific decision making. In
this chapter, we describe many of these
problems and the methodologies which
have been applied to solve them. We do
not mean to imply here that a specific
problem as interpreted by one agency
and that agency's approach to solving
it can be applied universally. There are,
however, certain classes of decision
problems which have been studied by
the law enforcement and criminal jus-
tice research and operational communi-
ties which do have general structures
and approaches for resolving them.
Hence, this chapter discusses such prob-
lems within the framework of classes of
models or decision areas (see Summary
Table).
As we are concerned with all of the
components which combine to form the
law enforcement and criminal justice
(LE/CJ) system, we first describe the
general structure of that system and
note that it is more an amorphous
structure than a true integrated system.
We can, however, subdivide the LE/CJ
by decision areas and we next describe
he range of decisions faced by admin-
istrators and operational personnel in
aw enforcement, courts and correc-
ions. Emphasis throughout is on law
enforcement as this area has been sub-
ected to a more intensive review (and
las received more funds) than the other
ireas.
Many basic law enforcement prob-
lems are concerned with the determina-
tion of the number of personnel (or
patrol units) to field during a particular
shift as a function of the expected num-
ber of calls for service. We review
statistical procedures for forecasting
calls for service and models which take
these forecasts and develop manpower
loadings which satisfy specified criteria,
such as immediate assignment of a unit
to a call for at least 85% of the calls.
Other related decision models which are
discussed deal with the division of a
city into patrol beats of equal workload
and the use of statistical procedures for
crime prediction and randomizing the
patrol pattern of a patrol unit.
Major projects are underway to de-
velop models which simulate the opera-
tions of the police dispatching and
patrol activities. Such models will enable
planners to evaluate proposed changes
to these areas prior to any field test, and
thus be able to select more viable alter-
natives for implementation. These mod-
els are reviewed, along with a discussion
of their future role in law enforcement
planning.
Court models and decision problems
revolve about the use of statistical data
for analyzing administrative and sched-
uling (calendaring) problems, and the
allocation of resource models to in-
crease the number of cases processed in
a given time period. Simulation models
have been effective here in evaluating
proposed structural changes, e.g. in-
crease in the number of grand juries,
and procedural changes.
Work in the corrections field has
been limited to models as an aid to
sentencing and the selection of proper
treatment of individuals, and as a means
233
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LAW ENFORCEMENT AND CRIMINAL JUSTICE
Models Discussed in Chapter
Summary Table
Model/Decision Area
General Type
Important Characteristics
Law Enforcement:
Resource Allocation
(St. Louis/LEMRAS)
Resource Allocation
(NYC/RAND)
Patrol Beat Design
Crime Prediction
Random Patrol (Edina)
Emergency Response
(District of Columbia/
MATHEMATICA)
Courts:
Allocation of Resources
Court Operations
Court Calendaring
Juror Selection,
Juror Waiting Time
Corrections:
Sentencing,
Rehabilitation
Forecasting and Queuing
Model
Dynamic Programming
Linear Programming
Multiple Regression,
Exponential Smoothing
Monte Carlo,
Randomization
Simulation
Queuing,
Linear Programming
Regression Analysis,
Simulation
Computer-Assisted
Logical Evaluation,
Simulation
Simulation
Statistical Analysis
Uses historical data to forecast
level of crimes by type and deter-
mines number of patrol units re-
quired to maintain a desired level
of response
Predicts the performance of a
specified manpower level and
police deployment in terms of dis-
patch delay, average response
time, patrol frequency and time
available for patrol
Divides a geographical area into
specified number of patrol beats,
each with approximately same
level of workload
Predicts crime levels by type and
area; determines if crime factors
are at specified levels and a crime
can be expected to occur in an
area
Assigns units to patrol areas
based on probability of crime
occurrence
Simulates movement of a patrol
force for evaluation of alternative
decision rules for dispatching calls
for service, assignment of patrol
units and general patrol strategies
Determines number of judges to
serve expected number of cases;
allocates cases to judges over time
to maximize number of cases
cleared
Evaluation of specific alternatives
for speeding up and improving
court operations
Develops calendar of cases so as
to reduce delays, over or under-
loading, and waste of personnel
time
To determine correct size of jury
pool to maximize utilization
Evaluation of different correc-
tional programs on recidivism
LE/CJ System:
Offender Flow and Cost
(Science and Technology
Task Force/JUSSIM)
Steady-State,
Probabilistic Linear
Flow, Simulation
Evaluation of parametric changes
and alternatives in the LE/CJ sys
tern in terms of total system cost
manpower, criminal population
234
-------
of analyzing correctional and rehabilita-
tive programs.
Attempts at analyzing the interrela-
tionships of the components parts of
the LE/CJ have produced models which
can be employed by State and jurisdic-
tional planners to aid in evaluating total
LE/CJ programs and their cost. Such
holistic models have also been used to
demonstrate to LE/CJ planners how
their decisions and particular activities
impact the rest of the LE/CJ system.
MODELS IN LAW ENFORCEMENT
Trial by Mathematics
In 1964 a black man and his white
wife were convicted of a mugging in San
Pedro, California mainly because they
were the only couple in the area who
matched the reports of witnesses on five
counts: the girl was a blonde, she had a
ponytail, her companion was black, he
had a beard, they drove a yellow car.
The prosecutor estimated the prob-
ability of each characteristic separately
—1/10 for the car being yellow,
1/1000 of the companion being black,
and so on. He multiplied the five frac-
tions and convinced the jury that the
probability was 1/12,000,000 that a
matching couple lived in the vicinity.
Not until four years later did the Cali-
fornia Supreme Court reverse the deci-
sion after a judge less ignorant of
mathematics persuaded the court that
he estimate should have been 41/100.
(News item, Time, April 26, 1968, p. 41, as
reported in Scientific American, October
1972, p. 111).
I. INTRODUCTION
The above news item serves to il-
ustrate how the use of mathematical
malyses and related decision-making
nodels in the areas of law enforcement
,nd criminal justice (LE/CJ) differs,
(i a sense, from the use of decision-
naking models in most other fields.
Although, as we shall see, the majority
f LE/CJ models do not deal with a
jecific individual or criminal situation,
ic decisions made with the help of
such models have a more direct bearing
on our daily lives than is the case in
other fields. Thus, it is felt that human-
istic considerations must always be
borne in mind when considering a
LE/CJ model—our models are not in-
fallible and rest heavily on assumptions
and available data.
Until the 1960's most LE/CJ models
were of the simple probabilistic variety
dealing with the probability associated
with a particular circumstance or set of
circumstances. If an impressively small
probability holds, then some contend
"that 'beyond a mathematical doubt'
transcends 'beyond a reasonable doubt'
in the court room" [1]. We shall not,
however, dwell on this restricted area
of criminalistics as more important and
exciting advances in LE/CJ models
have recently occurred and are becom-
ing an influential part of the LE/CJ
decision-making framework. We shall
review the background and develop-
ment of such models in this chapter.
The Criminal Justice System
We tend to use the phrase "Criminal
Justice System" as if it meant the dic-
tionary definition of "a regularly inter-
acting or interdependent group of items
forming a unified whole." Even a
cursory investigation shows that the
"unified whole" is an illusion. As noted
in [2], "every village, town, county, city
and State has its own Criminal Justice
System and there is a Federal one as
well. All of them operate somewhat
alike. No two of them operate pre-
cisely alike." The Criminal Justice Sys-
tem has three separately organized parts
—police, courts and corrections—each
having distinct tasks. Figure 1 shows a
general view of the Criminal Justice
System which is more or less applicable
to most jurisdictions [2]. There are
over 46,000 public agencies in the
Criminal Justice System [4].
Figure 1 can also be viewed as a
parital decision-making framework or
tree for LE/CJ, where a branch repre-
sents someone's decision that has to be
made, e.g. make an arrest, plead inno-
cent, schedule trial, determine length
of sentence. We note that there are
235
-------
many decisions which are not included
in Figure 1, especially those dealing
with the operations and planning of the
LE/CJ components. In what follows,
we do not mean to catalogue the full
range of LE/CJ decisions nor the full
scope of how models have been of as-
sistance. However, we shall describe by
major components—law enforcement,
courts, corrections—many decision situ-
ations, to be followed with discussions
of how specific models have been ap-
plied to aid the LE/CJ decision process.
Due to our tradition of assigning most
law enforcement and the administration
of justice activities to the States, we shall
emphasize State and local problems
over Federal concerns, recognizing that
This chart seeks to present a simple vet comprehensive view
of the movement of cases through the criminal justice system.
Procedures in individual jurisdictions may vary from the
pattern shown here. The differing weights of line indicate
the relative volumes of cases disposed of at various points
in the system, but this is only suggestive since no nationwide
data of this sort exists.
Prosecution
Courts
Information
Unsolved or Released Without Released Without Charges Dipped Charges Droppe
CrifflM Not A»ejled Proaecul'on Pioseculion or Dismissed ot Dismissed
May continue until trial
Administrative record of acres! First step at
which temporary release on bail may be
available
3 Before magistrate, commissioner, or justice of 5 Charge filed by prosecutor on basis of
peace Formal notice of charge, advice of
f iQhts Bail set Summary trials for petty
offenses usually conducted here without
further processing
4 Preliminary testing of evidence against
defendant Charge may be reduced No
separate preliminary hearing for misdemeanors
in some systems.
information submitted by poltcfl or citizens.
Alternative to grand iury indictment, often
used in felonies, almost always in
misdemeanors
i Reviews whether Government evidence
sufficient to justify trial Some States have n
grand jury system, others seldom use \\.
FIGURE 1—A general view of The Criminal Justice System
236
-------
there is some overlap, especially in the
areas of courts and corrections.
We first note that even though the
LE/CJ system consists of operating
entities which are administratively inde-
pendent and, in some situations, even
have conflicting objectives, we can
analyze the behavior of the system,
especially in terms of how changes in
the operation of a major component
impacts the ability of other components
to perform their functions. For ex-
ample, about 1.8 million persons were
arrested for drunkenness in 1971 [5].
If new approaches to the handling of
this problem were instituted on a large
scale, e.g. detoxification and treatment
Arraignment
>arge Dismissed Acquit
j Trial J
Sentencing
Arraignmenl
Appeal
Sentencing
centers, then this would change not
only the time the police would have
for performing other enforcement ac-
tivities, but the operations of the related
courts and jails would also be modified.
(The Commonwealth of Massachusetts
now considers drunkenness as an illness,
not a crime.) Changes like new ap-
proaches to correctional institutions,
new sentencing and parole procedures
and other proposals cut across the com-
ponents of the LE/CJ system and can-
not be evaluated in isolation. A system
analysis and related model of the total
LE/CJ system could enable planners to
measure such impacts and decisions.
We shall discuss such models below.
Probation
Penitentiary
M
it
Habeas
Corpus
Probation
Probation
Adjudicator Hearing J
12
Nonadjudicatory
Disposition
r
\
\_ \
\ Juvenile Institution V
\\ .. /
Parole
7 Appearance for plea, defendant elects trial by 9 Challenge on constitutional grounds to legality 11 Probation offi
judge or jury (if available), counsel for indigent of detention May be sought at any point in court action.
usually appointed here in felonies Often not
at all m other cases
10 Police often hold informal hearings, di
8 Charge may be reduced at any time prior to adiust many cases without further ore
trial in return for plea of guilty or for other
reasons.
12 Welfare agency, social services, co
medical care, etc , lor cases where
adjudicatory handling not needed
aurce: Reference [2]
237
-------
Law Enforcement Decisions
For our purposes we are concerned
mainly with the operation of an urban
police department. However, much of
our discussion is independent of the
size of a department and its demo-
graphic descriptors. As we take a close
look at what we define to be the set of
law enforcement agencies, we find ex-
treme diversity to be a major char-
acteristic. A Department of Justice sur-
vey [4] noted that there are over 14,000
separate agencies responsible for en-
forcing laws on the Federal, State and
local levels of government. Most of
these are located in boroughs, towns
and villages; with about 3,000 each in
the counties and cities. Their size ranges
from the one man police department
of Alpha, New Jersey to the 33,000
man department of New York City.
From an organizational point of view,
each police department has a full range
of decision-making problems, many of
which are similar to those encountered
in industrial or other governmental
settings. We next describe some of these
problems in law enforcement terms.
Much information is available which
relates the level of crime with demo-
graphic and socio-economic data [6].
Our approach to measuring the effec-
tiveness of our law enforcement agen-
cies ranges from the empirical measure
of the latest crime statistics, to the
emotional measure supplied by the
latest rash of unsolved murders. There
does not appear to be an agreed upon
measure. Unlike profit-oriented organi-
zations, the activities of a police de-
partment in terms of service to the
community cannot be measured in dol-
lars or even in terms of a more general
measure. (This is, of course, true for
most governmental organizations.) For
the police, this problem is further
compounded by the lack of consensus
on what the police should be doing, i.e.
what is their job?
The problem of police activity and
measures was studied in the report [7].
The authors were concerned with de-
cision-making in the area of police
patrol. They state that "the major func-
238
tions and activities of all police patrol
forces are (1) to prevent and deter
crime, (2) to apprehend criminals, (3)
to respond to calls for assistance from
the public, and (4) to regulate certain
noncriminal activities such as traffic."
They discuss problems in terms of effi-
ciency, effectiveness, and equity. Effi-
ciency deals with measures internal to
the system (the number of patrol
vehicles operating during a shift), effec-
tiveness implies measuring output or
external effects (the level of crime in
a city), and equity has to do with how
a service and its benefits are distributed
among the population. For our pur-
poses, we shall use the general term of
measure of effectiveness for any cri-
terion which aids the decision-maker
to select among alternative actions.
In addition to the level of crime by
crime types, other law enforcement
measures of effectiveness include the
average response time to a call for
service, the number of arrests, the num-
ber of crimes which are cleared (an
arrest or other disposition for a crime),
the number of convictions, the rate and
direction of change of the level of
crimes, the workload for a patrol unit,
the number of calls for service made to
the police. We might also consider such
subjective indicators as how the public
"feels" in terms of safety in streets, as
measured by a survey. For example, a
Gallup Poll [8] taken in December 1972
resulted in 21% of the urban respond-
ents stating that crime was their com-
munity's worst problem, and that fear
to walk alone in their neighborhooc
increased from 31% in 1968 to 49%
in 1972. Thus, one of the key oper
questions for this part of the LE/C.
system is how can we determine if th<
decisions and actions made by law en
forcement agencies improves their ef
fectiveness?
From a model point of view, the wa;
around this dilemma (which is not re
stricted to the LE/CJ area) is to offei
for a particular model, a specialize!
measure of effectiveness which enable
the decision-maker to select amon
available alternatives. The measur
-------
represents a surrogate measure which
is both understood and accepted by the
decision-maker and is more tractable
to formulate within the model frame-
work, e.g. the average response time for
a set of new patrol beats instead of the
change in the crime rate which results
due to the new beats. This is the ap-
proach which is used for law enforce-
ment models and other components of
the LE/CJ system. In many instances,
a single measure cannot be used and a
composite measure of effectiveness,
which could be a set of numbers or
set of information, must be employed in
making the decision.
Like most other organizational units,
law enforcement decisions can be
dichotomized into administration and
operations. We next look at some of
these decision situations stated in law
enforcement terms.
In the domain of administration we
find the police faced with the following
problems:
1. For given demographic parameters
—population, level of crime, urban
configuration, etc.—how many full-time
employees should a police department
have and how should they be dis-
tributed between patrol, detective and
administrative divisions? We find, as a
rule of thumb, that the police force in
large urban areas consists of about 4
employees per 1000 population and
ranges down to about 1 employee per
1000 population in the small cities and
towns.
2. Given a force level, how should
the manpower be allocated to police
districts, precincts, shifts and patrol
beats over time?
3. How should a city be divided into
jolice districts, precincts or beats based
Dn demographic, geographic and crime
jarameters?
4. How should a police district be
Broken down into individual police
)atrol beats so that each patrol unit
las equal work level? What definition
)f work do we use?
5. How should the patrol force be
ivided between a one or two-man car,
oot or scooter patrols and which
patrol type of types assigned to a par-
ticular beat?
6. In the long-range planning area
we need to determine manpower levels,
location of new facilities, contingency
riot and other emergency plans, equip-
ment needs, etc. How can we determine
the value of technological advances in
car locators, nonlethal weapons, patrol
vehicle design, communications?
In the operational area we have the
following problems:
1. How to identify a particular pat-
tern of crime which is related to the
same criminal or set of criminals?
2. Given that we have identified a
particular crime pattern, how do we
identify a probable set of suspects?
3. Given someone who has been ar-
rested, how can we determine which
crimes (if any) are associated with the
suspect?
4. With regard to the geographic
distribution of crime, how can we best
pre-position special patrols in order to
increase the probability of apprehension
and to increase the patrols' deterrent
power? How much preventive patrol
should a patrol put in? Is preventive
patrol effective in deterring crime?
5. How should the limited investiga-
tive effort be allocated and to which
crimes? (A preliminary study for the
President's Crime Commission [9] re-
veals that the investigative force usually
works on those crimes which have a
solid clue, e.g. named suspect, auto
license plate number, and do little Sher-
lock Holmes type work on the run-of-
the-mill crime.)
6. Given a call for police services,
which unit should be selected to re-
spond? As police forces respond to
such calls, how should the remaining
forces be dynamically re-allocated
based on current and expected de-
mands?
To obtain a better understanding of
specific law enforcement problem areas,
we next discuss the major set of activi-
ties of police agencies, termed the police
emergency response system. As back-
ground, we note that police activities
were first scrutinized in detail in light of
239
-------
modern systems analysis and modeling
procedures by the staff of the 1965
President's Crime Commission. The
technical studies done by the Crime
Commission were reported in [9] by the
Science and Technology Task Force.
The Task Force modeled the functions
of a generic police department in terms
of a flow chart of activities associated
with an occurrence of a crime. This
chart is shown in Figure 2. (The source
is [7] which modified the Task Force
Chart to include the noncrime activities
of the police.) The response process
begins with the detection of a crime
by a patrol unit or by a report to the
police by an alarm, a witness or a vic-
tim. After receiving the information,
an appropriate response must be made
and patrol officers are dispatched to the
scene. This is followed by search and
investigation (interrogation, data gather-
ing, suspect checking) and then, per-
haps an arrest.
To support the emergency response
process, decisions must be made and
activities performed, some of which are
based on analysis and some of which
are based on experience and intuition.
At this time, most such decisions are
made without the aid of formal models.
(Here, we include decisions required
in the planning function as well.) We
do note that crime detection and pre-
vention activities have used pin maps—
which in some agencies have been re-
placed by computer contour and density
maps—and basic statistical analyses,
e.g. the number of crimes which oc-
curred in the preceding day, to aid them
in prepositioning forces and developing
patrol routes and patrol beats.
The main measure of effectiveness
of the response system is considered
by most analysts to be the patrol re-
sponse time, i.e. the time from receipt
of a call for police services until the
arrival of a patrol unit at the scene
[7], [9], [10]. A Crime Commission
study in [9] showed that for emergency
calls for service for which an arrest
was made, the average response time
was 4.1 minutes; for those emergency
calls which did not culminate in an
arrest, the average response time was
6.3 minutes. A similar pattern existed
for nonemergency calls for service. A
short response time also has the benefit
of improving the public's view of the
department and thus, the public's
measure of effectiveness. A department,
concerned with response time, can
make appropriate changes in its mode
of operation, each such change repre-
senting a decision which has to be
evaluated in terms of improved effec-
Victim)
Witnewti
Othcn
Delected
Patrol
_
Police Car
Dkipaiched
By Radio
—
Police Can
Travel to
Scene of Call
—
Provide
r
FIGURE 2—The Police Emergency Response System
Source: Reference [7]
240
-------
tiveness and associated costs (person-
nel, equipment). To further illustrate
the law enforcement decision problem
area, we next describe the elements
of the emergency response process in
more detail. The reader will be able to
note those elements which can be
changed so as to improve the total re-
sponse time. Some of the decisions to
effect such changes can be supported
by decision models. We shall discuss
a few of these models in the sections
that follow.
Once a crime has been discovered,
he information has to be relayed to
he police communications center. De-
ays can occur if there are not enough
runk lines or operators. The operator
must determine the patrol beat location
}f the call and pass the request to a dis-
jatcher. Some departments combine the
•oles of operator and dispatcher. For
:xample, Chicago has organized its
:ommunications center so that a call
nade from any police district is auto-
natically assigned to an operator/dis-
latcher who only handles that district
nd is quite familiar with the district's
reels and patrol beats. New York City
as installed a computerized system
/Inch automatically matches the loca-
on of the scene with the patrol beat
nd displays this information to the
ispatcher. The use of a special police
mergency number (911) and the abil-
y to dial that number from a coin
:>x without using a coin has been insti-
lled in some localities. Special alarm
3xes for voice communication directly
' police and fire dispatchers are being
'aluated, while silent alarm and tele-
ionic alarm systems tied direclly lo
e police communicalions cenler are
use.
The police dispalcher must select an
ailable patrol unit to respond lo an
icrgency call. In many inslances, Ihe
al car is busy and a neighboring free
r is assigned, or Ihe call is slacked in
jueue depending on its priority. Each
jarlmenl develops unique dispalching
es for Ihe assignmenl of an emer-
icy call for service lo a palrol unil.
cision consideralions include Ihe
priority of the call (robbery in process,
drunk in the streel), which unil appears
to be closest in terms of travel time to
the scene, availability of the corre-
sponding beat car, the preemption of a
car servicing a lower priorily call, one-
man or Iwo-man unit response. Studies
have been made lo measure Ihe de-
crease in average Iravel lime based on
varialions in the dispatching rules. For
example, Ihe dispalcher does nol know
which patrol unit can gel to the scene
the fastest. Car locator syslems (which
can be ralher cosily) have been dis-
cussed in lerms of supplying Ihis infor-
mation to Ihe dispalcher.
The ability of the dispatcher lo reach
Ihe selecled palrol unil depends on Ihe
congeslion level of Ihe radio communi-
calions channels. Many departments
find Ihe radio waves overloaded in busy
periods and much lime is wasled before
a link is established. The analysis of
congestion in telephone and radio sys-
tems can be done by models which
indicale expecled delays and whal de-
crease in Ihe delay we could expecl by
addilion of a line or operator. As digital
informalion can be packed lighler lhan
voice over the same line, digital printers
are being experimented with for the
Iransfer of certain informalion.
Once Ihe unil arrives on Ihe scene,
Ihe law enforcemenl personnel are Ihen
faced wilh many relaled decision prob-
lems. These include the type of search
conducted, initiation and carrying out
of an arrest, the reassignment of Ihe
patrol unit to another call or lo pre-
ventive patrol, evalualion of evidence,
suspect determinalion, Ihe final clear-
ance of a crime.
From the above discussion the reader
should now have some understanding
of Ihe complex process associaled wilh
Ihe planning and operalions of a lypical
urban police department. Crilical deci-
sions ranging from whal nexl year's
manpower level should be lo how many
men should be on duly Ihe nexl shift
are being made on a routine basis.
Some of Ihe more imporlanl models
which have been developed to aid law
enforcement personnel in making some
241
-------
of their decisions are described in a
following section.
We continue our discussion of the
LE/CJ decision process by next review-
ing the court system decisions and the
correctional system decisions.
Court Decisions
The country's court systems are quite
diverse with over 13,000 State and local
courts [4]. Not all courts are criminal
courts, e.g. probate and family relations
courts. About 1,700 courts are located
at the State level of government, while
the remaining are at a local level
(county, city, township). The analysis
of court related decisions and the ap-
plication of models to aid in these de-
cisions is compounded by the lack of
central authority. As the President's
Crime Commission pointed out: "The
complex problems of court administra-
tion will not yield to any one simple
solution, but a well-structured and effi-
ciently organized system is a condition
precedent to further change. Rebuilding
the structure and organization of the
administration of criminal justice has
two aspects, the creation of a unified,
simplified court structure within a State
and the establishment of clear and di-
rect administrative responsibility within
that system [11]."
The decision framework of a court
system, as distinct from those made by
a judge in a particular trial, concerns
the administration and day-to-day man-
agement of the court's facilities and
personnel. This, as we shall see, has
been the main direction of application
for models in this area. A basic concern
of a court system is the reduction of
the delays in the processing of a case.
The major delays occur at the following
key points in the judicial process: arrest
to first judicial appearance, appearance
to formal charge, formal charge to pre-
trial proceedings, pretrial to trial, con-
viction to sentencing, sentencing to ap-
pellate review. A basic question here is
to determine what changes in a particu-
lar court system will be effective in
reducing delay, recognizing that such
changes call for financial, personnel
242
and even legal modifications of the
present system. Some decisions to have
more judges and juries, or to make pro-
cedural changes based on delay reduc-
tion can be evaluated with the aid of
models.
Other court management problems
include those of calendaring or schedul-
ing the cases for a particular date, the
assignment of a judge and the finding of
an available courtroom, and proper
utilization of jurors. Measures of effec-
tiveness for a court system could in-
clude the following: the average elapsec
time of court proceedings for each type
of case; holding the number of judges
and courtrooms to a minimum whih
the elapsed time for each case is kep
within certain limits: reduction of th<
backlog of total cases; or some measun
of the social good of the court process
i.e. the constitutional guarantees grant
ing an accused man the right to
speedy trial [12]. The minimization o
the average delay time for all case
might be an appropriate surrogat
measure.
Contrasted to the decision problen
in the management and administratio
of a court system is the set of decisioi
related to the disposition of a particuh
case. These include pretail release of
defendant, with or without bail; tl
granting of probation, the type ar
length of sentence; and the assignme:
to a particular correctional institutic
or process. We would hope, based (
the facts of a case and the particula
of a guilty party, that the sentencii
process would be such to increase t
chances that the guilty person wov
not become a recidivist. How to me!
ure this relationship has proven diffici
and little work has been done in t
important area. An additional area
the use of appropriate models
prosecuting and defending attorneys.
Corrections Decisions
The corrections section of the LE/
system is, like the other components
law enforcement and courts, basics
a State and local function. Of the o
7,bOO corrections agencies, there
-------
4,435 adult correction agencies, 724
juvenile correction agencies, and 2,445
probation offices under State and local
administration [4]. Over one million
offenders are assigned to the above
agencies at a cost of over one billion
dollars [13]. Like the court system, the
correction system decisions can be
dichotomized into (1) management and
administration decisions and (2) de-
cisions affecting an individual offender.
As noted in the President's Commission
Task Force Report on Corrections [13],
both areas are handicapped by the prob-
lems of data availability and relevance:
the data essential to the making of
sound decisions often are not available,
and information that is available may be
irrelevant to the outcomes which deter-
mine whether the decision was sound.
There is a major need to determine what
data are necessary, for example, to
iecide to parole an offender, or to insti-
ute a new type of rehabilitation pro-
;ram.
It is generally agreed that the estab-
ished goal of today's corrections system
n the United States is given by "Refor-
nation, not vindictive suffering, should
e the purpose of penal treatment" [13].
"his is contrasted to the deterrence
leory of correctional institutions. The
:form approach has led to a wide
mge of services and specialized insti-
itions directed to reforming the of-
ander: vocational training, prison
;hools and factories, probation and
irole, community programs, halfway
uises. "These and similar measures
tve never been tested definitively, and
e reform movement has led an uneasy
existence with the deterrence and
rlier harsher approaches" [13]. How
evaluate such different approaches
corrections is a viable area for the
plication of certain models. Similarly
" the decision areas associated with
: course of an offender within the
rrectional environment. This latter
•a. is an extremely difficult one as it
'olves about information which is
iically qualitative and open to wide
interpretations. The Corrections Task
Force noted [13]:
"Whether the decision is to invoke
the judicial process, to choose be-
tween probation or imprisonment,
to select the appropriate degree
of security in a correctional insti-
tution, or to determine the tim-
ing for release from incarceration
or the necessity for revocation of
parole, judicial and administrative
decision-makers are concerned
with very similar issues:
1. The degree or extent of threat
to the public posed by the indi-
vidual. Significant clues will be
provided by the nature of the
present offense and the length of
any prior record.
2. The nature of the response
to any earlier correctional pro-
grams.
3. The kind of personal stability
and responsibility evidenced in his
employment record, residential
patterns, and family support his-
tory.
4. The kind of personal de-
ficiencies apparent, including edu-
cational and vocational training
needs.
5. The personal psychological
characteristics of the offender that
determine how he perceives the
world and his relationship to it."
What measures of effectiveness can
we apply to the correctional process in
the evaluation of the success of the
process or in the selection of al-
ternative solutions to the decision
problems? On an individual basis, the
obvious measure is that the offender,
upon his normal return to society, does
not commit any additional crimes.
Variations of this theme include the ex-
pected proportion of the current con-
victed population that will be in prison
as the result of current or future con-
victions, the expected number of times
current prisoners will be reincarcerated
for new crimes, the equivalent annual
cost to society for each criminal career,
and based on estimates of first offender
input, the expected system population
over a 10-year period [14], [15].
243
-------
For corrections we must emphasize
that research and application of models
in this major element of the LE/CJ
system is extremely weak.
II. LAW ENFORCEMENT MODELS
Models for Manpower Resource
Allocation
The most important task of police
operations is the proper allocation of
resources to meet the expected demand
for service. Here we are basically con-
cerned with the level of the patrol force
on a daily or even shift basis and a
department's desire to respond to emer-
gency calls for service within a speci-
fied time.
There is a related planning problem
of determining the level of the patrol
force and total personnel for the next
budget period. Both problems require
some means of predicting the future
course of events. Such predictions, as
we shall note over and over again, must
be based on reliable and consistent data
gathering procedures.
We shall discuss the resource allo-
cation problem by first discussing
simple projection procedures and then
discussion a major contribution to police
resource allocation, that of the resource
allocation technique developed by the
St. Louis Metropolitan Police Depart-
ment.
In law enforcement, the use of simple
statistical models have a long history.
These include the use of pin and other
maps to locate crimes by types in an
attempt to glean some behavioral crime
pattern and predict the location of the
next incident or to highlight the dense
areas of crime, and graphs and tables
showing frequency counts over time
which indicate trends and which at-
tempt to convey some measure of police
effectiveness. More recently, with the
advent of computers, advanced statisti-
cal procedures are being employed. We
shall discuss some of these applications
which deal with the problem of predict-
ing the level of crime in future time
periods in specified areas of a city.
These types of models are useful in
244
scheduling the total level of patrol
forces required for the next period of
time and for the shifting of patrol forces
from expected low crime areas to high
crime areas.
For statistical analyses to be effec-
tive, proper reporting procedures must
be instituted to insure the reliability of
the results. Standard statistical pro-
cedures which can be applied by hand,
if the data is not too extensive, or
which are available for most computers,
can offer a full range of analytical pro-
cedures, coupled with the proper statisti-
cal tests for indicating that the assump-
tions of the model are correct. The
use of these type of analyess for plan-
ning purposes also requires that the
police department establish basic guide-
lines which relate to the level of crimi-
nal activity to workload for a patrol
officer, detective, and other personnel.
Given such planning ratios, and statisti-
cal predictions based on past events.
the department should then be able tc
estimate the desired total personne
level, as well as the breakdown betweer
the personnel divisions.
For a given patrol force, we nex
address the problem of how maff
patrol units should a department havi
during a particular tour of duty. J
very powerful resource allocation pro
cedure has been developed by the sta
of the St. Louis Metropolitan Polic
Department [19], [20], [21]. This coir
puterized system is available from con
puter manufacturers and others und«
the name LEMRAS: Law Enforcemei
Manpower Resource Allocation Sy
tern [22], We shall use the acrony
LEMRAS in the discussion below.
LEMRAS is designed to (1) predi
calls for service for each of a police d
partment's crime reporting areas (poli<
beats or other units) over the near ter
by eight-hour shifts, (2) the avera
amount of police time involved
handling these calls, and (3) the e
pected number of calls which can
handled without delay, i.e. immediatf
assigned to a free patrol unit in t
police district in which the call ori
nates. Thus, a police district co
-------
mander can determine how many calls
he can expect in his area and how many
units he should have during a shift
which will minimize the number of calls
delayed. This measure is a surrogate
measure of effectiveness for the implied
measure of minimizing the average time
to respond. The use of LEMRAS re-
quires that a district commander has
flexibility in establishing patrol beats
and the assigning of a different number
of patrol units during each shift. This
is not the case in many police depart-
ments as patrol beats and shift man-
power levels tend to be fixed, thus re-
moving the ability of the commander
and the department to have a more
effective flexible response to changing
conditions. Also to be more valuable,
a police department using LEMRAS
should gather its statistics by areas in
the city which are smaller than the
patrol beats. St. Louis and Washington,
D.C. Police Departments, for example,
lave established such reporting areas.
LEMRAS consists of two main pro-
cedures: a statistical procedure for pre-
dicting crime level by reporting area
md priority of calls, and a queuing
nodel for determining the ability of a
jolice district to respond to its predicted
:alls, by priority of calls, without delay.
The validity of these models is based
>n the following assumptions [22]:
1. Police workload, as measured
by calls for police service, has a
seasonal fluctuation that, within
reasonable limits, is repetitive from
year to year.
2. The distribution of police
workload over the hours of the
week is substantially the same for
all weeks of the year, and such
changes as do occur are slow in
developing.
3. Successive event occurrences
act as if they are independent.
4. The service times on succes-
sive calls for service act as if they
are independent.
5. All patrol units in an area
being analyzed (such as a police
district) are subject to being as-
signed to answer any call for serv-
ice in that area.
6. Any calls for service that
cannot be dispatched immediately
after being received are held by
the dispatcher until a unit is avail-
able for assignment. Calls are not
stacked in the patrol units.
7. Under normal conditions, a
unit assigned to one call will not
be pulled off that assignment to
handle another assignment with a
higher priority. Note that this is a
"normal condition" and will be
violated when necessary.
8. The assignment of the work-
load for an event (the time re-
quired to service the event) can
be totally assigned to the hour in
which the event is recorded with-
out substantial impact on the
analysis of workloads or events.
The statistical method used to pre-
dict the level of crime activity is called
exponential smoothing [23]. Expo-
nential smoothing is a method of time
series analysis which can be viewed as a
special type of weighted moving aver-
age. The more usual weighted moving
averages have a limited period and give
equal weight to each month within the
period. In exponential smoothing more
recent information is given more
weight. The weights decrease geo-
metrically, so that after a sufficient
number of periods have elapsed, the
weights for older data are so small that
the older data contributes essentially
nothing to the current average.
For LEMRAS, smoothed averages
of the number of calls for service and
the associated workload are maintained
for geographic areas in a city (entire
city, districts, beats, reporting areas).
Smooth averages are also maintained
on the number of calls for each hour
of the week and for each week of the
year. Using this information, predic-
tions are made by hour of the week
for the geographic areas. As noted in
[19], the element being predicted are
the emergency calls for service which
require police patrol response. To per-
form this prediction the historical data
must be collected by week of the year,
hour of the week and by geographic
areas. This data collection is a major
245
-------
enterprise in itself and requires a strong
commitment by the department in terms
of personnel and equipment.
As the number of events, i.e. calls
for service, have a seasonal effect, the
procedure is usually modified to com-
pensate for such weekly and hourly
variations. In addition, the estimated
calls can be broken into various cate-
gories of calls, e.g. crimes against per-
sons, crimes against property, etc. in
that each such call has an associated
average time for servicing the call.
St. Louis predicts for eight classes of
radio run emergency calls for service.
The final estimates are obtained for
the coming week by hours of the week,
based on the smoothed observations
of the previous weeks. These estimates
are then converted into minutes of
work required to service the estimated
calls for serivce. An example of such
predictions is shown in Figures 3 and 4
respectively. For example, Figure 3
shows that over the next three weeks
during the Monday hours of 7:00 to
11:00 A.M., a total of 63 calls is ex-
pected, while Figure 4 shows that dur-
ing these three weeks we expect a total
of 2,189 minutes will be used to service
these 63 calls.
Given these types of predictions for
the coming week—that is for each hour
of the week we have an estimate of the
number of calls for service and the total
time it will take to service these calls
for each geographic reporting area of
the city—we next want to determine
how many patrol units must be de-
ployed to maintain a specified level of
service. To approach this problem we
cast it into a standard queuing model
and assume that the pattern of the ar-
rival of calls for service, i.e. the queue
input distribution, is a Poisson process,
and that the service distribution, which
is derived from the distribution of time
required to service the calls, is expo-
nential. These are standard assumptions
for many queuing situations and appear
to be applicable to this problem [19],
[20]. The queuing analysis will enable
us to determine the number of patrol
units which must be assigned to a police
district in order to service a specified
percentage of the calls without delay.
The specified percentage is a commanc
decision and is controlled by the tota
force resources, available cars and per-
sonnel, the department's goals and ob-
jectives, and the district commander'!
analysis of his specific law enforcemen
situation. For the St. Louis Police De
partment, the number of patrol units i:
set so that at least 85% of all calls wi
be serviced by a patrol unit without de
lay. Thus, we see that the St. Loui
manpower allocation model and th
similar LEMRAS model are decision
aiding tools in that they afford the dis
trict commander or department admir
istrators some rationale for makin
patrol assignments over time whic
achieves a specified type and level c
effectiveness.
The assumptions of the LEMR.A
queuing model also states that it is
multi-server system, with the patr
The Ninth District, St. Louis, Mo.
Prediction period—3 weeks starting 03/06/67
Monday
63
83
113
104
61
27
(Number of calls per hour)
Tuesday Wednesday Thursday Friday
Day:
Hour
7-11
11-15
15-19
19-23
23- 3
3- 7
Day
Totals 451 428 427 442 554
Figures will not necessarily add to total due to rounding.
66
80
106
96
55
24
56
79
110
94
59
29
60
78
105
95
70
35
60
86
118
122
118
50
Saturday Sunday To
Source: Reference [19]
246
FIGURE 3—Predicted Calls for Service
67
104
133
133
107
43
587
56
78
84
81
50
27
375
-------
The Ninth District, St. Louis, Mo.
Prediction period—3 weeks starting 03/06/67
(Minutes of work per hour)
Day
Hour
7-11
11-15
5-19
9-23
'.3- 3
3- 7
Day
"otals
Monday
2189
2791
3669
3430
1974
906
14960
Tuesday
2223
2694
3426
3116
1807
803
14069
Wednesday
1880
2626
3569
3071
1898
965
14009
Thursday
2006
2584
3398
3103
2255
1143
14490
Friday Saturday Sunday Total
2024
2877
3863
3919
3786
1652
2231
3348
4201
4262
3423
1402
1862
2526
2662
2652
1635
888
14415
19446
24789
23553
16777
7759
18120
;igures will not necessarily add to total due to rounding.
FIGURE 4—Predicted Work
ource: Reference [19]
18866
12226
160740
mils representing the set of servers.
Vith these assumptions, standard queu-
ig formulas enable us to calculate the
ercentage of calls served without de-
ty, given a specified number of servers.
EMRAS does these calculations by
irying the level of servers and listing
>r each level the corresponding num-
:r and/or percent of calls which are
;layed, by priority (class) of calls.
The main formula used in these cal-
ilations is known as Erlang's formula
id it expresses the probability that
e number of calls for service in the
stem is greater than the level of
rvers. Using this formula, two tables
e generated, Figures 5 and 6, [19].
gure 5 relates the level of service
ained (the number of calls served
thout delay) to the number of patrol
its. This is shown for the St. Louis
,ht major classes of radio calls. For
imple, if six patrol units are on duty,
would expect 94 of the total of 169
ss 11 radio calls (crimes against per-
sons) to be handled without delay,
while almost all calls can be handled at
once if there are thirteen or more patrol
units assigned to the district. Thus, we
see that the table gives the maximum
number of units the district commander
must assign in order to obtain a speci-
fied level of service.
Figure 6 has more operational value
in that it shows service levels in relation
to the number of units assigned for
four-hour periods of a given day. For
example, it summarizes the predicted
activity in a district for Saturdays dur-
ing a three-week period, and breaks the
activity into four-hour spans, beginning
at 7:00 A.M. Across the top of the page
are the potential numbers of patrol
units, from 5 to 18, which may be
assigned. For each number of units we
are given, by four-hour periods, the ex-
pected total number of predicted calls,
the expected number which can be
answered immediately, the expected
number which must wait to be serviced,
Total
The Ninth District, St. Louis, Mo.
Prediction Period—3 Weeks Starting 03/06/67
(Number Serviced Without Delay)
nt Class
11
21
22
31
41
42
61
71
)tal
169
667
87
10
8
963
82
1279
3264
5
58
289
36
4
3
328
40
550
1308
6
94
432
55
7
5
543
57
823
2016
7
127
539
69
8
6
727
68
1031
2576
8
147
602
78
9
7
839
75
1152
2908
9
158
635
82
9
8
901
79
1217
3089
10
164
652
85
9
8
933
81
1251
3183
11
167
660
86
10
8
949
81
1267
3228
12
168
664
86
10
8
957
82
1274
3249
13
169
666
86
10
8
960
82
1277
3258
14
169
666
86
10
8
962
82
1279
3262
15
169
666
87
10
8
962
82
1279
3263
'RE 5—Predicted Number of Events Serviced Without Delay Vs. Number of Units Assigned
ce: Reference [19]
247
-------
These prediction are for areas in the Ninth District
Prediction period—3 weeks starting 03/06/67
This is for all Saturdays in the prediction period
Units
Hours 7-11
Total pred
No delay
Delay
Pet no delay
Pet delay
One more unit
Hours 11-15
Total pred
No delay
Delay
Pet no delay
Pet delay
One more unit
Hours 15-19
Total pred
No delay
Delay
Pet no delay
Pet delay
One more unit
Hours 19-23
Total pred
No delay
Delay
Pet no delay
Pet delay
One more unit
Hours 23-3
Total pred
No delay
Delay
Pet no delay
Pet delay
One more unit
Hours 3-7
Total pred
No delay
Delay
Pet no delay
Pet delay
One more unit
5
59
46
13
77
23
8
92
35
56
38
62
26
116
3
114
2
98
39
116
2
114
2
98
37
93
32
61
34
66
27
37
35
2
94
6
1
6
59
53
6
90
10
3
92
62
30
67
33
15
116
42
75
36
64
33
116
39
77
33
67
33
93
59
34
63
37
17
37
37
1
98
2
1
7
59
57
2
96
4
1
92
77
15
84
16
8
116
74
42
64
36
20
116
72
44
62
38
20
93
76
18
81
19
9
37
37
99
1
8
59
58
1
99
1
1
92
85
7
93
7
4
116
94
22
81
19
11
116
93
23
80
20
12
93
85
9
91
9
5
37
37
100
9
59
59
100
92
89
3
97
3
2
116
105
11
91
9
6
116
105
12
90
10
6
93
89
4
96
4
2
37
37
100
10
59
59
100
92
90
1
99
1
1
116
111
5
96
4
3
116
111
5
95
5
3
93
92
2
98
2
1
37
37
100
11
59
59
100
92
91
100
116
114
2
98
2
1
116
114
2
98
2
1
93
93
1
99
1
37
37
100
12
59
59
100
92
91
100
116
115
1
99
1
1
116
115
1
99
1
1
93
93
100
37
37
100
13
59
59
100
92
91
100
116
116
100
116
116
100
93
93
100
37
37
100
14
59
59
100
92
92
100
116
116
100
116
116
100
93
93
100
37
37
100
15
59
59
100
92
92
100
116
116
100
116
116
100
93
93
100
37
37
100
16
59
59
100
92
92
100
116
116
100
116
116
100
93
93
100
37
37
100
17
59
59
100
92
92
100
116
116
100
116
116
100
93
93
100
37
37
100
18
59
59
100
9:
9:
10
11
11
10
1
1
1(
1
1
Source: Reference [19]
FIGURE 6—Summary Queue Table
the corresponding percentages, and the
expected number of waiting calls which
would be answered at once if one
more unit were addded, e.g., between
7:00 A.M. and 11:00 A.M., it is ex-
pected that 6 units could handle 53 of
59 calls (90%), while 6 (10%) would
be delayed; by adding one more unit,
3 more calls could be answered at once.
It is expected, however, that 9 units
could handle all calls with virtually no
delay. The table enables the district
commander to determine explicitly
what the addition or subtraction of a
248
patrol unit will "buy" in terms
changes in the percentage of calls se
iced without delay. This is an import;
and new type of marginal analysis
previously available to police adn
istrators.
The above discussion illustrates h
the LEMRAS like models can be u
within the planning and operatic
framework of a police departmi
The type of decision-making infori
tion supplied by LEMRAS is new
just about all police departments
adds a whole new dimension to pc
-------
decision making and hopefully, they
will be able to integrate this information
into their total operations in a manner
which improves their effectiveness. This
type of manpower allocation model re-
quires a police department to be com-
mitted to effecting necessary changes.
The LEMRAS analysis can, for ex-
ample, indicate that to maintain the
specified level of service, two patrol
units must be added to the present
en patrol beat district. The district
commander must determine if he wants
o redesign his district into twelve beats
Dr to have the additional two cars act
as "floaters." Most departments do not
lave the flexibility to add or subtract
seats as required by LEMRAS—their
)eat structure is standardized, even to
he painting of expensive beat maps in
he communications center. Again we
;mphasize the data needs for these type
)f models in that most police depart-
nents do not gather their data in a
nanner which can be used directly by
J3MRAS. Also, data not usually tabu-
ited are required, e.g. time to service
lasses of calls for service.
Experience with LEMRAS has shown
lat it cannot be implemented without
oncern as to the requirement and
eeds of the user law enforcement de-
artment. For example, it is noted that
le use of LEMRAS in Los Angeles
aused conflicts with the department's
asic Car Plan, in which a patrol car
id personnel are assigned to a par-
:ular geographic unit and are expected
i spend 50% of the time working with
ie people of the area.
As final caveats to the use or misuse
LEMRAS, the following comments
e noted [22] :
1. LEMRAS does not predict exact
times and locations of calls for
police service. Using standardized
statistical techniques, LEMRAS
does forecast the average number
of calls for police service that
may be expected to occur in a
given area during a given period
of time, and the average amount
of police time it will take to serv-
ice that number of calls.
It should be noted that these
forecasts are based upon the nor-
mal stability that many observers
have noted in police workload
data, and that the unusual situa-
tions cannot be predicted. If and
when these situations occur, it
will be necessary for the police
administrators to allocate re-
sources on an emergency basis.
This caution is included here be-
cause it is recognized that such
situations may occur.
2. LEMRAS does not relieve field
commanders of the need for exer-
cising exceptional judgment in
the day-to-day depolyment of
manpower, and in evaluating the
LEMRAS predictions. LEMRAS
is designed and intended to make
available to the commander more
detailed and complete data on
which to base such judgment than
has ever been presented to him
in the past.
3. LEMRAS does not predict crime
nor does it provide guidance for
preventive patrol functions. Meas-
urement techniques are limited
to called-for services and the
manpower required to handle
them. The dispatch data collected
for LEMRAS is subject to analy-
sis, however, which can provide
insight into the development of
crime patterns and other condi-
tions which require or justify pre-
ventive effort. The form of the
preventive effort must be decided
by the commander concerned.
4. LEMRAS is not directly related
to the measurement of need for
manpower in investigative, ad-
ministrative, or support positions.
In addition to the manpower alloca-
tion models described above, there are
other models which aid in the evalua-
tion of manpower allocations. These
include simulation models (to be dis-
cussed below), the deployment analysis
and allocation method developed for
the Boston Police Department [33] and
the New York City Police Department
[7], [10], and the work done by the
Chicago Police Department [34], We
next present an extract of the deploy-
ment model description as given in [7].
249
-------
That effort involves an analytic model
which predicts the performance of a
specified manpower level and police
deployment in terms of dispatch delay,
average response time, patrol frequency,
and amount of time available for pre-
ventive patrol. The measures used are
flexible and any set of criteria which
can be analytically related to patrol
manpower may be utilized. This method
applies dynamic programming as its
mathematical allocation technique. It
allows the police to determine the man-
power necessary to provide acceptable
levels of service in terms of each of the
measures, and also to allocate a speci-
fied patrol force size to neighborhoods,
by time of day and week, so as to yield
the highest service level obtainable with
the given force. This model is more
comprehensive than the LEMRAS
models in terms of the multiple criteria
which may be used, and because it
addresses the preventive as well as the
response aspects of patrol.
The minimum levels of services pro-
vided may be set by the police and com-
munity and may vary with the neighbor-
hood or time of day, depending on
conditions. The various service level
criteria used in this method are flexible
but currently include the following: the
average number of preventive patrol
hours for each outside crime shall not
be less than a specified value in each
neighborhood, the average frequency
of patrol (which is related to outside
crime-detection probability) in a neigh-
borhood shall not be less than a speci-
fied value, the average time required
to travel to the scene of a reported in-
cident or call for service shall not ex-
ceed a specified value, and the number
of patrol cars for each neighborhood
shall not be less than an administra-
tively set minimum.
The use of these measures of service
is based on the assumption that addi-
tional preventive patrol and reduced
response time have a positive effect on
crime deterrence and on increasing the
chance of apprehending a criminal near
the scene of a crime. The existence of
such an effect and its actual degree
are not known and need to be in-
250
vestigated experimentally. The four
measures of service used in the current
model are clearly arbitrary and open
to revision to suit the local situation.
Procedurally, the number of cars
necessary to provide minimum levels o
service on each criterion for each dis-
trict and time period are calculated. The
remainder of the force is then deployec
(using dynamic programming) to mini
mize the dispatching delay due to un
availability of free cars.
For this technique, the data needec
for each command and shift to whic
police are to be assigned are: area
patrollable street miles, average trave
speed of a patrolling car by time o
day and day of week, average trave
speed of a responding car by time o
day and day of week, volume and distr.
bution over time of various types c
calls for service, volume and distribi
tion over time of reported outsic
crimes, and average total service tim
for each type of call.
The outputs of the deploymet
analysis and allocation method are: a
analysis of the present deployment gi1
ing (a) expected response time, (b
expected frequency of prevents
patrol, and (c) expected total numbi
of preventive patrol hours; a realloc
tion of current manpower to satisfy i
constraints on levels of service and
minimize delay in dispatching cars di
to temporary unavailability of a fr
patrol car; an analysis of the realloc
tion of manpower in terms of (a), (b
and (c) above; a determination of t
minimum force level necessary in ea
patrol district to just satisfy each servi
level constraint.
In a computational exercise usi
this model and data from New Yc
City, the predicted variation in serv
levels among precincts was greatly
duced, while average time delay in c
patching due to car unavailability v
cut from about 4 minutes to less tr
1 minute by reallocating the same ci
wide level of manpower. In addition,
measures of acceptable service le
were met, whereas they were not
satisfactory when the existing allocat
of manpower was used.
-------
Deployment analysis and allocation
models have aided decision-making at
the highest levels. As noted in f 10], such
analyses helped New York City to
demonstrate the extent to which effec-
tiveness of the patrol force was lower at
times of high demand than at times of
low demand. This demonstration was a
major impetus behind efforts of the
mayor and the police commissioner to
modify New York State's three-platoon
statute and to obtain a fourth platoon,
which now operates from 6:00 P.M. to
2:00 A.M. A revision of the law re-
sulted.
The deployment analysis and alloca-
iort model described above does rep-
•esent a conceptual advance over
^EMRAS like models due to its multi-
ibjective approach. No operational
omparisons between these approaches
re available. The manpower allocation
tiodels of St. Louis and LEMRAS
nodels are being used in a number of
ities. Those law enforcement agencies
lanning to implement such models
'ould do well to investigate the cur-
;nt and near future state-of-the-art
sfore selecting a particular approach.
atrol Beat Design
A problem which is related closely
i the manpower allocation problem is
at of determining the location and
se of individual patrol beats. For
.ample, a LEMRAS analysis might
dicate that two additional units should
: added to a ten patrol beat district.
ssuming two more units are available
d the police department does have
z ability to rearrange beats from time
riod to time period, how should the
itrict commander divide the district
o twelve beats? What measure of ef-
;tiveness should be used to determine
the beat designs are acceptable? A
mber of investigators [24], [25], [26],
'] have written on this subject and
;re appears to be applicable models
aid in this decision area. To date, no
ice department has used these
dels in any concerted manner; the
Louis Police Department has insti-
jd the most detailed study of this
>lication [25], [26]. The reasons why
h models have not been employed
include the need for a set of crime
statistics by small geographic reporting
areas in a city; and the lack of an
ability to run a more-or-less sophisti-
cated model on a computer, given the
available computer program. We next
describe a particular approach to this
problem [24]. The reader will note the
full set of data required and the in-
terpretive aspects of the model solution.
The basic problem is as follows:
given k patrol units to be assigned dur-
ing a patrol shift, how should the k cor-
responding patrol beats be determined
so that each patrol unit will, on the
average, have the same workload? The
area of a patrol beat must be contigu-
ous to itself and of such a shape to
allow for efficient patrol and response
tactics. (A long, narrow beat or star-
shaped beat would not be too efficient.
Studies have demonstrated the advan-
tage of square-shaped beats [10]. Of
course, geographical and political con-
straints often help shape a beat.)
The International Association of
Chiefs of Police (IACP) recommends
taking each zone of the city—usually
census tracts—and measuring in some
sense, the total crime workload in each
zone. Then, using heuristics, combining
the tracts to form k contiguous beats
having approximately the same relative
workload. To determine the workload
for a tract, weights are given to the
various incidents (investigate a criminal
act, arrest of a suspect) to yield the
weighted workload for a tract. The
weights tend to reflect the importance
of the incident and the time required by
a patrol unit to process the incident.
The IACP uses the following weights:
Type of Incident
Relative Weight
Criminal Homicide 4
Forcible Rape 4
Robbery 4
Aggravated Assault 4
Burglary 4
Larceny 4
Auto Theft 4
All Other Offenses 3
Arrests for all offenses
except Drunkenness 2
Traffic Accidents 2
Arrests for Drunkenness 1
Miscellaneous Police Services 1
251
-------
The first seven types of incidents are
called Index Crimes as they represent
the main categories of crimes reported
in the FBI's Uniform Crime Report.
Other types of workload measures or
"hazard" scores are in use and de-
scribed in [7] and [10].
One approach to the determination
of patrol beats is to attempt to employ
analytical procedures for the structur-
ing of the k beats. From the field of
operations research we find a situa-
tion analogous to the determination of
patrol beats, the warehouse location
problem. Here, we wish to locate a
specified number of warehouses and
assign customers to each warehouse
such that the total cost of servicing the
customers from their assigned ware-
houses is minimized. The cost could in-
clude transportation, delivery and cus-
tomer relations. This problem definition
has recently been extended to include
the problem of reapportioning a state
into legislative political districts [28].
The problem is to locate a specified
number of district centers and assign
population units to each district such
that the assigned district population
must be nearly equal—the one man,
one vote concept. The cost, or more
correctly, the measure of effectiveness
of a set of centers and assignments was
taken to be the population moment of
inertia, i.e. minimize the sum of the
squared distance of each person to his
district center. The computational pro-
cedure must, along with the measure of
effectiveness, allow for the need for
contiguous districts, no gerrymanders,
and for compact districts (more square
than rectangular). We next extend this
formulation and associated computa-
tional procedure to the structuring of
police beats.
Mathematically, the problem can be
formulated as an integer programming
problem, although the formulation does
not necessarily take care of the con-
tiguity requirement [28]. This require-
ment causes the combination of an
analytical procedure (basically solving
the transportation model of linear pro-
gramming) and an automated heuristic
adjustment.
252
To illustrate the process of beat de-
sign, we solve the problem by the
analytic-heuristic procedure of [28]. The
reason for this is that the integer pro-
gramming model can be quite difficult
to solve with available computational
tools, although an integer model for
beat design is given and solved in [25].
The sample problem to be illustrated
next uses data from the 1966 annual
report of the Cleveland Police Depart-
ment as the Department's crime sta-
tistics are gathered by census tracts and
the beats are formed by combining
census tracts. In general, it is recom-
mended that smaller reporting units
be used to gather the statistics (as in
LEMRAS) and the beats be formed by
combining these smaller units. This al-
lows for beats to be designed so tha
the beat workloads are more equitable
A number of different measures of ef-
fectiveness for workload are employee
that relate total crime, population, anc
area of each census tract interpreted a
an appropriate moment of inertia.
Again, the basic problem is to com
bine the census tracts of the City o
Cleveland to form contiguous am
compact beats. There was a total o
k = 58 beats and n = 205 census trac
to assign to six police districts. Figur
7 shows the number and percentage c
index crimes in each of the 1966 bea
in the first three districts and the rani
ing position in terms of index crime
The reader will note the wide vari;
tions in terms of crime rate, popul;
tion and area of the beats. The cor
putations used five measures of t
workload for a census tract: numb
of index crimes, population, area, lev
of crime multiplied by the populatio
and the level of crime multiplied
the area. It is felt that the worklo
in a patrol beat is some function
these three elements—plus relat
demographic and geographic data. T
computations kept the same six pol
districts as stipulated by the Clevela
police and attempted to readjust
beats in these districts in a more ec
table fashion. There was no attempt
-------
02,3,6,7
CM.5
B6,C8,9
01,2,3,4,5,7
06,8,9,64,5,6
B7,8,9,E1,2,3
F3,E7,8
361 747 1719 872 144,632 9,558
FIGURE 1—Crime by Police District and Beat (Zone)
ource: Reference [24]
construct beats based on any geo-
graphical, political or other considera-
ions.
The partial results of a complete set
bf computations for District 2 with
line police beats are shown in Table 1.
[he computational procedure for this
listrict yielded contiguous beats, al-
iough there were some minor non-
antiguous aspects in a few beats in
jther districts. For comparison pur-
DSCS, we show in Table 1 the total
umber of index crimes in each beat
District 2 for the actual 1966 beats
id the beats developed based on equal
rime. (Due to different population and
iavailability of data, such comparisons
Innot be made for other measures.)
le 2 shows for the five measures
amount of the total measure for
Ich of the nine beats.
[The decision process in the selection
a patrol beat design is complicated
two factors: there is no agreement
to what measure we should use to
tistruct equal workloads and, since the
iputational procedures do not neces-
Hly produce a single beat plan with
equal workloads, there is no apparent
guidance as to which beat plan to
implement. To resolve the latter point,
we can bring in other measures, e.g.
which beat plan causes the patrol units
to be out of their beats more often
[25]. But this type of evaluation calls
for the use of simulation (see discussion
below) or advanced mathematical pro-
cedures. Even though these factors can-
not be resolved to everyone's satisfac-
tion, the ability to change and produce
new beat plans readily, based on reason-
Table 1
No. of Index Crimes Per Beat (District 2)
Beats 1966 Actual Equal Crime
1
2
3
4
5
6
1
8
9
539
429
531
520
545
571
277
291
186
3,889*
453
429
460
373
400
478
477
435
421
3,926*
*Difference in totals attributed to errors in
data preparation.
253
-------
Table 2
Comparison of Measures
Beats
1
2
3
4
5
6
7
8
9
Crime (C)
453 crimes
429
460
373
400
478
477
435
421
Population (P)
19306 people
16417
14530
19272
17864
14922
20083
18604
15715
Area (A)
1. 1 59 sq. miles
1.210
1.189
1.136
1.047
1.017
1,207
1.308
1.234
CP/103
2010
1872
2216
1962
1507
1960
2227
1961
1800
CAxlO
1145
1182
942
1276
1209
1123
1135
1008
1256
Desired Average
436
17413
1.167
1946
1142
Source: Reference [24]
able assumptions, is certainly a major
step forward for most police depart-
ments. The model does not produce a
single plan for a given set of data and
time period which must be implemented.
It produces rational plans which en-
ables the cognizant decision maker to
evaluate better a range of alternatives
based on a wide range of requirements,
some of which may be external to the
model.
Crime Prediction and Random Patrol
From the above discussions, our
ability to predict future levels of crime
and police workload can greatly aid a
police department in its planning and
operational activities. As noted in [29],
". . . strategic decisions relating to
force structures and training emphases
would be easier if reliable long-range
forecasts of crime were available.
Tactical decisions on the day-to-day
deployment of forces would be eased
by accurate short-range forecasts or
by forecasts of specific crimes. Analysis
of the effectiveness of new (and old)
equipment can be performed more ac-
curately if appropriate crime prediction
capability exists. An understanding of
the relationships between social, eco-
nomic, political, and moral conditions
and crime, expressed in a model, could
be used to devise effective crime pre-
vention campaigns. These potential uses
have generated interest in the broad
technical problem of predicting crime."
The report [29] evaluates a number
of prediction models, basically varia-
254
tions of multiple regression and ex-
ponential smoothing, as applied to his
torical data collected for Los Angeles
Quarterly predictions for 27 crime type
and 24 geographical areas were com
puted and these predictions did mate
the actual crime levels within sta
tistical expectations. Given an ability t
predict gross crime levels by geographi
area over time (i.e. extrapolativ
models), we need ways of bringin
these predictions into evaluative mode
for police decision-making. LEMRA
is a good example of this ability. Othei
are needed, especially causal model
i.e. models which relate actions (alte
native solutions) to results and u:
crime level predictions as inputs. Wi
respect to prediction models [29] co
eludes: crime statistics can be predicts
with sufficient accuracy for some of t
possible applications by extrapolatic
of historical data; the potential applic
tions of crime prediction methodolo
are sufficiently diverse that no sinj
technical approach is appropriate
all; current qualitative and quanti
tive understanding of the causes
crime is grossly insufficient to perr
the construction of usable causal crii
prediction models; extrapolative crii
models rely upon the assumption t
trends will continue as in the i
mediate past. For example, changes
public policies (especially, but not
clusively, by police agencies), in e
nomic or social conditions, or in p
lie moral or philosophical attitudes i
invalidate this assumption.
-------
Another aspect of crime prediction
is the prediction that a crime will
occur at a particular time and place.
Jresently, law enforcement agencies use
jin maps, intelligence and other in-
'ormation to deploy stake-outs and
jatrol specific areas. Is it possible to
ase prediction models to aid in on-the-
icene crime detection and apprehen-
;ion? For this problem a multiple re-
ression model was tested for the seven
ndex crimes using data collected from
le Philadelphia Police Department
30]. The study tested out the relation
ietween crime type and 35 possible re-
ited crime factors. Included crime fac-
ers were day of week, phase of the
loon, temperature, age distribution of
opulation, number and type of schools,
c. The crime factors were used as in-
ependent variables of the regression
nalysis, and the level of crime type as
ie dependent variable. If the variables
ere properly related, in a predictive
:nse, then, for an area of a city, as cer-
in conditions obtained, we would ex-
:ct a crime to occur. Although the re-
Iting regression equations were not
iod predictors of crime, the analysis
d to further work using cluster analy-
i, a statistical procedure for grouping
events based on their attributes, here
me factors. This procedure has led to
computer driven query system from
lich a district commander can receive
•eport on the likelihood of a crime by
>e in the district or sectors which he
iignated. Based on his interpretation
the likelihood value, the com-
nder can then dispatch patrol forces
the area. Evaluation of this proce-
•e is not available at this time.
n general, our ability to predict an
nt by time and location is not too
at. Certainly, given information on
relative frequency of crime and
ses of crime, the number of suc-
iful predictions should increase.
at we need to do is to couple our
orical data with a patrol strategy
sh increases the probability of in-
epting crimes in progress. We are,
course, restricted to crimes visible
i the street. The concept of random
patrol has been introduced to aid in
this area. Random patrol is based on
the assumptions [31] that
1. irregularity of patrol schedules
will for a given patrol rate in-
crease the awareness of the gen-
eral population that patrol is tak-
ing place;
2. randomness of the patrol schedule
will discourage the potential
criminal who finds that he cannot
predict the arrival patterns of
patrol vehicles.
Patrolling in a random manner means
that there is no fixed sequence by
which the patrol visits each point in
the area, yet all points in the area are
visited within some average time [32].
It is shown in [32] and [10] that the
probability of intercepting a crime is
rather low, but even so, we should be
concerned with how to evaluate alterna-
tive approaches to patrol which can in-
crease that probability, without causing
deterioration of other measures of ef-
fectiveness. A rather detailed mathe-
matical model in [10] addresses the
problem "Given the recent pattern of
crimes and given limited amount of pre-
ventive patrol, how should the patrol
effort be allocated along streets to best
achieve some object?" The associated
analysis finds that the allocation that
maximizes apprehension probability
depends in a complicated fashion upon
recent crimes rates; patrol effort should
grow as the logarithm of the crime
density and that certain areas, where
the likelihood of crime is particularly
low, should not be patrolled at all.
An early application of random patrol
concepts was based on straightforward
Monte Carlo procedures for randomiz-
ing the areas visited by patrol units
while on preventive patrol. The town of
Edina, Minnesota has a 47 man police
department and in 1971 had a total of
1,075 index crimes. In 1962, the Edina
police, working with personnel from
the University of Indiana, initiated the
first systematic random patrol activity.
The town was divided into four zones,
with the four zones divided into a total
of 51 subzones. Data on the level of
255
-------
crime were gathered for each subzone
and four roulette wheels were designed
for each zone. The wheels were divided
such that the area of a subzone cor-
responded to the proportion of crime
in that zone. The experiment was run
just for the 11:00 P.M. to 7:00 A.M.
shift. When a car was free to patrol,
the corresponding zone roulette wheel
was spun and the car went to that
area. It was a very basic system. Folk-
lore about the Edina experiment relates
that the first time the wheel was spun
it caused the dispatch of the patrol unit
to a midnight visit to the city dump.
Of course, the officer found someone
stripping a stolen automobile. After
the first year of operation, burglaries
in Edina were down 38 percent on the
11:00 P.M. to 7:00 A.M. shift. Since
then, much more sophistication has
been brought into the system. Under a
Law Enforcement Assistance Admin-
istration Grant in 1968, the method
was computerized and applied on a
three shift basis. The guidelines of the
computerized Edina random patrol
model experiment were as follows [35]:
1. The entire uniformed police force
of the Village of Edina, on all
shifts, was involved; all were
given zone maps.
2. Two of the four zones were
patrolled using the random patrol
technique; the other two zones
were the control zones and were
patrolled in the conventional
manner. At the end of each week
the random patrol and the control
zones were interchanged.
3. At the start of each shift, each
officer was given a series of ran-
dom numbers and patrolled the
subzones corresponding to the
random numbers in the sequence
for a period of 15 minutes. After
15 minutes, he proceeded to the
subzone corresponding to the
next random number on his list.
If he received a call, he re-
sponded. When the call was com-
pleted, he proceeded to the sub-
zone corresponding to the next
random number on his list.
4. The field tests proceeded as out-
256
lined above for a period of three
months.
5. Patrol assignments were made so
that, if an officer was in a contro
zone one day, he would be in ar
experimental zone the next day
The Edina project had as its objectivf
the development of a random patro
procedure which would reduce ttu
response of the patrol units to emer
gency calls for service, i.e. the ran
domization of the patrol units locatioi
based on area crime levels was expectei
to preposition cars closer to the point
of need. A comparison between the yea
of the random patrol field test with th
preceding year showed a 40 percer
decrease in average response time froi
7.05 minutes to 4.22 minutes; this wz
achieved even though there was a 1
percent increase in calls for servic
It was also noted that while crime
Edina rose 11 percent during the e.
perimental year, crime in the rest <
the county rose 17 percent. This di
ference may be attributed to the ra
dom patrol. Another benefit of this ty
of project is that better data collectii
procedures resulted.
The Edina work is certainly trar
ferable to other departments, especia
those of comparable size. The imp*
of size and the many major and serio
events which can occur in large cit
would probably destroy any rando
ized process for patrolling undertak
by the usual beat cars. However, spec
preventive patrol units, which do i
answer emergency radio calls for se
ice, could probably be used in a fash
similar to Edina to insure a pro
level of preventive patrol time in criti
areas.
Simulation of the Police Emergency
Response System
Up to this point, our discussion
law enforcement decision-making m
els has been directed towards spec
problem areas, with such probl
having only a limited, but albeit,
portant scope with respect to total
enforcement concerns. Granted, at
time we cannot encompass withi
-------
single holistic model the complex law
enforcement framework; we can, how-
ever, attack major components in terms
of evaluating how changes in their sub-
components impact one another. And
having such an evaluative ability affords
us an important aid for selecting from
alternative decisions. The main means
of accomplishing this for law enforce-
ment, as well as the other areas of the
LE/CJ system, has been by the use of
simulation models. (However, the work
reported by [7], [10], [33] and others,
io represent many of the complexities
jy powerful analytical models. Refer-
ence [10] gives a rather complete dis-
;ussion of a wide range of models to
aw enforcement problems.)
The functions and the operations of
he police emergency response system,
.e. the dispatching and patrol of units
o respond to calls for emergency serv-
ce, was described above and is illus-
rated in Figure 1. Many aspects of this
ystem can be modeled and such models
sed to make measured changes, e.g.
ic determination of the number of
;lephone lines and operators, the de-
gn of beats, the number of patrol
nits during a shift. These models sup-
y the decision maker with quantita-
ve data by which an alternative policy
r operational change can be selected
nong a set of alternatives. For ex-
"nple, a beat design model will deter-
ine a specific structure or a set of
ually good structures for a district
ised on the assumptions and data
quirements of the model. There re-
ains an important consideration, how-
er. As every model is limited in its
iJlity to reflect the real world, how can
: test out the selected set of beats
Dlution) prior to actual field opera-
>n in order to insure against an un-
and solution? An important approach
answering this question, especially
• complex systems, is the develop-
:nt of a simulation model which can
:ompass in a more complete fashion
: total system and the interrelation-
3s of the system components, es-
:ially the random event nature of a
system like the emergency response
system.
As the simulation of the emergency
response system is rather rich in detail,
its execution requires the use of a com-
puter. Such computer simulations have
been or are being developed for a num-
ber of cities—Boston [36], New York
City [7], San Jose [37], Washington,
D. C. [38], among others. A detailed
description—both technical and non-
technical—of the response system
simulation is given in [10]. We shall
describe the use of simulation in this
decision-making environment as de-
scribed in [10], [36] and [38].
In a general sense, these simulation
models are of value to police admin-
istrators in the following ways: they
facilitate detailed investigations of
operations throughout the city or in
part of the city; they provide a con-
sistent framework for estimating the
value of new technologies and new ap-
proaches to the patrol function; they
serve as a training tool to increase
awareness of the system interactions
and consequences resulting from every-
day policy decisions; they suggest new
criteria for monitoring and evaluating
actual operating systems.
More specifically, the simulation
models can be used to test and evaluate
concepts such as the following:
1. What changes will result from
dispatching rules based on the priority
assigned to a call for service? For ex-
ample, rules which prohibit the dis-
patch of patrol cars to low priority
incidents at times when the system has
a high load level can be investigated.
Another example might be to divide
the patrol force into two groups, where
one group deals exclusively with low
priority calls on an appointment basis.
2. What will be the effects of modi-
fied or completely new patrol beat
structures? In other words, can system
performance be improved by adjusting
beat boundaries, by eliminating beats
altogether and assigning territorial
responsibility to small groups of cars,
by overlapping beats so that any given
area continues to receive preventive
257
-------
patrol even when many patrol cars are
servicing calls?
3. What will be the impact of add-
ing or subtracting patrol units? Using
more sophisticated performance meas-
ures, e.g. requiring that a given per-
centage of the highest priority incidents
receive a response within a set time
limit, the number of units required to
patrol an area may not equal the num-
ber as indicated by present allocation
schemes.
4. Which analytic procedures for
allocating manpower are in fact "best"
for a city? Recent analytic models, e.g.
LEMRAS, have advanced a number of
promising techniques that should allow
improved tour scheduling and deploy-
ment of patrol manpower. The simula-
tion model will permit evaluation of
these schemes for possible adoption.
5. What impact will new technolo-
gies have on the patrol functions, e.g.
car locator systems? Such investigations
will answer questions regarding the
locator resolution desired, the impact
on dispatch decisions, and the improve-
ments in total operational performance
which may be expected.
6. Are there viable techniques for
dynamically repositioning patrol units
before and after servicing a call? At
times, a rash of calls will draw patrol
units to a small area, leaving large gaps
in geographic coverage. Is it feasible
to reposition the remaining units so that
future service is maintained at a de-
sired level, given the present condi-
tions?
In addition to these basic questions,
further possible investigations include
saturation patrol, the interactions be-
tween radio-cars, scooters and foot
patrol, the effect of computerizing some
aspects of the dispatch function, and
the application of random preventive
patrol strategies [38].
The following description of the
simulation model approach is taken
from [36], augmented by material from
[38]. The model is designed to study
two general classes of administrative
policies: the patrol deployment strategy
and the dispatch and reassignment
258
policy. The patrol deployment strategy
determines the total number of patrol
units, whether units are assigned to
non-overlapping sectors, which sectors
constitute a geographical command,
and which areas are more heavily
patrolled than others. The dispatch and
reassignment policy specifies the set of
decision rules the dispatcher follows
when attempting to assign a patrol unit
to a reported incident. Included in the
dispatch policy are the priority struc-
ture, rules about inter-district dispatch-
ing, the queue discipline.
The simulation models use several
important measures of operational ef-
fectiveness. These include statistics on
dispatcher queue length, patrol trave
times, amount of preventive patrol
workloads of individual patrol units
the amount of inter-district dispatches
The simulation models under con
sideration work in the following way
They are organized to reflect the spatia
relationships inherent in patrol opera
tions, as well as the sequential timi
nature of events. Incidents are gen
erated throughout the city, distribute!
randomly in time and space accordin
to observed statistical patterns. Eac
incident has an associated priority num
ber. As each incident becomes known, a
attempt is made to dispatch a patrol un
to the scene of the incident. In attemp
ing this assignment, the simulation log]
is structured to duplicate as closely ;
possible the decision-making logic <
an actual police dispatcher. In certai
cases this assignment cannot be pe
formed because the congestion lev
of the force is too high. The incide
report then joins a queue of waitii
reports. The queue is depleted as pair
units become available [36].
The geography of the city under i
vestigation must be reflected in
realistic manner within the compu
in that as a patrol unit is assigned
call, we want to measure the distan
and time traveled. In [10] and [36], t
geography is organized by small po
gonal shapes called atoms, the sum to
of which form the city. Patrol be
and police districts are formed by co
bining these atoms. Crime statistics ;
-------
assumed uniform across the area of an
atom. In [38], the city is represented by
a set of city block centroids and their
coordinates (over 4,000 for Washing-
ton, D. C.) and the beats and districts
are represented by a list of correspond-
ing centroids. This model views the city
as a discrete collection of points and
all incidents which occur on a block are
assumed to be located at the centroid.
The simulations are event-paced
nodels. That is, once a certain set of
operations associated with one event is
:ompleted, the program determines the
lext event that occurs and updates a
imulation clock by adding to the
iresent time the time until the next
vent. The program then proceeds with
le set of operations associated with
lat event. Once the clock reaches some
laximum time, the simulation is ter-
linated and summary statistics are
ibulated and printed out.
The main type of event that occurs
a reported incident or a call for
olice service. The time of occurrence
' calls are generated by a Poisson proc-
;s. The location of the call is deter-
ined from historical patterns which in-
cate the fraction of calls that originate
om each atom or centroid. The pri-
•ity of the call is determined from his-
rical data which may vary by location.
Once the position and priority of
incident are known, the models
ecute the logic which attempts to
sign a patrol unit to the incident.
lis algorithm is governed by the dis-
tch policy specified by the user. One
mponent of the dispatch policy
;cifies the geographical area from
ich a unit may be dispatched. For
imple, only assign a unit whose
rol sector includes the geographical
a containing the incident, or only
ign a unit whose district designa-
i is the same as that of the in-
ent.
jiven that a patrol unit is within the
rect geographical area for a par-
ilar incident, the model then deter-
ics whether the unit is considered
ible for dispatch to this incident.
This determination focuses on es-
timated travel time to the incident, the
priority of the incident, and the current
activity of the patrol unit. In general,
the user may specify a dispatch policy
that allows very important incidents to
preempt (interrupt) patrol units servic-
ing incidents of lesser importance. In
addition, the importance of preventive
patrol may vary with each unit, thereby
giving the user the capability of as-
suring at least some minimal level of
continuous preventive patrol. If no unit
is found eligible for dispatch, the re-
ported incident is inserted at the end
of a queue of other unserviced in-
cidents. There may be separate queues
for each district and each priority
level. If at least one unit satisfies the
eligibility conditions, one is selected
for dispatch according to a prespecified
criterion such as minimal expected
travel time. The assigned unit's priority
status and position are changed ac-
cordingly.
A second major type of event oc-
curs when a patrol unit completes
servicing an incident. The logic is then
executed that either reassigns the re-
turning unit to an unserviced incident,
or returns the unit to preventive patrol.
The eligibility conditions regarding
priorities, travel distances, and geo-
graphical areas, which are necessary to
specify a dispatch policy, are also an
integral part of the reassignment policy.
In addition, it is necessary to specify
how one unserviced incident is given
preference over another [36].
The general structure of the simula-
tion process is as follows. Inputs and
initial conditions are classified into
three groups: Geography, Parameters
and Policies. Using this data, beats,
patrol assignments, the simulation
clock, dispatch queues, etc. are struc-
tured during initialization. Calls for
Service (CFS) are generated to follow
historical or hypothetical patterns. On
the basis of dispatch policies, units are
assigned to the CFS or are placed in
queue. If a unit is assigned, travel,
service and report/arrest times are
generated using the input parameters.
259
-------
Upon completion of service, a unit may
be assigned to a CFS waiting in queue
or it may resume preventive patrol.
During processing, operating sta-
tistics are gathered and, at the user's
option, may be printed out. In addi-
tion, provision has been made to dis-
play a snapshot of the entire state of the
system or to trace a number of units
during the simulation. At the conclu-
sion of the model run, summaries of
the simulation performance are printed
[38].
The input data requirements for
simulation models are quite enormous
and detailed. The geography data in-
cludes the structure of the city, dis-
tricts, and beats (by atom or centroid).
The operational parameters include the
number of patrol units, types and their
organization and beat assignment;
times, locations, types and priorities of
calls based on analyses of historical
data; response parameters dealing with
communication delay times, travel
times, service times, arrest and report
times. The gathering of the basic data
for the inputs and initialization of a
simulation model is an expensive and
time consuming task. Most police de-
partments are not now in a position to
supply such data. Hopefully, as better
data gathering procedures are initiated
and computers introduced, the neces-
sary parameters would be available.
In running a simulation to test out
a new dispatch policy or beat design
structure, there is no single measure of
effectiveness which dominates all the
others. In general, average response
time, which can be measured by the
simulation models, tends to be the over-
riding measure. However, the designers
of the simulation models have allowed
a wide range of measures to be
gathered and presented to the decision-
maker. These measures, plus the in-
tuition and experience of the police
commanders must be considered in
making the final determination. There
is a danger in relying on the com-
puter selected solution—based on an
agreed upon measure—to be field
tested or implemented without con-
260
sidering possible impact of the solutior
in the total police decision-makinj
framework.
The outputs and measures of effec
tiveness available from simulatioi
models of the emergency response sys
tern include a wide range of statistica
information which can be used ti
analyze the communications dispatc
delays, travel time to incidents, servic
times, preventive patrol, cross beat an
district service, workload of a patrc
car, etc. A test computer printoi
of a simulation run of the Washingtoi
D. C. simulation is shown in Figure
This output information can be pri
sented to the police decision make
in many forms which will allow the
to couple such data with their ow
experiences and intution. For examp
simulation runs can be made whi(
have all things constant except for
new district beat plan. The outp
measures for the new plan, especia
beat workload and response time, c
be compared to previous simulatii
runs and a decision made as
whether the new plan appears to
better. If so, then a field experime
with the new plan can be moun
with a higher level of success. In
similar fashion, we can evaluate ma
changes in the communications-c
patch area, e.g. computer aided c
patching such as New York Ci
SPRINT system, the advantages o
car locator system (see Reference [
for a discussion of this type of s
tern), the use of scooter patrols
dispatching to calls for service, i
many other major as well as mi
alternatives.
The simulation of the police en
gency response system have taken
forms with respect to mode of opi
tion. The Washington, D. C. sys
[38], which is in its final checl
stages at this writing, is run without
interaction from the analysts or u
after they have supplied the input c
while the system reported in [36]
used for Boston can be run in an ir
active fashion by the user who
input his data and assumptions v
-------
Simulation Run No. 35
Avg. Response Time
2.0 Min. for 17 CFS having priority 1
2.2 Min. for 19 CFS having priority 2
3.3 Min. for 14 CFS having priority 3
Time servicing CFS 30 percent
Time on preventive patrol 68 percent
Time on administrative out of service 0 percent
Time traveling to CFS 2 percent
Time for report & arrests 0 percent
Overall
HFS in waiting line
Percent placed in waiting line 12.0
Avg. time (minutes) 0.1
Percent exceeding 360 sec. 0.0
"ravel to incident
Avg. time (minutes) 1.7
Percent exceeding 720 sec. 0.0
Avg. distance (miles) 0.4
Percent exceeding 1.0 miles 8.0
.esponse time
Avg. time (minutes) 2.7
Percent exceeding 900 sec. 0.0
ervice time
Avg. time (minutes) 16.8
eport and arrest time
Avg. time (minutes)
Prio. 1
11.8
0.1
0.0
1.7
0.0
0.4
5.9
2.7
0.0
12.4
Prio. 2
10.5
0.1
0.0
1.3
0.0
0.3
5.3
2.2
0.0
18.1
Prio. 3
14.3
0.2
0.0
2.2
0.0
0.5
14.3
3.3
0.0
20.4
FIGURE 8—Computer Simulation Model of Police Dispatching and Patrol Functions
rminal. Both systems have output pro-
:dures which yield different levels of
:tail, depending on the needs of the
lalysis and the user's experience.
One additional use for such simula-
m models is for the training of new
Tsonnel and for demonstrating to
ilice personnel how their individual
tions impact the operation of the total
stem. New dispatch personnel can be
ssented with a scenario of calls for
•vice and asked to respond. The
nulation can then show how their
iponses did in terms of selected out-
measures. District commanders
i obtain more insight into the total
ponse system by working with the
mlation in a gaming exercise, where,
example, they are given a set of
rol units which they must deploy
inst a set of computer generated
s for service. Extreme situations, e.g.
Itiple bank holdups, can be put into
scenario. This type of training
aid probably be more effective if
simulation was tied to computer
ninals so that the gaming and train-
could be run in real, elapsed time,
e.g. an eight-hour shift over eight hours
of simulated calls.
Perspective of Law Enforcement
Models
From the above discussions we have
seen that models of many types have
been developed and are being used by
law enforcement agencies. Much of the
more advanced work has been sup-
ported by grant and other monies from
Federal and State offices. To date there
has been little carry-over of this work
from the originating agency to other
agencies. This has been due to lack of
continuing funds, lack of technical
personnel, and the inherent problems
associated with documentation and un-
derstanding of technical computer-
based models. There is no tradition for
research and development within law
enforcement agencies and professional
personnel familiar with management
science and operations research models
are quite rare. It is hoped that the
major police departments will fund
such personnel, along with continuing
Federal support. Until that time, the
261
-------
rich base of decision models for law
enforcement will continue to be under-
utilized and underdeveloped.
(There are indications that the use
of computer-based law enforcement
information systems have been and will
continue to be a prime mover in in-
creasing the technical abilities of an
agency and its use of models for deci-
sion making. Reference [39] shows that
every State and over 100 local jurisdic-
tions have such computerized systems,
some of which incorporate decision-
making models for the various compon-
ents of the LE/CJ.)
III. COURT MODELS
As noted earlier, court system deci-
sion models have been directed mainly
at court management problems. In what
follows, we shall discuss some of the
more viable approaches to these prob-
lems. There are related problem areas
which confront the prosecuting attor-
neys, public prosecuters and defending
attorneys. Little modeling work has
been directed in these areas, but we
note that some of the concepts dis-
cussed below, e.g. calendaring, simula-
tion, should be of value to this side of
the court system.
Court Statistics
In attempting to apply any type of
analysis to the management of a court
system, we are immediately faced with
two interrelated problems: what meas-
ures do we use to evaluate possible
changes in court operations and what
data can be obtained to aid in such
evaluations. An approach to what data
and how such data should be gathered
in order to modernize court admin-
istration is addressed in [11].
To illustrate how appropriate data
can be used to compare court systems,
we cite an experiment in the use of
court statistics as reported in [40]. That
study was directed towards developing
measures for courts in large urban juris-
dictions in order to provide a quantita-
tive basis for making comparisons
among cities as to how effectively their
262
local court systems were operating.
The selected indicators or measures of
effectiveness considered were the
amount of time taken to dispose of
criminal cases; the extent to which those
convicted have entered pleas of guilty;
the percentage of jail prisoners await-
ing trial; the amount of time prisoners
spend awaiting trial; the backlog of
criminal cases relative to the court's
caseload; the average number of cases
disposed of per judge; and the extent
to which probation is used as an
alternative to imprisonment.
These seven indicators do not ex-
haust the possibilities. Many more couk
be used to measure other aspects o
the judicial process. A more complete
list could include the following: th<
number of trial days; the length o
prison sentences according to type o
crime; cost per trial; cost per judge
ship; the extent to which conviction
are appealed; the portion of convic
tions overturned; the portion of de
fendants having adequate counsel, am
so on to cover more detailed aspects o
judicial processes. The selection mad
for this study was determined e;
sentially by the importance of th
measure and by the availability c
source data for its calculation. Th
lack of suitable data has severe
limited the choice of both indicate]
and cities.
As noted in [40], with few exce
tions, record keeping in court systen
is in a primitive stage; the most rue
mentary management informatk
needs are not being met in most jur'
dictions. Court statistics that are ava
able are fragmentary and in many i
stances the figures that appear in COL
documents are poorly defined.
The results of the survey and da
collection effort are gathered in Figu
9. Some cities were omitted from t
summary, primarily in instances whe
only a single indicator was availab
For certain indicators where measui
were available for only a few cities,
of the cities were included. Even thou
some selectivity was involved in ter
of the cities included in the summa
-------
Summary
Court Indicators for Urban Areas
Urban Area
Los Angeles
San Diego
San Francisco
Washington, D.C.
Urban New Jersey
Philadelphia
Chicago
Pittsburgh
Detroit
Minneapolis
Dallas
St. Louis
Miami
Baltimore
New York
dEAN
Number of
Days from
Indictment
to Trial
115
101
161
285
142
125
—
—
—
—
—
—
—
174
158
%
Convicted
of Pleas
of Guilty
60
89
96
—
—
67
83
53
86
77
92
77
62
—
97
78
% of Jail Ratio of
Prisoners Cases Number
Awaiting Pending to of Cases
Trial Dispositions Per Judge
55
45
55
33
—
73
65
38
52
33
75
49
—
76
48
54
.20 —
.14 —
.18 —
.17 —
— —
— —
— —
.37 1261
.31 —
.15 331
— —
— —
— —
— 655
.20 —
.21 749
% Placed
on
Probation
91
88
90
—
—
63
34
—
66
—
36
—
—
—
—
66
FIGURE 9
Source: Reference [40]
he fragmentary nature of the data be-
;omes obvious from the missing data
wints.
The purpose of the summary is to
issess particular court systems on the
lasis of a number of indicators. It can
ie seen from the summary that the
ourts in some cities are performing
etter than average according to cer-
iin indicators and poorer than average
ccording to others. This lack of agree-
ient is demonstrative of the risk in-
alved in assessing courts on the basis
a single indicator. The use of in-
cators in combination does not elimi-
ite the need for interpretation of the
ita but does give a picture of general
mrt performance.
The analysis illustrated above is an
ample of a rare, but important study
court operations. We still do not
tow, however, what values of the in-
;ators show that a court system is
>rking well. As we make changes in
; court operations, e.g. more judges,
ime history of the indicators would
least let us know if the change was
the right direction.
urt Planning and Operations
Research activities have produced a
nber of models which can be ap-
plied to decisions relative to court
planning and operations. We do not
believe that any of these models have
gone beyond the research stage.
Whether this is due to failings of the
models or to the inability of court ad-
ministrations to absorb and use new
management procedures is, at this time,
unclear. There are certainly few people
who have initimate knowledge of court
operations and problems who can com-
prehend and judge the adequacy of the
research work. There are fewer who
can implement these type of models.
Like in law enforcement, funds and a
commitment to investigate such ad-
vances for court systems are lacking.
Thus, in what follows, we shall describe
some models which appear to be of
value in analyzing specific court prob-
lems.
The study [12] describes particular
analytical models applicable to the
planning and scheduling problems of a
large criminal court system. A wide
range of measures of effectiveness can
be employed: minimize use of critical
resources subject to acceptable process-
ing times, maximize the number of
hearings processed by the court, mini-
mize the average waiting time for all
cases, [12]. No single measure applies
263
-------
across the range of problems, and thus,
the analyst and court administrator
must augment the results obtained by a
model with the usual experiential and
intuitive factors associated with good
management.
In evaluating alternative ways of
operating a system, we must develop a
proper cost function which expresses
the relationships between the applic-
able operating costs and decision varia-
bles. For a court system we have cost of
waiting (for defendants, lawyers and
witnesses involved in the case), and
the cost of overscheduling the system
(calling more cases than can be heard
in a single calling period) and under-
scheduling the system (running out of
cases to hear before the end of a
calling period) [12].
A queuing model approach to a
court system treats the hearings to be
processed as the arrivals and the judges
as servers. We can assume that the
arrival rate and service time distribu-
tions are Poisson and exponential,
respectively, and look at a court sys-
tem as a multi-server random process.
Here it might be appropriate to separate
the set of cases which arrive by type of
priority. Standard formulas then allow
us to determine average waiting time
and average length of a queue, given
the number of servers; or given the
desired operating rates of a multi-
server system, we can determine the
minimum number of judges required to
keep the system in equilibrium. Such
models are discussed in [12] and data,
which had to be gathered especially
for the study, were used to test the
model against present operations in
Allegheny County, New York.
If we look at a court system in terms
of the allocation of given resources, we
can formulate certain decision prob-
lems as linear-programming models. In
particular we consider a model which
maximizes the number of hearings proc-
essed, where the decision variables are
the number of hearings of each type to
be scheduled in a time period [12].
This type of model can be used to
evaluate planning changes in the court
system or to see how a system will
behave based on future projections on
the number of hearings which will
occur. Thus, bottleneck situations in
future time periods or oversupply of
judges can be anticipated. For this
model we define
s, = the number of judge-hours in
period t, t = 1, . . . , n,
hj = the number of hearings of class
j, j = 1, . . . , r, arriving each
period. Arrivals in period t can-
not be processed until perioc
t + 1,
p., = the number of judge-hours re-
quired to process a hearing o
class j,
bj = the backlog of hearings in clas:
j at the beginning of the periods
Xj, = the number of hearings of clas
j scheduled in period t.
The constraints due to the numbe
of available judges are given by
< st
t = 1,
The constraints due to the need
process the backlog are given by
and we require
Xjt — nonnegative integers.
The linear-programming model is
r n
maximize J^ 2 xjt subject to t
3=1 t=l
above set of constraints. If we so
this problem by continuous linear-pi
gramming procedures the xjt will n
in general, be integer valued; but
simple rounding scheme could suffi
This model is rather basic in its fo
and solution (schedule the short
hearings first), but it can be strenj
ened if additional constraints are ad(
which induce more realism, e.g. fo
a minimum of hearings of each case
be heard, insure against hearings be
delayed too long. Similar models i
be developed which minimize the m
ber of judge hours per period and m
264
-------
mize the total waiting time of all hear-
ings.
Another approach to analyzing court
changes on delay in a criminal court
is given in the report [411. Here stand-
ard statistical procedures, e.g. regres-
sion analysis, were used to evaluate
three possible alternatives to speeding
up court operations: increasing the
number of criminal case judges, in-
creasing the judges' time on the bench,
and a reduction in criminal jury trial
time. Data from the Criminal Division
of the U. S. District Court for the
District of Columbia were used. A
linear regression equation was devel-
oped which related, for each quarter,
the number of workdays having the
same number of trial starts to the
number of trials commencing on a
workday, i.e. a function which de-
scribed the probability that there would
3e x trials commencing on any given
workday in a particular quarter. For
he data studied this turned out to be a
inear function. This function was used
o determine new functions for each of
he proposed alternatives. For these
ilternatives, it turned out that none of
he courses of action individually
idved the problem of court delay. The
:ourse of action of adding one more
udge reduced the growth of court delay
o the slowest rate of growth. The
ddition of one judge full time as well
s a second judge for approximately
>ne quarter would stop the delay from
icreasing. Of course these conclusions
ssumed that the caseload of the Dis-
•ict Court would not increase.
The possibilities were then investi-
ated as to what would happen to delay
combinations of courses of action
•ere implemented. In each instance as-
iming no increase in the case load,
le expected backlog and expected wait-
g time for the cases were reduced.
L the instance of implementation of
1 three courses of action, there was a
$.3% decrease in case backlog and a
'% decrease in expected waiting time
•er a period of one court year. This
dicated that the best approach would
the implementation of several courses
of action rather than relying on one
method.
As noted in [11], "of all the court's
administrative tasks the one most diffi-
cult is to schedule its proceedings.
Schedules setting specific trials for a
fixed day are next to impossible to
achieve on either the criminal or the
civil side. Schedules must nearly always
be tentative. This may be the most
trying weakness of judicial administra-
tion and is caused by a combination
of the workload problems, administra-
tive methods, and the lengths to which
courts are willing to go to accommodate
the convenience of attorneys and
parties.
"The term 'calendar' seems to be
used in a number of different senses,
sometimes to mean all cases ready for
trial, but more often in the narrower
sense of only those which clerks have
tentatively earmarked for trial during
the court's current calendar year or ses-
sion. The calendar may be viewed as
those cases that have been put into wait-
ing order for trial." Models and com-
puter-assisted procedures for aiding this
process have been investigated for a few
court systems, [421 and [43]. The need
is manyfold: a scheduled case is held
over due to overloading, causing losses
in time and possibly money by wit-
nesses, lawyers and policemen; or not
enough cases have been scheduled and
prepared and a judge has to close down
early. A specific approach to this prob-
lem was developed for the New York
City Criminal Court, but it was not
implemented as the Court's present or-
ganization structure and data processing
abilities did not match what appear to be
inherent requirements of such models.
The major objectives or measures
of effectiveness of this model were to
prepare schedules so that: the prob-
ability of a judge running out of cases
in a given day is low; the probability
that a case would be adjourned due to
calendar overload is a minimum; at-
torney and policeman conflicts are
eliminated or minimized; policemen's
court appearances are batched and
scheduled for duty days; high priority
265
-------
cases are scheduled as early as pos-
sible; a maximum time is allowed prior
to which a case must be calendared. In
addition, the system would free the
judges and clerks from the chore of
preparing and calling calendars, and
date assignments would be made in real
time so that participants in a case are
informed immediately as to the time of
their next court appearance and con-
currence is obtained on the assigned
data [42].
The model formulation is based on
a set of logical rules dealing with
priorities of the cases in backlog, avail-
able judicial time, and date preferences
of the participants. The logical model
was tested out for a simulated court
system and did appear to perform prop-
erly. However, it was felt that basic
changes in the administration and
operation of court systems are a neces-
sary prerequisite to the proper solution
of the scheduling and other court prob-
lems. We also add that such changes
should include the employment of tech-
nical and other specialists, and a con-
tinuing commitment to fund research
and development efforts to study spe-
cific court operational problems.
Associated with the case scheduling
problem is the problem of juror selec-
tion and juror waiting time reduction.
A study conducted in the U. S. District
Court for the District of Columbia
covered juror utilization on 245 cases
[44]. It showed that an average of 125
jurors were used each day from an
available pool of 250. By use of a
simulation model, it was found that in
order to have a jury pool sufficient
to meet expected daily peak demand
for jurors, a 35 percent underutilization
of the pool would be necessary (com-
pared to the actual 50 percent). Al-
though the approach in [44] was not to
develop a particular decision model,
it did show that the jury utilization
process does have nice statistical meas-
ures and properties which could be used
for a more detailed decision model.
Necessary measures of effectiveness and
trade-off considerations, e.g. cost of not
having a trial due to jury shortage
266
versus jury costs and waiting time, must
be formulated and related to the prob-
lem of determining the correct size
of the jury pool.
Court Simulation Models
As the above court models do not re-
flect fully the complex interrelation-
ships of a court system, a more general
approach to the understanding of a
specific court system is by the develop-
ment of a computer simulation model.
Such simulations enable us to measure
experimental changes on the system
prior to their possible introduction into
the ongoing system. These type of ex-
periments on operational systems are
somewhat difficult, costly and not fully
controllable.
The President's Crime Commission in
its Science and Technology Task Force
Report [9] described a simulation model
for the processing of felony defendants
in the District of Columbia trial court
system (see also [45]). The main
emphasis of this study was to investi-
gate proposed changes directed towards
reducing delays in the court process.
As hardly any two court systems are
similar, a court simulation can not be
devised for a general case, but must be
directed towards a specific court en-
vironment. The Task Force study [45
investigated the following structure o
the District of Columbia trial cour
system, as shown in Figure 10.
The system is divided into thre<
parts: (1) the Court of General Ses
sions (the municipal court of the Dis
trict of Columbia) and the U. S. Com
missioner where defendants are brough
for preliminary processing, (2) th
grand jury section for indictments or in
formations, and (3) the U. S. Distric
Court for processing from arraignmen
to the final disposition. The processin
of felony cases was the only part of th
court system examined in detail be
cause the only adequate data availab
were concerned with this part. Th
numbers in Figure 10 indicate the flo1
of people accused of felonies throuj
the system in 1965.
Figure 11 shows some of the majc
-------
COURT OF
GENERAL SESSIONS GRAND JURY
U.S. DISTRICT COU«T
U.S. COMMISSIONER
FIGURE 10—Processing of felony defendants in District of Columbia courts (1965 data).
Source: Reference [45]
steps in the processing- of felony de-
fendants in the District of Columbia
and the measures of time between steps
obtained from the 1965 data, e.g. the
median elapsed time between the data
Df preliminary hearing and return of
indictment was 33 days, and the 80th
sercentile time was 54 days.
The simulation was calibrated and
/alidated for the 1965 data and showed
hat a queue had developed in the
,rand jury unit. This was a queue of
;ases waiting to be processed through
he grand jury unit either prior to or
ifter grand jury consideration. Typi-
:ally, in the simulation, a defendant's
ase spent 36 days in this queue waiting
o be processed. An additional grand
ury was simulated and added for one-
lird of the time, and an Assistant U. S.
Attorney and a clerk were added for
ae full time. The results of the experi-
ment showed that the time in queue was
reduced from an average of 36 to 8 days
with no significant increase in time after
arraignment. The time from present-
ment to arraignment was reduced to
25 days as opposed to the 53 days ob-
served in the 1965 data.
The problem of reducing the total
time with emphasis on the time from
arraignment to end of motions was
studied by imposing certain procedural
changes, including reduction of the
guilty plea rate. It was found that the
time for arraignment to first day of trial
was about half of that observed, namely
50 instead of 100 days. There was,
however, a longer time from end of
motions to trial. This is a result of
introducing less guilty pleas, i.e., more
defendants go to trial. A queue waiting
to be tried had developed.
Other simulation runs investigated
PRESENT- J^
MENT ^
42
72
PRELIMINARY
HEARING
\-
RETURN OF
GRAND JURY
INDICTMENT
ARRAIGNMENT
CURE 11—Number of days between steps in processing of felony defendants (1965 data).
urce: Reference [45]
267
-------
the effects of further increasing the
grand jury resources and testing varia-
tions of procedural rules. These analyses
showed that, if the input data repre-
sented the 1965 court system, a sig-
nificant reduction in time could have
been achieved, i.e., from an average
of five to six months to an average of
two to three months. Other simulation
runs addressed the question of resource
utilization.
As noted in [45], simulation can aid
the courts in planning, programming
and budgeting for future personnel and
facility requirements, and for evaluat-
ing alternative resource allocations and
operating procedures. It can be used
by the court administrator to investigate
and compare contemplated but untried
operating concepts, thereby allowing
him to experiment with possible
changes before putting them into effect.
Finally, it can perhaps lead to a fuller
understanding of the entire court sys-
tem—how it operates and how various
elements interact.
We must also stress here, as was
done for most of the models developed
for the LE/CJ area, that simulation
models require a detailed logical struc-
ture of the system and a firm set of
historical data. It is rare to find such
elements or even means for developing
them, e.g. data standards and defini-
tions, within court systems. Simulation
models for courts, as well as the other
court models have made little impact
on the planning and operational aspects
of our courts. Here we do not need new
technical advances, the state-of-the-art
is more than adequate. As in law en-
forcement, the court systems need a
continuing commitment to improve-
ment which calls for funds, legislative
and procedural changes, and the intro-
duction of qualified technical profes-
sionals as part of the court system.
IV. CORRECTIONS SYSTEM
MODELS
There is a paucity of models and re-
search into decision making as applied
268
to correctional problems. The deep be-
havioral aspects associated with these
problems does, of course, hinder logical
and mathematical approaches. However,
statistical techniques as aids to sentenc-
ing and selection of proper treatment
of individuals, and as a means of analyz-
ing different correctional programs ap-
pear to be feasible [9]. Research in
these areas is still embryonic, with refer-
ences [46], [47], [48] and [49] as typica
efforts. We do not know of any specific
models which have been employed ir
an operational context. The study [48
made for the California State assembly
was able to show, for the Californii
prisons, that recidivism was not foun<
to be significantly related to time-servec
but is closely correlated to the character
istics and history of the individua
These results did influence new parol
procedures and parole decision guide
lines.
One of the key problems of rehabil
tation is that of selecting a particuls
rehabilitative program to implemer
from among several alternatives. A
approach to this decision-making are
was developed by the Science and Tec
nology Task Force [9]. This model wi
based on analyzing the average numb
of career arrests and the costs of tho:
criminal careers under different circur
stances: the current rehabilitative pr
gram and new proposed progran
Changes in the career arrest rate ai
costs due to these new programs we
assumed (although they could ai
should be obtained experimentally). T
model established tradeoffs in terms
how much money could be spent
programs that reduce rearrest prc
abilities and thus, total criminal can
costs. This model approach, if it v
combined with a serious effort to obt;
data based on actual controlled expt
mentations, could be used to evalu
such programs in terms of recidivi
rate and correctional system costs, t
allowing for more rational decisii
making framework to be introdui
into this critical field.
-------
V. HOLISTIC APPROACHES TO
ANALYSIS OF THE LE/CJ SYSTEM
The above descriptions of the de-
cision-making problems and models
have viewed the LE/CJ system in terms
of its major component parts—police,
courts and corrections. Solutions af-
forded by these models tend to work in
isolation and neglect the secondary but
important impacts which a change in
one component can cause in the others,
;.g. the situation which could arise if a
new approach was taken to the arrest
ind processing of drunks. In general,
ittle consideration has been given in
he past to these interrelationships, espe-
;ially in terms of planning. However,
vith the increase of Federal funds to
Jtates and local agencies, criminal jus-
ice planning agencies now exist in most
najor jurisdictions, and some of them
lave demonstrated that integrated plan-
ling is feasible.
The Safe Streets Act of 1968 enables
ach State to establish and operate a
itate criminal justice agency, supported
y funds from the Law Enforcement
Lssistance Administration of the De-
artment of Justice. Representation on
n agency must include a supervisory
roup that represents all elements of the
E/CJ system, as well as citizen groups
id local government units. Each
jency must develop and submit a
Dmprehensive State plan. Although the
nplementation of general revenue shar-
g may change a State's approach to
ie development of such a plan, the
illowing comments are appropriate.
Each plan focuses on the problem of
ime: how much there is, what causes
how to prevent it, how to control it,
>w to treat people who commit crimes,
id how to improve and expedite jus-
•e. It examines the physical and hu-
an factors that produce crime, and
alyzes the needs of police, prosecu-
rs, defense attorneys, courts, the cor-
:tional processes and the offenders.
ich State plan must offer realistic,
xific goals; be action-oriented; and
:igh costs and benefits.
The State plan sets overall priorities
for each major LE/CJ area and priori-
ties for goals at the State and local
levels. It incorporates innovations and
advanced techniques; describes general
needs and problems, existing systems,
available resources, and administrative
machinery for implementing the plan.
It defines the direction, scope and gen-
eral types of improvements to be made,
and also encourages units of local gov-
ernment to make cooperative arrange-
ments with respect to services, facilities
and equipment [50].
To aid in analyzing such comprehen-
sive plans, agencies have been able to
use cost-benefit, program budgeting and
similar planning techniques. A holistic
LE/CJ model for evaluation of alterna-
tive plans in terms of their impacts
across the system was developed by the
Science and Technology Task Force [9],
[51] and [52]. (Other holistic models
are described in [53], [54] and [69].)
This model considers the flow of
offenders through the many branches
and stages of the LE/CJ system (Figure
1) and based on costs and probabilities
associated with passing through a branch
or stage, determines the workloads and
total costs under varying assumptions
of how the components do or should
operate. The following description is
excerpted from [51] where two ap-
proaches to this type of model are de-
veloped. First, there is a simple produc-
tion process, in which the principal
concern is the flow through the system,
and the accumulation of costs flowing
from a single arrest. This linear model
provides an opportunity to examine at
each stage the workload, the personnel
requirements that result, and the asso-
ciated costs; to attribute these to types
of crimes; and to project all of these
planning variables as functions of fu-
ture arrest rates. The second is a feed-
back model, which considers the recidi-
vism probability associated with each
released defendant, and his subsequent
processing for future arrests after he
has once been released by the LE/JC
system. Such a feedback model permits
estimating the costs of a total criminal
career and the consequences of alterna-
269
-------
live actions within the LE/CJ system to
lower recidivism probabilities.
Briefly, the linear steady-state model
is as follows [51]. It is used to compute
the costs and workloads at the various
processing stages and to establish man-
power requirements to meet the antici-
pated workloads. The workload is the
annual demand for service at the vari-
ous processing stages (e.g., courtroom
hours, detective man-hours); the man-
power requirement is derived from the
workload by dividing the annual work-
ing time per man; total operating costs
are allocated to offenders by standard
cost-accounting procedures.
The flow of persons through each
processing stage is described by a vector
whose ith component represents the
yearly flow associated with character-
istic type i (i = 1, . . . , I). These char-
acteristics can be any attribute associ-
ated with individual offenders, their
crimes, or their previous processing by
the LE/CJ system.
The independent flow vector to the
model, which must be specified as in-
put, is the number of crimes reported
to police during one year. The outputs
are the computed flows, costs, and man-
power requirements that would result if
the input and the system were in steady
state. Each processing stage is charac-
terized by vector cost rates and branch-
ing probabilities.
It is recognized that the model does
have certain simplifying features and
assumptions, but, given a set of con-
sistent data, it does yield acceptable first
estimate costs, workloads and flows by
crime type and processing stage. More
important, the model measures the ef-
fects of changes in one component on
the workload, cost and manpower re-
quirements of the other components,
e.g. changes in crime or arrest rate,
probation procedures, and also enables
the determination of future resource
requirements based on projections of
expected crime level.
The second model, the feedback
model, describes the recycling process
through the LE/CJ systems during the
course of an individual's career. The
270
applications of this model are far-reach-
ing for planning purposes: given the age
of an offender at first arrest and the
crime for which he is arrested, the
model computes his expected criminal
career profile (i.e., the expected crimes
for which he will be arrested at each
age); using the cost results of the linear
model, the model computes the average
costs incurred by the LE/CJ system
over a criminal career; recidivism pa-
rameters (e.g. rearrest probabilities)
can be varied to assess how each param-
eter affects criminal careers and cost;
and the model provides a unified frame-
work in which to study the process of
recidivism and in which to test the
effects of proposed alternative LE/CJ
system policies on recidivism.
The feedback model structure is as
follows [51], As in the linear model,
flows are distinguished by crime type.
In addition, each flow variable is broken
down by the offender's age. The input to
the model, rather than crimes reportec
to police, is the number of arrests dur-
ing a year, by crime type and by age, o
individuals who have never previousl)
been arrested for one of the crimes be-
ing considered. In the model, thesf
"virgin" arrests are added to recidivis
arrests to obtain the total arrests durin
the year. The total arrests then proceec
through the LE/CJ system just as the;
do in the linear model.
Since the offender flows compris
individuals who cycle back into th
system after dismissal or release fror
the LE/CJ system, it is necessary 1
compute the number that do recyc
when they are rearrested and for whs
crime. At each possible dismissal poin
the offender is characterized by a prol
ability of rearrest that is, in general,
function of his age and his prior crin
inal record. The expected number wh
will be rearrested at some later time
computed by multiplying the number i
the flow by the appropriate rearre
probability. Then, the age at rearrest
computed by using the distribution <
delay between release and the ne
arrest. Finally, the crime type of t
next arrest is computed from a rearre
-------
crime-switch matrix, where the matrix
element is the conditional probability
that the next arrest is for crime type j,
given that rearrest occurs and the pre-
vious arrest was for crime type i.
The data requirements for the above
models are quite demanding and few,
if any, jurisdictions are in a position to
supply the requisite data or to conduct
the necessary studies and data collection
procedures. The models were originally
tested with composite data which origi-
nated from California and other juris-
dictions. More recently, the linear model
has been modified and applied to the
City of Philadelphia and the State of
Alaska with good results [55]. The
actual Philadelphia model has 28 proc-
essing stages, 89 branches, 89 man-
power types, 20 non-salary cost types
and 29 crime types. Alternative plans
are evaluated against the base LE/CJ
structure and data and comparisons can
be made on such indicators as court
backlog, probation officer caseload, and
average population of prisoners.
These models can also play an im-
Dortant role in demonstrating to plan-
ners how their actions effect the other
dements of the LE/CJ system. To this
5nd, the linear model has been pro-
grammed to be run on a computer in
in interactive terminal mode and has
5een used as a training device [52], [56].
nhis program is used principally as a
lesign tool for testing a variety of
:hanges in the operation of the LE/CJ
system. These changes might include
introduction of additional public de-
fenders, discontinuation of arrests for
certain types of crimes, introduction of
additional judges or introduction of
innovative correctional programs.
In many cases, there is no theoretical
or empirical basis for assessing the de-
tailed consequences of a contemplated
change. In view of this difficulty, the
appropriate persons to make these esti-
mates are the LE/CJ system planners
and they can do this with an interactive
model. In response to inquiries from
the program, the criminal justice plan-
ner at a terminal makes changes to the
system parameters, runs the model, and
then notes the resource implications of
those changes. Thus, he can quickly try
a variety of changes, evaluate their
consequences, and use that feedback of
consequences to try further modifica-
tions.
The need for holistic models of spe-
cific LE/CJ systems is apparent. As
evidenced by the above models, we do
have valid approaches to the study of
the LE/CJ system, given that assump-
tions and refinements must be tailored
to each system. But these models can-
not be made functional unless concerted
efforts are made throughout all elements
of the system to mount continuing data
gathering activities. Only in this man-
ner will we ever be able to develop
measures and perform evaluations of
the LE/CJ system.
References
[1] Mode, E. B., "Probability and Criminal-
istics," American Statistical Associa-
tion Journal, September 1963, pp.
628-640.
[2] The Challenge of Crime in a Free So-
ciety, The President's Commission on
Law Enforcement and Administra-
tion of Justice, U.S. Government
Printing Office, Washington, D.C.,
February 1967.
[3] State-Local Relations in the Criminal
Justice System, Advisory Commission
on Intergovernmental Relations, U.S.
Government Printing Office, Wash-
ington, D.C., 1971.
[4] Criminal Justice Agencies in the United
Stales Summary Report 1970, De-
partment of Justice, U.S. Govern-
ment Printing Office, Washington,
D.C., 1970.
[5] "Report of the National Advisory Com-
mission on Criminal Justice Stand-
ards and Goals," Government Print-
ing Office, Washington, D.C., 1973.
[6] Crime in the United States, Uniform
Crime Reports, FBI, U.S. Govern-
ment Printing Office, Washington,
D.C., 1971.
[7] Kakalik, J. S. and S. Wildhorn, "Aids
to Decision-making in Police Patrol,"
(R-593-HUD/RC) The Rand Cor-
poration, Santa Monica, California,
February 1971.
[8] Gallup Poll: "One in Three is City
Crime Victim" and "Crime is Rated
Worst Urban Problem," The Wash-
ington Post, January 14 and 15, 1973.
[9] Science and Technology: Task Force
Report, The President's Commission
271
-------
on Law Enforcement and Adminis-
tration of Justice, U. S. Government
Printing Office, Washington, D. C.,
1967.
[10] Larson, R. C., Urban Police Patrol
Analysis, The MIT Press, Cam-
bridge, Massachusetts, 1972.
[11] The Courts: Task Force Report, The
President's Commission on Law En-
forcement and Administration of
Justice, U. S. Government Printing
Office, Washington, D. C., 1967.
[12] Lyons, N. R., "Analytic Models of
Criminal Court Operations," Gradu-
ate School of Business and Public
Administration, Cornell University,
Ithaca, New York, 1971.
[13] Corrections Task Force Report, The
President's Commission on Law En-
forcement and Administration of
Justice, U. S. Government Printing
Office, Washington, D. C., 1967.
[14] Pittman, J. T. and P. Gray, "Evaluation
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-------
[41] Reed, J. H., "The Application of Opera-
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sylvania, 1971.
[42] Shapiro, S. S., "An Automated Court
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Methods, Inc., New York City, New
York, October 1971.
[43] Isaacs, H. H., "A Study of Witness
Utilization and Case Scheduling in
the San Bernardino County Munici-
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geles, California, October 1970.
[44] Pabst, W. R. Jr., "Juror Waiting Time
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[45] Taylor, J. G. et al., "Simulation Ap-
plied to A Court System," IEEE
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Cybernetics, Vol. SSC-4, No. 4, No-
vember 1968.
[46] "Prediction of Criminal Conduct and
Preventive Confinements of Con-
victed Persons," Andrew von Hirsch,
Buffalo Law Review, Spring 1972.
[47] Clapp, p. E., "Parole: Viewed as a
Decision Under Uncertainty," The
Journal of Industrial Engineering,
August 1966.
[48] Pittman, J. T. and P. Gray, "Evaluation
of Prison Systems." School of In-
dustrial and Systems Engineering,
Georgia Institute of Technology, At-
lanta, Georgia, 1972.
[49] Daetz, D. and S. E. Kolodney, "Results
and Impact of an Analysis of Recid-
ivism in California," Department of
Industrial Engineering, Stanford Uni-
versity, Stanford, California, 1972.
[50] "A United Strategy for Crime Control"
Law Enforcement Assistance Admin-
istration, U. S. Department of Justice,
1968.
[51] Blumstein, A. and R. Larson, "Models
of a Total Criminal Justice System,"
Operations Research, Vol. 17, No. 2,
March-April, 1969.
[52] Blumstein, A. and R. Larson, "Analysis
of a Total Criminal Justice System,"
Chapter 16 of Analysis of Public Sys-
tems. A. W, Drake, R. L. Keeney and
P. M. Morse. MIT Press, Cambridge,
Massachusetts, 1972.
[53] "Prevention and Control of Crime and
Delinquency," Youth and Adult Cor-
rections Agency, State of California,
1965 (prepared by the Space-General
Corporation, El Monte, California).
[54] Abraham, S. C., "Simulation Modelling
in Criminal Justice: An Approach
and Demonstration Using System
Dynamics," Graduate School of
Management, University of Cali-
fornia. Los Angeles, California, July
1972
[55] Renshaw, B. H. et al., "PHILJIM, The
Philadelphia Justice Improvement
Model," Government Studies and
Systems, Inc., Philadelphia, Penn-
sylvania, October 1972.
[56] Belkin, J. A., et al., "JUSSIM: An
Interactive Criminal Justice System
Design Tool," Urban Systems In-
stitute, Carnegie-Mellon University,
1971.
Selected Additional References
feneral
[57] "Combating Crime," The Annals of the
American Academy of Political and
Social Science, November 1967.
58] "Crime Against Small Business," A Re-
port of the Small Business Adminis-
tration transmitted to the Select
Committee on Small Business, U.S.
Senate, Document No. 91-14 April
3, 1969.
59] "Criminal Statistics," National Insti-
tute of Mental Health, Center for
Studies of Crime and Delinquency,
Rockville, Md.. DHEW Publication
No. (HSM) 72-9094.
60] "Economic Crimes: Their Generation
Deterrence and Control," Harold L.
Votey, Jr., et. al., NTIS, Department
of Commerce, PB 194 984, 31 De-
cember 1969.
51] "Evaluation of Crime Control Pro-
grams," Michael D. Maltz, Law En-
forcement Assistance Administration,
U.S. Dept. of Justice, #2700-00163,
April 1972.
i2] "Federal Law Enforcement and Crimi-
nal Justice Assistance Activities," At-
torney General's First Annual Report
for 1971, #2700-0160.
[63] Foundations and Mathematical Models
of Operations Research With Exten-
sions to the Criminal Justice System,
Haig E. Bohigian, The Gazette Press,
Inc., 1971.
[64] "The Impact of Organized Crime on
an Inner City Community," Harold
D. Lasswell, Jeremiah B. McKenna,
The Policy Sciences Center, Inc.,
New York, New York.
[65] "Implementing Statewide Criminal Jus-
tice Statistics Systems—The Model
and Implementation Environment,"
Project Search, Law Enforcement As-
sistance Administration, January
1972, Technical Report No. 4.
[66] "Mathematical Methods in Criminol-
ogy," M. E. Wolfgang and H. A.
Smith, Intel national Social Science
Journal, Vol. XVIII, No. 2, 1966.
[67] "Property Crime as an Economic Phe-
nomenon," David L. Sjoquist, U.S.
Department of Commerce, NTIS, De-
cember 1970, PB-203-144.
[68] "Regional Criminal Justice Planning—
A Manual for Local Officials," Part
273
-------
I, National Association of Counties
Research Foundation," Washington,
D.C., June 1971.
[69] Ibid., Part II, November 1971.
Law Enforcement
[70] "Allocations of Resources in the Chi-
cago Police Department," National
Institute of Law Enforcement and
Criminal Justice, U.S. Department of
Justice, PB-212777, March 1972.
[71] "Analysis of Crime Prevention Strate-
gies," Ronald L. Rardin and Paul
Gray, 42nd National Meeting of the
Operations Research Society of
America, November 1972.
[72] "The Challenge of Productivity Diver-
sity—Improving Local Government
Productivity Measurement and Eval-
uation," Part III, Measuring Police-
Crime Control Productivity, June
1972, for The National Commission
on Productivity by The Urban In-
stitute.
[73] "The Collection and Analysis of Auto
Theft Data in Denver," July 1970-
June 1971, Final Report, Industrial
Economics Division, Denver Re-
search Institute, University of Den-
ver, Anita S. West, March 1971.
[74] "Computerized Allocation of Police
Traffic Services," A Demonstration
Study, NTIS, U.S. Department of
Commerce, PB-213 025, March 1972.
[75] "Computer Assisted Instruction Pro-
gram For Police Training," Richard
W. Brightman, U.S. Department of
Justice, National Institute of Law
Enforcement and Criminal Justice,
Pr 71-5, December 1971.
[76] "Crime-Correlated Areas," Frank S.
Rudnick, University of Rhode Island,
April 1972.
[77] Crime and Information Theory, M.A.P.
Willmer, Edinburgh University Press,
1970.
[78] "An Economic Analysis of the Distribu-
tion of Police Forces," J. F. Giertz,
U.S. Department of Commerce,
NTIS, 1 April 1970.
[79] "Measuring Auto Theft and the Effec-
tiveness of Auto Theft Control Pro-
grams," Robert Frese, Nelson B. Hel-
ler, for 38th National Meeting of the
Operations Research Society of
America, Sept., 1970.
[80] "Measuring the Response Patterns of
New York City Police Patrol Cars,"
Richard C. Larson, The N.Y.C. Rand
Institute, R-673-NYC/HUD, July
1971.
[81] "Measuring the Value of the Indianapo-
lis Police Fleet Plan," Donald M.
Fisk, The Urban Institute, Washing-
ton, D.C., Working Paper #108-70,
9/10/70.
[82] "Methods for Allocating Urban Emer-
gency Units," J. M. Chaiken and R.
C. Larson, The N.Y.C. Rand Insti-
tute, R-680-HUD/NSF, May 1971.
[83] "Minority Recruiting in the New York
City Police Department—Part I. The
Attraction of Candidates—Part II.
The Retention of Candidates," I. C.
Hunt, Jr.—Part I., B. Cohen—Part
274
II., The N.Y.C. Rand Institute, R-
702-NYC, May 1971.
[84] "Nonlethal Weapons for Law Enforce-
ment—Research Needs and Priori-
ties. Security Planning Corporation,
Washington, D.C., March 1972.
[85] "On the Measurement of Information
in the Field of Criminal Detection,"
M.A.P. Willmer, Operational Re-
search Quarterly, Vol. 17, No. 4.
[86] "Patterns of Burglary," Harry A. Scarr,
U.S. Department of Justice, National
Institute of Law Enforcement and
Criminal Justice, PR 72-10 February
1972.
[87] "Operations Research and Computers in
Law Enforcement: Some Case Stud-
ies of American Police Experience,"
A. M. Bottoms, Computers and Op-
erations Research, Vol. 1. pp. 49-65,
1974.
[88] "Police and Computer: Use, Accept-
ance, and Impact of Automation,"
Kent W. Colton. Joint Center for
Urban Studies of MIT and Harvard
University, Municipal Year Book,
1972.
[89] "Police Background Characteristics and
Performance: Summary," Bernard
Cohen and Jan Chaiken, For the
National Institute of Law Enforce-
ment and Criminal Justice, The
N.Y.C. Rand Institute, R-999-DOJ
(abridged), May 1972.
[90] "Police Training and Performance
Study," U.S. Department of Justice,
National Institute of Law Enforce-
ment and Criminal Justice, PR 70-4,
September 1970.
[91] "Some Determinants of Crime: An
Ec9nometric Analysis of Major anc
Minor Crimes Around Boston,'
George B. Weathersby, University o
California, for the 38th Nationa
Meeting of the Operations Researcl
Society of America, Sept. 1970.
[92] "Some Effects of an Increase in Polio
Manpower in the 20th Precinct o
New York City," S. James Press, Th
N.Y.C. Rand Institute, R-704-NYC
October 1971.
[93] "Urban Crime and Urban Planning, i
Pilot Study, Vol. I," Hubert C
Locke, U.S. Department of Con
merce, NTIS, PB 195 655, July 196'
[94] "The Use of Gaming Techniques '
Police Research," A. G. McDonali
Scientific Adviser's Branch, Londo
England, SA/POL 12, April 1966.
[95] "Watts Riot Arrests,"—Los Angele
August 1965, Bureau of Crimin
Statistics, Department of Justic
California, June 30, 1966.
Courts
[96] "Compilation and Use of Crimin
Court Data in Relation to Pre-Tr
Release of Defendants: Pilot Studj
J. W. Locke, R. Penn, J. Rick,
Bunten, and G. Hare, U.S. Depa
ment of Commerce. National Sure
of Standards. NBS Tech. Note 5'.
August 1970.
-------
[97] "Evaluation of the Manhattan Criminal
Court's Master Calendar Project:
Phase 1—February 1-June 30, 1971,"
John B. Jennings, The N.Y.C. Rand
Institute, R-1013-NYC, January 1972.
[98] "The Flow of Arrested Adult Defend-
ants Through the Manhattan Crimi-
nal Court in 1968 and 1969," John B.
Jennings, The N.Y.C. Rand Insti-
tute, R-638-NYC, January 1971.
[99] "The Flow of Defendants Through the
New York City Criminal Court in
1967," John B. Jennings, The N.Y.C.
Rand Institute, RM-6364-NYC, Sep-
tember 1970.
[100] "Quantitative Models of Criminal
Courts," John B. Jennings, The
N.Y.C. Rand Institute, P-4641, May
1971.
Corrections
[101] "The Bronx Sentencing Project of the
Vera Institute of Justice," J. B.
Lieberman, S. A. Schaffer, J. M.
Martin, U.S. Department of Justice,
National Institute of Law Enforce-
ment and Criminal Justice, PR
72-15, October 1972.
[102] "Parole Decision Making—The Utili-
zation of Experience in Parole De-
cision Making: A Progress Report,"
D. M. Gottfredson, L. T. Wilkins,
P. B. Hoffman, S. M. Singer, U.S.
Department of Justice, National In-
stitute of Law Enforcement and
Criminal Justice, January 1973.
[103] "The Measurement and Prediction of
Criminal Behavior and Recidivism,"
W. O. Jenkins et al., Draper Cor-
rectional Center, Elmore, Alabama.
December 1972.
275
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Chapter 9
Models in Educational Planning and Operations
By
Edmond H. Weiss
SUMMARY 279
I. EDUCATIONAL DECISIONS 281
Introduction 281
Decision Levels . 282
School District Level: Student Centered Decisions 283
Longer Run Student Decisions 284
School District Level: Curriculum Decisions 285
School District Level: Campus Operating Decisions 285
School District Level: District-Wide (Or University-Wide) Decisions
(Short Run) 286
District-Wide Decisions (Long Run) 287
District-Wide (Major Decisions) 288
Intermediate (County) Level Decisions 288
State-Level Decisions 289
Federal Decisions 291
II. ILLUSTRATIONS OF DECISION MODELS FOR EDUCATION 292
Introduction . 292
A Theoretical Model for Optimizing the Economy and Education 292
Forecasting Nationwide Undergraduate Enrollments and Federal
Financial Aid Requirements 294
A Model for Allocation of Vocational Education Funds 296
A State-Level Input-Output Planning Model for Local Educational
Agencies . 297
A Model for College Enrollment Forecasts 298
A Model for University Resource Requirements Analysis 299
A Model for University Facilities Analysis 300
A Model for School District Resource Requirements Planning 303
A Model for School Bus Scheduling 304
A Model for Class Scheduling 307
A Theoretical Model for Instructional Optimization 309
II. AN ASSESSMENT OF DECISION MODELS IN EDUCATION 311
Introduction: Assessment Criteria 311
Assessment 312
The Future of Models 313
REFERENCES AND SELECTED BIBLIOGRAPHY 313
277
-------
-------
Models in Educational Planning
and Operations
SUMMARY
American education is a complex of
institutions, governments and systems,
providing essential services to more than
50,000,000 children and adults. Sub-
stantial segments of this complex can
be found at every level of government
.from national to neighborhood) and
in both the private and public sector.
Decision models have grown increas-
ngly prominent in education manage-
ment. Most of the systems and tech-
liques have been developed to support
lecision problems which education has
n common with other large organiza-
ions: staff assignment, vehicle deploy-
nent, construction scheduling, cost
orecasting, and many others. In addi-
ion, several decision models have been
dvanced to solve decision problems
eculiar to education, such as: Delating
:arning to instructional techniques,
itisfying the skilled manpower require-
icnts of the economy, or achieving
icial integration in school programs.
In this chapter, a selection from the
rtually unlimited range of educational
:cision problems is presented. The de-
sions are organized according to a
erarchy of institutions—from the
issroom, to the school, to the inter-
ediate unit, to the state agency, to the
:deral Government. Interestingly, the
cision problems discussed (chosen
cause of their relative importance and
icnability to model-assisted solutions)
iicate that each level of the education
tnplex has similar decision problems;
ist of the differences are matters of
ipe, timing, and level of aggregation.
long the most prevalent decision
iblems at all levels are: forecasting
demand for service; calculation of
costs and resource requirements for pro-
grams; allocation of resources to pro-
duce optimum results; assignment and
scheduling of manpower and material
resources, to satisfy demand and achieve
economies; projecting the operational
consequences of alternative administra-
tive policies.
The chapter begins with a description
of the complex, its levels, and the main
decision problems. This section is fol-
lowed by a sampling of representative
and instructive models for national,
State, and local levels (see Summary
Table).
It should be noted that the majority
of decision models presented here are
not directly related to the conduct of
instruction. Administrative questions can
usually be more readily answered in
quantified terms than instructional prob-
lems. It is vastly easier to construct
simulations of the service systems in
education than it is to establish direct
and mathematically precise relationships
between resource utilization and student
growth. Even so, the benefits of these
models will ultimately be shared by
students, as a result of four related
consequences of their use:
• More efficiency in the non-instruc-
tional aspects of education, "free-
ing-up" instructional resources.
• More efficiency in the selection and
use of instructional resources, so
that there is a better match be-
tween apparent-student "needs"
and resources.
• More educational research, of
higher direct utility to educational
practitioners.
• More formal and explicit informa-
tion about the operation of schools
279
-------
EDUCATION
Models Discussed in Chapter
Summary Table
Model/Decision Area
General Type
National Level:
Macro-Economic
Planning (OECD)
Forecasting undergraduate
enrollments and financial
aid requirements
State Level:
Allocation of Vocational
Education Funds (Penna.)
Input-Output Evaluation
of Local School Districts
in a State (New York)
Forecasting State-Wide
College Enrollments
(California)
College/ University Level:
Resource Requirements
Prediction (WICHE)
Facilities Analysis Model
(CCHE)
School District Level:
Resource Requirements
Model (Trenton)
280
Simulation
Linear Programming
Probabilistic Flow Simu-
lation; Deterministic
Resource Requirements
Simulation
Linear Programming
Simulation
Multiple Regression
Probabilistic Flow
Simulation
Deterministic Simulation
Deterministic Simulation
Optimization
Deterministic Simulation
Important Characteristics
Determines optimum mix of na-
tional investment in education
and non-education sectors of the
economy, to insure economic
growth, provision of required
manpower, and a continuing
level of "non-material" educa-
tional benefits
Forecasts total undergraduate en-
rollments in the U.S., by socio-
economic group; calculates the
financial aid burden, under vary-
ing policies of student/govern-
ment financial obligation
Determines the optimum mix of
grant awards to vocational edu-
cation programs in the state, so
as to maximize the closeness be-
tween skilled graduates producec
and labor market demands
Evaluates the effectiveness o
programs in various school b)
comparing observed results will
results "expected" in the multiplf
regression equations for the dis
trict in question
Forecasts the enrollment in :
state-wide system of colleges, a
each year-level, as a function o
current enrollments in high schoc
and college and transitional proc
abilities
Calculates staff, facilities, equi]
ment, and other resource requin
ments as a function of enrpllmei
by program; relies on an "induct
course load matrix" which co
verts program service demands
resource requirements
Shows the alternative costs
various policies on the use
higher education facilities in
given institution; shows minimi
cost as a result of trading-i
operating costs vs. capital co
Forecasts the multi-year costs a
staff requirements for a sch<
district, based on current utili
tion, change in demand, inflati
etc; calculates consequences
current policies or simulates
consequences of alternative pi:
and policies
-------
Model/Decision Area
General Type
Important Characteristics
Vehicle Scheduling
(Tippecanoe)
School Level:
Class Scheduling
Classroom Level:
Optimizing Learning
Heuristic Simulation
Monte Carlo Simulation
Linear Programming
Determines school vehicle sched-
ules which minimize bus routes,
minimize mileage, overt overload-
ing; and keep route time below
constraint ceilings
Assigns students to courses, mini-
mizing the arbitrary effect of
"closing" sections on a "first-
come, first-served" basis; mini-
mizes the number of "unassigning-
able" cases
Develops a theoretical model for
assigning students to tasks, so as
to maximize achievement of de-
sired performance objectives
and colleges, so that "institutional
learning" will take place, and all
decisions will be more enlightened.
The chapter concludes with an assess-
ment of the adequacy of current models
(and forecasts of needed and probable
changes), as well as a resource bibliog-
raphy which will aid education adminis-
trators to apply models to their prob-
lems.
I. EDUCATIONAL DECISIONS
Introduction
The purpose of this chapter is to
introduce educational policymakers, ad-
ministrators, and program managers to
he range of decision problems for
which decision models are and (in some
;ases) are not available, and to give
jeneral and specific examples of the
nodels themselves. No technique or
nodel is described here in sufficient
icientific detail to allow an immediate
ipplication. In contrast, it is hoped that
he reader will learn from this discussion
hat certain analytical concepts are
ppropriate to his decision tasks: to
.cquaint him with the types or "styles"
if models he may choose from, to show
iim specific examples, and to provide
resource bibliography of modeling
terature.
The chapter is organized in four main
jctions:
—a discussion of the decision types at
all levels of educational planning
and operation, with an emphasis
on those which do now, or will
shortly, lend themselves to model
analysis
—a set of brief descriptions of actual
decision models used by diverse
planners and managers in various
levels of education
—an assessment of the overall avail-
ability, suitability, and potential of
education models
—a bibliography of education model
literature
Planning and operation of education
is a multi-level human service industry,
in which many of the decision problems
are peculiarly associated with the edu-
cational mission and many others are
common to the management of all large,
complex organizations. Interestingly, a
larger body of literature on formal
model development is found in connec-
tion with the administrative and organi-
zational functions than in connection
with teaching methods and instructional
decisions. Historically, the "profession-
alization" of school administration has
preceded the "professionalization" of
teaching, so that the development of
formal administrative models has a
head start of many years on similar
developments in instruction. The con-
281
-------
cept of "learning models" is as old as
empirical psychology, but the adaption
of psychological models of learning to
the engineering and design of instruction
is of relatively late vintage.
In this chapter, our emphasis is upon
models for educational decision mak-
ing, rather than models for the descrip-
tion of educational phenomena. This
emphasis is necessary in order to reduce
the number of examined approaches to
a practical level; an attempt to include
the full range of models used to de-
scribe education would involve exten-
sive representations from political sci-
ence, economics, sociology, urbanology,
epidemiology, communication theory,
and other disciplines. Instead, the ma-
terial which follows will address only
this question:
What are the actual decisions and
decision problems made frequently at
all levels of education, and what
models, or model types, are appro-
priate to these decisions?
Decision Levels
The American educational complex
is organized in the form of a pyramid,
with approximately 50,000,000 students
at the base and the Division of Educa-
tion of HEW at the apex. As should be
expected, the vast majority of decisions,
as well as the consumption of resources,
goes on in the bottom layers of the
pyramid, and, clearly, the time span and
scope of decision tends to be shorter at
the base than at the apex. As shown
in Figure 1 the base is comprised of
school districts and other educational
agencies (such as colleges and universi-
ties), and this base is further divided
into campus or sub-district, program or
curriculum, and individual student. It
is appropriate to show more detail at
the base level because, as already indi-
cated, most of the decisionmaking goes
on at this level. (Also included in the
base is the proliferating number of non-
college post-secondary schools and pro-
grams, both public and proprietary.)
At the next higher levels in the pyra-
mid are the Intermediate or Sub-state
units, and the State Education Agencies
282
(SEA's) or Departments. In many
states the SEA or the Intermediate unit
(which is typically a county or cluster
of counties) actually operates several
schools or program—for example, in
specialized service areas such as educa-
tion for the severely handicapped. For
the most part, though, Intermediate and
State units exist to regulate, lead, and
provide supportive services to the units
at the base of the pyramid, or to serve
as a funding conduit between higher
levels of government and the schools
and colleges. Typically, planning and
decisionmaking at these State or Inter-
mediate levels are with respect to the
basic level, and the State or Inter-
mediate plan is "driven" by the goals
and programs at the basic level.
Between the State and Federal level
are a few multi-state associations or
authorities, mainly in Higher Educa-
tion. These organizations are only quasi-
governmental, however, and make rela-
tively few decisions which directly
influence practices in schools and col-
leges.
At the Federal level, most decisions
regarding education are made in the
Division of Education of the Depart-
ment of Health, Education and Welfare
(although many educational programs
exist in other Federal agencies). The
Division consists of the Office of th<
Assistant Secretary, the Office of Edu
cation, and the National Institute o
Education. The differing responsibilitie
of these Federal units are still being de
fined. The authority for operation o
Public Schools and regulation of privat
institutions rests, of course, with th
States.
As indicated earlier, the different de
cisions made by each level frequentl
differ mainly in scope and timing, wit
swifter, more detailed decisionmakin
as the lowest level. Thus, each level
decisions admit of different forms c
mathematical quantification and requii
different levels of statistical precisic
. . . even when the parameters of tl
decisions (e.g. staff requirement!
appear to be the same.
-------
/Federal\
' Division!
of
' Education
(OE, NIK,
others"
Multi-State Regions\
or Authorities
State Units
Intermediate or
Sub-State Units
(usually counties)
School District or Institution of
Higher Education
School campus or Sub-District
Programs/Curricula
Students
FIGURE 1—Levels of Educational Decision
School Districts
or
Institutions of
Higher Education
(LEA'S)
School District Level:
Student-Centered Decisions
Most educational decisions are about
fhat to do to, for, or with individual
tudents. They are typically made by an
nstructor or classroom teacher, and
isually without a formal decision
lodel.
The most familiar educational de-
ision problems involve what to have
udents do (or what to expose them
>) over the next several minutes,
hours, or weeks. These decisions include
the choice of teaching methods and
materials, the making of student task
assignments, and the selection of rein-
forcements to be applied. Ordinarily,
this level of decision is based on intui-
tive models, "in the instructor's head,"
rather than formal quantified models;
this trend is probably attributable to an
absence of both theory and empirical
evidence supporting ideas of effective
instruction.
Averch, et al. [4] have recently re-
283
-------
leased a major study for the President's
Commission on School Finance, en-
titled How Effective is Schooling? . . .,
in which they address critically an
abundance of descriptive and evaluative
literature on educational innovations
and experiments. Searching for gen-
erally predictive program characteris-
tics, they are able to find numerous
cases in which treatments or program
types appear to be effective, but are
unable to identify any general or sys-
tematic patterns of effectiveness. This
finding leads one to conclude that the
factors which account for success in
both conventional and innovative pro-
grams have not yet been identified, nor,
indeed, conceptualized in a way that
admits of scientific appraisal. In short,
there is high uncertainty at this time
about what variables should be part of a
decision model for optimizing instruc-
tion through school management policy
decisions.
The areas in which modeling for
short-run student decisions do exist are
in curriculum engineering [63], and
behavior modification (or application
of operant conditioning to instructional
design [39]). In curriculum engineering
models, the course of study is conceived
as a branching program of student per-
formance objectives, in which students
are routed through consecutive steps on
a path which leads to attainment of the
major instructional objectives. Such sys-
tems are frequently computer assisted
(the computer terminal is the instructor)
or computer mediated. Behavior modi-
fication models are used largely in basic
skills training or therapy-like programs
to correct behavioral dysfunctions in
students. They operate by emphasizing
a formal reinforcement schedule, such
that positive sanctions and rewards are
allocated to student performances ac-
cording to a specific model, and be-
havior is thereby "shaped" to conform
with educational objectives.
It should be emphasized that, despite
the abundant literature in this area,
especially in curriculum engineering,
the overwhelming majority of short-run
student decisions are made without
benefit of mathematical models, or, in-
deed, formal models of any kind.
Longer-run Student Decisions
Longer-run student decisions are
usually associated with the guidance and
counseling function, which assists the
student in course and program selection.
Again, these decisions are mainly in-
stinctive and non-formal, although they
resemble a goal-programming approach,
in which interim decisions are made on
the basis of their probability of en-
hancing the attainment of the highest
practical level of student aspiration.
Typically, the inputs to this decision
model are test scores—intelligence,
basic skills, vocational preference, etc.
—augmented by preference statements
of the student and parents (the student
alone, in higher education). The al-
ternative courses of action available to
the decisionmakers are constrained by
the staff and programs available in the
institution, the financial resources of the
institution and student, and the belief
about the relationship between certain
courses and probable goal attainment.
Given this configuration, longer-run de-
cisions are highly sensitive to such
variables as the completeness of student
ability and preference data, the number
of alternatives to choose among, and
the firmness of knowledge about the
relationship between program selection
and results. Thus, it is not surprising
that guidance and counseling decision-
makers are increasingly employing
more ambitious student informatior
systems, as well as matching or search
ing logic which line up student need wit
available programs. This approach i
most effective in the selection of post
high school programs for secondar
students where the plan may be drawi
from the approximately 2,500 college
and universities in the data bank, plu
countless other post-secondary prc
grams, and a decision can be mad
which satisfies student objectives, an
constraints of locale, cost, and othe
variables.
In the lower grades, longer-run sti
dent decisions are made less formall1
284
-------
except in the cases of students with
diagnosed handicaps or disabilities. In
these instances, the plan is based not on
empirically verified models of prescrip-
tion and treatment but on the collective
judgment of a team of interdisciplinary
specialists (psychologist, audiologist,
social worker, etc.).
School District Level: Curriculum
Decisions
Curriculum decisions are generally of
two types: what curricula (or programs)
to offer; how to offer them. The former
decision is generally political, in re-
sponse to demands or preferences from
students, parents, and educators, made
within the constraints of public law
and availability of necessary instruc-
tional resources (such as teachers with
appropriate skills).
In basic education at the secondary
level, curriculum or course offerings are
frequently constrained by a minimum
enrollment, which will bring program
costs into a feasible range [21]. In
Higher Education, whole programs and
colleges within universities are some-
times evaluated on economic viability,
with favor often shown to self-sustain-
ing or even profit-making programs
[25].
There are, and can be no, purely
rational or deterministic models of what
programs should be offered in the edu-
cational program—since such a decision
is properly in the domain of political
values. The closest one might come to
such an approach would be the selection
of curricula on the basis of aggregating
individual student plans (mentioned
earlier) so that a program becomes, in
jffect, the intersection of several stu-
dent plans.
At certain macro-levels of decision-
naking, the choice of curriculum mix
nay be influenced by a cost-benefit
nodel, in which the relative economic
>enefits of alternative programs (e.g.,
eneral education versus vocational edu-
ction) are evaluated by projecting the
xpected return in student earnings or
educed public expenditures (welfare,
or example) and contrasting that re-
turn with the expected alternative costs
[40]. A less rigid variant is cost-utility
evaluation, in which decisionmakers
assign common unit weights to the non-
economic benefits of planned programs
and attempt to maximize the value of
the utility/cost fraction [74].
More directly applicable than cost-
benefit analysis is cost-effectiveness
comparison, in which, after goals have
been politically determined, alternative
methods or means to accomplish com-
mon objectives are compared. Depend-
ing on the decision problem the model
indicates the least expensive way to
achieve a given objective or the most
effective method which falls within an
upper bound of allowable cost [64].
The ability to use cost-effectiveness
decision models is constrained by the
limited knowledge of cause-effect rela-
tionships in instruction (necessitating
reliance on "Delphi" or other soft esti-
mation techniques [74, Appendix A])
and also the obscurities of educational
cost accounting, which tends to be
superficial and imprecise in relating
expenditures to outcomes. (The devel-
opment of education "production func-
tions" is concerned with solving these
analytical problems, and will be dis-
cussed again in this chapter.)
School District Level: Campus
Operating Decisions
Any school district or university is
faced with decisions about the assign-
ment of students, staff and resources on
a building or campus basis. These de-
cisions resemble those above, but the
emphasis is on specific dimensions of
physical space and time.
The problem of class scheduling is
one of finding an acceptable plan which
minimizes unsatisfied student demands,
while assuring a maximum utilization of
staff, facilities and equipment. A "class,"
thus, is a set of students assigned to an
instructor (or group), in a unique
space, at unique times. Because of the
dimensions of the problem, class sched-
uling lends itself to a number of well-
developed industrial management mod-
els in which conflict matrices are
285
-------
generated, and schedule conflicts are
minimized according to quantifiable cri-
teria such as to minimize:
• students not satisfied in course
choice
• unevenness in the utilization rate
for staff and physical resources
• interruption of sequenced courses
Such models and systems lower con-
flicts to a prescribed minimum, and
there is a growing body of models and
software available to perform this func-
tion. In addition, several of these sys-
tems include features which allow for
educational innovation, mainly by al-
lowing for the flexible aggregation of
small units of time (usually called
modules) into a variety of class con-
figurations. Such techniques allow for a
broader range of student choice, and
also a wider range of program design
alternatives (such as flexible or "modu-
lar" scheduling) [24, 28, 30, 33].
Close to half of the basic education
students in America go to school on a
bus, and most of those on a bus which
is operated by the School District.
Efficient vehicle scheduling also admits
of several mathematical decision ap-
proaches, based on assignment or queu-
ing models, which can serve to reduce
miles traveled, number of vehicles,
number of stops, mean travel time for
students, etc. When used in a simulation
mode, school transportation officials
can "try" policies in which, for example,
trade-offs are made between the distance
students must walk to a bus stop and
the net cost of the system.
Current opinion is that the use of
well-developed modeling methods in
school vehicle scheduling can signif-
icantly reduce cost and even minimize
accidents [2, 52].
In recent years, of course, vehicle
scheduling has been increasingly asso-
ciated with school desegregation. Vehi-
cle scheduling systems can be adapted
to respect constraints on the race-mix
in schools (see "Student-assignment,"
below) or to achieve desired race-
mixes, subject to contraints of efficiency
and cost. It is possible, for example, to
286
create a linear programming model in
which the variables in the objective
function are school boundary locations
and the objective is to minimize the
gap between actual and desired racial
distributions, subject to transportation
constraints on largest allowable travel
time, or mean travel time, etc. [20, 31].
Several modelling techniques may
also be applied to the general problems
of vehicle maintenance and replace-
ment, the goal being to determine opti-
mum times for the "trading-in" of
vehicles, as a consequence of trade-in
value, maintenance costs, and costs of
replacement vehicles.
Large campuses or school buildings
are repositories for large inventories of
supplies and equipment, some of it
consumable, some of it subject to de-
terioration and dysfunction. (In some
cases, a centralized warehouse facility
serves several buildings.)
The ongoing assignment of profes-
sional and non-professional personnel is
frequently aided by information sys-
tems which search through records of
staff abilities, certifications, and experi-
ences. Mathematical assignment models
can be used in conjunction with such an
information system to achieve such staf
assignment objectives as ethnic mix.
sex mix, age/experience mix, and sc
forth.
Personnel assignment can also be
done in conjunction with resource re
quirement models (to be discusse(
later). In these cases, the main focu
of the model is the estimation of wha
manpower and materials are requirei
to operate a particular program o
project. Several techniques familiar i
industrial engineering (such as Criticc
Path Scheduling) can be used in thi
process.
School District Level: District-Wide
(or University-Wide) Decisions
(Short-run)
So far, we have discussed sever;
student-centered, curriculum-centerei
and campus-centered decisions. In mo
cases, these decisions are related
short-run operating problems, with hij
-------
needs for precision. Clearly, staff assign-
ment in a particular school, at a par-
ticular hour, requires a type of decision-
making different in precision from esti-
mating, say, a university's staff needs
for ten years.
At the district-wide, or university-
wide, level, the shortest planning time
frame is usually a year, a period keyed
largely to the annual appropriations
cycle. For the most part, the short-run
decisions discussed below are likely to
be made in the annual budgeting cycle.
In addition, longer-term decisions are
also discussed, and, in these cases, the
limit on the number of years to be in-
cluded in the span of prediction can be
as long as the expected life of a facility.
Probably, the most significant educa-
ional resource decision is personnel
'election. Typically, one-year staff plan-
ling is based on a forecast of demand
number of students and program/
;ourse preferences), an analysis of
ivailable staff, and an estimate of new
taff requirements. In more sophisti-
ated planning, an expected attrition or
urnover rate is also utilized, so that
Dtal "positions" by staff type may be
djusted to show total "hires."
"Recruiting" may be a matter of
nding staff with scarce abilities (aided
y search of a talent bank data base),
ut, in basic education, is more likely
) be a system of selection rules for
loosing among the oversupply of avail-
jle teachers and administrators.
Little formal attention is paid to
>ricing" models in staff planning. Gen-
ally, decisionmakers intuit the rela-
mship between salary determinations
id effectiveness of recruiting.
Obviously, any analysis of staff re-
irements involves student population
d enrollment forecasting. In the area
basic education, one finds determi-
itic models, in which the school popu-
ion is determined by a set of demo-
iphic conditions in the community
ved by the schools [74].
n Higher Education, vocational and
i-public education, however, enroll-
nt forecasting is more complex, since
must include feedback from the
course/program offerings. Public ele-
mentary/secondary enrollment is de-
termined largely independently of what
is offered in the schools; other educa-
tional enrollments are affected by pric-
ing, "product line," and competition
[73].
Deciding the amount and type of
manpower and materials for mainte-
nance can be based on several ap-
proaches, most of them rule-of-thumb
planning factors about the size and age
of facilities to be maintained. Most
school districts maintain an administra-
tive distinction between maintenance
and custodial functions, with the latter
providing continuing, loosely monitored
service, and the former an ad hoc
utilization of a pool of staff and other
resources. Some school districts are de-
veloping more carefully planned pro-
grams of preventive maintenance, and
using modeling to schedule maintenance
activities, but, for the most part, edu-
cational maintenance consists of re-
placing lamps after they burn out and
repairing surfaces after they have de-
teriorated.
District-Wide Decisions (Long-run)
Many educational decisions require
more than one or two years to imple-
ment, and, for that reason, must be
based on forecasts and estimates of at
least three years.
In public school districts, where the
system is required to provide education
for everyone in the community, the
number and location of facilities is
determined largely by long-range popu-
lation forecasts, for which several
mathematical models exist [37]. In
higher education and non-public edu-
cation, the planners have a choice with
respect to how many people they will
serve, so that demand forecasts are
either adjusted downward (if the deci-
sion is made to not serve the full de-
mand) or upward (if the planners deter-
mine to expand student recruiting).
Other mathematical components in
the process are:
—calculating deterioration of exist-
ing plant,
287
-------
—computing or estimating the dif-
ferential costs of starting con-
struction in alternative years (fi-
nancing rates versus construction
costs),
—evaluating extended utilization of
existing facilities (by extending the
service day or year) [60].
Choice of facilities location is usually
made among relatively few available
plots of land, but may, in some cases,
include the full gamut of site location
variables used in industrial site selec-
tion models. The variables may include
not only the hard data above, but also
softer data regarding racial mix, esthet-
ics, convenience, employee preference,
and even environmental impact.
In public, basic education, student
assignment to new facilities is deter-
mined largely by propinquity, and
mathematical programming models
may be used to minimize distance from
school (or transit time), or a simula-
tion model may be devised to accom-
plish the same purpose.
Mathematical programming or simu-
lation models of student assignment
may also be employed in devising dis-
tricting plans which reduce racial im-
balances (see earlier discussion of ve-
hicle scheduling).
District-Wide (Major Decisions)
Decisions about the creation or elim-
ination of major programs are made
in a fashion analogous to the selection
of curricula (discussed earlier).
Rarely are such decisions made on
criteria which are quantified. Whatever
cost-utility evaluations are performed
are done implicitly through political
negotiation.
All educational organizations have a
need to estimate revenues in the short-
and long-run, although many are re-
luctant to project multi-year income.
Because most educational organizations
generate at least some of their own
revenues (by levying taxes or tuitions)
it is necessary to project the revenue
from all non-controlled revenue
sources, so that the appropriate rates
288
and schedules for one's own revenue
sources can be determined.
Public education revenue analysis,
given the current financial system, gen-
erally involves prediction of property
tax bases and the inflation of their
assessments. State subsidy revenues in-
volve, also, enrollment forecasts, staff
forecasts, and other variables, depend-
ing on the state. In recent years, school
districts must also estimate non-formula
income from state or Federal categori-
cal funding programs, whose year-to-
year funding levels are often quite diffi-
cult to project [74].
Still another area of revenue source
decisions involves the design of taxing
plans to raise educational revenues. If
models are used, they entail complex
relationships in which the base of the
proposed tax must be forecast, anc
alternative rates must be simulated tc
find a rate which will produce tht
needed money without having a nega
live impact on the base (e.g. liquor
cigarette taxes). In recent years, non
tax revenues must also be designed am
analyzed; in general the prediction o
income from lotteries and other gam
bling is even more difficult than fror
conventional revenue sources.
Intermediate (County) Level
Decisions
The education intermediate unit-
usually a county or cluster of counti
—is concerned with the public scho
districts in its region, the public tw
year colleges, and some vocational tec
nical programs. While such units fi
quently operate their own education
programs—often in the area of servic
for handicapped students—they a
more likely to be regulatory or suppc
live of the smaller educational units
the territory. Thus, their decisions £
of two main kinds: program and si
port.
To the degree an intermediate u
operates its own educational prograi
it must make decisions parallel to thi
made in the university or school (
trict: student plans, curriculum, ope
tions, scheduling, maintenance, i
-------
Intermediate units must frequently be
concerned with transportation schedul-
ing, construction, and the full range of
activities found in the more basic units,
and, thus, have parallel opportunities
for the use of decision models.
A major planning problem is the
creation and allocation of supportive
services to districts in the region. In the
current era of Ill's, these services tend
to be: data processing, instructional
materials loan, workshops and other
staff development, bibliographic and
abstracting services, proposal develop-
ment assistance, liaison with state gov-
ernment, and general education con-
sulting. Because the creation of such
units tends to stimulate demand for
them, the intermediate unit managers
are frequently faced with complex
short-run allocation problems for their
own small staffs and computer facilities.
In these settings, quantifiable criteria
can be used to ensure a desired alloca-
tion of services, and the criteria usually
are related to district size, wealth,
grade-span, urbanicity, or other statisti-
cal parameters.
State-Level Decisions
The state-level education unit is quite
difficult to describe, because it exists in
so many varieties and is usually in
transition.
In some cases, the State actually
operates basic institutions (such as state
colleges or state schools for the men-
ally retarded); in these cases its de-
cisions parallel those made in school
districts or universities. For the most
Jart, however, the state education
igency regulates schools, school dis-
ricts, and institutions which it does not
directly operate. Thus, an explication
)f state level decisions requires descrip-
ion of the relationships which may be
)btained between the state and the
Derating units.
Notice that the three general roles
or the state agency are regulation,
eadership, and service. That is, the state
nay enforce laws and codes, it may
stablish statewide goals and priorities,
ir it may provide supportive services
(like the Intermediate Units) to supple-
ment the resources of the operating
units. The most significant area of serv-
ice, of course, is the providing of sub-
stantial funds for the operating units
(usually 20 to 50% in public school
districts). But states also regulate the
local budgeting and accounting of the
operating units, and may even exert
leadership in recommending new re-
source allocation policies or expendi-
ture strategies.
The SEA tends to exercise its three
roles in regard to six functional areas:
finance, students, staff, curriculum,
facilities, school-community relations.
It is easy to conceive decision prob-
lems in each of the eighteen role/func-
tion areas. For example:
Finance
Regulation—How must school dis-
tricts handle their ac-
counting and auditing?
Leadership—To what purposes
should local and state
resources be applied?
Service —How much money
should be provided to
LEA's and colleges?
Students
Regulation—What students must be
served?
Leadership—What students ought to
be served?
Service —What resources should
be provided to augment
services to special needs
students?
Staff
Regulation—What certification re-
quirements must be
met?
Leadership—What staff types should
districts be encouraged
to find?
Service —What training should be
provided to upgrade the
abilities of existing
staff?
It is clear how parallel questions may
be raised in each area. In the sections
below, however, the most important
289
-------
decision problems—and their amena-
bility to decision models—are discussed
in more detail.
The most controversial and complex
area of state decision making at pres-
ent is in determining appropriate sub-
sidy formulas for organizations, insti-
tutions, and, in some cases, individuals
in the state. While there has been much
recent attention to the construct of
"equality" in support of education, the
notion of equitable distribution of
state/local burden has been a main
consideration throughout this century
[14].
Determining state subsidy approaches
requires a trade-off between equality
and equity. A straightforward levelling
of state support will penalize those com-
munities with limited local resources
and produce certain inequities. A pref-
erential treatment of less wealthy dis-
tricts, however, is often perceived as
inequitable by wealthier communities,
since many of them also feel their
local tax burden to be uncomfortably
large. (An interesting statistical pecu-
liarity is that any across-the-board in-
crease in state subsidy will reduce the
correlation between local wealth and
school expenditures.) State subsidies to
educational agencies are generally based
on a mathematical formula involving
enrollment (adjusted to reflect average
daily attendance, or attendance of
"weighted" pupils), and a per (weighted)
student subsidy rate. In some cases, the
subsidy is directly tied to the number
of students; in other states, the subsidy
is tied to an allowable number of teach-
ing positions (as a function of average
attendance), with the state providing
part of the teacher payroll. In those
formulae concerned with equalization,
certain communities receive a premium
if their taxable wealth (assessed prop-
erty valuation/student) falls below a
state standard; this subsidy is a func-
tion of the gap between actual taxable
wealth and the criterion, as well as the
local tax rate—to insure that local
communities will exert reasonable "tax
effort."
Certification of educational employ-
290
ees is both a quality and quantity con-
trol device. That is, it can be used both
to ensure that education personnel meet
certain minimum skill and preparation
standards, and also to arbitrarily limit
the size of the manpower pool.
Many states are currently engaged in
improving the definition of certification
requirements for educators, in order to
make them more "performance-ori-
ented," rather than oriented to "credit
hours" of training. Clearly, increasing
certification requirements and intro-
ducing more specialized certifications
has the effect of increasing students and
revenues at teacher-preparation institu-
tions—most of which are state-operated.
They also tend to raise the salaries of
educational personnel, because salaries
are tied to degrees and "credit hours."
It is not surprising that a major political
influence on state certification require-
ments has been the associations and
unions which represent education pro-
fessionals, as well as the administrators
of education programs in teacher-prepa-
ration institutions. The decision making
problem remains, however:
What certification regulations shall a
state adopt and enforce?
In addition to certifying staff, mos
states periodically evaluate or "approve'
schools and school districts—frequently
as a basis for continued or modifiec
financial support. There are at leas
three conceptually distinct approachei
to the problem:
—Performance Measurement: Per
haps the least frequently use<
approach is to evaluate the studen
product of the school or distric
by assessing the skills and pos
school performances of the stu
dents. While many states hav
state-wide testing data at the basi
and higher level, few use this in
formation as a basis for evaluatin
the schools.
—Operating Characteristics Measurt
ment: The most typical approac
is to use a checklist of salier
agency characteristics, such £
staff/student ratio, library hole
ings/student, ratio of certified t
-------
non-certified personnel, space and
specialized equipment, breadth of
course offerings, etc. The assump-
tion behind the use of this statisti-
cal and anecdotal data (used in
most high school approvals by re-
gional accreditation organizations)
is that these characteristics are pre-
dictive of educational quality and
efficiency. There is, of course, no
sound empirical evidence support-
ing such input-output relationships,
and, for that reason, the checklist
approach has begun to lose favor
in some states.
—Meta-evaluation: An approach cur-
rently receiving some attention is
the meta-evaluation, in which the
purpose of the state's investigation
is to see that the local unit is
evaluating itself competently, and
to provide guidance and assistance
in the evaluation process. This
approach necessitates agreement on
the allowable range of evaluation
methods (and standards for em-
ploying them), but this agreement
is more politically and technically
easy to reach than a set of output
standards would be.
There is much activity in standard-
setting and evaluation in SEA's. Little
3f it, however, employs decision models.
SEA's are also frequently required to
iefine the boundaries of new school
iistricts, or to design consolidated dis-
ricts, or specify the allowable location
)f new schools or college campuses.
\mong the parameters in such decisions
ire:
—projected populations and popula-
tion density.
—degree of contiguity with existing
governmental boundaries
—economies of scale versus dysfunc-
tions of excessive size
—feasibility of revenue base
—patterns of racial and economic
segregation
A related decision problem, men-
oned earlier, is the planning for loca-
on of intermediate or regional units
the SEA. In this case, a further im-
Drtant parameter is closeness of match
ith other regionalization plans of other
human service agencies in state govern-
ment.
Federal Decisions
Like the State Education Agencies,
the Division of Education, HEW, has
leadership, service, and regulation func-
tions—the last confined to those pro-
grams it funds and also to enforcement
of Federal laws and judicial decisions
affecting schools and colleges. In the
late 1960's the Federal government was
directly administering the Elementary
and Secondary Education Act, as well
as other programs, and dealing directly
with thousands of school districts and
colleges. While the higher education
contacts have persisted, in recent years
the Federal level has transferred most
funds and decision prerogatives to the
SEA, and, in fact, does most of its
communicating with local educational
agencies through the SEA's.
The policy making at the Federal
level tends to be of the broadest scope
and concerned with the largest planning
horizon of all levels in the system. And,
if there is a consolidation of several
Federal programs into Education Spe-
cial Revenue Sharing, it is to be ex-
pected that the Federal role will be
more and more detached from short-
run local decisions.
The Federal government's main de-
cision problem is to define its role in
the American education complex, most
significantly its financial role. Even with
the advent of revenue sharing, it will
continue to fund programs and projects
it judges to be in the national interest,
but a larger part of its funds will be
allocated at lower levels in the system.
There is no basis for determining the
Federal role, save the Constitution,
which provides constraints on allowable
roles.
An important series of subsidy and
grant decisions may face the Federal
government, if, in the next few years, it
is determined that Federal support is
necessary to achieve equitable funding
and financing of the public schools. In
this connection, and in all other de-
cision areas affecting the Division of
291
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Education, mathematical models will
be helpful—even if imprecise. Among
the analytic techniques which have been
and will continue to be, useful are:
—enrollment forecasts for higher and
basic education [37, 47]
—manpower needs projections [6,
55]
—models for estimating future Fed-
eral, state, and local revenues
—models for projecting the size of
special populations, including mi-
nority groups
—econometric models relating in-
vestment in education and man-
power development to economic
growth [23, 55]
—models relating educational attain-
ment to expected economic and
social benefits for typical individu-
als [13, 26]
A key educational concern of the
Federal Government in general is the
relationship between education and the
entire economy. Not only do specific
federal programs have economic impact
(like the National Student Loan pro-
gram), but also the entire education
complex has an impact on the growth
of the economy and federal tax base.
While ours is not a nationally con-
trolled education system, the Federal
government may utilize macro-models
developed for nations which control all
education. The Organization for Eco-
nomic Cooperation and Development
(OECD) has developed several mathe-
matical models which, for example,
relate educational plans to industrial
and social development, and which
simulate the flow of groups of persons
through the education system and the
labor market. Such approaches are not
directly applicable in this country, but
have been used in adapted forms in
state-level education decisions. (See
later discussion on models for optimiz-
ing education and the economy.)
In addition to the above there is an
emerging need for models which will
assist in managing R&D allocations.
The newly created National Institute of
Education will confront complex de-
292
cision problems analogous to those
faced by other major Federal Institutes.
II. ILLUSTRATIONS OF DECISION
MODELS FOR EDUCATION
Introduction
In the sections that follow, twelve
different decision models are described
briefly. The examples chosen are not
exhaustive but are a good representa-
tion of the range of analytical ap-
proaches currently being used, and the
typical decision settings in which they
often are applied. The illustrations in-
clude several levels, from nation-wide
forecasting, to specific problems in the
school or college, to detailed student
assignment. They incorporate determi-
nistic and probabilistic models, heuristic
approaches, simulators, and optimizers.
Each is presented with a minimum of
obscure technical information; the goal
is to show what they are, how they
work, and for whom they might be
useful.
The illustrative models are presentee
in descending level, from nationwide
decisions to the local classroom. The
levels and models are:
National Level:
• Macro-economic planning
• Forecasting college enrollment!
and financial aid requirements
State Level:
• Allocation of vocational funds
• Input-output evaluation of loca
schools
• Forecasting state-wide highe
education demands
School District Level:
• Resource Requirements Predic
tion
• Vehicle Scheduling
A Theoretical Model for Optimizing
the Economy and Education
The first model to be discussed w'
be treated more generally than tr
remainder in this chapter, partly fo
cause it is a theoretical decision mode
rather than an actual, useable managi
-------
ment tool, and partly because it con-
tains elements which will be detailed in
subsequent discussions. Thus, the con-
cepts in Benard's general optimization
model for the economy and education
[10] are presented without its elaborate
mathematical notation.
The Benard model addresses a ques-
tion of optimum investment policy at
the national level. Interestingly, it was
developed in France, where the school
system is nationally managed, and na-
tional economic planning includes di-
rect decisions about the nation's schools.
(According to Benard, in France 80%
of the schools are public, and the re-
mainder are subsidized by the govern-
ment.) Beginning with the most general
question—what proportions of national
"physical" resources should be invested
in each sector of the economy—a more
limited (though still quite global) ques-
tion is formulated:
If Education is regarded as a sector
of the commercial economy, how
shall investments be distributed be-
tween education and non-education
activities, so as to optimize economic
growth, subject to certain constraints?
In this conception, the economy has
a main output: "goods and services,"
expressed in a dollar value. Education is
viewed as a part of the economy,
namely that part which produces skilled
workers for business and industry. (The
sther educational outputs and benefits
ire mentioned by Benard, but play a
•ninor role in the model.) The output
)f the schools, thus, is expressed in
lumbers of "skilled" graduates, who, in
urn, flow into the other sectors of the
:conomy, or back into education as
eachers or administrators. Clearly, dif-
erent investment policies will produce
ifferent numbers of skilled graduates.
An essential concept in this model is
le notion of human flow, both through
ic various levels or cycles of the edu-
ational- program and through the levels
f the commercial sector (that is, levels
f skill). An important characteristic of
le model is the logic for flows from
;vel to level over time.
During any time period t, at any
level (education or otherwise), people
will have flowed from one of three con-
ditions in the just preceding time
period:
—at the just lower level
—at the same level
—from outside the system (either
outside the country, or, if educa-
tion is viewed as a separate system,
from education into the commer-
cial sector).
Similarly, at the end of time period t,
they will either move up a level, stay at
the same level, or leave the system.
It is possible, therefore, to develop a
representation of the human flow
through all levels of the education and
commercial sector, with calculated
transitional probabilities from level-to-
level, so that a change in any one
level will produce calculable systematic
changes in all other levels.
Skilled manpower is viewed as an
output of the education sector, in this
case, a linear function of the quantity
of physical goods and services invested
in education. (Factors causing enroll-
ment are considered, in this model, as
exogenous variables; investment is pre-
sumed to have no influence on enroll-
ment itself, only on the quality [in
skills] of the graduates.)
In contrast, investment in goods and
services in the commercial sector also
produces output in goods and services,
according to an empirically determined
input-output matrix, which is projected
in terms of the impact of technological
change on current productivity.
The choice, then, for policy-makers,
is between indirect investment through
education and direct investment in in-
dustry, knowing that under-investment
in education will eventually cause
counter-productive manpower shortages
in industry, along with reduced earnings
potential for citizens.
The model is a linear programming
model. The output is maximized for
each of a series of time periods, tj — tn.
(Of course, the statistical values of
parameters are recomputed periodically,
293
-------
and the model is re-run before the
end of the "global" time period.) Each
optimization is also a function, of
course, of constraints:
—two constraint vectors on maxi-
mum consumption, so that the total
output in goods and services does
not exceed that which can be con-
sumed by the projected popula-
tion.
—two constraint vectors on produc-
tion capacity, so that the input of
skilled manpower and investment
does not cause industry to grow
or produce faster than is possible.
—Three constraint vectors limiting
the transition of persons from level
to level, so that, for example, the
number of skilled persons flowing
into level 1 does not exceed the
number of openings at that level.
—A minimum growth rate for edu-
cation, that is, a kind of "safety
clause" which ensures that even
if the economic calculations justify
no, or very small incremental in-
vestments in education, there will
nevertheless be some guaranteed
investments in its cultural and non-
quantifiable benefits.
—A budgetary ceiling to reflect po-
litical constraints on the maximum
allowable investment in education.
The model is intended to allow policy
makers to "maximize the present dis-
counted value—over all periods con-
sidered—of the sum total of the varia-
bles representing the standard of living
of the population, of the production
potential of goods and services, of
skilled labour and of education con-
tinuing beyond the time limit (horizon)
of the model, and so enable the process
of growth to continue beyond that limit
[10, p. 226]." Obviously, the various
components of the output must be
weighted according to some preference
function or utility measure, and this
may prove to be the most sensitive or
politically difficult part of using the
approach.
The Benard approach has, in fact,
been adapted in an actual model by the
Organization for Economic Coopera-
tion and Development in Paris [54]. It
294
has also been adapted for use in state-
wide educational planning (the Edu-
cation Coordinating Council of the
State of Oregon) and it appears to have
influenced many other model-makers,
including McNamara [48] (whose vo-
cational education allocation model is
discussed later in this chapter). The
model has considerable conceptual
richness, and invites applications, even
though calculating the statistical values
of the various flow and productivity
matrices may prove quite difficult.
Forecasting Nationwide
Undergraduate Enrollments and
Federal Financial Aid Requirements
In 1971 the U.S. Office of Education
developed a system of probabilistic and
deterministic simulation models, whose
interim output is a probable projection
of the total undergraduate enrollment
in the United States, and whose ulti-
mate output is a determination of the
amount of Federal aid necessary to
support that population, and the dis-
tribution of aid types (loans, grants,
work-stipends, etc.) [47], Enrollment
projections are expressed as number of
students, by sex, by institution type
(2-yr., 4-yr., university), by private 01
public, for each year in the forecast,
These projections are subsequently in-
put into the aid calculation model, a;
summarized in Figure 2. (The sam«
project also produced procedures fo
forecasting post-baccalaureate enroll
ments and aid, but these are not dis
cussed here.)
As indicated in Figure 3 a potentia
student can be in one of three condi
tions: a high school graduate, a firs
year student in college, a student in
stage beyond his first year. Students
moreover, are categorized by sex an
family income group, data which i
both descriptively interesting and a
input to the aid calculation.
The sequence of calculations in th
series of models is as follows:
1. Number of high school graduate
by sex and income group, fc
each year in the forecast is pn
jected.
-------
1. Estimate the number of
high school graduates by sex
and family income
3. Estimate the probability
that a student is enrolled in
various types of institutions
in years following first en-
rollment
2 . Estimate the probability
distribution for the number
of years a student waits after
high school graduation before
first time college enrollment
STUDENT ENROLLMENT
MODEL
4. Estimate the total enroll-
ment by sex and family income
in various types of institutions
5. Estimate the expected con-
tribution from parents and stu-
dents by family income
6. Estimate the expenses in-
curred in various types of in-
stitutions
Source: [47]
FIGURE 2—Summary Flow of the Model
7.' Estimate the financial aid
requirements for students in
higher education
STUDENT AID
MODEL
2. An estimate is made of the proba-
ble number of years of delay
between graduation and starting
college for each sex/income
group.
3. First time freshman enrollment is
calculated from the first two
steps.
4. Next the retention or attrition
probabilities are estimated. The
probability of a freshman con-
tinuing to consecutive years is
different in each year, and the
existing data shows different rates
for the various sex/income
groups.
5. A distribution of students by type
of institution and "control" (pri-
vate vs. public) is introduced.
6. The enrollment forecast output
is produced by consolidating the
steps above and reporting the
enrollment by sex, income group,
institution type and control type
in each year of the forecast.
7. To use the enrollment projection
as input to the aid model, the
next step is estimating the pa-
rental and student contribution to
college expenses, which is a func-
tion of income, number of de-
pendent children, number of
dependent children attending col-
lege, student assets, and summer
income.
8. College costs are estimated by
type and control of institution,
including tuition, fees, room,
board, books, and miscellaneous.
Cost estimates are differentiated
for resident and commuting stu-
dents.
9. The final calculation measures the
gap between the expected capa-
bility to contribute and the pro-
jected costs.
The difficulties entailed in using this
model stem largely from the number
and complexity of sub-models required
to perform the various forecasts and
estimates. Referring to Figure 3, it
should be noted that there are seven
main components in the model, and
all but the seventh involve at least one
of 33 forecasting sub-models.
It is clear that the projections from
this model, because of the compounding
of errors in the several sub-models,
should not be treated as overly precise.
Recall, however, that its purpose is to
project, in broad terms, the long-range
financial consequences of college par-
295
-------
ticipation. We can assume that its
accuracy in forecasting these variables
is significantly greater than any intui-
tive, or less complete, prediction pro-
cedure currently available.
A Model for Allocation of
Vocational Education Funds
A recurring decision problem for
State Education Agencies is the alloca-
tion of a large pool of program funds
across a set of programs and projects in
local education agencies (LEA's).
McNamara has developed a linear pro-
gramming (LP) model for use by the
Pennsylvania Department of Education
in allocating Vocational Education
monies [48], (McNamara has also de-
veloped several review essays on the
application of mathematical program-
ming to educational planning; see [50]).
In McNamara's model, the objective
function is:
any optimal solution must satisfy the
constraint that
Maximize z =
x..
where
Xj, = the output in total students of
vocational program i from
county j.
i = 1, 2, . . . m (vocational-techni-
cal education programs)
j = 1, 2, . . . n (counties in Labor
Market Area)
A first constraint in the model is
capacity, the rate at which new students
can be added to existing facilities, or the
rate at which new resources can be
deployed. For this reason, each county/
LMA output must fall between the
minimum "desired" increase in capac-
ity of program i in county j, t^, and
the maximum "desired" increase in pro-
gram i in county j, TJJ;
Notice that the use of "desired" con-
straints allows for county level judg-
ments, as well as hard data on the num-
ber of student stations available.
Importantly, this model is also con-
strained by budget limitations. Thus,
296
3 = 1
where
hj = the fixed incremental cost for
each student added to program
i in n counties (Note: Common
programs cut across counties;
this incremental cost per stu-
dent is a program-specific in-
put).
rti = the ratio of the students in pro-
gram i in county j necessary to
produce the optimal number of
graduates in the program (Note :
this ratio is greater than or
equal to 1.0, and is the recipro-
cal of the expected drop-out or
failure rate for the program).
H, = the total marginal increase in
Vocational Education funds
from the State. The model al-
lows simulation by using sev-
eral different values of Hj.
The optimum State allocation is a
consequence of assembling sub-opti-
mum plans in each Labor Market Area
(LMA), each of which is a unique set
of counties. This X^ is a marginal in-
crease in the number of students the
state wishes to support in each county
of each LMA. There is an importan
constraint, however, on the number o
students in a county/ LMA, namely
the upper limit on the number o
graduates, from each occupation spe
cific program, which can be absorbec
by the Labor Market area manpowe
projection. Maximizing output also re
quires minimizing the percentage of un
met labor market needs (based on
projection of graduates by year) am
also minimizing the occasions on whic
school output exceeds the manpowe
opportunities.
This model, when accompanied b
appropriate sub-models which generat
the various forecasts necessary to th
LP model, generates a recommende
plan, in which each program in eac
-------
school district is expanded by an opti-
mum number of students (that is, a
number which minimizes unsatisfied
manpower needs). The plan, and budget
allocation scheme, is for the next year,
but also has a submodel which projects
the ith year on the basis of the first year
plan. While typical SEA allocations are
made annually, this multi-year extension
capability provides further data about
decision consequences to better inform
the short-run decision.
According to the author, there are
some limitations on the use of the
model. First, the optimal solution is a
function of the supply-demand relation-
ship, in which demand is manpower
demand in a given Labor Market Area.
The model assumes that first jobs for
graduates will be in the same geo-
graphical area as the school—an as-
sumption that the author argues is rela-
tively reasonable. Second, the man-
power demand is not offset by the "so-
cial demand," that is, what programs
students want to take. It appears, how-
ever, that the construct of "minimum
desired increase in student enrollments
in a program" provides a mechanism
for inputting social demand, even if
that is not exactly how its author con-
strues it. Third, and related, is that the
resource allocation model removes
monies from programs which over-
supply the LMA demand. McNamara
indicates, however, that this constraint
may be relaxed by the policy maker
and does not, therefore, impede a more
"social demand"-oriented planner from
achieving his own planning objectives.
Perhaps the most difficult data prob-
lem in the model is the projection of
LMA outputs from non-public schools.
As currently designed, the model as-
sumes that the state supported programs
will satisfy the entire unmet demand.
This problem can be solved through
closer scrutiny of the output and pro-
'ections of private and proprietary voca-
ional programs.
This model is clearly one of the more
advanced approaches to resource allo-
:ation in education, made possible in
jart by the more easily quantified out-
puts of vocational education. Its useful-
ness in both longer-range planning and
short-range allocation decisions is con-
siderable.
A State-Level Input-Output Planning
Model for Local Educational
Agencies
The New York State Education De-
partment has developed an ambitious
project known as Performance Indica-
tors in Education (PIE). As part of
the project, SEA staff have attempted
to develop the most elusive of educa-
tion models—the production function:
a mathematical model which relates in-
put and environmental variables to
performance outputs of local school
districts [68]. The developers have taken
an especially interesting approach; in-
stead of attending directly to the ef-
fectiveness of specific educational pro-
grams and treatments, they emphasized
the large set of non-instructional vari-
ables (including student and community
characteristics) which, according to
most research, have a greater predic-
tive power than typical instructional
variables (such as method or class
size). Given this view, the model is used
to calculate an expected performance
for a school district, given its char-
acteristics. To the degree that a given
program or treatment exceeds or falls
short of the expected performance
level, the program is judged to be
effective or ineffective. The model is
built on a simple conception of the
educational process. The concept argues
that the output of the schools is a
function of student characteristics and
environmental conditions, as well as
school processes.
The most problematical variable is
school processes, and effectiveness is
defined as the difference between what
is expected given all the non-school in-
puts, and what is observed. A particular
version of the model considered the
following as inputs, conditions and out-
puts:
(a) Input
Mean of 1967 and 1968 district
means in first grade readiness
297
-------
tests (1R67.68)
Mean of 1967 and 1968 district
standard deviations in first grade
readiness tests. (!Rsd67,68)
(b) Surrounding Conditions
FTV = Full Tax Valuation of dis-
trict, divided by enroll-
ment
PR70 = Proportion of Minority
Group Students in third
grade in 1970
S68 = "Size," enrollment in
grades 1-12, divided by
1000
D68 = "Density," square miles
in district divided by
number of pupils
(c) Output
3R70 = Third grade reading
mean for 1970
These variables—which are only part
of the list developed—are taken as in-
dicators of the input, environment and
output. By examining historical data on
the schools in New York State, the
model makers have been able to per-
form regression analyses, in which the
relationships of the variables are quanti-
fied. Equations are in the general form
OV = a (VJ + b (V,) + c (V3) . . .
-ft (Vn) -r k
where
OV = value of the output measure
V,, . . ., Vn = input and environ-
mental values
a,b,c, . . ., t = regression coeffi-
cients
k = a constant
In the case cited, the general equation
becomes:
3R70 = .298 (1R67.68) - .112 (IRsd
67,68) + .030 (FTV68) -
5.221 (PR70) + .13 (S68)
- 1.614 (D68) + 14.75
(This equation accounts for .332 of the
variance in actual scores.)
Thus, for any specific set of values
for a given school district, one may
298
calculate an expected value (and vari-
ance or range of probable values) for
"3R70," the third grade reading scores
of the district.
The PIE model is an advance on the
most elusive of educational problems:
the relationship between input and out-
put. There are objections, of course, to
any set of output measures, and, in-
deed, the developers admit that the
variables used may not be the most
sensitive or best predictors. Importantly,
users of this or other systems must
never treat the analyses as more precise
than they are, never confusing a fixed
value with a range of values, never im-
puting significance to non-significant dif-
ferences. In the authors' words:
"The PIE System is designed to
reduce the element of chance in
decision making. ... Its immediate
value will be to help local districts
recognize those program areas in
need of more detailed evaluation
and perhaps additional resources.
The system will eventually allow
the development of simulation
models for predicting the conse-
quences of decisions before they
are made."
Clearly, the developers of PIE make
no claims for the system beyond those
which are supportable in the data.
A Model for College Enrollment
Forecasts
There are two relatively distinct
problems in forecasting enrollments in
any basic or higher education program:
a. Projecting the number of persons
entering the programs or system.
and
b. Projecting the distribution of stu-
dents at each level (usual!)
years) in the program or system
The first problem usually entail;
modelling the relationships between the
principal education system and som<
other educational system or non-educa
tional system. For example, in basii
education, it is necessary to relate thi
number of incoming kindergarten o
first grade students to the demographic
of the community (e.g., birth rate
-------
housing changes, etc.); in higher edu-
cation, the main predictor of incoming
freshman is a mathematical model of
the impact of high school completion
on college enrollment. In the case of
projecting kindergarten students, it is
possible to build a deterministic model,
because there are direct legal connec-
tions between the census for certain age
cohorts and the obligations of the
schools.
In the other cases, however—grade-
to-grade transition in basic education,
basic-to-higher education, or year-to-
year transitions in higher education—
the process is stochastic rather than
deterministic. The process is described
simply in Figure 3.
Only some of the branching possibili-
ties are shown, but they illustrate the
principal concept. Notice that one of
the possibilities for high school grad-
uates is going to college; the transi-
tional probability for going to college
is TPlc. In the next year, one of the
possibilities for college freshmen is to
become college sophomores; this transi-
tional probability is TPj+j, c+1. Clearly,
if the transitional probabilities are
known, an estimate of the enrollment
at any one level, in any year, allows a
forecast of enrollments at higher levels
for subsequent years.
Oliver [53] has discussed the adapta-
tion of this approach for predicting
gross enrollments at the University of
California at the state level. In one
model, he describes, enrollment is based
on the fraction of students moving from
level to level, and number of students
coming in at something other than the
beginning level. The reader is referred
to [53] for the mathematical develop-
ment.
Enrollment forecasting is possibly the
most important input to long range
planning and resource requirements
analysis. Illustrations of its relation-
ships with other modelling problems
appear in the next sections of this
chapter.
A Model for University Resource
Requirements Analysis
Hussain [25] reports on an ambitious
resource requirements prediction model
(RRPM) for a university, developed by
the National Center for Higher Educa-
tion Management (NCHEM). This ex-
Other Post
Secondary
Year i+1
FIGURE 3—Simple Transitional Model for Three Years
299
-------
tensive projection system goes through
four analytical phases:
Instructional—calculation of all di-
rect instructional resources (staff,
space, etc.) and expenses for faculty,
supplies, travel, and equipment, by
discipline or department.
Unit Cost—calculation of unit in-
structional costs, both direct and in-
direct (allocated), by field of study
and student level.
Non-instructional Program—calcula-
tion of costs by sub-program, for all
sub-programs which are not instruc-
tional or academic support.
Space—calculation of space require-
ments and construction costs.
The principal input to RRPM is an
estimation of the number of students to
be enrolled in each major field of study,
at each undergraduate level, for each
year of the plan. From this data, and
an analysis of the historical distribution
of courses and resources for each field
of study, in each level of schooling,
NCHEM has generated the Induced
Course Load Matrix (ICLM).
The ICLM is essential in the projec-
tion of student credit hours (SCH),
weekly student hours (WSH), faculty
load (FCH) and full time equivalent
staff members (FTE). A portion of the
model is concerned with projecting
direct instructional expenses. This sub-
model corresponds to the Instruction
phase of the process.
The fourth phase, Space, addresses a
critical problem for most expanding
universities, namely the projection of
facilities requirements and attendant
construction costs. This process involves
taking data from the earlier resource
requirements projections and distilling
the incremental increase in space re-
quirements (in each of 22 defined space
types). As with other resources pro-
jected, the model calculates the quantity
of resource requirement (space, or staff,
or equipment) and multiplies by input
price schedules and estimates.
RRPM is a deterministic simulation
model, used to predict the consequences
of given policies (such as faculty load),
under conditions of different external
demand (enrollment by field of study).
Thus, like other resource requirements
models, its main function is to aid deci-
sion makers in testing the consequences
of current or contemplated policies.
Because its accuracy is constrained by
external variables (such as the student
forecast or the ICLM distributions) its
utility will vary from setting to setting.
As currently designed, RRPM can
be used in universities with as many as
90 Fields of Study ("Majors"), and can
accommodate 7 levels of students, 5
types of faculty, 4 non-instructional
staff types, 4 different modes of instruc-
tion (each with its own space require-
ments), and, as already mentioned, 22
space types. As such, it is a highly
flexible planning resource, particularly
for those institutions which have
adopted the NCHEM program-struc-
ture.
A Model for University Facilities
A nalysis
Sisson, Jacobson, and Robinson [60]
have developed a Facilities Analysis
Model (FAM) for use by the Califor-
nia Coordinating Council on Higher
Education (CCHE). The main objec-
tive of using the model is to develop
mathematically defensible standards for
facilities utilization (mainly hours of
service and scheduling of facilities), so
that the college may operate "near the
least cost point." As is apparent in
Figure 4 there is a Total Costs Curve.
which is a complex function of the
Operating Costs Curve and the Capita
(construction/equipment) Costs Curve
Intuitively, it is clear that heavie
utilization of existing facilities increase;
operating costs, while it decreases capi
tal costs. The mathematically interest
ing questions are:
—How do these two independen
curves behave?
—What institutional characteristic
are sensitive variables in influenc
ing the behavior of the curves anc
thus, the value of the lowest ToU
Cost point?
The policy-related outputs of th
model are, first, a set of utilizatio
300
-------
Costs
Total Costs
Operating
(faculty- related)
Costs
—• -- Capital-related costs
Less
Utilization
Stan rla rd
More
Utilization
FIGURE 4—Relationship Between Operating, Capital, and Total Costs
standards (justified by least cost analy-
sis) and an identification of policy-
related institutional characteristics which
offset current implementation of the
standards, or influence the determina-
tion of standards in subsequently de-
veloped colleges and universities.
Among these factors are:
—The age of the institution (and its
rate of growth)
—The gap between enrollment and
maximum capacity
—The client groups served, classified
by (1) day students, evening stu-
dents, (2) full-time, part-time, (3)
discipline or program, (4) degree,
certificate, transfer or non-degree
—Location of institution: urban, sub-
urban, rural.
Recall, that the FAM is not intended
is a continuing scheduler for facilities,
•ather as a policy formulating resource,
o be used only as often as the general
>olicies on facilities utilization are to
>e evaluated and revised by the user.
iach time it is used (which may be
>nly once in a given college or higher
ducation system) it is run several times
o calculate the impact on total costs
of alternative policies. The analytical
flow of one iteration of the model is
shown in Figure 5. The computations
and analyses are:
1. Forecast enrollment by program
or "major" and, using historical
data, calculate the demand for
classes (weekly student hours) in
each major.
2. Schedule the total number of class
hours over the course day (the
FAM treats all days the same),
assuming policy i about hours of
utilization. Deduce from this ap-
proximation of the master sched-
ule the demands on facilities.
Adjusting for any input policy on
percent of utilization, calculate
the space needs required to ful-
fill enrollment expectations (the
basis for capital costs).
3. Deduce the faculty contact-hours
from the scheduled class hours;
using the distribution of courses
(by discipline) within each major,
deduce the number of FTE
faculty members required by de-
partment, building in assumptions
about faculty work-loads (the
basis for estimating faculty oper-
ating costs).
301
-------
Input Enrollment
Projection by
"Major"
Source: [601
Devise Weekly Student-
Hours for Each Major
Distribute Class Hours
Over Week
Calculate Space and
Construction Needs
Calculate Total Costs
Source: [60]
FIGURE 5—Flow of the Facilities Analysis Model
4. Deduce support and indirect
operating costs, by applying
"planning factors" to the calcula-
tion of direct service needs.
5, Using unit costs planning factors,
calculate the capital costs, main-
tenance costs (keyed to sq. ft. of
plant), faculty costs, and indirect
costs (keyed to faculty costs),
and calculate the total costs in
each year of the projection.
Clearly, this calculation shows less a
prediction that the consequences of cer-
302
tain policy inputs, mainly on hours o
facility utilization. By re-iterating tht
model with several feasible sets of poll
cies, the lowest total cost can be ascer
tained, and the concomitant policies cai
be identified as most cost-effective.
In order to develop systematic con
tingencies on these policies, the mode
should be run for institutions wit
different characteristics, to ascertai
whether policies should be adjusted fc
different campuses within a heterogene
ous system of schools.
-------
A Model for School District
Resource Requirements Planning
The Trenton Public Schools, in New
Jersey, has developed a set of models
as part of an overall school district
planning system [74]. Included are an
enrollment forecasting model, a rev-
enue forecasting simulator, and a re-
source requirements (cost) forecaster
(STEP-RRM). In the STEP system, the
school district is first divided into
"planning units," the smallest division
of activities used in planning. A plan is
considered a set of planning units,
actual or proposed. Alternative plans
are produced by adding, deleting, or
replacing planning units. The resource
requirements model is used to calculate
the five-year cost consequences of al-
ternate plans. Figure 6 shows the overall
planning process; the resource predic-
tion occurs at steps 3 and 7.
(1)
(2)
(3)
(4)
(5)
Analyze Agency
into Planning Units
Collect Data about
Current Program or
Project Planning Units
Generate Multi-Year
Planning Unit
Resource Requirements
Forecast
Generate Alternative
Program-Structured
Outputs
Devise "Project Designs"
with Planning Unit
Data
Source: [74]
(6)
(7)
Specify Run
Combinations
Generate Alternative
Program-Structured
Outputs
Yes-
Approved
Flan
FIGURE 6—Resource Requirements Analysis Using the "Planning Unit" Concept
ource: [74]
303
-------
The model provides four alternative
resource requirements reports: The
Planning Unit Report; the Program Re-
port; and Project Report (special
clusters of Planning Units); and the
Site Report (costs by Facility). Each
of these reports can be generated for
current programs and projects (known
as the "base case" plan) or for planned
alternatives. Each report includes:
(1) The number of positions, by
each of fifteen staff types, for
Year 1-Year 5. (Staff types are
re-defined.)
(2) The salary cost, fringe benefit
cost, and total, for Year 1-Year
5.
(3) The total capital outlay cost,
Year 1-Year 5.
(4) The total non-staff/non-capital
outlay cost, Year 1-Year 5.
(5) The total gross cost, and the
total local cost.
(6) The total expected positions, by
staff type, and total "hires," Year
1-Year 5.
(7) Subsidiary data on planning
factors.
These data elements are relatively
constant in each of the reports gen-
erated by the module; the differences
are in the level or focus of aggrega-
tion. In the Planning Unit Report, the
above information is displayed for each
of the district's "planning units." In the
Program Report, the information is ag-
gregated in "programs," etc.
STEP-RRM operates by taking de-
tailed, current year data about the
"planning units" in the district, along
with other inputs about staff unit costs,
student/staff ratios, and turnover in the
district. Using these and a combination
of forecast options available to the
planners, the model projects the five-
year staff requirements and costs for
each planning unit. These planning
units are, then, aggregated into large
clusters, e.g., programs, projects, sites,
or the whole district, to produce the
main planning reports.
For each planning unit, users input
identification data and information
about the current staff, capital outlay,
and other resources being utilized in
the unit. In addition, appropriate en-
rollment information (taken from the
enrollment forecasting procedure) is
input to the planning unit description,
along with estimates of categorical or
"project" monies expected to accrue to
the unit. After data is collected for
each planning unit, district data is
added: mainly, the "fringe benefit per-
centage" associated with each staff type,
the expected turnover rates associated
with each type, and the forecast op-
tions chosen for each resource type in
each planning unit. The resource re-
quirements model then proceeds to in-
corporate the effects of projected en-
rollment change, inflation, turnover
rates, and other relevant variables, ac-
cording to the forecast options selected
by the users, and produces cost/re-
source requirements projections for
Year 1-Year 5.
The STEP-RRM, because of its
flexibly defined "planning unit" con-
cept, is argued by its developers to be
very adaptable to a wide range of
school districts and other public service
agencies, in both projection of unmet
operational costs, or calculating the
costs of alternative plans. An interesting
feature of the model is that it may be
used with any form of program-struc-
ture, or several simultaneous program
structures. Unlike most PPB-type cost
forecasting systems, the STEP-RRM
allows for alternative cost analyses
without extensive reprogramming or re-
coding. It is not designed for use as a
month-to-month program accounting
system, but rather as a long-range cost
forecaster.
A Model for School Bus Scheduling
The criteria for satisfactory pupi
transportation plans have escalated ir
recent years, at about the same rate a;
technology for vehicle scheduling has
developed. While, on the surface, th(
task of transporting thousands of stu
dents over hundreds of vehicle miles—
twice a day—may be considered suffi
ciently complicated in itself, the prob
lem is made more difficult when wi
304
-------
determine to minimize the cost of the
operation, or the traveling time for stu-
dents, or when the objective is tied to a
desegregation program.
The school bus scheduling problem
has many aspects which cause it to re-
semble a mathematical programming
problem or a "traveling salesman" prob-
lem. The unappropriateness of such
approaches, however, is apparent when
one considers the numbers of variables
that would be needed in such models
(an objective function with hundreds or
thousands of variables, one for each
student, for example).
Angel, Noonan, and Whinston [2]
have developed and implemented a
heuristic model which attempts to:
—minimize number of bus routes
—minimize vehicle mileage
—avert overloading capacity con-
straints on vehicles
—keep the route time below a maxi-
mum determined by policy
The approach developed does not
necessarily produce an optimal solution,
jut it does produce alternative sched-
jles which satisfy the constraints of the
jroblem, from which the schedulers
nay choose on both quantifiable and
ion-quantifiable criteria. The algorithm
s heuristic, in that it allows users to
eratively develop schedules which are
hown to be better or not better than
ome given schedule; the process is re-
ieated until users are satisfied that any
dditional runs will not be better then
ic "best" they have so far.
The scheduling system has three
mjor phases:
1. A data assemblage. Student cen-
sus, stop locations (on a map
grid), and distance data is input,
2. Using the data above, students
are assigned to stops, and a set of
stop loading cards and a time
matrix are generated (the matrix
is produced by a modified Moore
algorithm, a generalized algorithm
for calculating distances in net-
works), and
3. The stop loadings and time matrix
are then augmented with capacity
constraint data about number of
vehicles, capacity of vehicles, and
policy limits on travel time, out of
which a solution schedule is gen-
erated.
The third part of the process is the
most technically interesting and unique.
The steps (shown in Figure 7) are:
1. The bus availability table, time/
distance matrix, and bus stop
loading table are read in.
2. Each stop is assigned to an indi-
vidual route by entering the bus
assigned, the initial stop, the num-
ber of students and the total route
time into a route table. Stops on
a route are kept in a forwardly
ordered list.
3. The system calculates a measure
of closeness or "association" for
each pair of assigned routes, ac-
cording to several weighted fac-
tors (e.g., nearest points, distance
from school, current loads, re-
maining time until school, etc.).
4. Routes are merged as a function
of this association measure. The
ordering of stops on a given
merged route is determined by a
traveling salesman algorithm [52],
and the process is continued until
the number of routes does not
continue to decrease. The con-
straints, of course, are the capac-
ity of the vehicles and the maxi-
mum allowable route time.
In addition, the authors indicate that
the plan shown in Table 2 reduces by
one the number of routes in the district
and equalizes somewhat the burden on
all vehicles (factors which could, pre-
sumably, offset entirely the cost of the
scheduling job). The system was run on
a Control Data 6500 and, as currently
reported, can handle problems with as
many as 200 grid points.* The develop-
ers of the system foresee extensions of
the system into long-range planning for
fleet requirements.
Table 1 shows a sample model out-
put describing a single route for a given
vehicle.
The output includes the location of
* Larger districts could use the model by
partitioning the community into areas with
150-200 grid points.
305
-------
MERGE ROUTES AND APPLY
TRAVELING SALESMAN
ALGORITHM
WRITE fLEET
SUMMARY
WRITE
SCHEDULES
Source: [2]
FIGURE 7—Flowchart for Scheduling Sequence
306
-------
Table 1
School Bus Route Generation—Southwestern Route Number 3
Stop Numbers
Coordinates
9505
9255
11005
11005
10705
10505
10355
9005
10005
10505
11005
11005
11005
10305
9405
9255
8605
Source
222W
135W
200W
WOW
OW
55E
WOE
200E
154E
100£
100E
50£
10E
OW
OW
11W
WOW
Bus Capacity
Route Time
Loading Time
Driving Speed
Average Speed
: [2]
Old
129
121
128
108
833
829
1301
1340
1302
804
830
831
832
816
817
119
120
72
56.18
7.06
25.0
21.8
New
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
Students
2
2
9
2
5
3
1
7
1
5
2
13
10
2
2
4
1
Total Students
Total Stops
Miles Driven
Students/Mile
Student-Miles
Arrival
Times
4.30
7.24
13.48
17.06
20.24
22.12
23.54
29.36
33.48
36.24
38.06
39.30
41.48
44.42
47.06
49.24
52.00
71
17
20.5
3.5
1324.1
LO3U
Time
.12
.12
.54
.12
.30
.18
.06
.42
.06
.30
.12
1.18
1.00
.12
.12
.24
.06
the stops, in grid coordinates, the num-
ber of students at the stop, the arrival
ime (minutes after the start of the
route) and the load time. The report
also analyzes the salient characteristics
of the route, including total route time
and vehicle miles.
Table 2 shows the summary char-
tcteristics of the twenty-three routes in
i given plan for the Tippencanoe School
Corporation.
In the case illustrated, the policy con-
traints are 72 students per vehicle and
'0 minutes plus return maximum travel
me; the plan shown above clearly
atisfies the constraints.
Importantly, the principal motivation
Dr this project was to improve student
ifety, a concern shared by all managers
" school transportation services.
Model for Class Scheduling
Many colleges and secondary schools
ive begun to automate the process of
isigning students to schedules. While
may not be the soundest educational
Dlicy, the typical assignment problem
begins with a fixed master schedule, to
which students must adjust their course
preferences. Generally, the only impact
of student demand on the master sched-
ule is that undersubscribed courses or
sections will be deleted and, in some
cases, if the total set of student requests
has been tallied in advance, some
courses may have sections added to
the master schedule.
Macon and Walker [46] point out
that most automations of class sched-
uling behave much in the way that non-
automated systems behave. Instead of a
queue of students, the automated system
has a queue of student request cards,
with sections assigned on a first-come-
first-served basis, so that unsatisfied stu-
dent requests increase as the scheduling
proceeds. A slightly more sophisticated
automated approach involves the cumu-
lative calculation of students assigned,
so that requests for multiple-section
courses can be routed to the least sub-
scribed sections, thereby reducing the
number of student dissatisfactions.
Nevertheless, this approach is still, es-
307
-------
Table 2
Summary of Schedule
Number of routes:
Average load
Load
size:
size — range :
Maximum riding time:
Route
Number
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
Sched-
uled
Quan-
tity
67
65
72
69
72
71
65
71
65
70
61
72
64
66
70
62
63
60
57
70
70
61
57
Number
of
Stops
32
26
37
38
20
33
30
26
33
26
24
31
13
32
46
30
33
27
22
21
37
29
30
23
66
57-72
58 minutes
Number
of
Miles
13
13
12
14
13
12
8
11
12
10
11
25
15
15
7
8
24
28
12
13
25
21
17
Max.
Riding
Time
(min.)
43
38
50
52
31
48
40
40
46
37
33
47
25
25
41
40
44
44
31
34
47
45
47
Source: [2]
sentially, a first-come-first-served ap-
proach which unjustifiably penalizes
students who happen to come later in
the queue.
Macon and Walker propose a "fairer"
alternative to scheduling, using a "Monte
Carlo" model. They posit the most
difficult case, namely, that in which
students give only "first choices" (the
case is more typical in colleges than in
secondary schools), and consider any
requested student schedule which can-
not be assigned as "unable to be proc-
essed." Their goal, thus, is to minimize
the number of unprocessable requests.
To accomplish this goal, the total
number of requests for each section is
tallied in advance, and for each section
one computes a value p defined as
no. of seats available \
i = mini 1,-
' no. of requests remaining/
(i.e., minimum of 1 and the ratio)
In the first iteration, of course, the
number of requests remaining is the
total unprocessed set of student re-
quests. Given this index . . .
"processing a student's list of sec-
tions desired proceeds in the fol-
lowing way: A random r between
0 and 1 is compared to the p-value
of the first section requested. If r
p the other
sections of the same course are
tested one at a time for conflicts
with sections already assigned to
the student and the requests re-
maining on his list. If no conflicts
occur and the corresponding p-
value is greater than that associated
with the section requested, then the
section requested is replaced by the
section tested. This continues until
all sections of the course have been
similarly examined. The conflict-
free section with the largest p-
value is thus assigned. . . ."
Inevitably, if any section of any course
is closed, there is a possibility of beinf
unable to process a request. There is
the special case, however, in which the
assignment of students was based or
preferences, while another section as
signment would still have been feasiblf
(not conflicting with other requests b;
the same student). Macon and Walke
have also developed an assignment pro
gram which searches the individua
student assignments to see if section
can be changed for individual studen
without conflict, thereby opening som
sections which were previously closec
The assignment model increases th
probability of being able to process a
requests, and also distributes sectio
enrollments more easily.
Using an actual master schedule <
over 2000 sections, the users were ab
to assign 9000 students (averaging
section requests per list) in under foi
minutes of machine time. The autho
believe that with a few passes of t
model, the number of unprocessah
student requests will be reduced to
308
-------
or to so few that they may be solved
with special attention.
It should be reinforced that this, and
other sophisticated scheduling systems,
assume a given master schedule which
is relatively inflexible. As indicated
earlier in this chapter, this approach
satisfies administrative needs but may
be inconsistent with a more sophisticated
approach to determining what courses
should be offered in the first place.
A Theoretical Model for
Instructional Optimization
As indicated earlier in this chapter,
the most pervasive, and perhaps im-
portant, educational decisions involve
the minute-to-minute assignments of
students to instructional tasks. But, as
was also indicated, this process goes on
almost independent of any formal, let
alone mathematical, model of instruc-
tion. Of course, as Sisson observed
some years ago, what takes place in the
classroom decision-making is, in a real
sense, influenced by many models "in
the head" of instructors [61].
The discipline of curriculum engi-
neering is concerned with formalizing
instructional models and developing
ilternatives to the classroom teacher as
he decision-maker (alternatives such as
he student, a machine, a non-profes-
;ional monitor). The measures of in-
structional effectiveness which are to be
mproved include student performance
higher probability of achieving instruc-
ional objectives), time (reduced time),
ost, or motivation (by finding the opti-
num "style" or "strategy" for a given
tudent). The common attribute of the
iverse approaches to curriculum engi-
eering and instructional technology is
concern with defining a terminal ob-
;ctive for the instructional program,
efining a set of intermediate objectives
i route to the terminal objective, and
jecifying all these objectives in a form
hich allows accurate appraisal of the
udent's progress, to be used as the
isis for deciding what instructional
sk to be assigned to the student at any
ven decision point. There are, in such
stems, devices for providing instruc-
tion (people, machines, material) and
devices for monitoring progress (people,
machines, material). In the technique
known as CAI (computer-assisted-in-
struction), the computer is both the
provider and the monitor. In CMI (com-
puter-mediated, or computer-managed
instruction) the computer is the monitor
which evaluates data from or about
students and makes an instructional
assignment which is carried out by other
machines, material, or people.
The generalized approach to instruc-
tion assumed here is most familiar in
"programmed instruction" and the "pro-
grammed text"; this device, frequently
attributed to B. F. Skinner, makes it
impossible for a student to move
through a book without periodically
demonstrating mastery of an interme-
diate objective (an attribute of all engi-
neered curricula). Programmed instruc-
tional materials are generally designed
on a linear (not in the sense of linear
programming) or branching basis, as
shown in Figure 8.
As this representation shows, the
most typical arrangements allow for,
either:
a) the student repeats a task until he
can satisfy the criterion for the
intermediate objective, after which
he continues, (linear)
b) the student who fails a task is
routed to another path, another
task which is remedial or alterna-
tive in style; he can be re-routed
indefinitely, depending on the
complexity of the program de-
sign, until^ finally, he begins to
loop around one task (or is ran-
domly assigned to another, or
terminated as student, etc.). Thus
there are multiple paths through
the process, (branching)
Clearly, branching instructional pro-
grams can be rendered as a matrix, and
manipulated algebraically. Belgard and
Min [9] depict this array as shown in
Figure 9.
As shown in the illustration, a stu-
dent moves through a series of stages.
The "linear" path is K1]L-Kln, the initial
line; however, a student who fails to
309
-------
Linear Instructional Program
Branching Instructional Program
FIGURE 8—Design of Programmed Instructional Materials
^\j= 1, ..., n
Initial
S
T
A
Alternative -i
E
1
f 2
3
4
Im
STAGE
Task Task Task Task
(1) (2) (3) ... (n)
Kn K12 K,3 . . Kj,,
KV V V
21 ^22 **-2r, • • • ™~2\\
KV V V
41 ^42 ^4". • • • IS-4n
U
Kml Km2 Km3 ... K..
K2
K...
Km
K.I
Source: [9]
310
K.2
K.3
K.n
FIGURE 9—Matrix Representation of Branching Instructional Program
-------
move rightward on the initial path may
branch to another task at the same stage.
Actually, this matrix representation is
more general than a typical branching
program. For purposes of instructional
optimization, every permutation of tasks
may be considered a path to the ter-
minal instructional objective. Each path
has a differential probability of attaining
the terminal objective, and each path
has different costs (material and non-
material). Of course, several of the
possible permutations are highly im-
probable, but allowing the broadest
range of alternatives also allows the
broadest possible differentiation of stu-
dents, in terms of psychological needs
and "learning styles."
The Belgard-Min model is based on
probabilistic concepts of the teaching
learning process. Thus, at each stage in
the matrix, the student performance is
measured, and the probabilities are cal-
:ulated for every candidate next stage.
Dptimality is a function of maximizing
jrobability of attaining the terminal
objective (assuming that it can be esti-
nated) within physically and psycho-
ogically defined constraints, and it is
irgued that global optimality for any
tudent is the sum of next-task optimali-
ies (the State-Increment Model).
The further mathematical details of
le model are less important here than
n appraisal of the general approach.
LS already mentioned, there are cur-
cula which are, in fact, constructed as
matrix or network through a set of
leasurable objectives, and there are
atomated systems which monitor and/
r provide instruction in these curricula.
le limitation on such a concept is,
early, that many educators believe they
)ject to this conception of instruction,
owing that it may be suitable for
raining," or even "skills instruction,"
it not for "education." It is difficult to
y where the burden of proof lies in
ch a debate, but it is clear that there
11 be increasingly larger branches of
itruction which lend themselves to
s approach. It also appears that im-
imentation will occur more readily in
litary, industrial, vocational, and
profit-oriented instruction, and that the
public schools and colleges will be
among the last to make significant
moves in this direction.
III. AN ASSESSMENT OF DECISION
MODELS IN EDUCATION
Introduction: Assessment Criteria
Models in educational planning and
operation exist to serve a wide variety
of purposes—particularly in the broadly
defined area of planning. For that rea-
son, assessments should be function-
specific, a review of the adequacy and
availability of models devised for each
specific purpose.
In the next section we shall attempt
to assess the models available to per-
form various functions for various
levels of the education complex. Some
rating, therefore, will be involved,
based on the following scale, from high-
est to lowest:
—Best: Models are available, ac-
cessible, and in limited use.
(4)
— Models are available and
accessible, but little used.
(3)
— Models are available, but
largely inaccessible and in
little use at this time. (2)
—Worst: Models are of limited
availability, or virtually
non-existent. (1)
Models will be appraised according
to the following functions:
a. Models for specific short-run op-
erational decisions
b. Models for longer-range forecast-
ing and predictions
c. Models for informing non-quanti-
fiable policy decisions (including
some of b.)
d. Models for stimulating research
and inquiry related to decision
problems (including some from
all the above)
Below, we shall indicate judgments
about the rating of models, for each
311
-------
function, at the key decision levels
mentioned in the early part of the
chapter. Finally, we shall speculate
about developments in the near future,
including factors which will impede or
facilitate further development.
Assessment
Table 3 shows the author's assessment
of current models in educational plan-
ning and operation. While it would be
improper to attach too much signifi-
cance to these ratings, the table does
indicate some interesting general trends:
1. The level for which models seem
to be most available, accessible,
and used, is the national level
(except in the area of short-run
operational decisions, which is not
applicable). The national level
makes relatively heavy use of
forecasting systems, and projec-
tion models are in many respects
easier to build for large, gross
forecasts than small, detailed
ones. Several units of the Division
of Education are concerned with
modeling, particularly forecasting,
and it is not surprising that this
relatively high level of develop-
ment and utilization exists. (The
use is not universal, but intensive
in certain units.)
2. Forecasting and Prediction mod-
els are the functional area with
greatest development and utiliza-
tion at all levels, approximately
equalled by short-run operating
decision models, which, when
applicable, seem to be highly
developed.
3. Forecasting and prediction mod-
els are more likely to be used
strictly for projections than in a
simulation mode, that is, to
project the consequences of alter-
native policy decisions. Thus, they
are infrequently used in the func-
tion of informing non-quanti-
fiable policy decisions.
4. One of the most advanced area;
of model development is in the
variety of detailed operating de
cisions made at the school, schoo
district, college, or college systerr
level. These include a variety o
approaches to scheduling, inven
tory, staff assignment, vehicle de
ployment, etc. Interestingly, th
advances in these areas may b
due to the wide availability o
comparable models already de
veloped to solve analogous prot
Table 3 Assessment of Education Models
Level
Function
Short-Run Forecasting Policy Stimulatir
Op. Decisions Prediction Informing Research
National: Policy /Program
State: Subsidy/Finance
State: Staff
State: School Approval
State: Boundaries/ Jurisdiction
School District: Student Decisions
School District : Operating Decisions
School District: Program/Policy
College: Student Decisions
College: Operating Decisions
College: Program/Policy
n/a
3
2
n/a
3
3
4
n/a
4
4
n/a
4
3
2
1
4
3
3
2
4
4
4
3
2
2
2
2
2
2
2
3
3
3
3
2
2
2
2
3
2
1
3
3
2
Ratings: 4 = available, accessible, limited use
3 = available, accessible, little use
2 = available, largely inaccessible, little use
1 = limited availability or non-existent
312
-------
lems in business and industry.
Also, one should attribute the
prevalence of modelling in these
areas to the activities of dis-
seminating agencies such as the
National Center for Higher Edu-
cation Management, the Center
for the Advanced Study of Edu-
cational Administration, the Na-
tional Center for Educational
Statistics, private consulting firms,
and other organizations dedi-
cated, in part, to the extended
utilization of quantification in
educational decision-making.
The Future of Models
Whether there will be extended use of
models in the future depends on at least
the following four factors.
First, modelling as a science and
craft poses its own theoretical and tech-
nical problems, which frequently must
3e solved before the model can be used
with a level of effort and cost propor-
ionate to its value. The increased use
}f linear programming in recent years
;an be partially attributed to the devel-
opment of solution algorithms and effi-
:ient computer procedures which make
inear programming feasible to use. At
>resent, for example, many simulation
nodels used for resource requirements
irojection require enormous machine
apacity and cost. More efficient ap-
iroaches are needed.
Second, there are many theoretical
roblems inherent to education itself
'hich limit the possibility (or, at least,
le precision) of models. We still lack
nportant theoretical insights into the
aching-learning process, for example,
id can construct instructional decision
odels based only on the most super-
;ial measures, very few of them re-
lated to the important "soft" outputs of
education [5, 11, 12, 13, 17, 18].
Third, there is the need to appropri-
ately document, publish, package, and
market modeling materials, to close the
time gap between development and im-
plementation. The key marketing de-
vise, here, is training of potential users
in the value and technique of modeling,
assuring that in each candidate agency
there is at least one manager who can
identify a decision which will be served
by models and can communicate his
needs to appropriate technical staff or
consultants.
Fourth, and finally, the barrier of
emotional resistance to quantified meth-
ods must be overcome. This resistance
in education comes from two main
sources: (a) politically oriented educa-
tional leaders who prefer politically
attractive solutions to technically justi-
fied ones, and (b) educators who, for
good or bad reasons, believe that an
emphasis on quantification and for-
malization of educational decision proc-
esses is inconsistent with the well-being
of students.
The first and third of the factors
(better modeling technique and market-
ing) are not severe impediments; both
can be ameliorated by the application
of more resources to the area. The
second and fourth (educational theory
and emotional resistance) are vastly
more difficult to overcome or skirt. To
have an impact on these two barriers
will require many years of effort by
modelling advocates; it will require
better models, better packaged; and it
will also probably require appropriate
changes in the professional training
given to educators.
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316
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Chapter 10
Models in the Field of Energy
By
Kenneth W. Webb
SUMMARY . 319
I. INTRODUCTION , . 320
Categories of Decisions . 321
II. INDUSTRIAL DECISION MAKING AND THE USE OF ENERGY MODELS 321
Sources of Energy . . , 322
Exploration Decisions . 323
Mining Decisions . . . 323
Transportation to Energy Manufacturing Plants 323
Manufacturing and Distribution Decisions . 324
II. GOVERNMENT DECISION MAKING AND THE USE OF ENERGY MODELS 325
Projections by Trend Extension , , 326
A Demand Estimation Model 327
A Dynamic Demand Model With Interfuel Competition 328
A Pollution Policy Model . 331
A Model for Rate Making Proceedings 332
A Model for Federal Procurement of Fuels ... 333
A Model to Locate Needed Research 334
A Model of Oil Supply and Distribution 335
A State Government Demand Model . 338
V. RECENT DEVELOPMENTS AND NEW DIRECTIONS 339
REFERENCES . . 343
317
-------
-------
Models in the Field of Energy
SUMMARY
Rising fuel prices, shortages, and the
estimates of future shortages, if not
depletions, has caused increased con-
cern in the energy industry and Federal
government. The procedures of envi-
ronmental protection have further com-
plicated the energy supply and price
picture. Pollution abatement and facility
siting problems have delayed construc-
ion of facilities, decreased production
ind increased cost. The question of how
serious an energy problem we are going
o have and alternative strategies for
illeviating the problem can be answered
>y statistical estimating procedures and
tiore extensive models. The adequacy
if the available models and the promises
f the models under development are
nder sharp review.
This chapter is concerned with the
ecision making that occurs in the field
: energy and the models that are used
> aids in making those decisions. The
ederal government makes use of mod-
s in many decision areas such as
imulating exploration, determining
tes, conserving energy, import quotas
id environmental quality. State and
:al government are beginning to use
Ddeling for problems of locating fa-
ities, pollution control, safety and
lers.
Non-governmental institutions have
2n using models far longer than their
yernment counterparts in such de-
ion making areas as manufacture of
and gas, financing projects, distribu-
rt of products, and market analysis.
2 first section of this chapter describes
decision making in the industrial
rid, and the models that are used by
ustry. The exploration for reserves
of oil, natural gas, uranium and coal
has increased modeling efforts in terms
of statistical estimation of sampled re-
serves and economic evaluation of the
field. Mining operations use PERT and
simulation for developing and testing
operational designs. The transportation
systems from reserve areas to manufac-
turing sites makes use of scheduling
techniques and inventory control meth-
odology. Many linear programming
models are used in the manufacturing
of energy, especially in the oil industry.
Complex models that represent several
refineries are in operation as aids to
reducing cost and increasing output.
Electricity utilities are using network
analysis to determine the optimum con-
figuration of plants and transmission
systems. In general, the industrial uses
of models have been to increase profit
or supply more service in the case of
utilities. The questions of degradation
of the environment and social issues are
only recently forcing their way into the
industrial decision processes.
The main body of this chapter on
energy modeling is on the models of
use to the government. The Federal
government needs models that will per-
mit the analysis policy affecting demand,
supply and cost. The models do not
exist today that will answer these needs;
however, models are being used and
studied which partially respond to the
needs. This chapter reviews models that
are used in trend projection of explora-
tion, manufacturing, demand, price and
other components of the estimating
problem. The problems of using trend
projection, where there appears to be
complete changes in relationships of
supply and demand, is discussed in
detail.
319
-------
Econometric models that are useful
to government planning are also dis-
cussed, including a dynamic demand
model with interfuel competition, a
pollution policy model for testing new
government pollution policies, and a
linear programming model for the pro-
curement of fuels by the Federal gov-
ernment.
The chapter contains a description of
a model useful for determining the
areas of energy supply where research
monies can best be allocated, a model
that was used by the Canadian govern-
ment for the assessment of the effects of
the Arctic oil findings, and a State gov-
ernment model for examining the effects
of price changes in power and devel-
oped for a twenty year power plant
citing plan. Recent econometric models
and research efforts are also described
to illustrate the complexities that occur
in modeling when more comprehensive
estimates and models are required. The
following summary table contains the
main models discussed in this chapter.
I. INTRODUCTION
Energy decision problems are among
the most critical ones confronting both
Federal and State governments. For the
past thirty years, the relative costs of
most forms of energy have been de-
creasing and the availability far ex-
ceeded the demands. However, the year
1971 was the first year that the average
price of electricity rose; and, in 1972,
shortages of natural gas, oil and elec-
tricity prevented expansion of usage in
certain sections of the country.
Predictions indicate that the supply
of energy to meet demands will con-
tinue to be a problem and that costs
will increase. Economists feel that in-
creasing costs will tend to slow the use
of energy and have a depressing effec
on the economy.
The problems of supply and cos
have been complicated by the recen
increased demands for environmenta
protection. The location of facilities t<
preserve the environment, the use o
ENERGY
Models Discussed in Chapter
Summary Table
Model/Decision Area
Stimulation of Exploration
for new sources
Determination of Rates
Conservation of Energy
Stimulation of new methods
of manufacture
Import Quotas
Purchase of products for
government consumption
Power Plant Siting
Pollution Abatement
General Type
Important Characteristics
Dynamic Model
Regression
Dynamic Model
Engineering Equations
Network Model
Linear Programming
Deterministic
Scenario Analysis
Linear Programming
Combines supply, demand a
price with interfuel compe
tion. Assesses the effects
new reserves
Models exploration, resid<
tial, commercial and industi
consumption
Combines supply, demand •<.
price with interfuel comp
tion
System models to deterrr
the benefits of changes in
system
Assesses the effects of reset
and imports
The least cost selection
energy vendors to fill gov
ment needs is determined
A State government ana
of demand projections ant
cation effects of facilities
Subject to sulfur controls
model predicts supply,
mand and price by air qu
regions
320
-------
pollution abatement procedures, and
general conservation restrictions have
added cost and retarded new produc-
tion of energy.
The continuance of supply problems
may require the government to make
difficult decisions concerning the con-
servation of energy. These may include
changes in building codes such as in-
creased insulation, tax incentives to use
less energy, and advertising the benefits
of conservation practices. A more care-
ful use of our energy could ease some
environmental problems and lessen the
need for imports which impact our
balance of payments.
Categories of Decisions
Insuring an adequate supply of energy
has become a critical decision making
area at all levels of government. De-
cision making at the Federal level of
government is concerned with the fol-
lowing :
• stimulation of exploration for new
sources
• determination of rates
• conservation of energy
• stimulation of new methods for
manufacturing energy
• import quotas
• direct purchase of products for
government
• environmental quality
• assuring the growth of the economy
through sufficient supplies of
energy.
Decision making at the local govern-
lent level is concerned with the fol-
iwing:
• location of facilities such as new
power plants
• pollution control and other envi-
ronmental impacts
• safety considerations
• direct purchase of products for
local government
• assuring growth of local economies
relative to their dependence on
energy
• in some localities, the operational
problems of operating government
power utilities.
In addition to these governmental
areas of decision making are the de-
cisions of many institutions concerned
with the production and distribution of
energy. They include the following:
• companies that manufacture oil,
electricity, natural gas and other
products
• national agencies that manufacture
electricity such as the Tennessee
Valley Authority
• commercial banks that finance
projects
• the courts that adjudicate the prob-
lems of location of facilities, rates
and regulation
• scientific groups that are concerned
with all aspects of energy supply
and use
• environmental and conservation
groups that bring suit and use
persuasion on problems affecting
the environment
• the general public which makes
decisions by voicing attitudes and
by referendum.
The use of models in decision making
in industry is well developed. The use
of models by government is in the
beginning stages. By way of introduc-
tion to models in energy, we shall first
briefly review the industrial models to
illustrate the extensiveness of their use.
Following this, detailed descriptions
will be made of governmental decision
making relative to the use of models.
II. INDUSTRIAL DECISION
MAKING AND THE USE OF
ENERGY MODELS
Energy for the use by society is
generally supplied by private enterprise.
The exceptions are the electricity utili-
ties that are sometimes part of city
government or such bodies as the Ten-
nessee Valley Authority. In general,
however, the production of energy prod-
ucts such as coal, natural gas, oil and
electricity is in the private domain. These
321
-------
products are dependent on basic sources
that are found in or on the surface of
the earth, as shown in Chart 1.
By far, the largest basic source of
energy is solar radiation at the surface
of the earth. Solar energy is captured
by leaves of plants where it is stored
by the process of photo-synthesis. The
leaves get buried and eventually pro-
vide the fossile fuels. A recent analysis
of the possible total of the world's
mineable coal indicates 7.6 trillion tons.
The current production rate is 3 billion
tons each year. Thus, there are two to
three centuries of reserve coal if the
present production rate does not double
more than three times. Oil and natural
gas are estimated to be in much shorter
supply. For instance, the peak of pro-
duction of natural gas is estimated to be
about 1980.
Heat from the interior of the earth
is presently a very minor source of
energy. Several plants exist for the pro-
duction of electricity. One has been in
operation in the Larderello part of Italy
since 1904 and currently has a capacity
of 370 megawatts. The use of tidal and
wind power is still experimental. One
tidal power plant for the production of
electricity is on the Channel Island off
the coast of France and produces 240
megawatts.
In the field of nuclear energy, the
basic input is Uranium 235. The Atomic
Energy Commission estimates that it
will take 206,000 short tons of U3Og to
meet the needs of the decade 1970 to
1980. Extrapolating trends, the AEC
estimates that the quantity of ore pro-
ducible at $8 per pound in the United
States is 243,000 short tons, indicating
a need for additional reserves to be
found.
The descriptions of the supply picture
for several energy products is charac-
terized by diminishing resources. This is
going to result in both short supply for
Basic Sources of Energy
Solar Radiation
Heat from the center of
the earth (geothermal)
Tidal and Wind
w
W
Products
Coal
Gas
Oil
Hydropower
Uranium
M Electricity
Uses
Manufacturing
Transportation
Commerce
Government
Homes
CHART 1—Sources of Energy
322
-------
the United States and ever increasing
prices as less rich deposits are used. It
is of course possible that in the next
decade innovations for alleviating short-
ages may appear such as gassification of
coal and breeder reactors. However, the
experiences with the long lead times to
get nuclear plants into operation cause
us to believe that we should not rely
on such innovations for the near term.
The several steps in the manufacture
of energy are the following:
Exploration
Mining
Transportation to energy manufac-
turing plants
Manufacturing of energy
Distribution
In the remaining part of this section
on the industrial decision making, dis-
cussions of the types of models used in
he above steps will be presented.
Exploration Decisions
Exploration for new reserves of oil,
natural gas, uranium and coal is im-
portant to the longevity of the compa-
lies involved. The use of modeling in
ixploration is poorly documented be-
ause of the confidential nature of the
echniques. In the exploration for petro-
;um there were some early attempts to
se game theory to answer questions of
loving to drillings in new fields. This
ielded poor results and more recently,
le methodology of decision theory has
een applied. Underground oil surveys
lake use of other modeling techniques
icluding magnetic, gravimetric, and
ilynological. The model which com-
nes all these into a comprehensive
;cision system has not been developed.
Prospecting for uranium ore and for
ial generally takes on the following
ree decision making stages:
last two years to use search theory. This
generally takes the form of a model to
do a rough search to narrow down the
likely points, which is then followed up
with a more costly search on the
selected areas. The use of sampling
theory models in the second step has
produced forecasts of value in deter-
mining where and how close to make
test borings. The third step is a market
analysis to arrive at expected profit if
the ores go on the world market.
Mining Decisions
When a company makes the decision
to build a mining operation and exploit
a deposit, it frequently makes use of a
PERT network analysis to provide a
schedule for each of the steps in the
construction. It is almost standard prac-
tice today to build a simulation of the
mining operation, including the opera-
tion of the railroad to remove the ore,
the operation of a port facility, hourly
rates of mining and schedules of the
ore ships. The purpose of the simulation
is to determine the best schedules for
each part of the operation to prevent
backlogs and excessive use of storage
facilities. For an illustration see [30].
Transportation to Energy
Manufacturing Plants
In the petroleum business, the sched-
uling of crudes from the wells to the
refinery plants via tankers and pipelines
is a complex problem which must also
take into account the ability of the re-
finery to accept the delivery. Storage
costs money and storage capacities are
limited. A tanker fleet is composed of
ships, each with several compartments
for different grades of crudes, and is
severely affected by weather delays and
difficulty in port entry. A pipeline is a
"irst, a search for
ndicators of deposits
fe
W
Second, if there are
indicators, the deposit
has to be estimated
for size and quality
Third, the economics
of the deposit has to
be evaluated
ie first stage makes use of all the tools
d models of a geological nature. A
v attempts have been made in the
continuous flow of shots of different
crudes and is subject to difficulties of
predicting arrival times and correct
323
-------
amounts. The requirements of the re-
fineries for different grade crudes is
subject to much change. Simulation
models have been used to study this area
by different companies without signifi-
cant success and the use of models here
is very limited. Some companies have
used heuristic models for generating
schedules.
Manufacturing and Distribution
Decisions
The manufacture of petroleum prod-
ucts is an area where a great deal of
successful model building has taken
place to support decision making. The
earliest use of models was for answer-
ing questions on blending. This opera-
tion is the mixing of a variety of manu-
factured components to yield products
that meet industrial specifications. For
instance, to yield a gasoline of a certain
octane and with other specifications, as
many as half a dozen different com-
ponents may be blended. The early
blending models were linear program-
ming models using about 40 equations
and about 80 variables. The equations
were constraints on components, prod-
uct requirements, specification con-
straints and an objective function to
minimize cost. The blending models
generally gave cost savings of about
2% over the manual methods of arriv-
ing at the solutions. These models were
gradually enlarged to aid in decision
making on such problems as desulfuri-
zation and catalytic cracking.
Following this phase, more massive
models were made of complete refineries
to identify the operations and com-
ponents that would minimize the cost.
General opinion seems to be that the
cost savings with the complete refinery
models was not appreciable. However,
the models did provide very valuable
information to management on the mar-
ginal costs associated with limitations of
the plants and finished products.
Petroleum companies have investi-
gated complex models of several refin-
eries. The aid to decision making in this
case is the testing of many inter-refinery
strategies to see what interchange of
324
components, sources of supply, and
allocation of products would minimize
the cost of the operation. These have
proved most useful for long range
planning of facility changes, allocation
of product manufacture, and allocation
of supply of the different types of
crudes. These models have shown con-
siderable cost savings for the companies.
The conversion of energy from coal,
oil, gas, and nuclear energy into elec-
tricity is characterized by very large
scale operations. Electricity utilities are
generally joined together in large power
pools for the solution of peaking prob-
lems and the borrowing of electricity
when equipment fails. Utilities require a
continuous heavy capital investment.
New plants and transmission facilities
have very long lead times and are
expensive. The optimal configuration of
networks and facilities and the efficient
use of the equipment are two majoi
areas of industrial decision making
where modeling is playing an importan
role. Utilities normally have the exclu^
sive franchise for the area that the?
serve, prompting (in recent times) thei,
concern for social and other considera
tions. For instance, new environmenta
control measures are causing utilities ti
consider the social and environmenta
impact of the location of plants am
transmission lines. These restriction
are being modeled along with resultar
costs to the utilities and then to the cor
sumer.
Since electricity cannot be storec
the prediction of demand is the star
ing point for many of the investmei
decisions that must be made so that tl
facilities will be available in time
meet the demand. Short term demar
estimating models are required to sche
ule the manning, the start up of gener
tors, and to resolve the decision pro
lems of what to do about peakin
Longer term, ten year estimates, a
used to decide on the investments
new plants and transmission lines. Ea
utility has its own method of predictk
but most of these methods are sim
extensions of trend, e.g. the fitting
an exponential curve to the data.
-------
Demand projections are art forms
rather than science, because a variety
of extensions of trend can be made
from past data. Some analysis has been
made to assess the risk of shortage if
the exponential trend is followed. The
large amount of growth, averaging
about 7% per year, has so far protected
the utilities from overinvestment in
plant. Thus the decision making models
did not have to be so very accurate.
Management's attention has been di-
rected towards reducing the risk of
undercapacity to an acceptable level.
Linear programming models have
been used to determine the optimal
choice in changes of equipment and
plant over the long term. These models
seek to minimize investment and oper-
ating costs using a demand figure pro-
duced by the estimating methods. Monte
Carlo simulations are used by utilities to
assess investment options. The simula-
ions allow modeled equipment to break-
down, allow time to overhaul the equip-
ment, assume demand irregularities, and
input of power from the pool. The
simulation results allow management to
issess a variety of options by simulating
heir operational characteristics.
A network of plants in a utility com-
>lex requires scheduling to find the
iptimal level of production for each
Jant to meet the overall system de-
tiand. Plants differ in efficiency at dif-
erent load levels and the loss of about
5% in transmission plays a part. Sev-
ral modeling techniques including the
alculus of variations, dynamic pro-
ramming and integer programming
ave played significant roles in provid-
ig management with schedules. Linear
rogramming has been useful in model-
ig the shipment and storage of fuels for
le plants. Simulation has been used
>r modeling the properties of hydro-
ectric systems for assessing the fluc-
ations of production resulting from
iriation in the water sources.
In summary, the use of models to aid
dustrial management decision making
the production of energy is well de-
oped. The objective in most of the
plications has been cost minimization
and profit maximization. The questions
of what is best for the local community,
the State or the nation have not been
explicit in these modeling efforts. The
growing shortage of energy to meet
rising demand and the growing resist-
ance to environmental degradation due
to energy production, are bringing new
and more complex decision problems to
industrial management. This will call
for the extension and new applications
of models.
III. GOVERNMENT DECISION
MAKING AND THE USE OF
ENERGY MODELS
The Federal government needs mod-
els that will permit energy policy analy-
sis affecting demand, supply and cost.
These models, which do not exist in an
operational sense today, should be able
to provide guidance on matters of what
the government should do about import
quotas, stimulation of new exploration,
conservation of energy and the stimula-
tion of new methods of manufacture of
energy. Thus, Federal government de-
cision making in this area is dependent
on the estimates of supply, costs and
demand. Correct assessment of future
energy characteristics is important for
planning regulatory, tax, environmental
and other policies. It is critical in
determining the best allocation of gov-
ernment funds for research and develop-
ment, as the time from initial commit-
ment to major commercial use may be
decades.
In 1970 almost 10% of the useful
work in the country was done by elec-
tricity. This required 26% of the gross
consumption of fossile energy to fuel
the plants. The difference is due to the
inefficiencies of power generation and
transmission. The rate of growth in the
use of electricity has been changing
from 7% per year in 1961-1965 to
8.6% in 1965-1969 and 9.25% in 1970.
The energy consumption for industry,
homes and commerce has increased at
a fairly steady rate in the last decade,
but transportation has had a sharp in-
crease since 1966. The GNP, one of the
325
-------
traditional dependent variables for en-
ergy prediction, has fallen off and the
ratio of GNP to energy consumption
has suddenly started to climb since
1967. These facts illustrate the difficul-
ties of modeling energy consumption by
way of simple methods of trend exten-
sion.
Battelle Memorial Institute [43] re-
viewed and compared the significant
forecasts of energy for the purpose of
assessment of the methods and the pre-
dictions. Most of the forecasts studied
had only limited information about their
methods, and practically none provided
quantitative information on the standard
errors of estimate or other measures of
uncertainty. All of the projections were
based on trend analysis or simply judg-
ment. Most of the projections were
made from additions of the projections
from each energy source such as coal,
oil and natural gas. Of the thirteen
projections analyzed, the variation was
fairly large. For instance, the projec-
tions of energy requirements for 1980
varied from 74,542 trillion BTU to
97,000 trillion BTU.
The models analyzed by Battelle are
those that influence government policy
in the field of energy. One major criti-
cism of these models is that they ignore
the relationships among demand, price
and supply and they ignore fuel sub-
stitutability. Recent model developments
are going beyond simple energy trends.
For instance, the Federal Power Com-
mission estimates that the demand for
electricity will double by 1980 and
double again by 1990. These estimates
include extrapolations of economic and
population growth. The projections will
be accurate if the predictions of the
economy and population are accurate
and the assumed energy consumption
relationships continue. More sophisti-
cated models are appearing [2], with
alternative scenarios, multivariable rela-
tionships with demand and separate
estimates for different consumers. We
note, of course, that it is possible that
the Federal Power Commission estimate
could be in error and research on the
326
measure and estimate of such errors is
required. For further reading see [1].
Models do exist which analyze the
supply and price of different forms of
energy [16], [17], and [18]. Models and
studies have been made on the demand
for energy [21], [22], and [20]. How-
ever, these models do not explore in
depth the interdependencies of price,
supply and demand, nor do they esti-
mate the effects of fuel substitution.
For instance, if the price of natural gas
should rise, it is to be expected that
customers will, to some extent, switch
to oil and coal. This ease of substitution
is an important omission in the model-
ing efforts made so far.
Projections by Trend Extension
As an illustration of the basic energy
projection model using trend extension
and judgment, we cite the National
Petroleum Council's study of the na-
tion's energy outlook [13], [14], spon-
sored by the Department of Interior.
The projections were to be made to the
end of the century, were to encompass
all ranges of possibilities and were tc
examine areas where Federal policies
and programs could contribute to ar
optimum posture. The study includec
shale oil, synthetic oil and gas, and nu
clear stimulated gas supplies. The de
scription which follows only cover;
natural gas and conventional oil.
The study was done without econc
metric and demographic inputs, with rt>
price or production optimizing logic
The computational model computes
schedule of annual oil and natural ga
reserves based upon assumed trends i
drilling, reserves in fields discovered t
data and future changes in oil recover
From this, the model computes schec
ules of oil and gas production. Tl
computations also cover annual e
penditures required for the exploratio
development and production of oil ar
gas reserves. The model also calculat
the annual revenue required for d
mestic oil and gas production to earn
given rate on investment. Five rates
return are assessed in the model, ai
-------
for each, five prices of production are
calculated.
Fourteen geological regions were
analyzed, each having different success
rates in exploration, drilling require-
ments, producing characteristics and
costs. The overall model is composed of
three submodels, one for oil, one for
natural gas, ond one for economic in-
vestment calculations. The input to the
oil submodel is composed of many
factors such as: annual rate of change
in exploratory drilling footage, alloca-
tion of drilling to each region, years of
delay in recovery projects, existing re-
serves, investment required.
The model consists of accounting
type relationships to manipulate the
more than twelve input factors for each
of the fourteen regions. The output of
the oil submodel consists of the follow-
ing projections: annual exploratory
footage drilling, distribution of annual
footage to regions, annual footage by
well type, oil in place discovered
annually, annual reserve additions,
annual natural gas discovered, annual
oil and gas production, annual reserve
additions, annual well abandonments,
annual investments, annual producing
expenses.
The gas submodel has similar inputs
md outputs to* calculate future produc-
ion schedules of non-associated gas and
latural gas liquids based on continua-
ion of production from current re-
erves and trends in drilling and finding
>f gas.
The economic submodel computes
le tables of investments and operating
xpenses. Using oil and gas investments
i net fixed assets at the start of the
udy, an annual schedule of net fixed
ssets devoted separately to oil and gas
aerations is developed. Then the
nnual revenue required to provide each
' five rates of return on the net fixed
>sets is determined. The required
inual revenues from oil operations and
is operations are divided by their pro-
iction schedules to obtain schedules
revenue per unit of production
mce).
The model was developed by many
individuals whose experience in the oil
and gas operations is extensive. The
development of a model using expert
judgments on factors and trend exten-
sions is the most simple of all possible
approaches. The accounting type equa-
tions tie together all the variables using
judgment and expert opinion. This il-
lustrates the lack of modeling in the
supply area in terms of developed
formal functional relationships that
allow optimization and insight in the
overall process. Usually, when modeling
is performed with expert judgment, it
is of additional value to know the range
of expert opinion on the most sig-
nificant factors. These ranges can be
used to test the sensitivity of the out-
put to the range of likely error in the
variables.
A Demand Estimation Model
The Subcommittee' on Science, Re-
search, and Development of the Com-
mittee on Science and Astronautics of
the House of Representatives was con-
cerned about the multiude of energy
estimates and their validity and in June
1972, accepted a study [2] which ana-
lyzed some of the problems of elec-
tricity estimation. The study developed
a national electricity demand growth
model for testing projection method-
ology.
•It is a premise in this model that the
projections of demand for electricity
used in the past, which have been suc-
cessful and are based on population and
GNP growth, will not work in the
future. Many of the factors influencing
the demand for electricity and depart-
ing from long established patterns. For
instance, the increasing concern for
environmental effects is going to force
cost increases in the forseeable future
marked by the price increase in elec-
tricity in 1971. This modeling effort
assumes that there are four main factors
affecting demand in the future, they are
listed in order of decreasing impor-
tance: (1) price of electricity, (2) pop-
ulation growth, (3) income, (4) gas
prices.
There is a wide variation in the pub-
327
-------
lished estimates for future cost in-
creases. This model uses two estimates
which span the variety of estimates.
The first, a National Power Survey esti-
mate of 19% between 1968 and 1990
and the second, a doubling in 30 years.
It is assumed that there will be a 13%
increase in the price of natural gas
from 1970 to 1990. Two estimates of
population growth are used. The first,
based on a Bureau of Economic Anal-
ysis estimate of 1.4% per year, and
the second, that the fertility rates will
stay about the same resulting in a
stable population in 2030. Per capita
income growth is assumed at 1.4% per
year.
Thus the model uses two alternative
projections of population growth and
two projections of price, and the other
two factors (income and gas prices)
are fixed. The projections of demand
are made with the equation:
where i is the consumer class, j is the
region, t is the year, Q is the demand
for electricity, A is a constant, 6 is a
time response parameter, PE is the
average price of electricity, N is the
population, Y is the per capita income,
PG is the average price for gas, and
a, /8, y and a- are short run elasticities
for electricity price, population, income
and gas price.
The results of the four combinations
of inputs are shown in Table 1 along
with a fifth case, assuming no change in
electricity prices, and a sixth case with
a 24% decline in prices to 1980 and a
12% decline thereafter. The combina-
tions are based on the Bureau of Eco-
nomic Analysis (BEA), Federal Power
Commission (FPC) the estimate from
the National Power Survey of the FPC
and zero population growth to 2035
(ZPG2035).
Some conclusions that can be drawn
from this output are the following:
1. At 1975 there are small differ-
ences. Supply problems by 1975
will not be eased by adjustment
of prices.
2. The population assumption is
relatively unimportant for the
next 20 to 30 years.
3. The generally accepted projec-
tions and estimates of the influ-
ence of causal factors (price,
population) are incompatible.
4. Previous projections of demand
growth from FPC, National
Petroleum Council, and others
were too high.
This research was prepared for a
committee in the House of Representa-
tives, and was aimed at an investigation
of the multiude of estimates of the
energy crisis. The predictive mode
that was designed, an iterative year by
year calculation process, allows the
input of many assumptions about causa
variables. It is assumed that demand foi
electricity can be projected without re-
gard to the demand pattern that wil
develop for the other fuels.
A Dynamic Demand Model With
Interfuel Competition
"We next describe a model that com
bines the supply, demand and price in
Table 1 Electricity Demand Forecasts
Electricity Demand :
Population Assumption
Bureau of Economic Analysis
Bureau of Economic Analysis
Zero Population Growth 2035
Zero Population Growth 2035
Bureau of Economic Analysis
Bureau of Economic Analysis
Price Assumption
Federal Power Commission
double by 2000
Federal Power Commission
double by 2000
constant
decline
1975
1.98
1.88
1.98
1.88
2.02
2.14
1980
2.38
2.07
2.37
2,05
2.54
3.05
1990
3.01
2.11
2.95
2.07
3.56
5.66
200
3.4'
2.0
3.2
1.9
4.5
9.8
* Trillion Kilowatt Hours
328
-------
medium to long range dynamic model
of interfuel competition for the United
States [7]. This model, developed by
M. L. Baughman, has not been used in
a decision making framework as yet,
but agencies of the government are re-
viewing its applicability. It is included
here because it represents a major ad-
vance in energy modeling and is likely
to be used extensively in the govern-
ment. The results of the model will be
of direct use in policy analysis.
The model contains the interactions
between supply and demand within the
market clearing process. The market
clearing process yields the price and
quantity of the different fuels. For the
market to clear, supply and demand
must be equal. The overall model is
sketched in Figure 1.
The demand by sectors and the re-
source characterization are the exoge-
nous inputs. Sector demands are time
series for transportation, space condi-
tioning, industrial processing, etc. Some
part of the total sector demands will be
going to the market place to buy energy
from the market sensitive demand part
of the model. These inputs are func-
tions of the rates of growth of demand
and rates of turnover in consumers
equipment. The total of consumers who
continue to use the same fuels is called
the base demand.
The market clearing process, based
on price, matches supply to meet market
sensitive demand in the classic economic
supply-demand equilibrium. This is re-
lated to supply schedules, demand
schedules and a theory for the market
clearing process.
The dash line in the schematic indi-
cates the boundary of the system that
was modeled. It is assumed that the
variables inside the model do not affect
the variables outside the model. The
assumption that price inside the model
does not affect demand by sectors im-
plies that demands are elastic. Addi-
tional assumptions are that if all prices
change proportionately, the level of
demand will not change in that there
Jemand by SectorS
Model Boundary
-V
Environmental /
Effects '
Market Sensitive Demand
1
Market Clearing Process Fuel, Quantities, Prices
A. r •
\
Supply, Capacity, Costs
t
.Resources Economical to Develop'
Technological Change Resource Characterization^
FIGURE 1—Dynamic Demand Model Interactions
-Exploration
329
-------
will be no substitution, and that levels
of demand are dependent on variables
outside the model such as GNP, popu-
lation and other demographics.
In addition, exploration activities and
the effects on reserves are not depend-
ent on the model variables. The rela-
tionships between investment in ex-
ploration and the resulting returns on
investment are not well understood.
Another assumption is that there is
perfect competition in that prices of
supply are equal to cost. It is hypothe-
cated that this is reasonable in spite
of regulations and the fact that imper-
fect competition does exist. It is also
assumed that import and export quotas
are exogenous variables. Electricity
which consumes fuels and competes
with them on the market is treated as
both a supply and a demand with a
price dependent on fuel price and proc-
ess cost.
The level of aggregation is at the
coal, oil, natural gas and electricity
levels of supply. Thus prices are really
price indices over the subcomponents of
the supply aggregates. This creates a
loss of sensitivity to the changes in
demand for subcomponents and re-
sultant changes in production. It also
assumes that there is an adequate
shipping system for all products, and
that costs can be treated afterwards.
Geographical considerations are not
included in the model.
One output of the model is the market
shares and levels of consumption for
the fuels and electricity. This output
might aid in developing policies on
pollution, as well as energy. Another
outut, the supply and price of energy,
might be valuable to the government in
terms of predicting economic growth.
The levels of investment in the fuel
suppliers, as a model output, might be
helpful for predicting energy costs and
the availability of investment for other
fields. To illustrate the level of mathe-
matical statements used in the model,
the following are the cost functions for
the cost of petroleum.
Given an oil reservoir developed to
capacity q0, the output would appear
as the solid line below, in Figure 2:
output
time (years)
FIGURE 2
The dotted line shows increased ca-
pacity. This can be approximated by an
exponential q(t) = q0e~Dt where D is
the rate of decline in output.
Using this formula, the total capacity
of the reservoir can be estimated. The
government policy decisions on invest-
ment in development can then be
assumed. These include:
• money for speedier recovery of the
oil
• investment for a more complete
recovery of the site
These options can be tested by formulas
that yield the marginal development
cost, which is the cost of the next barrel
resulting from investment in more ca-
pacity, i.e.
MDC =
b(q0 + r0R0)-
where
MDC = the incremental cost of the
next barrel resulting from
investment in more capac-
ity,
r0 = the discount rate,
R0 = the total resources in the
reservoir,
q0 = the initial output of the
reservoir, and b and r art
constants.
The MDC formula is really a submode
in the overall sets of equations. I
provides the marginal development cos
for each of the overall tests of thi
model. The overall model is an equi
librium seeking, dynamic system tha
searches for the equilibrium of suppl;
and demand.
330
-------
The model has been validated by
using it to predict the behavior of
prices, demand and supply of the sev-
eral fuels over a historic 50 year period.
The match to the historical data was
considered good.
This model, as illustrated by the
example of finding the marginal de-
velopment cost of petroleum, does not
need a great deal of data input since
most of the activities of price, demand
and supply are represented by formula.
The many assumptions and conditions
noted previously suggest that this model
requires further development and vali-
dation. However, it is felt that its use
by the Federal government in its pres-
ent form would be helpful for making
applicable decisions as there is a definite
lack of valid other approaches.
Demand
Submodel 1
Demand
Submodel 2
was to link together three submodels
on demand, transportation and bidding,
then solve for fuel prices and alloca-
tions to regions over the entire United
States.
The model is formulated as a large
linear programming problem. Ten types
of fuel covering the types of oil, coal
and gas have a total of 300 sources of
supply. The model is to answer two
questions:
(1) How do the 300 fuel sources get
allocated to the air quality re-
gions so as to minimize cost and
still meet the specified air quality
constraints?
(2) What is the price for each fuel
type in each of the regions?
The linear programming problem can
be outlined by the following diagram.
— Demand
— Constraints
— Demand
— Constraints
Capacity constraints of the sources
Objective function (cost)
A Pollution Policy Model
The previous model is significant in
;nergy model building for decision mak-
ng purposes because of its compre-
icnsive characteristics. As noted, one
rf its outputs is the market shares of
he several fuels and the levels of con-
iumption. This can be used for pollu-
ion analysis and testing government
>olicies on pollution. Another model,
^hich we describe next, is the Energy
Duality Model [8], being developed for
le Environmental Protection Agency
or testing pollution policy.
This effort was aimed at determin-
ig the effects of sulfur limitations on
ie allocations of fuels to regions of
le country. A mathematical model was
eveloped for predicting fossil fuel
apply, demand, cost and distribution
Jr the air-quality control regions sub-
:ct to sulfur limitations. The approach
— Demand
— Constraints
— Capacity
Constraints
= Minimum
The model requires as input the
following:
• Selling prices for the fuels in each
of the regions
• Values describing the physical
characteristics of the power plants,
Btu requirements, and sulfur emis-
sion limits for each region
• Demand for coal, gas and oil by
the non-power plant users.
The output of the model is the fol-
lowing :
• A fuel price for each fuel used in
each region
• The amount of each fuel used in
each region. This model does not
include the use of fuel for trans-
portation in each region, but does
include commercial, home and
industrial usage
• The amount of each fuel shipped
from each supply district to each
use region.
331
-------
This is intended to be a predictive
model in that it is to be used for esti-
mating the effects of sulfur policies
several years in the future.
Demand for each of the air quality
regions is assumed to be fixed for each
of the fuel types. Fuel cost is estimated
by adding production costs and profit.
The output will also include the cost of
transportation. Power plants are
allowed fuel options including fuel
switching from type and grade, and the
installation of gas cleaning equipment.
These costs are added to the fuel costs.
As an illustration of the type experi-
mental runs, a predictive run for 1975
was desired. The AQCR's in this case
were aggregated to match states so that
the state implementation plans could be
studied. Some AQCR's were in two
states, requiring fragmentation. In addi-
tion, 12 critical metropolitan regions
were included. The final aggregation
included 46 states, 10 metropolitan re-
gions and 5 fragmented metropolitan
regions. Fuel supply districts were
aggregated to 112 regions. This illus-
trates the flexible nature of the model
in that it can be aggregate or disaggre-
gate as required by the study.
The Energy Quality Model is still in
the developmental and testing phases
and, as far as can be determined, it has
not yet been used for decision making
or policy analysis. The model should
be of value in pollution policy analysis
by testing the effects of pollution con-
straints on the national or regional
distribution of fuels and the resultant
prices to the consumers. The model is
significant because it points the way for
modeling of interactions of environ-
mental quality policies and the effects
on society in terms of the availability
and price of fuels.
A Model for Rate Making
Proceedings
The procedural steps in Federal regu-
lation are defined by law, but the proc-
esses for each of the steps are not
clearly spelled out. The use of econo-
metric models for future decision mak-
ing is a real possibility. In 1961, the
332
introduction of an econometric rnodel
on the Permian Basin Area Rate Case
was the first use of the results of a
model in a rate case before the Federal
Power Commission [10]. The model
projected the impact that various ceiling
prices would have on the demand and
supply of natural gas.
The model as conceived by the eco-
nomics staff of the Federal Power Com-
mission, used as inputs an assortment
of hypothetical gas prices which re-
sulted in estimates of future exploratory
effort, additions to gas reserves, gas pro-
duction, gas consumption and other
factors affecting the natural gas in-
dustry. The model was developed in
three separate parts: exploration activi-
ties, residential and commercial con-
sumption, and industrial consumption.
The basic analytical approach was
regression analysis. Each of these parts
was represented as a dependent var-
iable in the regression approach. For
example, to create a dependent variable
for exploration activity, the Office of
Economics selected the number of
exploratory wells. The associated inde-
pendent variables included the expected
future price, the production of oil and
gas, the cost of money, and exploration
success ratio, an index of the probable
depths of new reservoirs and finally, a
grouping of many factors in one index,
These variables were identified for the
period from 1940 to 1961 and wen
inputs to the regression analysis. Th<
residential-commercial and the indus
trial submodels were developed in ;
similar way.
The basic finding of the model imple
mentation was that when there is a ga
price increase there is a tendency t
lowering of the quantity of gas sole
The supply of gas is essentially th
underground inventory of proven ga
reserves. Inventory levels are referre
to as life indexes in which proven ga
reserves are divided by annual gas coi
sumption to determine how many year
gas supply is available at any give
time. With reduced consumption, aft<
a price increase, the life index vak
would rise, meaning that more g:
-------
would be available without new re-
serves. The conclusion is that price in-
creases do not stimulate new explora-
tion.
The model was severely criticised by
industry experts and others. Oil and gas
producers felt that the model was in-
accurate, full of subjective manipula-
tion and not a useful tool. The hearing
examiner felt that the model was not
relevant or material to the problem.
The subjectivity, the problems of multi-
collinearity, bias, problems of auto-
correlation and aggregation were all
spelled out as rendering the modeling
inadequate as a predictive tool.
A Model for Federal Procurement
of Fuels
One of the decision making areas
for the Federal government is to deter-
mine the sources for the purchase of
fuels for use by the agencies of gov-
ernment. The Defense Fuel Supply
Center (DFSC) has been purchasing
fuels since the mid-sixties using a linear-
programming model for the selection
of bids from suppliers for delivery all
over the country [14]. The procurement
is for the entire defense establishment.
It is the world's largest purchaser of
fuels, and the U. S. petroleum industry's
biggest customer. This case history in-
volves the jet fuel procurement pro-
gram which accounts for more than
lalf of the one billion dollars DFSC
spends each year.
DFSC procures more than two bil-
ion gallons of jet fuel for the armed
"orces every six months. It must be
ihipped to fill the requirements of over
00 air bases, air fields, and air sta-
ions on the continental United States.
ivery six months DFSC must consider
.bout 100 bids from petroleum com-
>anies throughout the United States
nd South America, and award con-
racts to the companies so that the total
elivered cost is the least possible.
Although the total volume of fuel
ffered by all bidders exceeds the total
;quirements, it is never possible to
ivard contracts such that the require-
lents of each base can be completely
supplied from the least expensive
source. Import quotas and limited offer-
ings by each bidder preclude this.
Simple procedures of awarding con-
tracts to the cheapest sources, then to
the next cheapest sources for unfilled
requirements, and so on, do not provide
the least-cost solution.
As an illustration, suppose there are
four bidders, labeled A, B, C and D and
three supply depots or destinations
labeled 1, 2, and 3. The four bidders
offer the following quantities of the
same product:
Bidder A offers a maximum of 800
units
Bidder B offers a maximum of 1200
units
Bidder C offers a maximum of 1100
units
Bidder D offers a maximum of 3000
units
Total is 6100 units.
The three supply depots require the
following quantities of the product:
Supply depot 1 requires 1000 units
Supply depot 2 requires 1500 units
Supply depot 3 requires 2000 units
Total is 4500 units.
The bid price per unit of the product
by each bidder, fob destination, is indi-
cated in the following table:
Supply depots
1 2 3
Bidder A
Bidder B
Bidder C
Bidder D
52
48
60
52
30
32
40
41
4H
., > Bid prices
60J
According to this table, the price per
unit bid by A and shipped to depot 1
is 52 cents. The cheapest source for
depot 1 is bidder B at 48 cents, for
depot 2, it is bidder A at 30 cents and
for depot 3 it is also bidder A. Bidders
A and B do not offer enough product
to satisfy the needs of the three depots.
Other bidders must be considered. If
the reader attempted to award bids
even in this simple case, he would find
that the least-cost set of awards totaling
$2,051 is difficult to arrive at.
333
-------
In addition to complexities of amount
of product, a bidder may indicate a
minimum quantity, indicate a choice of
shipping points, tie his offer to another
bidder, quote different prices for dif-
ferent amounts and many other com-
plexities. The awards must be made in
conformance to the Small Business Act,
import quotas, and the criteria may be
fob origin or destination.
The problem is treated as a standard
linear programming transportation prob-
lem, i.e.
Minimize S £ C« Xij (total cost),
i j
subject to S Xjj = TJ for all i
SXy 0 for all i, j
i denotes the installation
j denotes the bidder
rj = the requirement by installation
bs = the maximum offered by
bidder j
Xjj = the quantity shipped to i from
bidder j
Cij = the delivered cost per gallon
to i from j
The above formulation does not
handle certain possible bidding strate-
gies, e.g., increasing for additional lots
from the same bidder, but mathematical
and computational procedures can
account for these complexities. The
system using the transportation method
of arriving at the least cost had reduced
total cost by more than 2 percent, re-
duced the bid evaluation time to a 1
hour run on the computer, allowed
quick reaction to changes, eliminated
computational errors, and the model
can be used for a multiplicity of plan-
ning studies.
A Model to Locate Needed Research
A significant function of the Federal
government is the awarding of grants
and contracts to solve technical prob-
lems in the energy field. The purpose
is to produce innovations to increase
supply or to increase efficiency of the
operations. Models of systems can be
very helpful in identifying particular
334
aspects of operations that would benefit
from research. The models can also be
used to determine the benefits from
changes in technology in terms of
greater production, reduced pollution,
lower cost and other features. The fol-
lowing model is one of a series designed
for this purpose [6], It is a techno-
economic model of an electricity gen-
erating plant, using coal, gas and oil.
For a variety of such studies, including
locational studies, see [23], [24], and
[26].
At present, fossil fueled steam elec-
tric plants produce 80% of the electri-
cal energy in the United States. The
fruits of R&D in cost reduction in these
plants would have a substantial effect
on the economy. This model is intended
to predict cost reductions based on
hypothesized advancements.
Since the model is to assess techno-
logical advancement, it must contain
technical detail of sufficient depth. For
example, to assess the cost reduction
resulting from improved heat transfer
coefficients in the condenser, the model
must be able to include detailed com-
putation of the size and related cost of
the condenser for various heat transfer
coefficients.
The first step in the modeling effort
is to make a schematic diagram of the
typical plant, Figure 3. For each of the
elements of the schematic, cost equa-
tions are developed related to design
characteristics. To demonstrate the
methodology, one component for watei
treatment, a wet tower with natura
convection will be made into a cos
equation.
The method to develop the equatior
is to use known engineering relation
ships of performance to produce th(
following:
Cost = (0.015) (X)(Y) (0.8),
where X is the heat removed from th
water by the tower, Y is a performanc
coefficient as a function of the desig
characteristics. Using regression metr
ods, the validity of the cost equatio
was checked against actual results c
specific power plants.
-------
I Exhaust Gases
Exhaust Gas Treatment
Fly Ash
Air
Air
Preheater
Fuel
Treatment
Jvfeke up
Waste
Fuel
FIGURE 3—Steam Electric Plant Schematic
The outputs of the model are based
on. postulates for engineering advance-
ments (changes). Table 2 illustrates the
typical output.
The usefulness of models of this type,
aimed at identifying significant research
srojects for engineering research, is
imited by the simplifications which
must be made. As far as we can deter-
nine this model has not been used to
evaluate alternative decisions.
4 Model of Oil Supply and
Distribution
As has been illustrated above, the
-ederal government has depended on
imple trend analysis methods for de-
termining supply, price and demand.
Interfuel competition has not been
analyzed in the models used thus far.
Of late, the Baughman model and the
EPA Energy Quality Model have shown
promise of increased quality of model-
ing. The use of the recently developed
models described in this paper in deci-
sion making appears to be small or
non-existent. However, agencies such
as the National Science Foundation,
Environmental Protection Agency,
Council on Environmental Quality and
the Federal Power Commission are
funding efforts to develop modeling
approaches that will be of direct use in
answering specific decision problems.
335
-------
Table 2. Engineering Advances vs. Cost Savings
Advancement
Result
Coal Oil Gas
Savings-mills/KWH
Reduce size and cost of
cooling tower by 20%
Increase boiler outlet
temperature from 1000°
to 1400°
Eiliminate fouling in
condenser
Lower construction
costs
Reduction in fuel
consumption
Reduction in
condenser size
.5375
.0604
.117
.5086
.0604
.117
.5037
.0604
.117
In contrast, the Canadian National
Energy Board has an Operations Re-
search Branch which has developed
several models that are contributing to
that nation's policy decision domain,
see [15], [46], [47], and [48].
A model conceived for the National
Energy Board was used in the assess-
ment of the effects of the Arctic oil
findings on the Canadian oil industry.
Although the decisions that were made
based on use of the model have not yet
been divulged, and even though it is
rather complex, we feel that the model
is an important one and we next dis-
cuss its structure.
The problem called for a global
solution at a macro-economic level and
in addition, answers at a micro-eco-
nomic level concerning linking of
supply and demand distribution points
by pipelines to include pipeline ca-
pacity, cost, effect on field prices, and
investments and producing capacities in
the various regions. It was assumed that
profit was the prime motive of compe-
tition between producing centers.
Major assumptions were as follows:
• Price changes are triggered by the
leader in the industry who is the
major operator in the producing
region.
• The Arctic region will be able to
compete with other continental
regions on its own terms in order
to maximize its profit.
• The base price is set by the price
leader at the most competitive
producing region, determines the
maximum value or opportunity
cost of crude at all other points in
the distribution system.
336
• The cost to find, develop, and pro-
duce oil in a region has little
bearing on the posted field price of
oil in this region.
• Price is a determining factor in the
decision to invest in oil producing
capacity.
• The oil distribution system tends to
minimize the cost of fuel delivered
at the demand centers.
The data base is quite extensive and
consists of five categories of informa-
tion.
1. By 1° latitude and longitude dif-
ferences, detail of terrain and
province boundaries.
2. Regional cost of pipe, mean
winter temperature, and marginal
cost relationship characterizing
the economics of exploration and
production.
3. Sixty supply and demand nodes
are identified by latitude, longi-
tude, and characterized by addi-
tional data. Supply nodes are
characterized by field price bei
barrel, a list of regions for which
the node acts as a collection
point, and the production of the
regions. Demand nodes are char-
acterized by demand levels anc
growth factors.
4. Pipeline route data are piece-wis*
linear curves, a chain of straigh
line elements. Each link on th<
chain is characterized by th<
latitude and longitude of the enc
points, the capacity of the link
the direction of flow, cost o
transportation and the pipelin
diameter.
5. Parameters which include th
discount rate, cost of servicin
-------
pipelines, oil import quotas, price
of steel and oil and similar
factors.
The demand for oil and the field
price is related to a level of exploration
and development by a production func-
tion. The allocation of crude from
supply to market is constrained by the
producing capacities and by oil import
restrictions. These capacities are a func-
tion of recoverable reserves which in
turn are a function of investments in
exploration and development. These in-
vestments depend on the economics of
exploration and development, price of
crude and the cost to find, develop and
produce oil. While the price of crude is
a result of competition, the cost to find
and produce oil depends on the available
geological information.
The model requires an estimation
method for the amount of investment
in exploratory and development opera-
tions. This is done by first deducing the
relationships among probability of finds,
estimated volume of basins, depleted
and discovered basins and hydrocarbon
reserves. This resulted in an equation
of investment between the current
known year of data and the year n.
This was then expanded by integration
to a linear equation which was approxi-
mated by regression analysis.
A capacity expansion function was
devised to estimate regional investments
n exploration and development for oil
md gas, based on field prices and de-
mands for oil, as determined by the
:ompetitive position of the respective
iroducing regions in the supply distri-
mtion system. A choice had to be made
•etween the traditional econometric
egression model and a deduced behav-
jral model. The poor results of regres-
ion and the lack of data indicated that
deduced model was the best choice.
'he model was validated against 100
jgregate annual investments for 40
reducing regions and was adjudged
itisfactory for the purpose of the over-
1 model.
Finally, a flow allocation model was
eveloped. At every yearly time step,
lis model solves for the minimum cost
allocation of oil in the supply and dis-
tribution system and determines which
existing pipelines should be expanded
and which new lines should be built.
The distribution network is modeled as
a set of capacitated arcs. This is trans-
formed into a network flow graph
amenable to mathematical flow opti-
mization procedures. Figure 4 shows a
simplified network. Dummy demand
and supply nodes are included to absorb
any slack in the system.
All demand centers are connected to
a dummy demand center with imagi-
nary pipelines having minimum and
maximum capacities equal to the respec-
tive demands at each center. These links
incur no costs of transportation. AH
supply centers are connected to a
dummy supply center with imaginary
pipelines with maximum capacities
equal to the producing capacities of the
supply points and with minimal capaci-
ties equal to zero. The unit transporta-
tion costs through these imaginary pipe-
lines are the field prices of oil at the
respective points of supply.
Other imaginary nodes and links
were necessary to describe certain con-
ditions of the system. For example, the
tariff imposed on Canadian oil exported
to the United States is represented by
introducing two imaginary points at
each side of the border along pipelines
crossing the border. The trans-border
link between these two nodes is assigned
a zero length, an unlimited capacity
Dummy Demand
Point
Overseas Source
Dummy Source
FIGURE 4—A Simplified Version of a
Flow Network
337
-------
and a positive import tariff for south-
bound pipelines.
The system is then represented by a
graph N composed of arcs (i, j) each
characterized by: a maximum capacity
Q1( going from i to j, a minimum ca-
pacity M13 going from i to j, a unit
cost of transportation Cy. The optimi-
zation problem is to find a way to solve
for a flow amount q(j on each arc that
minimizes the total cost satisfying the
minimum capacity constraints and sub-
ject to the maximum capacity con-
straints. This can be stated mathe-
matically as a special linear-program-
ming problem as solved using computa-
tional procedures which allow for fast
and efficient solution of network prob-
lems.
An iterative procedure for solution
was adopted because the costs Clf in
reality are dependent on the qa. This
procedure consists of correcting costs
in a second run through the computa-
tion based on the q(1 values from the
previous run.
This model is significant because it
points the way for the United States to
model the supply points and the de-
mand points in such a way as to allow
testing of alternative arrangements of
supply and distribution facilities. In the
years to come, when shortages of oil
become severe and prices increase, the
need for a more efficient national dis-
tribution system will assume increased
importance.
A State Government Demand Model
State governments have not used
modeling to any great extent in their
planning and decision making. One
noteworthy exception is the State of
California, which has developed several
energy planning models. The model
described below was aimed at providing
a basis for a twenty year power plant
citing plan in terms of projected de-
mand [9].
One possible method of building a
State model that was considered was
to simply add together the projections
of all the utilities in the State. It was
decided that this would not be practical
338
because each utility has variations \n/
their methods, but all methods
amounted to simple trend projections.
Since the growth rate is generally ex-
ponential, it was felt that this cannot be
realistic for future projections. Modi-
fications of this rate would have to
occur.
The model approach used was to
view the State as a whole and develop
a forecasting model with social, demo-
graphic, technical, geographical and
other factors. Five cases were devel-
oped for possible future conditions, all
reasonable projections of economic and
demographic growth and with some
anticipated increases in the price of
electricity. The likelihood of any one
of the cases actually occurring cannot
be evaluated; however, there was a
base-line case which is classed as a
surpirse-free scenario. The base-line
case is bracketed by two cases, one with
lower estimates and the other with
higher estimates. The remaining two
cases of the five accounted for the pos-
sible effects of increasing energy prices.
The five cases are as follows:
(1) Base case
(2) Base case with price increases
(3) Low-growth case with price in-
creases
(4) Low-growth case with constan
prices
(5) High-growth case with constan
prices
The model outputs and therefore ths
conclusions are, of course, sensitive tc
the structure and relationships of tht
model, as well as the assumptions ii
the scenarios. For instance, a few o
the assumptions in the base case wit
price increases are as follows: in th
early 1970's pollution restrictions hav
stopped construction of all fossile fue
plants in the south region; nuclea
plants have been obstructed by consei
vationists and safety consideration;
only limited development of geotherm;
capacity takes place; and by the 1980
brownouts and blackouts are frequei
and may last an entire day.
The model represents all of Cal
-------
fornia and is not a summation of dif-
ferent utility marketing areas. It does
account for different meteorological
conditions and population densities.
Price increases in the model effects de-
mand by causing shifts to other energy
sources and decreased consumption.
The model consists of a set of six
main submodels for the following com-
ponents: residential, industrial, com-
mercial, transportation, government,
agricultural.
The residential submodel is com-
posed of three main factors: number of
households, devices in the homes, con-
sumption of electricity by devices,
which are functions of demographic
change, factors affecting use of appli-
ances, climatological factors, relative
prices of energy sources, dwelling unit
characteristics, utility promotional ac-
tivity.
The industrial submodel is composed
of 21 industrial group models. Con-
sumption is measured as a function of
the output of the group and the elec-
tricity required for that output. Assump-
tions are made about the changing tech-
nology, e.g. canning will be supple-
mented by freezing processes.
The commercial submodel involves
ive elements of trade, finance, insur-
ance and real estate, communication,
slectricity, gas, sanitary services, con-
struction. The method of estimating the
consumption for the commercial sub-
nodel is based on regression with the
ross State product (GSP). The future
s estimated by simple trend projections
or GSP.
Transportation is such a modest
onsumer, that the submodel reduced to
n assumed constant. The agriculture
equirements for electricity are related
> the electricity used for irrigation
'hich is fairly stable. A constant factor
•as also used! for this component.
Government uses include street light-
ig and office buildings. The method of
itimating consumption is by a relation-
lip of the government contribution to
te GSP.
This energy prediction model, as has
;en noted, is a set of estimating equa-
tions where the variables are input
factors arrived at from source material
on projections of the economy, tech-
nology, demographic characteristics and
other factors. It is a deterministic model,
however the use of the five scenarios
allows analysis of possible errors of
estimate. The output of the model of
course is the demand figure for the
State. Model results, running the five
cases have led to the following con-
clusions :
1. Demand could be much lower
than would be projected by
simple extrapolation of trend such
as each utility is doing.
2. Price increases will mainly affect
the commercial and industrial
sectors.
3. Demand is very sensitive to eco-
nomic and demographic varia-
tions.
IV. RECENT DEVELOPMENTS
AND NEW DIRECTIONS
New modeling research efforts are
underway in the United States stimu-
lated by the growing concern with the
problems of energy. Resources for the
Future (RFF), Inc. conducted a semi-
nar in January 1973 where many of the
new efforts were presented. The presen-
tations are briefly outlined here to indi-
cate the various directions that current
research is taking. It should be noted
that the work outlined below does not
include all research on modeling energy
problems; they do point up many of the
new approaches that are being investi-
gated.
Use of Input-Output and
Econometric Techniques for
Energy System Modeling
The main drive of models of this
type is the relating of energy consump-
tion and/or production to comprehen-
sive economic models. This approach,
using many economic sectors, allows
more than the usual detail modeling
of residential, commercial, industrial,
transportation and electric utility sec-
tors. The availability of data delimits
339
-------
the extent to which the model can
be detailed. Different investigators use
various devices to disaggregate his-
torical energy statistics. The way in
which energy consumption is related to
the economic model for forecasting is
one of the features of interest. This can
be simply a constant relationship be-
tween energy consumption and eco-
nomic activity. Usually data indicates a
trend and more complicated relation-
ships must be used. At the other ex-
treme, full interaction between the
energy model and the economic model
(in the equilibrium concept) with
energy prices affecting energy produc-
tion and consumption as well as pro-
duction and consumption of other
goods and services. Several models were
presented at the RFF seminar. In a
paper by William A. Reardon [50], the
disaggregation is carried to much
greater detail than previously in the
construction of input/output tables.
Reardon's tables covered three years of
time and 35 economic sectors. The
trends found for the input/output co-
efficients indicates trends for energy
consumption per unit of output in the
35 individual sectors.
In an Inter-Industry Forecasting
model, under development at the Uni-
versity of Maryland [51], there is a
division of the economy into 185 in-
dustries. The model is used to estimate
the sales of each industry to each of the
other industries, 112 types of capital
investment, consumers, government and
export. More than 1000 regression
equations were employed in forecasting
consumer demand, investment, export
and import behavior, labor productivity
and changes in materials used in the
185 industries. Forecasts are generated
year by year for a ten-year span. In
order to forecast demand for petroleum,
the model relates each major petroleum
product to each industry. In a paper by
Verleger [52], there is an attempt to
more fully couple the energy and eco-
nomic models. He makes use of
partial and general equilibrium models
in which energy and nonenergy de-
340
mands of the economy are put in a
simultaneous equation framework
where prices are determined so that all
markets clear at every moment of time.
Use of Linear Programming in
Energy Models
Linear programming provides a basis
for another class of energy models gen-
erally making use of the classic trans-
portation problem. Since this is a class
of optimizing models, they are not par-
ticularly useful for projection. Linear
Programming models are attractive to
research on planning and policy anal-
ysis. Linear programming features the
ability to use constraints such as pro-
duction capacity limitations. Thus, the
outputs of the model can be used as
standards to measure the efficiency of a
given or proposed system. Hoffman
[53] offers a model for planning and
technology assessment. The model en-
compasses the entire energy system and
represents full inter-fuel substitutability.
The analytic approach is to use n
alternative supply categories, yielding
n X m possible supply-demand com-
binations. The current research has n
at 13 and m equals 15. The objective
function is the minimization of cost
bounded by the demand and supply
constraints. Another linear program-
ming module by Deonigi and Engle [54
is concerned with the generation o
amounts of electric power which it
specified exogenously. The model equa
tions are formulated as electric utilit;
decision variables, yielding a mode
4,000 X 9,000 in size. Griffin [55] in
troduces a model applied to the petro
leum refining industry using a linea
programming description of the pro
duction process. The demand estimate
are based on conventional econometrf
approaches using stocks of petroleui
and consuming equipment. Once th
demands are obtained for products, tt
requirements for the major produc
become constraints. The objective fun<
tion seeks to minimize the cost of pr<
duction using demand, quality speci
cations and capacities as constraint se
-------
Econometric Models of
Individual Sectors
Several papers given at the RFF
seminar are interesting because of their
simplicity. A paper by Erickson, Spann,
and Ciliano [56] uses five consumption
sectors with consideration of the role
of each fuel in each sector. The model
is a regression approach relating de-
mand to a series of variables covering
new uses, prices, density of urbaniza-
tion, income and temperature. In
another research paper, by Spann and
Erickson [57], there is a focus on long-
run oil and gas exploration using econo-
metric techniques. The model seeks to
estimate the response of supply to
econometric factors such as prices, in-
terest rates, and time. The model con-
tains cross-elasticities of supply between
oil and gas and cross-elasticities with
demand. Gas and oil are produced and
discovered by the same companies in
actuality, thus they can be considered
as joint products. The supply and de-
mand interdependence is taken into
account by using a simultaneous equa-
tion framework.
The models outlined above represent
the classes of approaches that are being
experimented on in current research.
Whether input/output, dynamic equi-
ibrium, or linear programming, the
rend seems to be models of consider-
able complexity, requiring extensive
iata. Interestingly enough, modeling in
ransportation when challenged to pro-
luce better models went to models of
(reat complexity and high data cost.
during the last decade, the transporta-
ion models have become more prag-
natic and simpler approaches are again
icing used. It would appear that the
unding of these research efforts in the
nergy field should nurture both com-
licated and simple models to insure a
sefulness of the research results.
However, the usefulness of modeling
) examine some of the newly arrived
roblems of energy is dependent on the
jvelopment of new comprehensive and
.teractive techniques. For instance, the
ipacts of new energy technology on
ic economy and air quality was treated
with an input-output model by Just
[74]. This model was used to examine
three new technologies that might be
significant in 1985:
(1) High BTU coal gasification;
(2) Low BTU coal gasification;
(3) Gas turbine topping cycle (com-
bined gas and steam cycle).
The major results show the sensitivity
of total capital investment to changes
in the energy use growth rate and to
the adoption of new energy technology.
They also show that very small changes
in the overall growth rate of personal
consumption or government spending
can restrain total investment to within
its historical limits as a percent of GNP.
Thus the United States can sustain the
high investment costs created by rapid
energy demand growth by reducing the
growth rate of consumption and gov-
ernment spending by less than 0.1%
per year through 1985.
The core of the model contains the
actual and projected input-output struc-
tures describing the 1963, 1970, and
1980 economics. The noneconomic
quantities are referred to as accessory
variables and are summarized in the
bottom half of the Figure 5. These are
model outputs and are assumed to be
proportional to the total output of each
sector.
The boxes in the upper half of Figure
5 show the various means for interact-
ing with the model, in terms of the
alternative future being investigated,
including changes in technologies and
composition (or size) of GNP.
Alternative futures are constructed
by developing a final demand vector to
represent the conditions of the scenario
and modifying the technology and cap-
ital coefficients to include the amount
and kind of new technology that is
specified. Once these changes are made,
the total outputs and investment require-
ments can be calculated. The values of
the accessory variables are then ob-
tained by simple multiplication.
In making projections of final de-
mands, it is necessary to calculate the
investments required to support the
341
-------
Alternative Final
Demands
Price Elasticities
Alternative Futures
Price Changes
Gross and Cooling
Water Usage
New Technologies
(coal gasification,
gas turbine
topping cycle)
The U. S. economy
Basic Input-Output
Structure and Final
Demands
1963, 70, 80
Energy Use by
Fuel Type
Model Outputs
FIGURE 5—Input-Output Energy Model
level of final demand, which depends on
investment level.
A simple two-period model can be
used to illustrate this. Assume that:
(1) The same technological coeffi-
cient matrix A applies to both
periods.
(2) Total final demand Y consists of
final demand purchases by
households and government
(YF) and capital investment
purchase by all sectors of the
economy (Y1), thus,
Y = YF + Y1
(3) The capital matrix C is defined
as C = (csj) where cu is the
marginal capital purchase from
sector i by sector j, required to
expand the capacity of sector j
by one dollar of output. Thus,
if X0 is the total output in period
T0 and X\ is the total output in
period T,, the new investment
required is C (Xt — X0).
The objective is to find for
period t; the total output (X{)
and total final demand (Yj),
given the total output in period
t0, (X0) and the noninvestment
final demand in period tj, (Yjp).
The basic equations for the model
are:
and
These can be solved for total outpu
(*,) and total final demand
X!=(I-A- C) > ( Y!F
These can be used to investigate th
effect on investment Y1 and the tots
output X of changes in the growth rats
of components of YF.
Projections of alternative futures fc
some year involve the same GNP s
that meaningful comparisons can I
made.
Estimates for 1985 using this mod
were made using alternatives involvir
various energy growth rates both wi
and without the three new technologic
The projections were made with a G^
342
-------
of $1.34 trillion 1958 dollars for 1985.
Some illustrations of the results are
as follows:
• total investment becomes a larger
percentage of GNP especially with
high BTU gasification, however the
other two technologies tested actu-
ally decrease investment.
• output of coal mining with coal
gasification increases dramatically.
• total employment is nearly con-
stant.
These types of outputs lead to the
following types of conclusions:
• total investment in general and
capital good industries are quite
sensitive to energy use growth
rates.
• major impacts of introducing new
energy technology will be on the
capital goods industries.
• aggregation of demand for invest-
ment funds will occur with intro-
duction of high BTU coal gasifica-
tion, whereas the gas turbine top-
ping cycle will decrease demand
for funds.
The advantages of the input-output
approach to evaluating new technol-
ogies are apparent from the above con-
clusions which show that the interac-
tions with all sectors and factors of the
economy can be measured. The level of
detail is only restrained by the avail-
ability of data for the base years. Some
of the potential uses for the input-output
approach are as follows:
• Evaluating air quality standards
time tables in terms of what can be
done and at a reasonable cost.
• Evaluating the impacts of multiple
investment programs.
• Evaluating the impacts of alterna-
tive technological thrusts.
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Edward W. Erickson, Robert M. Spann
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1973, pp. 190 to 208.
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345
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Chapter 11
Models in Planning and Operating Health Services
By
Boyd Z. Palmer
SUMMARY 349
I. THE HEALTH SERVICES SYSTEM . 349
Introduction . 349
Health Services as a System . . 351
Performance Measures , . . . 353
II. NATIONAL POLICY MODELS . 354
National Policy . 354
Population Growth Policy . . . 355
Health Services Supply . 355
Delivery Systems Design 359
National Program Evaluation and Comparison 360
III. COMPREHENSIVE HEALTH PLANNING MODELS . . .361
Regional Health Planning Decisions 361
Adaptive Control Models . 361
Probability Models . . 362
Utilization Simulation Models . . 363
Econometric Models . 365
Mathematical Programming Model 365
Ill-Health Generation Models . 366
V. COMMUNITY HEALTH SERVICE ALTERNATIVES . 366
Community Health Service Decisions 366
Blood Bank Models . 366
Emergency Medical Care Models . 367
Planning Alcoholism Programs . . . . 367
Maternal and Infant Care Programs 367
Family Planning Programs 367
Narcotics Control Models . . 367
V. INSTITUTIONAL PLANNING AND CONTROL MODELS 368
Facility Planning and Control Decisions . 368
1. ASSESSMENT OF HEALTH SYSTEM MODELS FOR POLICY ANALYSIS . 368
Model Types Versus Level of Decision 368
Prognosis and Conclusion , 369
REFERENCES . 370
347
-------
-------
Models in Planning and Operating
Health Services
SUMMARY
This chapter reviews health services
models and concludes with a general
assessment of these models from the
viewpoint of decision-makers in health
planning or in health service organiza-
tions. The discussions emphasize the
modeling approaches taken, their devel-
opment stage and the performance
measures used, rather than specific
technical details of model construction
or data estimation. The basic question
to be examined is: "to what extent
have models been or can be used to
estimate future effects of alternative
proposals for improving health."
The chapter begins by reviewing dif-
ficulties of developing useful models of
health services and the general ap-
proaches that modelers have taken to
overcome these problems. Major prob-
ems noted include the lack of agreed-on
measures of health status, the lack of
3stablished relationships between re-
source use and health conditions, and
he large number of dimensions that
nust be built into any realistic repre-
;entation of health services.
The applications of models are re-
'iewed in three areas: Federal policy
ecisions; regional, state and area-wide
Janning decisions; and community
icalth service alternatives. Models are
Iso useful for institutional planning
nd control decisions and this opera-
onal use is surveyed briefly. These
reas do not exhaust the application of
lodels to health problems (for ex-
mple, there are many models of the
srvous system and the circulatory
'stem, diets, and biomedical research),
jt they should serve to give an over-
ew of the possibilities and problems
of the use of models to analyze health
system decisions with scope ranging
from community to national.
The Summary Table lists the more
important models discussed in this
chapter.
I. THE HEALTH SERVICES
SYSTEM
Introduction
Models of health services date back
to the early 1950's in the U. S. and
perhaps somewhat earlier in Great
Britain. Those early efforts were pri-
marily concerned with the application
of probability concepts to relatively
small portions of a particular health
service, such as a radiology department
of a hospital. More recently, several
factors have led to great interest in
analytic techniques that might help ex-
plain what happened as a result of past
actions, e.g. the introduction of Medi-
care, and predict what might happen if
proposed actions were to be taken, e.g.
national health insurance.
The need to analyze health systems
results from the emergence of health
services as a major, fast-growing sector
of the U. S. economy, the realization
that large groups of people receive in-
adequate care because of their inability
to purchase services, and the realization
that there is uncertainty as to even first-
order effects of Federal actions to al-
leviate maldistribution problems.
Several models have been developed
to estimate, on a national scale, effects
of Federal policy actions affecting sup-
ply of hospitals, training of health man-
power, changing the organization of
the health service delivery system, and
349
-------
HEALTH SERVICES
Models Discussed in Chapter
Summary Table
Model/Decision Area
General Type
Important Characteristics
National Policy Models:
Population Growth
Health Service
Health Services Demand
Delivery Systems
Program Evaluation and
Comparison
Dynamic feedback
Macroeconomic
Microeconomic
Simulation
Statistical
Mathematical
programming
Simulation
Statistical
Mathematical
programming
Comprehensive Health Planning:
Regional Health Planning Adaptive control
Probability
Demand and Supply
Health Services Impact
Utilization of Services
Vancouver and Quebec
Health Care System
Comprehensive Health
Planning Agency
Minnesota Health
Planning Agencies
Mental Health Services
Ill-Health Generation
Community Health Service:
Blood Bank
Emergency Medical
Alcoholism Program
Maternal and Infant
Care Program
Family Planning Programs
Narcotic Control
Simulation
Analytic
Deterministic
Statistical
Simulation
Econometric
Simulation
Simulation
Econometric
Econometric
Mathematical
programming
Simulation
Statistical
Inventory
Simulation
Statistical
Simulation
Probability
Simulation
Econometric
Simulation
Simulation
Probabilistic
Simulation
Analysis of long-term impact of popula-
tion growth and health policies
Evaluation of manpower programs, medi-
care, credentialling rules, hospital services
required for population and demand
alternatives
Estimate of demand for hospital care,
physician, etc.
Evaluation of HMO's, alternative health
delivery organizations
Analysis of disease control programs
Analysis of alternative actions, health
goals and objectives, estimate future
resource requirements
Estimate demand and supply of health
services and measure system performance
Evaluation of how a health services sys-
tem reacts to major shocks, e.g. disasters
Forecast of resource requirements
Study of health care system within total
social environment, evaluation of alter-
native resource allocations
Use by agency to forecast and evaluate
policies
Use by agencies to forecast and evaluate
policies
Analysis of alternative policies
Estimate of air pollution medical effects,
health service needs
Evaluation of management policies,
forecasting requirements, allocation of
supplies
Determine the location and number of
ambulances
Evaluation of alternative programs
Evaluation of effects of changes in
population or nursing staffs
Determine patient flow requirements for
budget estimating
Cost benefit analysis of alternative pro-
grams, analysis of the economics of
control programs
Institutional Planning and Control:
(No detail discussion given—see Section V for range of problems treated)
350
-------
enabling people to buy more services
through greater insurance coverage.
The advent of a legislative require-
ment for comprehensive health plan-
ning at the state and regional level has
led to the development of regional
health models. At the same time, model-
ing has continued as a technique to aid
institutional management, particularly
hospitals, to assist in the evaluation and
comparison of programs such as blood
banking, emergency medical services,
alcoholism, and tuberculosis treatment.
This chapter describes some of the
more important models developed to
analyze decision problems which arise
in the health services area. Before pro-
ceeding to example models, we first give
an overview of the health services
system.
Health Services as a System
In order to appreciate the difficulty
in developing models which depend on
visualizing health services as a system,
it is necessary to understand the com-
slexity of health services interactions,
and the lack of general agreement on
definitions and classifications.
Health services are now provided by
i variety of institutions, independent
practitioners, governmental and private
tgencies. The interactions among these
igencies are very loose, being con-
lected only by those processes which
:onnect any institutions within a so-
:iety: its economic markets, overall
,overnmental (executive and legisla-
ive) processes, and normal methods of
oordinating human activities. There is
ot, in any region, a central health
5rvices delivery, management or plan-
ing authority. Thus, health services are
laracterized by most health profes-
onals as a "non-system." The separate
;rvices are regarded as autonomous,
id the service providers have simply
/olved as the result of a variety of
irces, internal and external, acting
son them. The present "non-system"
so complex that it even involves
,encies with dual authorities, the prime
.ample being the separation of ad-
inistration and medical direction in a
hospital. Each institutional provider of
health service can make its own de-
cisions on which persons to accept as
patients, and which to refer to other
providers, without follow-up to see if
the referred people actually are ac-
cepted by any other provider. Each
provider can create his own data sys-
tem, using different classifications. Men-
tal health services are completely sepa-
rate from physical and dental services,
and personal health services are con-
sidered to be separate from environ-
mental health services. There are differ-
ent entry points and procedures among
providers, depending to a large extent
on location, e.g., urban, suburban,
rural; and on the financial resources of
the consumer available for health
maintenance.
These characteristics of health serv-
ices have posed formidable problems
to health system modelers, because
many potentially relevant model types
depend on defining the jumble of serv-
ices as a system, not in the sense that a
central seat of power exists that can
control (or manage) all services in the
system, but in the sense that health
services and the flows of people from
one service to another, can be defined,
measured, and analyzed. If health serv-
ices can be assumed to be components
of a system, traditional systems con-
cepts of input, output, capacity, proc-
essing, and system performance can
then be utilized, and a model con-
structed based on application of these
concepts to the decision area to be ana-
lyzed. A further problem confronting
health modelers is that suitable meas-
ures of health service system perform-
ance and data consistent with a systems
representation cannot be obtained. Per-
vading the whole analysis effort is the
dimensionality of the health area which
necessitates aggregation in the major
variables, and disregard of many rele-
vant variables, if the effort is to be at all
feasible.
Figure 1 illustrates the complexity
and dimensionality problems using the
common approach that health services
should be evaluated fundamentally by
351
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comparing demand (or need) with sup-
ply (or capacity). Assumptions incor-
porated into this figure are: (1) The
basis for relating supply and demand
is via services, the processes of provid-
ing health care; (2) The health services
system should include physical, dental,
mental, and environmental health serv-
ice activities; (3) The need for services
is created by the processes of living
which are outside the health services
system; (4) In general, need is not the
same as demand; the latter is created
when the perception of the need is
combined with recognition of an avail-
able, accessible source of help (serv-
ice); (5) The capacity for health serv-
ices must be created by providing the
proper combination of basic resources;
(6) Even the smallest geographic scope
of interest (a neighborhood) can in-
clude virtually the entire range of fac-
tors associated with demand for, and
supply of health services.
Most modeling efforts which attempt
to represent a broad range of serv-
ices (rather than institution specific
models) can be located on Figure 1 by
specifying geographic scope and the
demand and supply factors. Which par-
ticular factors are selected for repre-
sentation in a given model depends, of
course, on the purposes of the model-
ing effort and the decisions to be
analyzed.
In general the existing health models
have dealt with the problems of com-
plexity, lack of standard measures, di-
mensionality, and lack of data, in the
following ways:
• through use of a "non-system"
model (i.e. statistical regression
model), which does not require
consistent measures of input, out-
put, resources, and performance.
• through use of a system (formal)
model, with relatively few highly
aggregated variables, and using
hypothetical data values.
• by narrowing the scope, in terms
of services covered and/or geo-
graphic area, to a feasible system
which can then be modeled with
available, consistent data.
• by designing but not constructing
a detailed broad scope model to
show how problems could be ana-
lyzed if adequate data were avail-
able and measures used were ac-
ceptable.
All models do not fit neatly into
these groups; many are hybrids of sys-
tems and non-systems models, and many
use a scope just a little broader than
available data will fit, thus requiring
reasonable estimates of some of the
data. Just about all models narrow the
scope to either physical health services,
excluding mental and environmental
health services, or mental health serv-
ices alone, or environmental services
alone. Measurements to link service
utilization and resultant changes in
health conditions do not exist, so system
performance measures have to be de-
fined in other ways. In fact, the variety
of definitions of performance used in
models within the same decision area
is a major factor affecting the useful-
ness of the models for decision analysis,
and greatly hampers comparison of
models for such purposes. As measure-
ment of health services activities is
of such critical importance to the policy
maker, as well as the model maker,
we next review some approaches to
performance measures.
Performance Measures
These can be grouped into two gen-
eral types: outcome measures, which
concentrate on health status of people
using health services, and process
measures, which represent various char-
acteristics of the service process; we
discuss examples of each type in turn.
Data series which are used to meas-
ure health status of individuals are
usually built on states of disability.
Garfield [36] proposed a classification
of well, worried well, early sick, sick,
and very sick categories, so health serv-
ices appropriate to each category could
be assigned.
Torrance, et al. [110], conceptual-
ized a three dimensional disability state
measure, based on physical function,
emotional function and social function.
353
-------
A linear interval scale was proposed
with a value of 1 being equivalent to
"perfect health" in all functions, and a
value of 0 being equivalent to death.
Rather than define all disability states,
an index value based on this scale is
suggested. This utility index was used,
with hypothetical data, in a mathe-
matical programming formulation of a
health program ranking procedure.
Chorba, Miller, and Sanders [14] sug-
gest a "deprivation" index based on
time spent seeking health care, time
spent in bed due to sickness, and time
lost due to death before age 90. This
index was used in a model analyzing
tuberculosis program alternatives [15].
Blum [6] suggested a similar index for
use in assigning priorities to programs.
Fanshel and Bush [26] derived a dys-
function index based on ability to func-
tion in society. This work has been
further refined by Bush, et. al. [8 and 9]
in a Health Index Project at the Uni-
versity of California. Thirty status cate-
gories have been defined for evaluating
success of health programs. Success
means moving people into better status
categories. This approach results in a
single-valued health index; it has been
used in a model to evaluate tuberculin
testing programs [11].
Many variations of morbidity and
mortality measures have also been used.
So far, none of the proposed health
status measures have received the pres-
tige of official approval by professional
organizations nor general usage by a
large number of health researchers.
A common procedure in health
modeling is to use process measures, i.e.
calculate demands for services and sup-
ply of those services, and estimate "un-
met demands" by the difference. The
implied assumption is that all persons
who received services needed the serv-
ices and such persons gained improved
health status as a result. Thus, process-
oriented performance measures empha-
size utilization of services, rather than
improvement in health.
At this time, models which use proc-
ess-oriented performance measures or
none at all are predominant among
354
health models. They represent a feasible
compromise between the desire to build
models that can optimize health levels
using accepted measures of health, and
the known limitations of data now
available.
II. NATIONAL POLICY MODELS
National Policy
The economy of the United States
has traditionally operated on a "market"
basis which incorporates the concept of
price mechanisms. In the area of health,
these mechanisms mean that some
people are unable to buy services in the
main delivery system. A series of gov-
ernment actions has attempted to help
people purchase services, or to set up
alternative delivery systems. The Fed-
eral government has in the past chosen
to allocate an increasing amount of its
resources to increase the overall na-
tional supply of hospitals, mental health
centers, and physicians. It has provided
subsidies to encourage reallocating re-
sources and services to the elderly, the
young, and the disadvantaged, both in
the core city and in isolated rural areas.
As a result of continuing problems and
disagreement about the success of prior
actions, basic questions have arisen
about the proper role for the Federal
government in health. Some of the im-
portant questions are: Should the Fed-
eral government supply funds to build
hospital facilities? Should it support
categorical disease-control programs di-
rectly or by revenue-sharing? Should it
begin a national health insurance pro-
gram? If so, should such insurance have
limited or comprehensive coverage?
Should Health Maintenance Organiza-
tions be encouraged? If so, what type
of organization would give best health
care? Should the Federal government
actually operate any health services di-
rectly, or simply supply incentives to
affect market forces? Should basic re-
search in health services be increasec
or decreased?
Many alternative answers to these
questions have been suggested [35,58
63,102,113]. Programs adopted in the
-------
next few years will guide actions, fund-
ing, legislation, and regulations for some
time to come. We next discuss models
which address some of these questions
or which have a bearing in determining
national health programs.
Population Growth Policy
The broadest health policy question
to be supported by models is what
should be the rate of population growth
to produce the "best" health of the
population. Meadows, et al, [67] con-
structed a world model which included
one aggregate measure of health serv-
ices and its delayed impact on life ex-
pectancy. This model contains feed-
back processes, has only a few, highly
aggregated variables and uses estimates
of parameters. It computes values for
important variables many years into the
future. It is not intended for detailed
policy analysis; its main use is to indi-
cate the need for population growth
policies (among others) by demon-
strating the general impact of alterna-
tive values of the key parameters.
A similar type of model was used by
Kane, Thompson and Vertinsky [56], to
investigate aggregate effects over 25
years of three Canadian health policy
intervention strategies on population
size, mortality rate, availability (capac-
ity) of health services, total health ex-
penditures, level of diagnostic screen-
ing and the delegation of physician
functions.
The three intervention strategies used
were:
Policy A—"Fire-fighting." The model
assumed incremental ad-
justments in health service
whenever morbidity got too
high, expenditures got too
high, or availability got too
low.
Policy B—Maintain high availability of
health service. Two meth-
ods were used: (1) keep
population at zero growth,
and (2) increase facilities
and delegate more physi-
cian functions to para-
medics.
Policy C—Increase screening to detect
health problems. Screening
was tripled over the first
five year period, with no
further intervention there-
after.
Policies B and C amount to major re-
structuring of the health services sys-
tem. They are general policies which
would be realized by a multitude of
specific actions, each of which could be
done in alternative ways.
The model results showed that Policy
A was a "clear failure, giving very little
in return for its added expense," and
the others were also regarded as too
expensive. The only solution that might
avoid future financial crises would be to
alter the productivity of medical re-
sources.
Health Services Supply
The question which has attracted the
most attention from health service re-
searchers deals with the national supply
of health facilities and health man-
power: what is the current gap between
supply and demand, and how will the
gap change in the future? The most
common model form used to examine
such questions has been aggregated,
macroeconomic models, consisting of a
large number of equations designed to
explain variables expressing supply of
medical manpower and hospital beds,
utilization of physician time and hospi-
tal beds, and some prices, costs, and
government expenditures. Generally,
they estimate effects of past policy
changes and explain what has already
happened. Feldstein [27] developed
such a model to study the impact of
Medicare and make projections of pos-
sible future changes; see also [28] and
[94].
In 1969, the U. S. Bureau of Health
Manpower Education contracted for
pilot studies in the development of
microsimulation models (that is, de-
tailed simulations) for health man-
power estimation. During the summer
of 1970, a two day conference was
held to present and discuss results of
the designs. The two-volume proceed-
355
-------
ings of that conference constitutes a
basic reference for health manpower
modeling, and on microsimulation
models in general.
Volume One [121] presents an econo-
metric microsimulation approach which
was investigated by the Human Re-
sources Research Center of the Uni-
versity of Southern California. This
group also developed macroeconomic
models of the national health system
(Yett, et al. [124,125]). The research
effort conceptualized two highly com-
plex models, called Mark I and Mark
II. While most econometric models deal
with only one "population" (such as
health manpower), both I and II use
five populations: individuals, health
service institutions, health manpower,
health professions educational institu-
tions, and students. Using three compu-
tational modules, for health services,
health manpower, and health education,
the five populations interact in four
basic types of markets: for outpatient
services, inpatient services, manpower,
and training. This is diagrammed in
Figure 2. Mark II is a scaled down
version of I, but still involves hundreds
of equations.
The proposed use of these models
would be to concentrate on manpower
issues although other policy issues could
also be evaluated. The report discusses
ways in which the Mark I model could
be used to test changes in Medicare
coverage, introduction of new health
occupations (e.g. physician assistant),
and changes in credentialling rules (e.g.
education requirements in nursing pro-
grams). Neither model can handle
issues about geographic maldistribution
of services, and neither includes dental,
mental or environmental services.
Volume Two of the proceedings pre-
sents a probabilistic microsimulation
model developed by the Research Tri-
angle Institute (RTI) [48]. RTI was
required to produce a working model,
using whatever data they could find.
This led the RTI researchers to con-
centrate on the hospital portion of the
health system. Figure 3 shows a dia-
gram of the more complete model de-
HwlthSwvlcw Modulfi
Hutth Education ModuU
Source: Yett, et al. [121] "Conceptualization of a Health Manpower Simulation Model"; Vol. I
of Proceedings of Conference on a Health Manpower Simulation Model, HEW, NIH,
Dec. '70; Page 29.
FIGURE 2—Basic Structure of the USC Micro-Simulation Model
356
-------
Population
Generation 1
and |
Projection |
1
u.
Initial Population Generation
\
f
Vital Events Generation Over Time
Simulated Population
Generation
of Health
Demand
Health Need Generation
Conversion of Health Need
to Demand for Services
Demand for Health Servicss
id
Demand Allocation Submodel
Hospital
Submodel
Health .
Services I
Jtilization I
Extended
Care
Submodel
JL
Group Practice
Submodel
Private
Practice
Submodel
£
Integrating Submodel
I
Health Services Requirements
Personnel and Facilities
Source: Horvitz, et al. (48] "Methods for Building a Health Manpower Simulation Model",
Vol. 2: Proceedings of Conference on A Health Manpower Simulation Model, HEW,
NIH, Dec. '70, page 49.
FIGURE 3—Health Care Demand System Model
357
-------
sign rather than the actual programmed
model which considered only hospital
services and hospital manpower. The
uses of the model centered on measur-
ing variations in requirements for hospi-
tal services when population distribu-
tions and demand estimates changed.
The differences between the micro
and macro approaches, at least using
econometric models, is discussed in a
relatively non-technical article in Yett,
et. al. [122], which compares the Mark
I model with a macro model for re-
gional planning.
A continuation of the above efforts
developed a scaled down, but opera-
tional version of the Mark II model,
Yett, et. al. [123]. This represented
a significant achievement in data as-
sembly and econometric analysis and
has the potential to be a useful econo-
metric model of the health services
system. While the model has not as yet
been used for prediction purposes, the
current version demonstrates that it is
possible to obtain an integrated working
representation of services, resources
supply, consumer demands, and market
prices, within the constraints of avail-
able data. Figure 4 shows a block
CONSUMERS
age
sex
race
Inco.ne
condition (diagnosis)
jTiarkets for pc*tfent visits
[ Deraands for non-phys ician manpower j
7)
PHYSICIANS
age
special ty
act ivi ty
U.S. or foreign graduate
V
\
HOSPITAL SERVICES
[Demands for patient days
Markets for patient days
"".; i —-
Supply of patient days
—~ i
ZX 1
non-physician manpower!
HOSPITALS
ownership
size
length of stay
Markets for non-physician
manpower
Supply of non-physician
manpower
NOM-PHYSICIAN MANPOWER
Registered Nurses (by age)
Licensed Practical Nurses
Allied Health Professionals
Other Personnel
Source: Yett, et al., [123] "The Preliminary Operational HRRC Model" Human Resources
Research Center, U. of So. Cal., 1973.
FIGURE 4—Block Diagram of the HRRC Microsimulation Model
358
-------
diagram of this model, which is com-
posed of 5 sub-models.
The first submodel generates a popu-
lation of consumers or individuals who
demand medical services. It estimates
the nation's annual population sub-
divided into cells according to the at-
tributes age, sex, race, income, and
condition or diagnosis. The three major
events which change the overall popula-
tion are birth, death, and immigration.
The second submodel generates a pop-
ulation of physicians, providing annual
estimates of the supply of doctors, sub-
divided into cells according to their
age, specialty, and type of professional
activity. The physician services or third
submodel computes: (i) the demands
(by each consumer group) for patient
visits with physicans in private practice
and on hospital-based clinics; (ii) the
supply of patient visit capacity provided
by doctors in office-based practice; and
(iii) the doctors demands for aides
(i.e., non-physician manpower). The
fourth submodel computes the demands
for patient days at short-term and long-
term hospitals, and the fifth submodel
computes the supply of non-physician
manpower. The solution procedure bal-
ances the variables among the sub-
models for each period (year) of the
simulation.
Many other econometric models re-
lating to health services have been de-
veloped. A review of the economic
factors used in projecting requirements
for health manpower is given in Klar-
man [59]; Yett, et. al. [125] contains a
comprehensive review of economic re-
search studies covering many aspects of
the health service system. However,
most of these studies are difficult for
non-economists to understand, and do
not directly relate to public policy de-
cisions. For example, Grossman [40]
investigated the demand for health,
rather than health services, and used
1963 survey data from the Chicago
based National Opinion Research Cen-
ter to estimate coefficients of his econo-
metric equations. He treats good health
as a commodity; specifically, as a "dur-
able good" that depreciates over time,
but can be increased by investment in
medical care. The analysis can then
compare investments in health care in
relation to other investment opportuni-
ties, such as in housing, recreation, and
good. The purpose of the study was to
develop a theoretical, model and test it
with empirical data. No predictions re-
lated to public policy were contem-
plated. But the understanding gained
about the relationships between health
levels and medical expenditures may
prove of value to future work in econo-
metric modeling of health problems.
Non-economic approaches to estima-
tion of health services have also been
developed. Navarro and Joroff [76]
studied the distribution of physicians in
the urban areas of the U. S., using
statistical multi-variate analysis. Wirick
[118] used a statistical model to esti-
mate demand for hospital days of care,
physician visits, dental visits, expendi-
tures for prescribed medicines, and ex-
penditures for other medical expenses.
Finally, the impact of changes in
several Federal political policies in
hospitals was investigated statistically
by Jaeger [51]. Availability, accessibil-
ity, cost, financing, manpower, effi-
ciency, and quality measures were used
as dependent variables, with fiscal
policy, discrimination "policy," popu-
lation growth, education, and economic
ability used as independent variables.
The concept of the model, and the
measures used, are of interest; numeri-
cal results proved inconclusive and of
little value for policy makers.
Delivery Systems Design
There are strong indications that the
real problem of health care in the U. S.
is not the demand-supply relationship
(which might be stabilized by increas-
ing capacity or even by decreasing de-
mand), but the way in which health
care is organized. For example, Glazer
[37] and Joyce [55] examine paradoxi-
cal evidence which indicates that there
may already be a sufficient supply of
health care. The evidence, based on
wartime depletion of medical man-
power, shows that a direct relationship
between supply of physicians and mor-
tality rates cannot be established. Gar-
field [36] examines health service
utilization differences between pre-paid
359
-------
care (Kaiser-Permanete Plan) and fee-
for service care, showing fewer physi-
cians can handle more people in al-
ternative organizational arrangements.
Lewis [63] advocates different organiza-
tional delivery systems to eliminate ex-
cessive duplication of services.
Delivery system policy questions in-
clude: What if we changed the or-
ganization? What should it be changed
to, and what can we predict about the
effects? Will Health Maintenance Or-
ganizations (HMO's) improve the situ-
ation? To answer these questions we
would need a model whose design
does not depend on existing patterns of
delivery, but allows representation of al-
ternate systems.
Many models have been formulated
around this problem, though none have
attempted to represent the general de-
sign problem. We cite four such
models:
Schemer [97] formulated a non-linear
mathematical programming model to
search for an optimal size for a group
practice. Schneider et. al. [100] investi-
gated design of HMO's as mathematical
programs in terms of three measures of
effectiveness—(1) minimize cost to the
subscriber, (2) minimize the number
of professional manpower to serve a
given set of subscribers (and maintain
quality), and (3) maximize services
provided by a given set of professionals;
these require integer solutions. The re-
search effort did obtain enough data
to compute an illustrative output, and
more analysis will be forthcoming.
Schuman, et. al. [103] developed
an integer-mathematical programming
problem for a hypothetical neighbor-
hood health center and expressed the
problem as one to determine the mix
of personnel and services, the level of
technology, and the amount of con-
struction and community resources
necessary to minimize the total "cost
to society" of providing health services,
subject to the constraints of quality of
service, service requirements, available
personnel, capacity of facilities, finan-
cial considerations, and relationships of
personnel and services. Milly and Po-
360
cinki [69] developed a simulation model
based on service-treatment stations; it
will be used to evaluate alternative de-
livery system designs for neighborhood
health centers, medical group practices
and cooperative pre-paid group delivery
systems.
None of the above models are able
to incorporate health status measures
in any explicit way. In the models,
people arriving at services require re-
sources. Their various diseases and dis-
abilities are represented as, demands for
particular services. Only the Milly and
Pocinki approach seems, at this time,
capable of including other considera-
tions such as patient satisfaction, and
some connection with morbidity and
mortality in the population served.
National Program Evaluation and
Comparison
Two related policy problems are
health program evaluation and health
program comparison. Evaluation is a
retrospective analysis of an existing
health program to see if the effects pro-
duced by the input of resources justi-
fied, in some sense, the cost of those
resources. Program comparison can ap-
ply either to a comparison of two (or
more) program evaluations, to see if
one program produced more effect than
others for the same relative resource
input; or to predict for several existing
and/or proposed programs, which ones
should produce the most effect per dol-
lar, and thus help policy makers decide
on priorities for program expansion or
development when funds cannot sup-
port all programs. In addition, the de-
sign of a single new program may re-
quire comparisons of effects at different
levels of funding, [18,39]. An important
program evaluation effort was the HEW
analysis of selected disease programs,
which was designed to answer the
policy question: "If additional money
were to be allocated to disease control
programs, which programs would show
the highest payoff in terms of lives
saved and disability prevented per dol-
lar spent?" Grosse [39]. The resulting
estimates and background analyses have
-------
influenced HEW allocations since 1966
[114]. For example, they helped in
setting a high priority on educational
activities to convince people to wear
seat belts in motor vehicles.
The Indian Health Service con-
structed a "Q index" to determine pri-
orities among several problem areas
Miller [68]. The procedure was de-
signed to put high priority on health
conditions that tend to reduce total time
lost due to the health problem, includ-
ing lost time due to early death. The
index tends to assign highest priority
to accidents, because so many happen
to children.
Levy [62] collected a set of operating
data on the Illinois mental health pro-
gram to determine if sufficient data
could be acquired to evaluate the pro-
gram. This led to the need for measur-
ing the "quality of life" of discharged
patients, but this relies on indirect evi-
dence given by available statistics, i.e.
the patient did not come back.
A complex program evaluation
model, specific as to tuberculosis pro-
grams, was designed by Chorba and
Sanders [15]. Benefits were calculated
primarily from program savings result-
ing from prevention and early cure, so
that expensive later treatment would
not be needed.
As part of an ongoing Health Index
Project (Bush, et al. [8,9]), a mathe-
matical programming approach was de-
veloped by Chen and Bush [13] for the
selection of health programs. This in-
cluded budgetary constraints, specific
programs and in effect selected people
for program treatment so as to mini-
mize the time people would spend in
highly dysfunctional health status
categories.
A mathematical programming model
was also used to choose "best" actions
in another specific health program, that
of family planning, Correa and Beasley
[17]. The measure of effectiveness was
he difference between actual and de-
sired children per family, and the
'ormulation included six contraceptive
methods and the costs of providing the
sontraceptives and doctor visits.
Correa [16], also demonstrated the
use of mathematical programming in
allocation of national resources toward
either preventive care or curative treat-
ment. Results suggested that all uncom-
mitted resources should go into preven-
tive services, to minimize death and
disease.
III. COMPREHENSIVE HEALTH
PLANNING MODELS
Regional Health Planning Decisions
The policy questions associated with
regional (State and local) planning, in-
clude: maldistribution of health re-
sources; unmet need for particular
health services; specific problems such
as infant mortality and air pollution;
optimum utilization of present services;
and state credentialling of manpower
and certification of facilities and
services.
There have been a few models de-
signed specifically for regional planning
use. Because of a lack of data, and
lack of an organizational focus for the
user of a model, such models are ex-
perimental at best. The models are
used to speculate on how policy ques-
tions could be handled if proper data
could be developed and if funds were
available to convert the model design
into operating reality. The designs are
generally simulation models, rather than
the econometric national policy models.
The discussion of models below is
organized by main headings of model
type, e.g. econometric, with related
problems discussed in each section.
Adaptive Control Models
Adaptive control models which could
encompass all health services in an area
would logically seem to fit planning
needs better than other model types;
their application to health services has
been discussed by Howland [49 and
50]. One of the most important features
of adaptive control models is the con-
centration on information needed for
decisions.
Figure 5 shows the conceptual ele-
ments of a control-oriented model. As-
361
-------
sumptions include: (1) a comparison
of input and output is made, to see
what changes have occurred as a result
of using the services; (2) the results
of the comparison are used by a regula-
tion function, which can then make ad-
justments to the system activities or sys-
tem resources; and (3) the comparison
of input and output is guided by objec-
tives derived from goals. Thus, this
representation assumes that the plan-
ning function can influence system per-
formance by regulating the health sys-
tem processes, or by changing the sup-
ply or resources.
Palmer, et al. [83] presents a plan-
ning system within which a model of
the entire health services system would
be useful. The planning system as a
whole is considered to be an adaptive
control system, with objectives serving
as the basis for comparing actual data
with desired results. Projects, persua-
sion, and recommendations for legisla-
tion become the control actions. The
model would be used to predict the
effects of the control actions, recogniz-
ing the long time lag before measurable
effects can be expected.
Probability Models
The probability approach separates
a population into different categories,
and calculates how transitions will oc-
cur among the categories from one
time "snapshot" to the next. This ap-
proach has been described by Navarro
[75] and [77], Schach and Schach [96],
Newheiser and Schoeman [78], and
Nakamura [74], To some extent, the
models of disease development dis-
cussed by Bush, et al. [10], and Ortiz
and Parker [80], and also the model
of epidemic contagion by Thomas
[107], could be considered in the re-
gional planning context, even though
the models do not include specific health
resources. The next two paragraphs de-
scribe some of the approaches to defin-
ing the probabilities of transition.
General Health Status Categories.
These models incorporate probabilities
SOCIETAL
( Knowledge about GOALS
conditions that
create health
problems
J
1 Characteristics of
people entering
I
1 INPVI
(ie., people
with health
problems)
\
1
HEALTH SYSTEM •** ~™~ "X
SERVICES' *• "~*~ OBJECTIVES \ ""^ ,
SYSTEM 1 | (
1 1
X' PLANNING &
COMPARATOR: REGULATING
Input vs output _—--""" FUNCTION
process vs 1
objectives "• " ~ — _ _J_
f T--~
1 Characteristics of 1
HEALTH SERVICES SYSTEM
Components, Services, Activi
\?sv/\r^'
— — — 0 » ENVIRONMENT
^ , HE« HEALTH
SERVICES
"*~" ^~*~ ~"™" *' RESOURCES
/ ^\ Chacactetistio o£
j X people who used
ties \
__^ OUTPUT \
^^ (Ie.» people
who have i
received health /
services) I
., 1
Resources, inputs, outputs
Information
Control activities
FIGURE 5—Simplified Adaptive System
362
-------
of transition from one health state to
another. Palmer [82], attempts to do
this by postulating three sets of transi-
tion probabilities: one based on no
health services being received, one
based on "ideal" care being received,
and a third based on actual services
received, which is usually somewhere in
between "no care" and "ideal care."
Papell and Crocetti [84] assign people
to "risk categories" which are close to
general health status categories, but are
primarily designed for an ambulatory
care service.
Health Services Categories. This
method of classification estimates the
distribution of people receiving various
health services at a given time. The
probability estimates are for transi-
tions to a different type of service be-
tween time periods. Navarro [75] used
6 medical care categories for a regional
population: not under care, primary
medical care, consultant medical care,
hospital care, nursing home care, and
domiciliary care. These "utilization"
probabilities were used to estimate re-
source requirements for each type of
care. The concept was extended to age-
specific probabilities, decreased number
of care-categories, and shortened time
intervals, Navarro, et al. [77]. This for-
mulation was simulated to obtain annual
averages over a ten year period. Schach
and Schach [96] used the same ap-
proach to estimate the averages and
standard deviations of resources needed.
The need in turn was based on the
distribution of people using each type
of health service.
These formulations still do not cover
the full range of health services; mental,
dental, and environmental are left out,
as well as preventive and promotional
activities. The distribution of services
has not been represented either. The
emphasis is basically an estimation of
future resource requirements, assuming
past utilization rates will continue to
change in line with past trends. Data
problems are almost insurmountable
with probability models, even with ag-
gregated categories.
Utilization Simulation Models
Zemach [126] has designed a simula-
tion model to combine the many factors
related to production, utilization, and
cost of health services. The model may
be used to simulate a few proposed
changes in the health system, if esti-
mates on changes in utilization rates
can be provided. By estimating future
population, a forecast of resource re-
quirements can be derived, assuming
the utilization units per person and re-
source-service relationships remain
about the same. The linkage to changes
in health status as a result of resource
useage is not included. Mental and en-
vironmental health services are not
modeled.
The California State Office of Com-
prehensive Health Planning has de-
veloped a deterministic procedure for
computing demand and supply esti-
mates for health services (California
[12]). A Personal Health Services
module computes people who will be
attended by health services, a Com-
munity Health Systems Analysis module
computes the health system capacity,
and an Evaluation of Community
Health System module will compute
various measures of system perform-
ance, including impact on health status.
This model represents an ambitious at-
tempt to relate data from many sources
into an integrated framework. Much
of the data is being derived from a
1964 study of a pre-paid group health
plan in New York City, Avnet [4], and
National Health Interview data. The
model is very much disease-oriented
and excludes dental, mental, and en-
vironmental services.
A model using a combination of
model types has been developed by
Richie, et al. [90] and [91], and a varia-
tion has been described by Lawless and
Richie [60]. The overall procedure uses
a regression analysis to predict entry of
people into the health care system,
by estimating initial visits for each of
nine age groups. A simulation proced-
ure then estimates useage of inpatient
and outpatient care, to produce re-
source useage data. A series of equa-
363
-------
tions then determines costs and com-
pares resources needed against known
resources available to identify short-
ages. The model is shown in a simpli-
fied flow chart in Figure 6. The pro-
cedure was originally designed to study
effects of sudden "shocks" applied to
the health services system, such as
epidemics and disasters. The supply-
demand estimates would be about in
balance under normal system condi-
tions (especially since the regression
equations use past data). The major
interest would lie in the supply short-
ages to be expected under sudden,
unusually heavy demands on services.
Work with the model has placed more
emphasis on estimates under normal
conditions, and suggestions have been
made to use the model to gauge the im-
pact of national health insurance,
HMO's use of paramedical personnel,
and other proposed changes.
A group at the University of British
Columbia developed an aggregate simu-
lation model of the health care system
Physician
Public
Policy
(expenditures)
Simulated
Crises
1
Supply
DEMAND PREDICTIONS
Initial
Visits
(outpatient)
Population
DemoKrachv
Health
Medical
Experience
SIMULATION OF
PATIENT-SYSTEM INTERACTION
Current
System
Occupancy
isti
Exiting
System
Structure
Physical
Constraints
1 1
Public
Policy
(proposed
system
revisions)
Allocated
Resources
Medical
Prognoses
ECONOMIC ANALYSIS
Cost
Source:
364
T Including
cost of
noneffectivaness
Richie, et al. [91] A Model for Health System Parametric Studies and Utilization Pre-
dictions, mimeo paper, Texas Hospital Assoc.
FIGURE 6—Health Services Simulator Model
-------
in Vancouver, Canada (Milsum, et. al.
[70]). While the Canadian health serv-
ices system is very different from the
U. S. system in many respects, the
project is worthy of note because the
health service model was built for re-
gional planning purposes and is a part
of a larger modeling effort designed
to include other systems such as trans-
portation, land-use, and education. In
addition, the model includes a scale of
social impact as a method for gauging
psychological effects of not providing
health services when people need (or
want) them. The model simulates
people in various disease categories,
with a seriousness of illness rating scale
constructed from 126 diseases. The
general idea is that available resources
are considerably short of demand, so a
conscious effort is needed to allocate the
available resources to high priority
health problems, as derived from the
seriousness scale. The social impact
scale is then used to estimate the effect
in terms of cases not treated. By build-
ing the health planning model as a part
of a larger model, a simulation run
could show the effect that changes in
external environmental conditions have
on health. By simulating for future
time periods, the value of preventive
services can be demonstrated.
The health portion of the overall
Vancouver model is being adapted for
the province of Quebec (Quebec [86]).
Development efforts are now in prog-
ress to use data being generated as
part of a new Quebec health care de-
livery system. Disease-specific data
should eventually include virtually
every transaction between individuals
and health care providers. Initial model
computations have been limited >o in-
surance data which shows the use of
physicians and hospitals by disease cate-
gory. While the model does not include
dental, mental, or environmental serv-
ices, vital questions on hospital planning
and delegation of duties to paramedi-
cal personnel are being simulated.
Econometric Models
An econometric model has been de-
veloped specifically for the use of
Comprehensive Health Planning agen-
cies at the areawide (sub-state) and
statewide levels, Yett, et al. [120], The
model requires data for over 100 varia-
bles as well as some familiarity with
econometric concepts and techniques.
The general plan is to provide to Com-
prehensive Health Planning Agencies
the model with a manual describing
how to use it for forecasting and policy
purposes. The model does not include
dental, mental, or environmental health
services, nor a measure of health status.
Another econometric approach to
modeling a regional health system was
developed by Davidson and Dahl [19]
for the Minnesota Comprehensive State
Health Planning Agency. Data from
1970 were obtained for 86 of Minne-
sota's 87 counties (the county contain-
ing the Mayo clinic was omitted to
avoid distortion). Forecasts for 1975
and 1980 were computed under several
assumptions. Major results were the
estimates of requirements, by county,
for health manpower, as well as esti-
mates of patient days in hospitals, out-
patient clinic visits, emergency visits,
patient days in nursing homes, primary
care physicians, and secondary care
physicians.
Mathematical Programming Model
A model of a state formula for financ-
ing mental health services in New York
was successful in analyzing related
policy problems, Bodin, et. al. [7]. The
amlysts worked closely with state legis-
lators to incorporate politically feasible
value- of county contributions in a
shared-funding formula. The analysis
produced an alternative proposal to one
already in committee. The model was a
mathematical program with a non-
linear (quadratic) objective function. It
used an optimizing criteria based on
minimizing the deviations of projected
future county expenditures from pres-
ent expenditures, i.e. do not let the
deviations vary too drastically or politi-
cal feasibility will be impaired. While
the close association between the
analysts and the legislators produced
a politically feasible analysis, the scope
365
-------
of the problem was extremely narrow.
Alternatives for treating the mentally
ill were not included in the analysis.
Ill-Health Generation Models
Two other models should be men-
tioned in connection with regional plan-
ning; one because of the attempt to re-
late environment conditions to changes
in health, and the other because of the
use of a different modeling technique.
The Environmental Systems Group
at the University of California at Davis,
Watt [116], has been developing a
Model of Society, simulating the Cali-
fornia air pollution environment. It
computes expected medical effects on
the population, as well as on plant
growth, agriculture and meteorological
conditions. The model does not include
the health services system; it models the
extreme lefthand portion of factors
shown in Figure 1, the generation of
ill-health conditions. In an associated
study, Hickey [46] used a correlation
analysis to associate air pollutants with
chronic diseases and found strong evi-
dence of such association.
Anderson [3] also studied the illness-
generation factors and constructed a
model of health services which included
many demographic variables associated
with poor health based on data from
the 32 counties in the state of New
Mexico. A form of statistical regression
model, called path analysis, was used
which depends on hypotheses concern-
ing the direct and indirect effects of the
variables on health delivery and on the
health status of the population. Results
showed that hospital beds per 100,000
population appears to have a small posi-
tive direct effect on the mortality index;
per capita income appears to have a
negligible effect on health; and un-
employment has a large direct effect on
the mortality due to accidents, on sui-
cide, and on cirrhosis of the liver. Since
the variables used are not considered
controllable by the health services sys-
tem, the results are difficult to use in
giving guidance to health planners.
366
IV. COMMUNITY HEALTH
SERVICE ALTERNATIVES
Community Health Service Decisions
Community health problems include:
rat control, alcoholism, narcotics addic-
tion; service delivery problems include:
maternal and infant care, emergency
medical care and ambulance services,
coronary care, food sanitation, and
blood bank inventory control. These
problems require coordination of a
variety of agencies in developing al-
ternative solutions. The alternatives are
sufficiently narrow so that modeling is
quite feasible. Many health problems
at the community level have rather well-
defined treatment actions that can pro-
duce measurable effects. Once a re-
sponsible group in a community has
either already started a program, or
has determined that a health program
action is needed, models can be used
to choose among alternative actions, to
monitor an on-going program, or to
evaluate prior programs.
This section discusses briefly some
of the models used in analyzing com-
munity health service program alterna-
tives.
Blood Bank Models
Analysis of blood banking procedures
are necessary due to the problems of
shelf-life, cross-matching, and the impli-
cations of a blood shortage or errors
in matching.
Rabinowitz and Valinsky [87] con-
structed a simulation model of an indi-
vidual hospital blood bank, keeping
track of 8 different blood types and in-
corporating the reservation policies
actually in use. The model was used
to test policies for managing the in-
ventory. Frankfurter and Pegels [34]
constructed a blood inventory forecast
model for a hospital, based on past dis-
tributions of useage by day of week,
and other variables. These models are
used to aid blood bank managers in
ordering and assigning units of blood
within individual hospitals. Jennings
[53, 54], Jelmert and Pegels [52], have
modeled a distribution center responsi-
-------
ble for allocating daily supplies to par-
ticipating hospitals, and policies related
to inter-hospital transfers of blood.
Pegels and Jelmert [85] applied a prob-
ability analysis to calculate average
wastage rates and average life of an en-
tire city's inventory.
Emergency Medical Care Models
Emergency medical care systems
have been modeled primarily by simula-
tion. Typical decisions supported by
models are the optimal number of
ambulances to cover a service area
(given probabilities of emergency inci-
dents) and the optimal location of the
ambulance dispatch centers so as to
minimize response time to the scene of
randomly occurring emergencies, New
York City (Savas [95]), Detroit (Hall
[42, 43]), and Los Angeles (Fitzsim-
mons [32, 33]). Stevenson [104] de-
signed an analytical probability model to
study the use of less efficient auxiliary
vehicles when primary vehicles are all
in use. A detailed simulation model of
the total emergency medical service
from time of injury to time of release
from the emergency medical facility
was developed by Hare and Wemple,
[44].
Planning Alcoholism Programs
Holder and Hallan [47] describe the
use of a simulation approach in plan-
ning alcoholism programs in 20 coun-
ties of North Carolina. The project
identified ten intervention points for
dealing with problem drinkers. Pre-
liminary simulations were used to guide
establishment of potentially effective
programs. Performance was judged by
changes in personal drinking behavior,
as measured by data collected on clients
served during 4 two-month periods.
Maternal and Infant Care Programs
Kennedy and Woodside [57] describe
a maternal and infant care (MIC) simu-
lation model. It was used to evaluate
effects of changes in population or nurs-
ing staffs on project operations in three
North Carolina counties. Four regres-
sion equations were developed to pre-
dict the number of visits a mother
makes to the prenatal clinic and the
number of infant illnesses. The link
between needs and resources was based
on the time required of all resources
in the clinic to care for a patient. Initial
data were obtained from an MIC clinic
and the model was then tested against
data from other clinics.
Family Planning Programs
O'Connor and Urban [79] reported
on a model of patient flow in family
planning programs in Atlanta, Georgia.
The analysts worked with directors of
family planning services to define spe-
cific flow patterns, data and costs in the
model. By participating in actual build-
ing, program directors understood the
model and the necessity for appropriate
data. Projections obtained using the
model aided in annual budget discus-
sions.
Narcotics Control Models
A cost benefit analysis of various
programs for treating heroin addicts
was constructed by Maidlow and Ber-
man [65]. The model evaluated two
main programs: the therapeutic com-
munity as an abstinence approach, and
methadone maintenance as a substitu-
tion approach. Direct costs, maximum
benefits (if everyone were cured) and
probabilistic net benefits (adjusting for
drop-outs) were calculated for each
treatment program. Most of the benefits
were due to addicts refraining from
stealing to support the habit.
A feedback model was used by Levin,
et al. [61] to simulate the economics of
narcotics control programs. This model
searches for stable conditions among
the supply, addict-population, and other
variables associated with narcotics ad-
diction problems. Results from the
model suggested that a variety of com-
munity response actions would be best;
i.e. police response without rehabilita-
tion and education drives up prices and
increases crime proportionately; re-
habilitation alone leaves a tempting sup-
ply to reinfect the addicts; and com-
munity education alone is simply in-
effective. Only if all three program
responses are used does the model show
367
-------
some stability of conditions after a
3-year period.
V. INSTITUTIONAL PLANNING
AND CONTROL MODELS
Facility Planning and Control
Decisions
The planning decisions which are
concerned primarily with an institution
as a whole can be grouped into cate-
gories. The categories with references
to models developed for these areas fol-
lows. As we will not describe these
models, the reader is referred to [105]
for an overall review.
1. New Facilities:
(a) Design decisions—how does
architecture and layout of the
physical plant affect hospital
efficiency and patient care? [20,
22,23,92,93, 111, 117]
(b) Location and size decisions—
where in a given geographic
area should new facilities be
built? Should one large facility
be built, or several smaller
ones? [1, 24. 38, 71, 72, 99,
101]
2. Existing Facilities:
(a) Overall efficiency: management
control decisions. [5, 21, 29,
30,31,66,89, 109, 112]
(b) Patient admission decisions—
how should elective admissions
be scheduled, when combined
with stochastic elements of
emergency admissions? [108]
(c) New services decisions—how
would addition of a new inten-
sive care unit, for example,
affect operations of a hospital
as a whole? [25, 41]
(d) Staff assignments and bed-use
decisions—how to allocate staff
and beds to improve service
and use skills most effectively?
[115, 119]
(e) Department/Clinic workload,
staffing, inventory, and schedul-
ing decisions. [2, 45, 64, 88,
98, 106]
368
VI. ASSESSMENT OF HEALTH
SYSTEM MODELS FOR
POLICY ANALYSIS
Model Types Versus Level of
Decision
The preceding sections show that
many health models have been devel-
oped at each decision level. No one
model type has been determined to be
best for any given decision lev el. Rather,
researchers with a particular way of
viewing the health care system have ap-
plied familiar methodology to their
areas of interest. For example, staff
of the Johns Hopkins University have
been the source for many probability
models of institutional problems, with
extensions to community services and
then to areawide planning. Work from
the Research Triangle Institute has ap-
plied simulation models to institutional
and community services, with extension
to national health manpower decisions.
A group at the University of Southern
California has specialized in econo-
metric models of the nation's health
services and manpower policies, with
extensions to regional planning, while
researchers at the Massachusetts Insti-
tute of Technology are working on
feedback models of large scale systems,
with applications to health care systems.
Many individuals, as noted in the previ-
ous sections, have also pioneered and
applied specific models to the health
area.
Our general assessment of models in
the health services field is, however,
that most of the modeling efforts are
used infrequently or not at all by the
appropriate decision makers. Although
no specific answer can explain the gap
between model developer and policy
maker, we offer the following com-
ments.
The insights and understanding to be
gained in the building of a health model
are valuable in themselves. Researchers
have constructed econometric models
partly, if not mostly, to gain an under-
standing of economic market forces
that have been at work to produce the
current pattern of physicians, nurses,
-------
hospitals, prices, and government ex-
penditures. Others have constructed
detailed simulation models of hospitals
and nursing homes at least partly to
understand how the work tasks of em-
ployees, such as nurses, affect the over-
all profits and output of the institution.
This may help explain why some model-
ing efforts do not get beyond the de-
sign stage: the modeler already gained
enough of the understanding he was
after, and foresaw too many data prob-
lems to justify further work.
There are serious measurement limi-
tations in health models as there is no
agreed upon measure of health status
that can summarize physical, dental
and mental health conditions. An ac-
cepted overall measure of health would
help modeling be more useful in policy
decisions.
The objectives of most of the models
have been specified by the modelers,
rather than by policy makers. The
policy makers must be involved in the
analysis if they want useful results. In
health this means decision makers from
HEW to County Health Departments.
Also, in the health field (as well as in
other social fields) data are not col-
lected in consistent categories suitable
for model use. There is no data at all
for many variables and parameters that
must be specified. Models tend to
build-in the present system and are
therefore difficult to use in predicting
effects of major changes in that system;
some policy questions arise because
there is a suspicion that past relation-
ships should change. Proposals, such
as national health insurance and HMO's
are advanced concepts which should,
if successful, substantially alter the en-
ire health services system. Further-
nore, as the Swedish economist Myrdal
73] points out, parameter estimation
lepends on the time period chosen, the
)opulation included and the geographic
irea encompassed. Parameter estimates
ire not constant over time or area.
'herefore, a prediction of effects using
nodel parameters derived from past
elationships can be inaccurate at best
nd may be highly misleading.
Prognosis and Conclusion
Are any limitations so serious that a
person in a position of real responsi-
bility should not even consider using a
model and its results as major guides
to health legislation, planning or operat-
ing decisions? There are many current
efforts which will substantially reduce
some of the limitations. For example,
research on health status measures will
probably produce a useful, generally ac-
cepted measure of health condition.
The Federal-State-Local Cooperative
Health Statistics program will eventually
standardize data definitions and cate-
gories, and produce data useable in
models. Problems of inadequate objec-
tives and semantics can and must be
overcome by establishing closer liaison
between modelers and policy makers.
It seems that health system modeling
will continue and even expand, mostly
as part of academic studies. The utility
of health models as policy analysis
instruments will depend on developing
a rapport between analyst and persons
in responsibility, probably requiring
new organizational arrangements. The
flavor of what will be needed has been
suggested by Dr. Charles D. Flagle, as
given in Horvitz, et al. [48]:
"Our pediatric clinics simulation
model is one in which the resident who
runs the clinic sits at the computer ter-
minal and decides experimentally
whether he wants four doctors or five in
a simulated morning session, or decides
whether he would like to have only a
walk-in clinic instead of walk-in and
scheduled clinic or decides to see what
would happen if some day twice as
many people come in. The simulation
model demonstrates the effects of his
decisions in terms of delays and con-
gestion.
"The point is from the time the physi-
cian administrator sits down at that
terminal, the model is his and not ours.
It was ours in the beginning, and when
it was only ours he didn't care very
much. But having made it a part of his
own activity and working on it in the
context of the very organization in
which he has the authority to make
369
-------
decisions it becomes very much a part
of his existence. We might ask, How
do we reproduce that situation in the
context of regional planning or compre-
hensive health planning? How do we
set up a health planning game, as it is
possible in cases of military war gaming
or industrial management games?
"We need situations with a scenario,
the running dialogue. We need to have
analysts and decision-makers in the
same room with all sorts of displays on
the wall, displays coming quickly from
the computer, showing people the re-
sults of the decisions they have made
in their role in the simulation. Such
an alliance may permit us to avoid some
of the connotations of the word
'utopian,' the notion of naivete, of
dreaminess, of leaving out something
important. Perhaps we can avoid this
if we can bring into effect the necessary
coalition of practical and theoretical
decision-maker and scientist."
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Chapter 12
Econometric Models for Policy Analysis
By
E. Philip Howrey
SUMMARY 377
I. INTRODUCTION 377
What is Econometrics? 377
Uses of Econometric Models . 382
Types of Econometric Models . 384
II. NATIONAL ECONOMETRIC MODELS . 386
An Expository National Econometric Model 386
Uses of a National Econometric Model . 388
Operational National Econometric Models 389
II. REGIONAL ECONOMETRIC MODELS 390
An Expository Regional Econometric Model 391
Uses Regional Econometric Models 393
Operational Regional Econometric Models 394
V. FORECASTING AND POLICY ANALYSIS: AN EXAMPLE 397
Forecasting With an Econometric Model 398
Policy Analysis With an Econometric Model 401
Concluding Remarks . 402
REFERENCES . . 403
Econometric Methods 403
National Econometric Models 404
Regional Econometric Models . 405
Miscellaneous . 406
APPENDIX: Construction and Use of Econometric Models 406
Econometric Models 406
Forecasting, Analysis and Control 412
375
-------
-------
Econometric Models for Policy Analysis
SUMMARY
The purpose of this chapter is to
introduce the policymaker to econo-
metric modeling and to indicate how
econometric models can be used in
forecasting and policy analysis. It is
readily apparent that this chapter is
substantially different from the other
chapters of this Guide in that econo-
metric modeling is a set of analytical
techniques rather than a subject area
such as urban economics or waste
management. Econometric methods
have been used to develop models in
virtually all of the problem areas which
are studied in the Guide.
Two areas in which econometric
models have had or are expected to
have an important impact need to be
covered explicitly. These are national
economic models and regional eco-
nomic models. The purpose of these
models is typically to forecast the level
of economic activity as measured by
jross national product for example and
o provide a framework for the analysis
)f alternative tax and expenditure
Dolicies.
The discussion of this chapter is
'ramed primarily in terms of what
nodel builders generally hope to ac-
omplish through their modeling ef-
orts. Ideally, this would be accompa-
lied by examples of the ways in which
conometric models have been used in
le actual formulation of economic
olicy. Unfortunately, it is virtually im-
ossible to document the role of econo-
ictric models in policy design. The
;ason for this is that the use of models
L the policy-making process is seldom
>rmalized. This is not to say that
icdels are not used; rather they are
>ed in a rather informal way.
In order to provide the policy-maker
with some appreciation of econometric
models the elements of econometric
modeling are reviewed briefly and in as
nontechnical a way as possible. This
is followed by a review of national
econometric models and regional econo-
metric models. The final section of the
text provides numerical examples of
how a national econometric model can
be used in forecasting and policy analy-
sis. The technical materials on model
construction and validation as well as
on the use of models in forecasting and
analysis is relegated to an appendix.
I. INTRODUCTION
What is Econometrics?
The use of econometric models in
economic forecasting and in the design
and analysis of public policy has in-
creased substantially over the past sev-
eral decades. Forecasts based on an-
nual and quarterly econometric models
are regularly produced by a number
of academic research groups and con-
sulting firms. In addition, these groups
also periodically conduct analyses of
public policy issues with the use of these
models. In view of the increased avail-
ability of econometric models for policy
analysis, it is desirable for policymakers
in responsible government positions to
be aware of the types of models that
are available and how these models can
be used to aid in the formulation of
policy recommendations.
This chapter attempts to introduce
the basic elements of econometric
modeling and to indicate in some detail
the types of models that have been de-
veloped over the past several decades.
The remainder of this section is devoted
to a brief, non-technical overview of
377
-------
Econometric Models For Policy Analysis
Discussed in Chapter
Summary Table
Model/Decision Area
Characteristics (Econometric Models)
National Econometric Models
Bureau of Economic Analysis
Model
Brookings Model
DHL III Model
DRI Model
Fair Model
Federal Reserve Bank of
St. Louis
The MPS Model
Wharton Mark III
Wharton Mark III
Anticipations
H-C Annual Model
Wharton Annual Model
Liu-Hwa Monthly Model
Regional Econometric Models
Alaska
California (Burton and Dyckman)
California (Ratajczak)
California (Roberts and Wittels)
Southern California
(Moody and Puffer)
Hawaii
(Chau)
Massachusetts
(Bell)
Ohio
(L'Esperance, Nestel,
and Fromm)
Puerto Rico
(Dutta and Su)
Puerto Rico
(Stahl)
Other Regional Models
Lakshmanan and Lo
Ready access to preliminary data
One of the first attempts at large-scale modeling; sec-
toral disaggregation
Large-scale, academic model
Available on a time-shared basis
Primarily a forecasting model relying on anticipations
data
Small-scale, monetarist model
Extensive monetary sector
Interaction with industrial subscribers in forecast prepa-
ration
Extensive use of anticipations data
Designed to study structural change
I/O table used to derive industry projections
Monthly model limited to some extent by data availability
Quarterly forecasting and policy analysis model
Model designed to analyze effects of national policy on
the California economy
Econometric forecasting model
Forecasting and policy analysis with complete linkage
between national economic variables and detailed Cali
fornia economic variables
10-county model using demand components of gros
regional product
Short-run forecasting model for civilian personal incom
and employment
Regional forecasting model linked to a national forecas
ing model
Forecasting and policy analysis model
Structural model with emphasis on relationship to U.
economy
Sectoral model to examine productivity trends and re
tionship of these to domestic investment, trade and i
come
Regional model for assessment of air pollution abateme
programs
378
-------
econometrics. This introduction in-
cludes a discussion of what the term
econometrics means and how econo-
metrics differs from industrial dynamics
as well as what these areas have in
common. The general principles of
econometric model construction are
briefly reviewed. The general uses of
econometric models are summarized
and the section concludes with a con-
cise outline of the types of econometric
models that are currently available.
Sections II and III which follow are
concerned specifically with the develop-
ment of econometric models for na-
tional and regional economic analysis.
The format of each of these sections is
the same. Included in each section is a
discussion of the structure of national
(regional) models, the ways in which
national (regional) models have been
used, and a short survey of national
(regional) models that are currently
available.
In section IV, alternative uses of
econometric models are considered.
Three areas of particular interest to
policymakers are singled out for ex-
tended discussion:
1. the use of models in forecasting
the future;
2. the use of models to investigate
the impact of alternative policies;
and
3. the use of models to design opti-
mal policies.
Primarily for expository purposes, a
ecent forecast of the Michigan Quar-
srly Econometric Model of the U. S.
iconomy is reviewed. In addition, the
esults of several policy experiments are
iscussed. The qualifications to which
lese numerical results are subject are
iscussed in some detail so that the pol-
:ymaker will have an appreciation of
hat can and cannot be expected from
n econometric model.
The Appendix to this chapter includes
technical discussion of the construe-
jn and use of econometric models.
lis material is much more mathemati-
il than the text and should be read
ily by those familiar with econometric
modeling who wish to gain a further ap-
preciation of the technical aspects of
model construction, validation, and use
in forecasting and policy design.
What is Econometrics? Econometrics
is concerned with providing empirical
content to economic theory. Economic
theory is in turn concerned with the de-
velopment of concepts and relationships
which can be used to describe and in-
terpret observable events. In this sense,
econometrics can be thought of as a
quantitative approach to the study of
economic behavior.
The emphasis in econometrics is on
measurement. Two types of measure-
ment are involved: observation of basic
data and the estimation of unobserved
parameters. The basic data with which
the econometrician operates are pre-
dominantly non-experimental data
which are routinely collected in the
course of economic transactions. It is
frequently impossible for the economist
to generate experimental data which
provides the basis for empirical work
in the "hard" sciences. This necessitates
the development of research strategies
in the social sciences and economics
in particular which differ from those
used in the physical sciences.
An example may be useful to clarify
the relationship between theory and
measurement in econometrics. To keep
the example simple, consider an econo-
metric model of commodity price de-
termination. The policymaker may wish
to know the mechanism by which prices
are determined in a particular com-
modity market so that he can introduce
policies to stabilize price fluctuations
over time. Presented with this prob-
lem the econometrician would first turn
to economic theory to specify a set of
functional relationships that character-
ize the market. That is, the econo-
metrician-would recognize at the outset
that a system of relationships is re-
quired to describe the market.
A minimal system might involve only
three relationships: a demand function,
a supply function, and a market clear-
ing equation. More complicated models
could easily be constructed but this
379
-------
three-equation system is sufficient to
illustrate the basic points and yet simple
enough to be manageable. The demand
function might be written as
D = D(p, q, y, t)
(1)
where D denotes the quantity of the
commodity demanded by consumers
per month, p is the unit price of the
good, q is the price of competing
goods, y is consumer income, and t is
the unit tax on the commodity. The
economic theory which underlies this
relationship imposes certain conditions
on this function. If the commodity
is a normal good (as opposed to an in-
ferior good), then a price increase will
result in a reduction in quantity de-
manded, while an increase in income
will result in an increase in the quantity
demanded. If the price of competing
goods increases, the quantity demanded
also increases as consumers switch from
the higher to the lower-priced com-
modity.
If the policymaker wished to dis-
courage the consumption of this com-
modity or to raise revenue by levying
a tax on the commodity, it would be
necessary to determine empirically the
demand function. Only then would it
be possible to determine the revenue
that could be raised by the imposition
of a tax on the commodity. However,
it is readily apparent that the demand
function alone is not sufficient to pro-
vide this information. An increase in
the unit tax on the commodity would
reduce the quantity demanded by con-
sumers by increasing the effective price.
But the process of adjustment is not
likely to stop here. The reduction in
demand is likely to have some impact
on suppliers and their response must
also be considered.
This indicates that it is necessary to
specify a system of relationships to
avoid drawing misleading implications
from the analysis. Economic theory
again suggests that the supply function
is of the form
S = S(p,x) (2)
where S is the quantity supplied per
month, p is the unit price received by
380
suppliers, and x is an uncontrolled or
exogenous variable (i.e. a variable
that is taken as given rather than ex-
plained by the model) such as the
weather that affects production and
hence the supply of the commodity. It
is generally true that the quantity sup-
plied is an increasing function of the
price received by the supplier. In order
to close the system, an equilibrium or
market clearing equation is required.
For this model, it is assumed that prices
adjust instantaneously so that the quan-
tity demanded is always equal to the
quantity supplied.
D = S (3)
These three equations, (l)-(3), de-
termine the equilibrium values of p,
D, and S given the values of q, y, and t.
In order to see exactly how this
model works, it is convenient to con-
sider linear approximations to equa-
tions (1) and (2).
D = a0 - Mp +1) +
S =
(2')
The way in which the demand equation
is written indicates that the buyer pays
an effective price of p + t per unit bu
the supplier receives only p, the differ-
ence being the tax payment. If (!')
and (2') are solved simultaneously witl
the equilibrium condition (3), the re
suiting equilibrium price is
p =(ttl + jSj)"1 (<*„-&,
+
-------
then
D + tdD/dt
= D + t(dD/dp) (dp/dt)
= D + t
-------
D, S
FIGURE 2—Observations Generated by Shifts
in the Demand Curve
estimate all of the parameters of the
interdependent system. This would not
be a serious problem if controlled ex-
perimentation were possible for then the
type of sample data that is required for
the estimation problem could be gen-
erated. However, as mentioned previ-
ously, controlled experimentation is
generally not possible in the social sci-
ences. Hence, the econometrician has
devised methods to analyze nonexperi-
mental data generated by simultaneous
equation systems. Several of these pro-
cedures are described below. The point
to be emphasized here is that single-
equation methods are generally not ap-
propriate since the variables are simul-
taneously determined. Although this
may seem like an obscure technical
point, it is necessary to underscore it
since many otherwise excellent studies
use an inadequate estimation method-
ology.
In summary, econometrics can be
thought of as a branch of statistics con-
cerned with the analysis of non-experi-
mental observations on the variables of
an economic system. By way of con-
D, S
FIGURE 3—Observations Generated by Shifts
in the Supply Curve
382
eluding this brief discussion of econo-
metrics, it may be useful to compare
econometrics with industrial dynamics.
Viewed as research methods, the dif-
ferences among these areas would ap-
pear to be primarily differences in
emphasis rather than substance. In-
dustrial dynamics as described by For-
rester [7, 8], for example, is concerned
with the construction of complex dy-
namic models that describe physical or
social processes. The complexity of the
models that have been developed in this
area lead to two serious problems. First,
typically the data required to estimate
the parameters are not available. Even
if they were available, the functional
forms that are postulated are such that
parameter estimation is difficult if not
impossible. The second problem associ-
ated with the complexity of industrial
dynamics models is that analytical solu-
tions are difficult to obtain. It is there-
fore often necessary to resort to nu-
merical procedures to analyze the
resulting models. This is not a majoi
difference between econometric and in
dustrial dynamics models however. Thi
critical difference is the relative im
portance of parameter estimation in thi
approach to modeling.
The estimation problems inherent i
industrial dynamics models are ofte
quite severe. However, this is not
serious problem if one of the basi
postulates of the industrial dynamic
methodology is satisfied. Specifically,
is asserted that the behavior of comple
systems is not critically dependent c
the parameter values. If this is tru
that is, the same conclusions are o
tained for wide ranges of paramet
values, then the problem of paramet
estimation is not so serious. Trie emph
sis in econometric modeling is <
parameter estimation. In essence, t
postulate that the system behavior
insensitive to parameter variation is i
jected, at least initially. This frequen
leads the econometrician to consk
models which offer some promise
parameter estimation and to rej
models that are too complicated
allow estimation to proceed with
data that are available.
-------
Uses of Econometric Models. The dis-
tinguishing features of econometric
modeling are the use of economic theory
in the specification of the economic sys-
tem and the use of statistical theory to
estimate the parameters of the specified
model using non-experimental observa-
tions. The process of model construc-
tion, including estimation and valida-
tion, will be discussed at length in the
Appendix. For purposes of exposition,
it is assumed that this stage of the analy-
sis has been completed. This section
discusses briefly the ways in which
econometric models can be used by de-
cision makers.
Returning to the commodity market
example, the parameters of the linear
model (l')-(3') are now assumed to
be known. If a, denotes the estimated
value of f simplicity.
This model can now be used in two
vays: prediction of future values of
ic system and analysis of policy
hanges. The empirical system (le),
2e), and (3) can be used to predict in
dvance the commodity price and the
uantity sold. The solution for the equi-
brium price is
= (ax + b^-1 (a0 — b0 + a^
+ a3Yj - MJ — b2Xj) (4e)
redictions are obtained by substituting
•edicted values for q^, yp t,-, and x.j
this expression and solving for PJ.
le resulting prediction is a conditional
ediction in the sense that is is the
ice that is expected to prevail if the
edicted values of the independent
riables are realized. The conditional
prediction given by (4e) is subject to
error from three sources. First, if the
independent variables deviate from
their projected values, this will intro~
duce an error. Second, even if the
independent variables are forecast cor-
rectly, any errors in the coefficient esti-
mates will lead to prediction error.
Third, the fact that the model is not
exact will introduce a further error in
the prediction.
This last source of error is not ap-
parent from the overly simplified way in
which the model has been presented.
In point of fact, the system (l)-(3) is
considered to be not an exact system but
rather a stochastic system. Hence a
more realistic representation would be
D = D(p, q, y, t, u) (Is)
S = S(p, x, v)
(2s)
(3s)
where u and v are random disturbances.
These random disturbances arise be-
cause the quantity demanded is not an
exact function of p, q, y, and t. Simi-
larly, the quantity supplied does not
depend exclusively on p and y but also
on other influences which are lumped
together in the random variable denoted
by v. In going from the nonlinear
formulation (Is) -(2s) to the linear
formulation (l')-(2') another source
of error — misspecification of the form
of the relationships — may be involved.
In any event, the linear model should
have been written as
S=&,+Ap + j82x + v (2's)
It is now apparent that the solution of
(1's), (2's), and (3) for ps will depend
onu and v, i.e.,
(4's)
where p is given by (4). Hence the
error in using p to predict the actual
price ps is (ax + ft)-1 (u —v). The
other two sources of error result from
the use of p to estimate p.
383
-------
The analysis of these sources of error
is an important part of any applied
econometric study. A lack of data often
prevents a detailed analysis of predic-
tion error but as discussed in detail
below, prediction error analysis is an
extremely important part of the process
of validation of a model. Recent work
of Howrey [14] and Dhrymes, et. al. [5]
suggests that three types of tests are of
special importance in connection with
validation of a model. These are
• Tests of data conformity,
• Comparisons of alternative models,
and
• User-oriented criteria of success.
The statistical aspects of these tests
are described in detail in the Appendix.
It is perhaps sufficient to note at this
point that these tests all depend on fore-
cast errors in one way or another.
The second general way in which the
model can be used is in the study of
policy issues. For example, with the
empirical model, the policy-maker is
able to estimate the magnitude of the
response of price to a change in the tax
rate. That is, the derivative calculated
in (5) can now be assigned a value
equal to —at(a! + taj)-1. This is only
an estimate since the true values of the
parameters are not known. How good
an estimate of the policy impact this
yields depends on the extent to which
the model is a valid representation of
the system and how close the parameter
estimates are to their true values.
In more complicated models, alterna-
tive policies can be compared in this
way. Suppose, for example, that the
independent variable x in the supply
equation represents a unit subsidy to the
supplier. The supplier now receives
p + x for each unit produced and sold
on the market and the consumer pays
p + t for each unit purchased. The
model can be used to compare a subsidy
program with a tax-reduction program.
For example, suppose that it is desired
to increase the production of a com-
modity that is currently taxed at the
rate t. The alternative policies that are
under consideration include a tax re-
duction or a subsidy to producers. A
tax reduction in the amount At will
result in an estimated price reduction of
Ap = a!(a! + b1)~1At
An increase in the subsidy by Ax will re-
sult in an expected price reduction in
the amount of
Which of these two policies results in
the larger price reduction will depend
on the values of the parameters o^
and y82 of the model. The estimates at
and b2 can be used to provide evidence
on this issue.
These examples illustrate the use of
the model to compare different ad hoc
policies. If an objective function is
introduced, then the model, together
with the objective function, can be used
to determine the best of several alterna-
tive policies. Returning to the taxation/
subsidy comparisons, the policymaker
might introduce as the objective func-
tion the change in output that results
from the policy and the cost of the
policy. If two policies achieve the same
expansion of output but one policy costs
more than another, the least-cost policy
is preferable. The objective function
thus permits the ranking of alternative
policies on the basis of the results tha
they produce and the model provide;
the basis for the estimation of the re
suits of different policies.
This evaluation procedure can be car
ried one step further. Suppose that th
policymaker wishes to increase outpu
by a specified amount but to do so i
the least cost way. The policymaker ha
two variables that can be controlled, th
tax rate and the subsidy rate. Th
problem is to find the optimal combin;
tion of these two rates that achievs
the output goal and minimizes cos
This optimization problem illustrati
the use of econometric models in t"
selection of optimal policies. This su
ject will be described in greater dett
in the Appendix.
Types of Econometric Models. T
field of econometrics consists of tv
types of activities: econometric theo
and applied econometrics. Econometi
384
-------
theory is concerned with the develop-
ment of statistical techniques which are
used in estimation and hypothesis test-
ing. Applied econometrics is the ap-
plication of these techniques in concrete
modeling situations. It is difficult to
construct a complete catalogue of
econometric models because econo-
metric methods have been applied to so
many diverse problems. Many of the
models that have been discussed in
other chapters of this book could quite
properly be called econometric models.
Broadly defined, an econometric
model is any model dealing with eco-
nomic relationships in which statistical
methods have been employed to esti-
mate unknown parameters or to test
hypotheses. This definition is clearly
so broad that it encompasses all but the
most theoretical of economic models.
Perhaps a more useful way to cate-
gorize econometric models is in terms
of the subject matter with which they
are concerned. In this regard, a first
broad distinction could be made be-
tween microeconomic models and
macroeconomic models. Microeconomic
models are concerned with the behavior
of individuals or small groups of indi-
viduals. Thus models dealing with the
expenditure decisions of a household,
he investment decisions of a firm, or the
Jrice of a particular commodity would
•>e microeconomic models. Macroeco-
lomic models are concerned with be-
lavior in the aggregate. The main vari-
ibles of these models are aggregate
ncome, the unemployment rate, wage
md interest rates, and the price level.
Models which attempt to describe the
lational economy or the economy of a
tate or region are examples of macro-
conomic models.
The models that are carefully re-
iewed subsequently are national and
3gional macroeconomic models. There
re several reasons for choosing this
rea to review. First, by far the largest
mount of coherent, systematic model-
uilding effort has been devoted to
mcroeconomic systems. Hence there
a fair amount of agreement on the
2neral structure of such models and a
substantial number of applied results
for national econometric models. Sec-
ond, methods of regional economic
analysis are advancing quite rapidly and
several operational regional models
have recently been constructed. This is
an area which is likely to experience
significant breakthroughs in the near
future in response to urgent needs of
economic policy-makers. Finally, na-
tional and regional models lend them-
selves quite naturally to a decision-
making context. Moreover, the devel-
opment of these national and regional
models as decision-making tools would
benefit enormously from a more direct
input from policy-makers.
Confining specific attention to na-
tional and regional models means that
several important areas of applied work
are not discussed. In particular, com-
modity or industry models are not re-
viewed in any detail here. The exposi-
tory example of the introduction should
give the reader a good feel for what is
involved in the construction of a com-
modity market model and how it can
be used for decision-making purposes.
For a more detailed discussion of this
type of model, the interested reader is
referred to the recent book by Labys
[91].
Within the broad area of national
and regional economic models, it is
possible to make the following distinc-
tions.
• Long-term/Short-term Models
• Forecasting/Policy Models
• Large-scale/Small-scale Models
Short-term models are concerned pri-
marily with near-term prediction and
policy analysis. There are several na-
tional models that produce eight-quarter
forecasts each quarter. The methods of
construction and implementation of
these short-term models are somewhat
different from those used to build mod-
els which are intended to provide ten or
twenty-year projections.
It is also possible to distinguish be-
tween models primarily designed for
forecasting and those designed for
policy analysis. Forecasting models,
385
-------
particularly short-term forecasting mod-
els, can make use of anticipations data,
that is, data obtained from preliminary
surveys of household and business in-
tentions. Less attention is devoted to the
introduction of detailed policy variables
and the channels through which the
policy variables operate. Policy models,
on the other hand, must necessarily be
concerned with this aspect of the sys-
tem.
The scale of the model can often
be varied almost continuously depend-
ing upon how much detail is required
and the amount of resources available
for the construction and operation of
the model. National models range in
scale from five or six equations to two-
hundred or more equations. Slightly
different strategies are involved in the
construction of very large-scale models
than in smaller models. The problem of
coordination as it affects the logical
consistency and completeness of the
model becomes acute if a number of
investigators are involved in the de-
velopment of the model. However, the
overall approach to the model is not
critically dependent on the scale of the
model.
II. NATIONAL ECONOMETRIC
MODELS
In order to gain an appreciation of
the potential uses of national economic
models, it is necessary to understand
the structure of these models. A fairly
elementary expository model is intro-
duced to illustrate the basic relation-
ships of a macroeconometric model.
This expository model is then used to
indicate the uses of such a model for
policy analysis. This section is con-
cluded with a brief survey of opera-
tional econometric models of interest
to policy-makers.
An Expository National Econometric
Model. The structure of the most
complicated econometric model of the
national economy can be grasped fairly
easily once this expository model is
386
understood. The way in which large-
scale, operational models differ from
this system will be explained after the
model has been introduced. It should
be noted at the outset, however, that
most econometric models are dynamic
in the sense that they include lagged
values of the dependent and independ-
ent variables. In the interests of econ-
omy of presentation, this expository
model will, at least initially, suppress
the dynamic elements in order to con-
centrate on the general form of the
relationships.
The reader will recall that the simple
commodity market model introduced
previously consisted of three equations:
a demand equation, a supply equation,
and a market clearing or price de-
termination equation. A national
macroeconomic model typically has the
same three blocks of equations: a set of
demand equations, a set of supply equa-
tions, and a set of price equations. The
demand equations of the model attempt
to explain broad expenditure aggregates
such as personal consumption expendi-
tures, gross private domestic investment
expenditure, and net foreign invest-
ment. These aggregates closely follow
the national income and product ac-
count data which are typically used to
estimate the parameters of the models.
The following equations provide an
example of the block of demand equa-
tions of a national econometric model,
C = C(y, r, m) (9;
I=(X,r, K) (10.
X = C + I + G (11
The symbols used in these equation
are denned as follows.
C : real (constant-dollar) persona
consumption expenditure
y : real disposable income
r : the interest rate
m : real balances held by househok
-------
I : gross private domestic invest-
ment
K : the stock of capital
X : real aggregate demand
G : real government expenditure
Personal consumption expenditure is
assumed to be a function of real dis-
posable income, the interest rate, and
the stock of real balances held by
households. This equation is based on
the idea that consumption expenditure
depends on the resources of households
as reflected in their income y and
wealth m. In addition, the opportunity
cost of consuming and hence not saving,
as reflected in the interest rate, may also
have an impact on the level of con-
sumption expenditure.
The investment function states that
the level of investment is a function
of the level of aggregate demand, the
cost of capital as measured by the in-
terest rate, and the current stock of
capital. If the current stock of capital
is large relative to aggregate demand
so that there is excess capacity, then in-
vestment spending will be low. On the
other hand, if the current stock of
capital is low relative to current aggre-
gate demand, there will be pressure to
expand production facilities and invest-
ment spending will be influenced to
some extent by the availability and cost
of funds. Hence the interest rate is
included in this equation to capture this
effect.
The final equation of this block
simply sums the individual demand
components to arrive at the aggregate
demand for output. The level of gov-
ernment expenditure, as in most mod-
els, is assumed to be exogenous. The
model does not attempt to explain
variations in government spending;
rather, these are taken as given.
The supply block of this model con-
sists of four equations.
X=X(K,L) (12)
Lf=L(w/p) (13)
D=SK
(14)
(15)
The new symbols which appear in this
block are as follows.
L : the level of employment
Lf : the full-employment supply of
labor
w : the wage rate
p : the price level
D : the level of capital consumption
The first equation of this block is the
production function which indicates
how capital and labor are combined to
produce the output X. The second
equation states that the supply of labor
depends on the real wage rate. The
last two equations determine the supply
of capital. The capital stock available
for current production is equal to the
stock inherited from last period plus
the amount of gross investment less re-
tirements. Capital consumption is as-
sumed to be proportional to the stock of
capital.
The block of price equations for this
model can be written in the following
way.
p=p(wL/X) (16)
Aw=w(L'-L) (17)
m = m(y, r)
(18)
The price equation (16) is based on the
notion that prices depend on unit labor
costs wL/X. The wage adjustment equa-
tion indicates that wages adjust in re-
sponse to unemployment since Lf — L
is the difference between the full-em-
ployment labor force and the amount
387
-------
of employment currently available. The
final equation is a very simple charac-
terization of the monetary sector in
which the interest rate adjusts to equili-
brate the demand for money m(y, r)
with the supply of money m which is in
turn determined by the banking system
and the financial sector of the economy.
Several definitions and accounting
identities are needed to close the system.
Y= pX-Tx + Tr-pD (19)
y=Y/p (20)
m=M/p (21)
The new symbols introduced in these
identities are defined as follows.
Y : disposable personal income
M : the stock of money
Tx : federal, state, and local tax pay-
ments
Tr : federal, state, and local transfer
payments to households
The first of these identities indicates
that disposable income is equal to the
market value of all output produced
less taxes paid plus transfers to house-
holds less capital consumption allow-
ances. The other two identities indicate
how the real and nominal values are
related.
This system of 1 3 equations describes
how the 13 endogenous variables C, I,
X, L, Lf, K, D, p, w, r, Y, y, and m are
determined. The exogenous variables
of the model are G, Tx, Tr, and M.
Thus given the values of these exoge-
nous variables, it would be possible in
principle to solve for the 1 3 endogenous
variables of the model.
The implementation of this model
requires that the general functional re-
lationships be specified in a form in
which the unknown parameters can be
estimated. This involves two things.
First, the general functional form must
be replaced by a specific, parametric
relationship. Using the consumption
function as an example, this function
might be written as
C = c0
c2r + c3m
(22)
In this form, the unknown parameters
c0, CL . . ., c4 could be estimated from
observations on C, y, r, and m. The
disturbance term u is added to the equa-
tion to indicate that the equation is not
exact but rather a stochastic relation-
ship. This error term arises because the
functional form may not be correct,
variables that are relevant to the deter-
mination of personal consumption ex-
penditure may have been omitted from
the equation, or consumption behavior
of households may be inherently ran-
dom rather than deterministic. The
specification of the properties of this
error term is the second aspect of the
specification phase that is required be-
fore estimation can proceed.
Each of the equations in the model
which involves unknown parameters
must be specified in this way. Of course,
the identities need not be modified since
they do not involve unknown param-
eters and hold exactly. In the above
system there are eight stochastic equa-
tions: (9), (10), (12), (13), (15),
(16), (17), and (18). The remaining
five equations, (11), (14), (19), (20),
and (21) are identities.
Uses of a National Econometric
Model. Once the parameters of the
model have been estimated, the model
can be used for forecasting and policy
analysis. In connection with the system
described above, forecasts of all of the
endogenous variables of the model, i.e.,
variables that are explained by the
model, can be obtained once the exog-
enous or independent variables art
predicted. Thus in order to forecast tht
level of gross national product nex
period, it is necessary to forecast th<
level of government spending, tax col
lections, transfer payments, and thi
money stock. Once these are given, th
system can be solved to obtain a fore
cast of the level of output next perioc
It should be emphasized that this fore
cast is a conditional forecast in the sens
that it depends on projected values c
the exogenous variables. Forecast erroi
arise from three sources: the use c
estimates in place of the unknown ce
efficients of the system, the disturbanc
388
-------
errors in the stochastic equations, and
errors in forecasting the exogenous
variables.
In addition to the use of a national
econometric model as a forecasting de-
vice, it can be used to analyze the
impacts of alternative policies. For ex-
ample, modifications of the tax system
which affect Tx in the system can be
investigated. Changes in welfare pro-
grams which alter the value of Tr are
likely to have an impact on income,
employment, and prices and these ef-
fects can be estimated using the model.
Finally, changes in government spend-
ing which affect G or changes in mone-
tary policy which result in changes in
M can be investigated. After an investi-
gation of a number of alternative policy
changes, the policy which seems most
appropriate can be chosen by the de-
cision-maker.
Operational National Econometric
Models. The simple expository model
introduced above is intended to provide
an overview of the structure of an op-
erational econometric model. The op-
erational models that are currently in
use are typically much larger than this
simple model. The block of demand
equations typically contains many more
equations than those shown in the ex-
pository model. For example, personal
consumption expenditure is disaggre-
gated by type of expenditure to give
;onsumption of durables, consumption
)f non-durables and consumption of
ervices. Durables consumption is some-
'mes further subdivided into automobile
xpenditures, expenditures on household
oods, and expenditures on other dur-
bles. Since the prices of these different
omponents do not always move to-
ether price equations must be intro-
uced for each component of consump-
on expenditure.
The single investment function (10)
typically replaced by a set of invest-
ient functions corresponding to differ-
it types of investment expenditure
itegories. For example, a separate
nation might be included for invest-
ent in plant and equipment, residential
instruction, and investment in inven-
tory. These investment equations could
be further disaggregated by industrial
type. Again since prices of these differ-
ent types of investment goods do not
move together, price equations would
be introduced for the different com-
ponents.
In most models export and import
equations are added to the system. These
additions result in the modification of
the identity (11) to
X = 2C, + 21, + Ex - Im+G (11')
where Q denotes the demand for con-
sumption of type i, I; is investment
demand for the ith type of investment
good, Ex denotes exports, and Im de-
notes imports.
The supply block can be expanded
by introducing production functions for
different types of broad product groups.
Similarly, the production functions can
be modified to include different types of
labor. The labor supply and capital
supply functions can be expanded in the
same way.
It has already been noted that the
introduction of consumption and invest-
ment components necessitates an ex-
pansion of the block of price equations.
If different types of labor are intro-
duced, then a corresponding set of wage
adjustment equations can also be intro-
duced in place of the single wage
adjustment equation (17). The rudi-
mentary monetary sector embodied in
(18) is typically expanded to explain
long-term and short-term interest rates,
the levels of demand and time deposits
and the response of financial institutions
to changes in the discount rate and open
market operations conducted by the
federal reserve system.
These modifications result in rather
large and complex nonlinear systems of
equations. Although they are used in
exactly the same way as the simpler
models that have been used here for
expository purposes, solution by numer-
ical methods is frequently required. The
size and complexity of these models
means that the operation of these
models is a very specialized activity.
An excellent tabular survey of a num-
389
-------
her of econometric models is given by
Nerlove [56]. This survey is somewhat
dated now, but it provides an overview
of the state of the art as of about 1965.
A recent paper by Fromm and Klein
[46] provides some comparisons of the
properties of the models that are most
readily available and widely used today.
The models included in this survey in-
clude the following.
• The Bureau of Economic Analysis
Model, A. Hirsch, M, Leibenberg,
and G. Narasimham [48, 53]
• The Brookings Model, The Brook-
ings Institute, G. Fromm, L. Klein,
and G. Schink [39, 40, 47]
• The DHL III Model, University of
Michigan, S. Hymans and H.
Shapiro [49]
• The Data Resources Inc. Model,
O. Eckstein and E. Green
• The Fair Model, Princeton Univer-
sity, R. Fair [44]
• The Federal Reserve Bank of St.
Louis Model, L. Anderson and K.
Carlson [33]
• The MPS Model, University of
Pennsylvania, A. Ando, F. Modi-
gliani, and R. Rasche [34]
• The Wharton Mark III Model,
University of Pennsylvania, F. G.
Adams, V. J. Duggal, G. Green,
L. Klein, and M. McCarthy [55]
• The Wharton Mark III Model, An-
ticipations Version [32]
• The H-C Annual Model, Stanford
University, B. Hickman and R.
Coen
• The Wharton Annual Model, Uni-
versity of Pennsylvania, R. Preston
• The Liu-Hwa Monthly Model,
Cornell University, T. C. Liu and
E. C. Hwa
With the exception of the last three
models, all are quarterly models. It is
difficult to provide a concise, up-to-date
description of these models because they
are all in the developmental stage in the
sense that minor modifications are made
periodically. A complete description of
the current version of the model can
often be obtained by writing directly to
the model builder.
390
The paper by Fromm and Klein re-
ferred to above gives comparative
figures on a number of characteristics
of these models. These characteristics
include
• Sample-period solution errors
• Post-sample-period solution errors
• Dynamic tax multipliers
• Dynamic government expenditure
multipliers
These results provide a basis for making
some judgments about the accuracy that
econometric forecasts can be expected
to achieve. In addition, the differences
in the dynamic multipliers obtained
from the different models indicates the
range of the uncertainty which accom-
panies such estimates.
Another set of model comparisons is
contained in the paper by Cooper [37].
These results have generated a certain
amount of controversy and have been
responsible, at least in part, for a sub-
stantial amount of research activity
which is only now being completed. Of
special note along these lines is the
recent paper by Nelson [96] which com-
pares the forecast accuracy of the MPS
model with naive autoregressive models.
This methodology of model evaluation
has been examined in some detail by
Howrey, Klein, and McCarthy [16]. A
discussion of the predictive accuracy of
Wharton forecasts is contained in Green
and Klein [11],
III. REGIONAL ECONOMETRIC
MODELS
The demand by policymakers fo
more detail at the state and local leve
has led to the development of regiona
econometric models. Most of thes
models have been constructed along th
same lines as the national macroeconc
metric models discussed in the precedin
section. These regional models are usi
ally concerned with state aggregate:
This is perhaps not the ideal level c
aggregation but what little data exis
are usually collected on a statewic
basis.
This review of regional models fo
-------
lows the same format as that of the
preceding section. The structure of a
typical regional model is introduced
first. Ways in which regional models
can be used for policy analysis are then
described. The review concludes with a
few comments on operational regional
models.
An Expository Regional Econometric
Model. In an excellent survey paper,
Klein [76] has outlined the structure of
a representative regional econometric
model The actual models that have
been constructed depart from this struc-
ture in some areas to account for the
peculiarities of the area under investiga-
tion. However, the general structure
proposed by Klein is followed to a large
extent and is extremely useful in under-
standing the nature of regional econo-
metric models.
The usual approach that is pursued in
regional econometric modeling is to
follow the outline of a national model
fairly closely. Some adjustments are, of
course, required by the nature of eco-
nomic activity in the region. What this
means in terms of regional modeling is
that aggregate production and employ-
ment is explained by the model through
an aggregate demand equation. The
alternative approach is to develop a set
of interrelated models for each of the
major industries of the area and then
to aggregate these industry relation-
ships. This approach has not been fol-
owed primarily because of lack of de-
ailed data that this approach would
require. However, another reason for
lot pursuing this approach to regional
nodeling is the success that has been
ittained by national models that are
instructed from aggregate data.
The block of demand equations of a
epresentative regional model can be
/ritten as follows.
C=C(Y/pc*)
I = I(X,r*,k)
G= G(Tx,N, r*)
,x= Ex(X*, pe/pm*)
n = Im(X, p/pm)
(23)
(24)
(25)
(26)
(27)
pX = pc C + q*I + G + G*
+ peEx —pmlm (28)
The variables included in this block are
defined in the following way. An as-
terisk denotes that the variable is a
national aggregate. Otherwise the varia-
ble is a regional variable.
C regional personal consumption
expenditure
Y disposable personal income
pc* national index of consumer
prices
I gross private domestic invest-
ment
X gross regional product
r* the interest rate
K the capital stock
G state and local government ex-
penditure on goods and serv-
ices
Tx state and local taxes
N regional population
Ex exports of goods and services
X* gross national product
pe price of exports
pm* the price of imports
Im imports of goods and services
p gross regional product deflator
q* cost of investment goods
G* federal government expendi-
ture on regional goods and
services
The reader will recognize that these
functions are similar to those given
previously for the national model. The
important difference is the mixture of
national and regional variables in this
model and this requires further com-
ment.
The regional consumption function
states that consumption expenditure in
the region is primarily a function of
disposable personal income of house-
holds in the region deflated by the
national price index of consumer goods.
The reason for the use of the national
index is that consumer purchases in
any region will usually contain a large
number of items produced outside the
region. It is therefore more appropriate
to use a national price deflator than a
regional price deflator. The regional
investment function is of precisely the
391
-------
same form as the national investment
function. The use of a national interest
rate r* is appropriate here since busi-
ness firms can usually obtain funds in
a national market. They are not con-
fined to borrowing in local markets.
A major difference between national
and regional models is that in regional
models it is thought to be appropriate
to consider state and local government
expenditure as an endogenous variable
to be determined within the system.
State and local expenditure is usually
closely tied to tax receipts, population,
and the cost of borrowing funds. This
link between receipts and expenditures
is much stronger at the state and local
level than it is at the national level.
The fact that regional economies are
much more open than national econ-
omies means that the export and im-
port functions play an especially impor-
tant role in regional models. The export
function postulates a relationship be-
tween regional exports and gross na-
tional product, the regional export price,
and the price of imports from all other
regions. The idea is that a region can
expect to export more to other regions
during periods of prosperity. There are
two reasons for this. High levels of
activity will generate demands for in-
puts. High levels of activity also gen-
erate high incomes and hence lead to
bouyant demand. In addition to ex-
panded activity, exports are higher if
export prices are low relative to domes-
tic prices in other regions. Hence the
introduction of the price ratio pe/pm*
in the export equation. The import
equation is based on the same reasoning.
Imports are expected to vary positively
with regional production and income
and directly with the price ratio p/pm*.
An increase in p/pm* means that
domestic goods are more expensive rel-
ative to imported goods and this would
be expected to stimulate import demand.
The final regional demand equation
aggregates the individual regional de-
mand components. The only completely
exogenous variable in this equation is
the federal expenditure on regional
goods and services. None of the other
392
components of demand is completely
endogenous in the sense that each one
depends in part on a national economic
variable.
The supply side of the regional model
is characterized by four equations.
X = X(K,L) (29)
K = K_j + I - D (30)
D = D(K) (31)
Ls = L(N) (32)
The new variables introduced in this
block are as follows.
L
D
Ls
regional labor force
regional capital consumption
regional supply of labor
Since these equations are quite similar
to those of a national model, detailed
comment is not required. It might be
noted that a very simple labor supply
function is introduced here in which
the supply of labor depends on regional
population and not on the regional
wage rate as in the national model.
The price equations of the regional
model are of a simple form.
p= p(p*,w, pm*) (33)
pe= pe(p*, w, pm*) (34)
w = w(u, u*, pc*) (35)
The new variables introduced in thi;
block are the following.
w
u
u*
regional wage rate
regional unemployment rate
national unemployment rate
These price equations are somewhat a<
hoc formulations. However, they ar
similar to the price equations that ar
employed with considerable success i
national models.
A rather detailed tax and transfe
system can often be constructed for
regional model. The following system c
equations provides an example of sue
a system.
Tx=Txi + Txd (3f
Txi=Txi(pX) (3"
-------
Txd = Txd(w L, TT) (38)
Txf = Txf (w L, *•) (39)
Tr = Tr(u, N) (40)
These symbols have the following
meaning.
Tx total state and local taxes
Txi indirect state and local taxes
Txd direct state and local taxes
Txf federal tax collections in the
regional
Tr regional transfer payments
•n- nonwage income
Finally, two identities are needed to
close the system.
•n = pX — qD — wL •
u = L* - L
Txi
(41)
(42)
This completes a system of twenty equa-
tions in the twenty endogenous varia-
bles C, I, G, Ex, Im, X, L, K, D, Ls,
p, pe, w, Tx, Txi, Txd, Txf, Tr, *-, and
u. In order to solve for these twenty
endogenous variables, the values of the
national variables pc*, r*, X*, pm*, q*,
and u* are needed as well as the exog-
enous variables N and G*.
Uses of Regional Econometric-
Models. Regional econometric models
are used in much the same way as na-
tional econometric models are used. In
the context of economic forecasting,
predictions of the endogenous regional
variables can be obtained by solving
the regional model with projected values
inserted for the exogenous national and
regional variables. The use of regional
models in conjunction with national
econometric models is of relevance in
his connection. The national model can
56 used to generate forecasts of the
rational variables that are used in turn
is inputs to the regional model.
Regional models are particularly use-
'ul to the policy-maker in connection
vith projecting future tax receipts. Un-
ike the Federal government, State and
ocal governments often are faced with
ifficulties in borrowing to cover un-
'oreseen deficits. It is therefore impor-
ant to be able to anticipate potential
deficits in State and local government
budgets and to make contingency plans
to cover these deficits. Regional models
can also be used to obtain forecasts of
unemployment and the demand for
transfer payments through welfare
programs.
Regional models can be used in policy
analysis to explore the impact of alter-
native tax and expenditure policies. For
example, the impact of revenue-sharing
proposals can be investigated using a
regional econometric model. One of the
variables in the model described above
is the level of Federal spending on
regional goods and services. The re-
gional impact of changes in Federal
spending can be derived with the use
of a regional model.
A recent interesting use of regional
economic models is provided by Laksh-
manan and Lo [95]. They develop a
model to predict the cost of air pollution
control in a region under alternative
control schemes. Since the model is one
of the few ventures in this area, it is
worth reviewing briefly the basic ele-
ments that are involved. The model
incorporates four sets of interrelation-
ships, namely,
1. A Keynesian-type regional macro
model of the type discussed
above;
2. A set of production relationships
by industry;
3. A set of regional fuel and elec-
tricity demand equations by in-
dustry; and
4. A set of relationships linking
regional industrial activity with
national industrial activity.
The impacts of alternative air pollution
abatement policies are determined by
assuming that the cost of the products
of high-emission industries will in-
crease. This will result in a reduction in
the demand for these products and will
have regional effects on income and
employment that can be traced through
the model. Although the model is still
in the experimental stage, interesting
results on the distributional effects of
393
-------
pollution abatement policies have been
derived. For a detailed discussion of the
model and the policy results that have
been obtained, the reader is referred to
Lakshmanan and Lo [95].
Regional modeling is a relatively new
venture. The results that have been ob-
tained to date are sufficient to establish
regional econometric modeling as a use-
ful research area. However, progress
has been relatively slow and the models
that have been constructed are anal-
ogous to national models. As this area
develops, it is likely that new applica-
tions will be found for these models.
Operational Regional Econometric
Models. The major U. S. regional eco-
nometric models have recently been
reviewed by Glickman [70] and Chen
[64]. The models reviewed by Chen
include the following:
• The Alaska Model, G. H. Tuck
[90]
• The California Model, R. P. Bur-
ton and J. W. Dyckman [62]
• The California Model, D. Rata-
jczak [84]
• The California Model, B. F. Rob-
erts and G. Wittels [87]
• The Ten Southern California Coun-
ties Model, H. L. Moody and F.
W. Puffer [79]
• The Hawaii Model, L. C. Chau
[63]
Table I
Stated Objectives of the Ten Regional Econometric Models
Model
ALASKA
Tuck
CALIFORNIA
Burton
Dyckman
CALIFORNIA
Ratajczak
CALIFORNIA
Roberts
Wittels
SOUTHERN
CALIFORNIA
Moody
Puffer
HAWAII
Chau
MASSACHUSETTS
Bell
OHIO
L'Esperance
Nestel
Fromm
PUERTO RICO
Dutta
Su
PUERTO RICO
Stahl
Stated Objectives of the Model Builder
Construct an aggregate income model of Alaska for quarterly
economic forecasts, 4 to 6 quarters in advance, for policy analysis,
and systematic organization of data.
The basic purposes of the Phase 1 version of the model were for
economic forecasting and analysis of the effect of national policy
upon the California economy.
The Phase II version attempted to refine the Phase I model by im-
proving estimation reliability of certain sectors, reclassifying certain
industry groupings, and securing better predicting equations through
improvement or augmentation of basic data.
Develop an econometric forecasting model of California.
The CEEP California model was intended for use by decision
makers for systematically projecting images of the California econ-
omy and for posing meaningful economic questions. The structure
of the model draws complete linkages between national economic
policies and detailed California economic variables.
Construct an economic model of the 10 southern-most counties of
California utilizing the demand components of Gross Regional
Product.
Construct an economic model for making short-run forecasts of
civilian personal income and employment in Hawaii.
Develop a regional econometric model which can be linked to
national forecasts and apply this model to Massachusetts.
Develop a set of social accounts for estimating the gross state prod-
uct of Ohio, Construct an econometric model describing Ohio's
economic behavior which is useful for forecasting and policy analy-
sis.
Construct an econometric model which incorporates all important
features of her economic structure, especially her close economic
relationship with the U.S.
Use a model similar to L. R. Klein's model of the Japanese economy
to examine trends in labor productivity in various sectors of the
economy and the relationship between these productivities, invest-
ment, external trade, and the level of income in Puerto Rico.
Source: Dean Chen [64].
394
-------
• The Massachusetts Model, F. W.
Bell [58]
• The Ohio Model, W. L. L'Esper-
ance, G. Nestel, and D. Fromm
[78]
• The Puerto Rico Model, M. Dutta
and V. Su [66]
• The Puerto Rico Model, J. E.
Stahl [88]
Glickman's survey includes the Burton
and Dyckman California Model, The
Massachusetts Model, and the Ohio
Model. In addition, the following
models are reviewed by Glickman.
• The Michigan Model, D. B. Suits
[86]
• The Northeast Corridor Model, R.
T. Crow [65]
• The Philadelphia Model, N. J.
Glickman [68]
The potential uses of these models
can be inferred, at least partially, from
the stated objectives of the model-
builders. These objectives have been
summarized by Chen for the models in
his review and the tabular summary is
reproduced in Table I. It is apparent
that the objectives of the model-builders
are similar and stated only in general
terms. The development of a forecasting
model for the region is most frequently
given as the stated objective of the in-
vestigation. Policy analysis is also
mentioned specifically by some of the
model-builders but no specific policy
issues are mentioned.
Table II, also constructed by Chen,
Table II
Type of Data of the Ten Regional Econometric Models
Model
ALASKA
Tuck
CALIFORNIA
Burton
Dyckman
CALIFORNIA
Ratajczak
CALIFORNIA
Roberts
Wittels
SOUTHERN
CALIFORNIA
Moody
Puffer
HAWAII
Chau
MASSACHUSETTS
Bell
OHIO
L'Esperance
Nestel
Fromm
PUERTO RICO
Dutta
Su
PUERTO RICO
Stahi
Type of Data
Period Covered
Quarterly 1960-67
Quarterly 1950-62 for all equations which do not contain
predetermined defense variables
1954-62 for all remaining equations which do con-
tain exogenous defense variables
Quarterly 1953-1971
Quarterly 1961-1 to 1971-III
Annual 1953-61
Annual 1951-68
Annual 1947-62
Annual The model was estimated with varied lengths of
period for different equations. The maximum length
of period covers 1945-64.
Annual 1948-64
Annual 1947-61
Source: Dean Chen [64],
395
-------
indicates some of the characteristics of
these models. The type of data and the
sample period used to estimate the pa-
rameters are given for each model. Most
of the models have been estimated by
ordinary least squares. However, the
models for two states, Massachusetts
and Ohio, have also been estimated us-
ing two-stage least squares.
The scale of these regional models is
indicated in Table III which was also
compiled by Chen. For each model, the
number of stochastic equations and the
number of identities are given. The sum
of these two numbers is the number of
endogenous variables of the model.
These models range in size from Stahl's
thirteen-equation model of Puerto Rico
to the 294-equation model of California
devised by Burton and Dyckman.
The final table that has been extracted
from Chen's review is Table IV which
gives the number of exogenous variables
in each model. These are separated into
the number of regional exogenous vari-
ables and national exogenous variables.
The larger the number of exogenous
variables, the more difficult it is to use
the model for prediction and policy
analysis. The reason for this is that to
obtain a prediction of the endogenous
variables it is necessary to forecast the
exogenous variables. The models range
from a low of eight exogenous variables
Table III
Number of Endogenous Variables of the Ten Regional Econometric Models
Model
ALASKA
Tuck
CALIFORNIA
Burton
Dyckman
CALIFORNIA
Ratajczak
CALIFORNIA
Roberts
Wittels
SOUTHERN CALIFORNIA
Moody
Puffer
HAWAII
Chau
MASSACHUSETTS
Bell
OHIO
L'Esperance
Nestel
Fromm
PUERTO RICO
Dutta
Su
PUERTO RICO
Stahl
Source: Dean Chen [64].
396
Stochastic
Equations
Total
Endogenous
Identities Variables
14
240
32
33
13
25
8
16
23
11
18
54
32
43
11
12
32
294
64
76
18
31
14
27
35
13
-------
Table IV
Number of Exogenous Variables of the Ten Regional Econometric Models
Model
ALASKA
Tuck
CALIFORNIA
Burton
Dyckman
CALIFORNIA
Ratajczak
CALIFORNIA
Roberts
Wittels
SOUTHERN CALIFORNIA
Moody
Puffer
HAWAII
Chau
MASSACHUSETTS
Bell
OHIO
L'Esperance
Nestel
Fromm
PUERTO RICO
Dutta
Su
PUERTO RICO
Stahl
Regional
Exogenous
Variables
49
340
30
77
6
35
1
13
17
11
National
Exogenous
Variables
0
17
12
11
3
3
8
3
5
2
Total
Exogenous
Variables
49
357
42
88
9
38
9
16
22
13
Source: Dean Chen [64].
for Stahl's model of Puerto Rico to the
astonishing number of 357 exogenous
variables for the Burton-Dyckman
model of California.
A more detailed summary of these
models is contained in the review ar-
ticles that have been cited above. In
view of the fact that the models are
essentially elaborations on the represen-
tative regional model that has been dis-
cussed in some detail, no useful purpose
tvould be served by introducing these
detailed summaries here. To conclude
his brief survey of regional models on
in optimistic note, it is apparent that
he results that have been obtained to
late establish the fact that useful re-
,ional econometric models can be con-
tructed. On a somewhat less optimistic
lote, very little experience has been
,ained in the use of these models so that
he validation process for any one of
these models is far from complete.
Moreover, the problems of data avail-
ability impose very serious constraints
on the detail that can be incorporated in
these regional models. Much of the
ingenuity of these models lies in the use
of proxy variables in place of missing
data. In spite of these difficulties, sub-
stantial progress has been made in
regional econometric modeling over the
past decade. And there is every reason
to believe that future progress will be
just as rapid.
IV. FORECASTING AND POLICY
ANALYSIS: AN EXAMPLE
In an attempt to illustrate the use of
econometric models in concrete terms,
a recent forecast produced by the
Michigan Quarterly Econometric Model
of the U. S. Economy [92] is examined.
397
-------
In addition, several policy experiments
also based on this model are reviewed.
These numerical results are intended to
provide the policy-maker a realistic view
of what can be expected from econo-
metric models.
Forecasting With an Econometric
, Model. The Michigan Model [49] con-
sists of 61 equations and is similar in
outline to the model described in Sec-
tion II. A recent set of forecasts pro-
duced by this model is shown in Tables
V and VI. A careful examination of
these tables reveals that the Michigan
model prediction shows a reduction in
the rate of growth of gross national
product over the next two years.
Nominal GNP is expected to grow at a
rate of 11.8% over the 1972-73 period
and taper off to 8.6% over the 1973-74
period. The forecast shows that real
gross national product, i.e., nominal
GNP corrected for price changes, is
expected to grow at 6.2% over the
1972-73 period. A meager 2.4% in-
crease is predicted over the following
year.
At the same time that the economy
is slowing down, the unemployment
rate is expected to increase from 4.85%
in 1973 to 5.35% in 1974. This increase
in the aggregate unemployment rate is
expected to be accompanied by an in-
crease in the rate of inflation. Using
the gross national product deflator to
measure the price level, the projected
rate of inflation is 5.2% for 1973 and
6.1% for 1974. Projections of various
components of gross national product
are given in these two tables.
Of perhaps more interest than these
figures themselves is the way in which
the forecast was constructed. In this
connection the specification and estima-
tion of the model is only the first step
in the projection procedure. Since this is
a true ex ante forecast, i.e., a forecast
that is made before the fact, it is neces-
sary to forecast a number of variables
which are not explained by the model
and which are therefore referred to
as exogenous variables. The more im-
portant exogenous variables of the
Michigan model are
398
• The Federal budget,
• State and local purchases of goods
and services,
• Monetary policy variables such as
the discount rate and the money
supply,
• Farm prices, and
• Import prices.
Any error involved in the projected
values of these and the other exogenous
variables of the model will lead to an
error in the forecast values of the en-
dogenous variables or variables that are
explained by the model. This is, of
course, not the only source of error and
it is possible for these errors to offset
one another to some extent.
The likely error to which these pro-
jections are subject can be inferred from
past forecasts. The usual method used
to evaluate forecast accuracy is to de-
rive what are called ex post forecasts.
This involves the use of known values
of the exogenous variables as inputs to
the model. The corresponding values of
the endogenous variables are then cal-
culated and these solution values are
compared with the actual values. Error
statistics for selected endogenous varia-
bles are shown in Table VII. These
error statistics were calculated for the
period 1960.1-1969.4. The variables in
this table are defined as follows:
GNP : Gross National Product,
billions of 1958 dollars.
GNP$ : Gross National Product,
billions of current dollars.
u : Unemployment Rate, per-
cent.
PGNP : Gross National Product Im-
plicit Deflator; 1958 = 100.
These results can be used to deter-
mine the precision of the one-quarter
forecasts that are obtained on the basis
of perfect information about the exo-
genous variables. For example, if the
forecast errors are normally distributed
a 95% confidence interval (2-standard
deviations) would be approximately
± 5.6 billion for real GNP. A 95%
confidence interval for the unemploy-
ment rate would be ± .38. Using this
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TABLE VII
Ex Post Forecast Error Statistics,
The Michigan Model,
1960.1-1969.4
Variable
GNP
GNP$
u
PGNP
Root
Mean
Squared
Error
2.808
2.941
.190
.149
Error
Statistic
Mean
Absolute
2.287
2.370
.152
.129
Mean
Absolute
Percentage
Error
.397
.370
4.316
.115
Source: Hymans and Shapiro [93].
historical experience as a guide, the
most likely value of the unemployment
rate for the third quarter of 1973 is
4.68%. A 95% confidence interval
would be 4.68 ± .38 or 4.30 to 5.06. It
would be surprising indeed if the actual
unemployment rate were to fall outside
this interval. This rare event is expected
to happen no more than once in every
twenty forecasts.
These calculations of the precision of
the model forecasts are conservative in
the sense that they do not take into
account potential errors in the projec-
tion of the exogenous variables. As
mentioned previously, actual ex ante
forecasts are conditional on the exogen-
ous variables. If fiscal or monetary
policy turns out after the fact to be sub-
stantially different than was predicted,
the forecast error of the endogenous
variables is also likely to be much larger.
The entries in Table VII relate only
to one-quarter forecasts. It is also of
interest to examine how forecast ac-
curacy deteriorates as the forecast
horizon is increased. Error statistics for
multiperiod predictions are shown in
Table VIII for the same variables that
are contained in Table VII. The point
to note is the rate of deterioration of
forecast accuracy. For example, four-
quarter error in the unemployment rate
forecast is double the one-period stand-
ard error. The errors in the GNP pro-
jection do not accumulate as rapidly
but the deflator errors build up even
more rapidly. These results are con-
sistent with the qualification that usually
accompanies an eight quarter forecast
to the effect that the second year is
illustrative only and indicative of likely
broad tendencies.
Other types of error statistics can be
calculated for models such as the Mich-
igan Model. For example, the number
of business-cycle turning points that are
accurately predicted can be computed.
The use of these and other ex post error
statistics to validate and compare
models is considered in the appendix
to this chapter. Perhaps the most im-
portant point of this discussion is that
the policy-maker should be aware that
econometric models are subject to pre-
diction error. He should insist that error
statistics such as those described above
should accompany the model and any
forecasts that are presented. Only then
will he have an idea of the range of
error that is likely to be observed.
Policy Analysis With An Econome-
tric Model. Alternative economic pol-
icies can be examined with the aid of an
econometric model. Two policy changes
that illustrate some of the dynamic
properties of the Michigan Model are
discussed in this section. The first in-
volves a permanent increase of $1 bil-
lion in State and local government pur-
chases of goods and services. The other
involves the use of monetary policy to
lower the treasury bill rate by 100 basis
points.
The numerical results of the fiscal
policy experiment are shown in Table
IX. The new variable in this table,
UM%, is the unemployment rate of
males, 20 years of age and older. The
TABLE VIII
Root Mean Squared Errors for One to
Four Quarter
Forecasts Over 1961.1-1969.4
Variable
GNP
GNP$
u
PGNP
Number of Quarters
1 2 3
3.19
3.43
.21
.14
3.60
4.18
.27
.27
4.81
5.66
.30
.24
4
4.76
5.87
.42
.32
Source: Hymans and Shapiro [93].
401
-------
TABLE IX
Fiscal Policy Simulation With the
Michigan Model: Response to a One
Billion (1958 Dollars) Increase In
State and Local Government
Purchases
Quarter
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
GNP
.85
1.64
2.16
2.59
2.92
3.17
3.32
3.39
3.36
3.22
2.96
2.59
2.10
1.45
.65
-.22
Response
UM%
-.04
-.10
-.15
-.20
-.22
-.24
-.25
-.25
-.25
-.23
-.21
-.18
-.13
-.08
-.02
+ .05
PGMP
.02
.02
.02
.01
.02
.04
.05
.09
.14
.20
.27
.35
.43
.56
.58
.63
Source: Hymans and Shapiro [93].
results show that the response to the
increase in government spending reaches
a peak some eight quarters after the
policy is initiated and then begins to
lose its impact. At the end of fifteen
quarters, the income effects are negli-
gible. The unemployment rate reflects
this same pattern with a cumulative
reduction in the unemployment rate
until the eighth quarter followed by an
increase. At the 16th quarter, the econ-
omy ends up with no change in real
GNP, no change in the unemployment
rate, but a higher price level than would
have been the case without the increase
in government spending. However, all
during the period GNP has been higher
and the unemployment rate lower than
would have been the case. The price of
this increase in real output is the infla-
tion that would be experienced over the
period.
The results of the monetary policy
experiment are shown in Table X. The
interesting point of this simulation from
the point of policy design is the long
lag in the response to monetary policy.
Not until after the eighth quarter does
the response begin to build. Indeed, it is
402
almost three years before the increase
in real output is significant. Just as the
predictions described previously are
subject to error, so to are these policy
simulations. These simulations give only
likely affects on the assumption that
there are no other changes except the
policy change. But since these impacts
are based on a model with estimated
coefficients, the results may be quite
misleading. Unfortunately, it is very
difficult to calculate tolerance intervals
for these multipliers. The reason for this
is that there is generally a large number
of unknown parameters which must be
estimated, as many as 100 or 200. It is
just not feasible to vary these param-
eters both individually and jointly to
determine the sensitivity of the solution
to these parameter variations. Such sen-
sitivity analyses, even on a small scale,
would be extremely valuable in an
evaluation of the usefulness of the
model for policy analysis purposes. The
policy-maker should routinely insist on
such studies so that undue precision will
not be attached to the results of policy
simulations.
Concluding Remarks. This section
has attempted to illustrate the use of
econometric models in forecasting and
TABLE X
Monetary Policy Simulation With the
Michigan Model: Response to a 100
Basis Point Reduction In the
Treasury Bill Rate
Quarter
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
GNP
0
-.02
-.06
-.09
-.10
-.09
-.06
.03
.19
.40
.61
.99
1.74
2.66
3.34
3.60
Source: Hymans and Shapiro [93].
-------
policy analysis. The general theme that
has been emphasized is that the models
that are available today are subject to
error. In some cases, these errors are
substantial. The policy-maker should
insist on tolerance intervals for forecasts
and on sensitivity studies for simulation
experiments. Otherwise, he is likely to
be misled as to the accuracy of the
results generated by the model.
The scale of many of the models that
are available may at first appear to be
a deterrent to their use by policy-
makers. However, with the spread of
time-shared systems, it has become a
relatively simple matter to use these
models. Policy simulations of the variety
described previously can be performed
routinely with the software that is now
available. It is possible to subscribe for
a nominal fee to DRI, the Wharton
Model, and others. Such a subscription
typically includes quarterly forecasts
and entitles the user to access the model
for policy experimentation. Thus the
use of even very complex models should
become rather routine in the next sev-
eral years. With such ready access, it is
imperative that policy-makers under-
stand the limitations of these models lest
they be disappointed in the results.
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-------
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Appendix
The purpose of this appendix is to
provide a brief technical introduction
to the construction and use of econome-
tric models. In the first section of this
appendix, model construction is con-
sidered. The interrelated steps of spe-
cification, estimation, and validation are
described in some detail. Various simul-
taneous equation estimation methods
are reviewed and several validation tests
are summarized. The second section
outlines the use of econometric models
in forecasting and policy analysis.
Econometric Models
An econometric model was previ-
ously defined as an empirical economic
model. There are three essential steps in
the construction of an econometric
model. First, the relationships of the
model must be specified explicitly in a
form amenable to statistical analysis.
Second, the unknown parameters must
be estimated from data on the variables
contained in the model. Finally, the
model must be validated to determine
the extent to which the model is con-
sistent with known properties of the
system that is being modeled. These
three aspects of model construction:
specification, estimation, and validation,
are discussed in this section.
Specification. The specification of the
equations of the model is perhaps the
most critical step in the construction of
an econometric model. The reason for
this is that the statistical procedures
employed in estimation and hypothesis
testing are predicated on the assumption
that the specification is correct. An in-
correct specification can lead to incor-
406
rect or misleading inferences being
drawn from the model.
In the specification stage of an econ-
ometric study the basic functional re-
lationships are set out. Returning to the
example of the Introduction, the de-
mand function is written as
D=D(p,q,y,t)
(A-l)
where the variables D, p, q, y, and t
are as defined previously. Writing the
demand function in this general form
is not without content. For even in this
general form, the function indicates
which variables are being entertained as
direct determinants of the quantity de-
manded per unit of time. In this con-
text, only four variables are included in
the demand function.
In addition to the selection of var-
iables, it is necessary at the specification
stage to distinguish between endoge-
nous and exogenous variables. Endoge-
nous variables are those variables that
are to be determined by the model.
Exogenous variables are those variables
determined outside the model which
have a bearing on the determination of
the endogenous variables of the model.
The set of exogenous variables can be
further subdivided into these variables
that can be controlled or partially con-
trolled by the policymaker and those
which cannot be so controlled. In the
commodity market example, the tax
rate t can presumably be controlled by
the policymaker whereas the price o
competing commodities, q, cannot be
directly controlled.
The number of variables included ir
the model depends to some extent or
-------
the purpose for which the model was
constructed and on the nature of the
process being modeled. The division of
the variables between endogenous and
exogenous similarly depends on these
same considerations. For example, if
the policymaker is specifically con-
cerned with the development in a single
commodity market, it may not be too
great a distortion to assume that in-
come, y, is exogenous. If the commodity
market were the market for onions, this
would be more appropriate than if it
were the automobile market. In either
case, the feedback from market devel-
opments to the level of national income
would not be significant. If the single
market is the only consideration, then
the price of competing goods might
also be taken as exogenous. However, if
the policymaker is concerned with the
agricultural support program, a single-
market approach might not be appro-
priate since developments in one market
may have important repercussions in
other markets. In this case, it would
not be appropriate to regard the prices
of other goods as exogenous.
This may be summarized by noting
that a systems approach is necessary at
the specification stage of econometric
modeling. All the important variables
must be included in the system and all
of the important interdependencies
should be taken into account. The spe-
cification of the system is partially a
matter of the nature of the problem and
partly determined by the interest of the
policymaker.
The formulation of the general sys-
tem relationships is only part of the
specification process. It is necessary, in
addition, to decide on the functional
forms to be employed. Here, statistical
theory imposes certain constraints on
the types of functional forms that can
be employed. In general it is very diffi-
cult to deal with equations which are
not linear in the unknown parameters
of the system. Thus a linear approxima-
tion to (A-l), given by (!') in the
text, or a log-linear approximation to
(1), given by
In D = a0 — at ln(p + t)
+ a2 In q -I- 0,3 In q (A-2)
are linear in the unknown parameters
cc0, a,lt a,, and a.,. However, an equa-
tion of the form
D = a0(p + t)-<»q« + a3y (A-3)
is not linear in the parameters and
would lead to severe problems in
parameter estimation.
Ideally, the theory on which the
model is based would indicate the func-
tional forms to be used. However, eco-
nomic theory is frequently not suffi-
ciently precise to indicate the variables
that should be included in the equa-
tion, not to mention the functional
form. This is particularly true when it
comes to dynamic systems. It is gen-
erally true in commodity models, for
example, that the quantity demanded
per month responds with a distributed
lag to price changes, That is, because
of inertia in buying habits and lack of
information about potential substitutes,
consumers adjust with a lag to price
changes. This might lead to the dynamic
linear specification
D, = a0 — Mp + t)j + a2qj
+ a-jj + aJVi (A-4)
for example. However, this is only one
of a variety of lag patterns that could
have been introduced and economic
theory often provides almost no guid-
ance in this matter.
A final aspect of the specification
phase of an econometric study involves
the introduction of the stochastic prop-
erties of the model. No matter how
complex the model, it is extremely
unlikely that the model will correspond
exactly to the real system that is mod-
elled. This inexactness is recognized by
introducing an error term with certain
properties in the equations of the sys-
tem. For example, the equation (A-4)
becomes
+ a3yj + o^Dj,! + Uj (A-5)
where Uj is a random variable with a
zero mean and finite variance a2. In
addition, it is often assumed that the
407
-------
error term exhibits no serial correlation
so that us and us_7 are uncorrelated for
j T^ 0. A specific density function such
as the normal density is also frequently
assumed for the disturbance term but
this is not always the case.
By way of summarizing the specifi-
cation stage of econometric modeling,
the standard linear econometric model
is introduced. The model contains n
jointly dependent, endogenous variables
denoted by the vector y and m pre-
determined variables denoted by the
vector z. These predetermined variables
include both exogenous variables and
lagged values of the endogenous var-
iables. The model is written as
By + rz = M
(A-6)
where B is a matrix of dimension
n X n, r is a matrix of dimension
n X m, and w is a vector of n disturb-
ances, one for each equation. The point
to note is that there is one equation for
each endogenous variable, otherwise
the model would not be complete. Eco-
nomic theory is used wherever possible
to select the variables for each equation.
Thus some of the elements of the co-
efficient matrices B and r will be zero.
The problem now is to estimate the
non-zero elements of these coefficient
matrices.
Estimation. The unique feature of the
linear econometric model (A-6) is the
fact that the n endogenous variables in
the vector y are simultaneously deter-
mined. Econometric theory has de-
veloped methods to estimate the param-
eters of the matrices B and r which take
this simultaneity into account. Indeed,
a number of estimation procedures have
been developed and it is necessary to
choose from among a set of estimators.
The choice turns on several considera-
tions. In some instances the form of
the model will be sufficient to determine
the appropriate estimation procedure.
More often than not, however, the
estimation procedure that is used will
be a compromise between the ideal
estimation procedure and a procedure
that is feasible from a computational
point of view. The following discussion
408
attempts to acquaint the reader with
several alternative estimation proce-
dures and some of the criteria that can
be used to choose among the esti-
mators.
The simplest estimation procedure
both conceptually and from the point
of view of implementation is the method
of least squares applied to each equa-
tion. If /Jj denotes the ith row of B and
yj. denotes the ith row of r, the least
squares estimator is obtained by mini-
mizing
N
with respect to the elements of &. and
7i. The sum of squared errors, Sj, is
defined over the sample of N observa-
tions on y and z. The entire set of
parameter estimates, obtained by re-
peating this procedure for i = 1, 2,
. . . , n, are referred to as ordinary
least squares (OLS) estimates.
The OLS estimates do not, in gen-
eral, have very attractive properties. In
particular, the estimates of the param-
eter /3j are not consistent. That is, as
the sample size increases without limit,
the estimate of /J( does not generally
converge to BL. This rather serious
problem does not arise in one particular
case; that is, if the model is fully recur-
sive. A model is said to be recursive if
the matrix of structural coefficients B is
triangular and the covariance matrix of
the disturbance vector u is diagonal.
What this means is that y± is jointly
determined by y2, y3, . . . , yn; y2 is
jointly determined by y3, y4, . . . ., yn;
and so on. In addition the disturbance in
the first equation is uncorrelated with
the disturbances in all other equations.
In this special case, ordinary least
squares yields best linear unbiased esti-
mates of the parameters. That is, the
expected value of the least square esti-
mates of the parameters are the actual
values and the estimates have a smaller
variance than any other estimator that
is a linear function of the observations
on y. Except in this special case, ordi-
nary least squares is not recommended.
It might be useful to point out that
-------
the problem with the use of ordinary
least squares arises in the attempt to
estimate the structural coefficient in
the matrix B. One way around this
problem is to focus attention on the
reduced form of the model which is
given by
Yn + S &JYJ +
t = ul
y = ir z + v
(A-8)
where -rr = — B~1r and v = B~lu. Each
equation is now a function of only pre-
determined variables and the simul-
taneous equation problem does not
arise. The application of ordinary least
squares to each reduced-form equation
yields an estimate •& of the coefficient
matrix -a. Provided the predetermined
variables are uncorrelated with the dis-
turbances, this estimate has the de-
sirable properties of a least-squares
estimator.
There are several potential problems
with this approach, however. First, the
full vector z which now enters each
equation of the reduced form system
(11) may have a large number of ele-
ments. Indeed, it is not unusual in large
models for the dimension of z to ex-
ceed the number of observations that
are available to estimate •£. In this case
the reduced-form estimator cannot be
used. A second problem is that the
reduced form estimator does not use
any of the restrictions on the coeffi-
cients matrices B and r to estimate -n.
A more efficient estimation procedure
would use this information. Finally, the
coefficients of B and r are typically of
direct interest to the policymaker. Only
in the special case in which the model
is exactly identified is it possible to
unscramble the relationship £ = — B'^r
to obtain estimates of B and r. For
these reasons, reduced-form estimation
is not generally advocated.
Perhaps the most popular estimator
that avoids the pitfalls of ordinary least
squares but retains much of the sim-
plicity of the least squares procedure is
Two-Stage Least Squares (TSLS). The
essential features of TSLS can be
illustrated by a consideration of the
first equation of the system which is
written as
Typically, a number of the coefficients
jSij and y13 will be zero. Let &/ and j^'
denote the nonzero coefficients. Then
(A-9) can be written as
Yu + £ /3'uYjt + 2 -/i
j=2 3=1
= u
lt
(A-10)
with an appropriate reordering of the
endogenous and predetermined varia-
bles, if necessary. In the first stage of
the two-stage estimator, the endogenous
variables included in this equation, y2,
YSJ • • • > Yn'> are regressed on the pre-
determined variables as in the reduced
form equations (A-8). Reduced-form
predictions of yz, ys, • • - -, yn- afe then
obtained from
yt = irzt (A-ll)
for the sample period t= 1, 2, . . . ,
N. The parameters in (A-10) are then
obtained by minimizing the sum of
squared errors
N
2
t=l
Yit + 2 /
J=2
+ £ -
(A-12)
with respect to the unknown param-
eters.
This estimation procedure is not
without its difficulties. If the number of
predetermined variables exceeds the
number of observations, the first-stage,
reduced form estimator cannot be com-
puted. In this case a procedure that is
employed is to regress y} not on the
full set of variables z, but rather on
the first m" principle components of
this set. This circumvents the problem
but introduces the need to choose m"
and the first-stage estimates and hence
y and thus the second-stage estimates
may be sensitive to the value assigned
to m".
Other estimation procedures are often
discussed but seldom used in practice.
These alternative estimators will only
be mentioned here. The two-stage esti-
mator uses some of the information
about the complete system but not as
much as it might. In particular, it takes
409
-------
into account the fact that ylt y2, . . . ,
yn are jointly determined but it does not
use the fact that the deviations ut may
be correlated with the deviations Uj
(j = 2, 3, . . . , n). If the covariance
matrix of the disturbances process is
not diagonal, this should be taken into
account in the estimation of the param-
eters. The estimation procedure referred
to as three-stage least squares accom-
plishes this. The estimation procedure
has not been employed very frequently
in the estimation of parameters of
econometric models so it will not be
discussed further.
The two- and three-stage procedures
make use of system information but
do not incorporate potential knowledge
about the distribution of the disturbance
vector. The method of maximum likeli-
hood can be applied to derive parameter
estimation procedures if the distribu-
tion of the disturbance vector is known.
It is generally necessary to assume that
the error process is normal for lack of
further information. The computational
problems become rather prohibitive in
all but the simplest cases. Hence, maxi-
mum likelihood procedures are not used
very frequently in the estimation of
national and regional econometric
models.
By way of summarizing this discus-
sion of parameter estimation, the prac-
tical choice among estimation pro-
cedures usually reduces to ordinary least
squares applied to the structural equa-
tions, ordinary least squares applied to
the reduced form or two-stage least
squares. There is no simple rule-of-
thumb that can be given to select the
best estimator from this group. The
preference from the point of iew of
the theory of estimation is for the two-
stage estimator if the model is cor-
rectly specified. This is a severe quali-
fication. It means that the investigator
should be convinced that the constraints
imposed on the system in the form of
zero coefficients for some variables are
correct. Otherwise more may be lost
by imposing incorrect constraints than
by disregarding the constraints alto-
gether and applying ordinary least
410
squares to the original system, equation
by equation.
Validation. An important aspect of
any econometric study is the validation
of the model that has been constructed.
Validation generally refers to the proc-
ess by which the validity of the model
is established. This process generally
involves successive confirmation of the
model as a useful decision-making de-
vice. A sequence of successful applica-
tions of the model provides the basis for
the determination of the circumstances
in which the model contributes sig-
nificantly to the decision-making proc-
ess. In this sense, the validation of a
model is a continuing process.
In view of the fact that the specifica-
tion and estimation of an econometric
model are frequently an interdependent
process, the model that eventually
emerges from this stage of the investiga-
tion may be sample-dependent to an
undesirable degree. What typically
happens in model construction is that a
preliminary model is specified and the
parameters are estimated. Some of the
estimated parameters turn out to be
insignificant so those variables are
dropped from the model. Inevitably
other variables are added to the model
and the dynamic, distributed-lag rela-
tionships are empirically determined to
a large extent. Thus the empirical model
that emerges may depend on the pecu-
liarities of the sample data to an un-
warranted degree. It is desirable to test
for this possibility, if at all possible,
before using the model in a decision-
making context.
At the present time, there is no uni-
versally accepted set of tests of validity
of an econometric model. However, the
work of Howrey [14] and Dhrymes,
et al. [5] suggest that it is useful to view
the problem of validation in the fol-
lowing way. Three types of tests are of
particular interest in connection with
validation. These are
• Tests of data conformity,
• Comparisons of alternative models,
and
• User-oriented criteria of success.
-------
These tests are discussed in detail in
Howrey [14] and are merely sum-
marized here to give the reader an idea
of what is involved.
Tests of data conformity attempt to
determine the extent to which the data
are consistent with the empirical model.
Some of the tests that have been intro-
duced in this connection can be based
on the same data that are used in
parameter estimation. However, more
powerful tests are generally obtained if
a different set of data is used to validate
the model. A type of test that uses post-
sample data, i.e., data beyond the
sample period that was used in the esti-
mation of the parameters, is the test for
structural stability. Returning to the
first equation of the system (A-6), the
empirical equation is
(A-13)
where b1( is the estimate of y82j and c^
is the estimate of ylr It is assumed that
these parameter estimates are based on
a sample of N observations (t = 1, 2,
. . . . , N). Now suppose that r addi-
tional observations for t = N+l,
N + 2, . . . , N + T are available. To
test for structural stability, the proba-
bility that these additional observations
were generated by the empirical equa-
tion (A-13) is calculated. If this proba-
bility is small, say less than .05, then the
model is rejected. Otherwise the data
are consistent with the model and the
model is retained.
The model might fail this test for a
variety of reasons. The coefficients
might have changed between t= 1, 2,
. . . , Nandt = N+ 1, N + 2, . . . ,
N + r. The coefficients bj, or c13 may
have erroneously large or small values.
Relevant variables may have been
omitted from the equation. An incorrect
functional form may have been em-
ployed. There are clearly a number of
potential errors in the model. On the
other hand, a significant departure from
(14) is required to reject the model.
Thus it is not clear in general how
stringent such a test might be. As indi-
cated by Cooper [37], the test does
discriminate against several aggregate
econometric models that have been
published.
A battery of tests based on the
sample data used to estimate the param-
eters of the model has been developed
by Ramsey [24]. These tests are con-
cerned with testing for correct func-
tional form, testing for omitted varia-
bles, and testing for correlation of the
regressors with the disturbance process.
Although these tests are not now per-
formed routinely, they provide useful
information which is relevant to the
validation of a model. If a model passes
all these tests it is retained, otherwise
it is rejected.
The tests described thus far are con-
cerned with the evaluation of a single
model and are aimed at providing an
answer to the single question "Is the
model consistent with the data?" A
second phase of the validation process
involves comparisons of the model with
alternative descriptions of reality. This
is an exercise in hypothesis testing in
which the model under investigation is
treated as the null or maintained hy-
pothesis while alternative models are
considered as potential candidate mod-
els. The motivation for tests of this
type derive from a consideration of the
prediction accuracy of a model. If the
predictions of a complicated econo-
metric model are not at least as good
as those of a simple extrapolative model,
the econometric model is rejected.
Formal tests of this sort turn out to be
very complicated unless one model can
be written as a submodel of the other.
If this is true, then the two hypotheses
are nested and classical statistical
methodology can be used to test the
hypotheses. If the hypotheses are not
nested, a relatively simple test procedure
is not available. In this case several
approximate tests are discussed in
Howrey [14].
A final set of tests of the validity of
a model involves an evaluation of the
ability of the model to aid the policy-
maker. Zarnowitz [31] has considered
the problem of validation from a user
411
-------
point of view and finds that it is not
easy to implement. The conditions that
must be met include the following:
• the errors must be identifiable
• the preferences of decision makers
must be known
• the constraints under which the
decisionmaker operates must be
known
• the cost of using the model must
be known.
If all these are available then the "suc-
cess" of the model can be measured by
the reduction in the cost of incorrect
decisions which are avoided by the use
of the model. This user-oriented ap-
proach to model validation is to some
extent subjective and depends heavily
on the specific objectives of each user.
Hence, there are no published examples
of this type of validation. Nevertheless,
it is an important element in the
evaluation of an econometric model. As
models are used in the decision-making
process, it is expected that their use
will be under continuous review.
Forecasting, Analysis and Control
One of the primary reasons for the
construction of an econometric model
is to use the model as an aid in eco-
nomic forecasting. In addition to this,
however, models are also extremely use-
ful in the examination of alternative
economic policies. Going one step
further, a model can be used to aid in
the design of optimal policies. These
three areas constitute the important
potential uses of econometric models
and will be considered in some detail in
this section.
Forecasting With An Econometric
Model. In this discussion of the use of
an econometric model in a forecasting
context, it is convenient to rewrite the
reduced-form system of equations (A-8)
+ Bryt_r + C jct + vt (A-14)
This result is obtained from the re-
duced-form equation by separating the
412
lagged endogenous vectors yt_l5 yt_2,
. . . , yt_r from the exogenous variables
*t in the vector zt of predetermined
variables. The matrices B^, B2, . . . ,
Br, and C are obtained from TT and
denote matrices of estimated coeffi-
cients. The vector vt of disturbances is
assumed to be serially uncorrelated.
Several types of forecasts can be gen-
erated using this equation. It is useful
to distinguish among these different
types of forecasts especially in connec-
tion with the analysis of forecast error
and in connection with the comparison
of alternative models. A first distinction
that is useful is between ex ante and
ex post forecasts. An ex ante forecast
refers to a forecast that is made before
the values of the exogenous variables
are known. If yt] denotes the predicted
value of yt one period in advance, then
it follows from (A-14) that
t1 = S Sp-t-i +
(A-15)
is the one-period, ex ante forecast of the
vector yt. The one-period, ex post fore-
cast of yt is given by
t1 = 2 Jtyt-j + c *t
(A-16)
The difference between (A-16) and
(A-15) is that in (A-15) the exogenous
variables are forecast whereas in (A-16)
the actual values are used.
Ex post forecasts are particularly use-
ful for an investigation of the validity
of the model. The ex post forecast error
depends on the disturbance vt and the
errors in the estimates of the coefficient
matrices. The ex ante forecasts include
an additional component that results
from errors in the predictions of the
exogenous variables. This ex ante fore-
cast error is useful for determining the
potential range of error of uncondi-
tional forecasts whereas the ex post
forecast error indicates the range of
error of conditional forecasts.
In addition to the one-period fore-
casts, y,.1, multi-period forecasts can be
-------
generated using (A- 14). For example,
the two-period, ex ante forecast is
In general, a ^-period forecast is given
by
+ S
k=x
t-k + C *t» (A-17)
An additional source of error arises in
the multiperiod forecast since the lagged
endogenous vectors yt_l5 yt_2» • • • ,
>'t-y+i must be forecast in advance. This
dynamic forecast gives rise to the accu-
mulation of forecast error which is of
interest in the comparison of models.
A model that exhibits a slow error
buildup is generally preferable to one
with a rapid error accumulation.
This discussion of forecasting with an
econometric model has been couched
in terms of the linear model (A-14).
However, many current econometric
models contain some nonlinearities so
that this discussion is not completely
relevant. Fortunately, it is not difficult
to modify the results given above to
include the case of nonlinear models.
In particular, it is assumed that the
reduced form can be written as
(A-18)
where F[-J denotes a vector of func-
tions. By analogy with the linear model,
a one-period, ex ante prediction is de-
fined by
= F(yt.lt yt_,,
Xf1, 0)
(A-19)
As Howrey and Kelejian pointed out
[15], this is not an unbiased forecast
since, in general, the expectation of a
function of a random variable is not
equal to the function of the expectation
of the random variable. More recently,
Haitovsky and Wallace [12] have found
that the bias in (A-19) is indeed statisti-
cally significant for at least one macro-
economic model.
An unbiased one-period, ex ante fore-
cast could be obtained by numerical
methods. By averaging over a number
of replications of
^t1 = F(yt.1, yt_,, . . . , 3Vr> Xt1, vt)
(A-20)
an unbiased forecast is obtained. Each
replication in (A-20) involves an evalu-
ation of the function F(-) with a ran-
domly generated value of x^ and vt.
The situation is even more complicated
in the multi-period prediction case. In
order to obtain an unbiased forecast,
replications of
must be obtained and averaged. Al-
though no empirical work has been
conducted on this problem, it is almost
certain that the unbiased multi-period
prediction would deviate significantly
from the corresponding biased f-period
prediction given by
y,.,
, . . . ,y\ r+1,
. ,yt_r.V>0)"
(A-22)
For any particular non-linear model,
there is a need to investigate the impact
of nonlinearities on the predictions
generated by the model.
Policy Analysis With An Econo-
metric Model. Policy analysis with a
linear econometric model can be il-
lustrated by returning to the reduced-
form system (A-14). The vector xt of
exogenous variables is partitioned into a
subvector of control variables, denoted
by gt, and a subvector ht of independ-
ent, or uncontrolled, variables. The
matrix C is partitioned conformably so
that the reduced form system can be
written as
(A-23)
Alternative policies are characterized by
assigning different values to the ele-
ments of gt. The properties of alterna-
413
-------
tive policies can be determined from
this reduced-form system.
The impact multiplier associated with
a change in one of the elements of the
vector of control variables is defined by
. = Pj
(A-24)
which is the jth column of the matrix P.
The immediate impact of a unit change
in gjt on ykt is thus Pkj. The matrix P
is the matrix of impact multipliers that
are used to compare the immediate
effects of alternative policy changes.
This same system of equations can be
used to calculate the dynamic multi-
pliers associated with a policy change.
The term dynamic multiplier refers to
the time path of the response of the
vector yt to a change in gjt. That is,
the response in period t + k to a unit
change in the control variable g3 in
period t is
+
(A-25)
for k= 1,2, . . . .
The impact and dynamic multipliers
for a nonlinear model can be defined
in an analogous way. For example, the
vector of impact multipliers correspond-
ing to a change in g5 is given by
, yt-r
(A-26)
where F(') is the vector of functions
of the reduced-form (A-18). It is again
necessary to point out that, in general,
this is a biased estimate of the impact
multiplier. It is, nevertheless, the multi-
plier that is usually calculated. An
equally important point to notice about
this multiplier is that, in general, it will
not be a constant but will depend on
the values assumed by the predeter-
mined variables. This added complica-
tion is one of the features that makes it
rather difficult to work with nonlinear
models.
The dynamic multiplier 3yt+k/3gjt is
given by
414
(A-27)
Once again, the sequence of multipliers
defined in this way is biased. Moreover,
the sequence is a function of the time
paths of the variables of the system.
It is useful to consider briefly the way
in which the dynamic multipliers de-
fined in (A-27) are calculated in prac-
tice. First, a control solution ytc for
t = r+ 1, r + 2, ..., r + T cor-
responding to the initial conditions, yrc,
yVi> • • • , yic and the control path
gf, hf t = r+l, r + 2, . . . , r + T
is obtained from (19) with vt = 0. This
control solution provides the basis for
comparison of alternative policies. A
new solution corresponding to gt' is ob-
tained starting from the same initial
conditions and using the same values
for htc. The difference between the new
solution yt' and the control solution ytc
is the response path to the policy change
given by §t' — gf. Generally, an itera-
tive method is used to solve the non-
linear system. Some of the algorithms
that have proved to be useful in this
connection are described by Fromm
and Klein in [9].
Optimal Economic Policy. In addi-
tion to the analysis of alternative ad hoc
policies as described above, it is pos-
sible to use an econometric model in the
design of optimal economic policy. In
order to do this, it is necessary to intro-
duce explicitly an objective function
which compares alternative outcomes
of the system. The objective or welfare
function is written as
gi,
, yT;
• ,8?)
(A-28)
to indicate that the policymaker is con-
cerned with the values of the endoge-
nous variables yt as well as the values
of the control variables gt over the plan-
ning horizon t = 1, 2, . . . , T. The
values assumed by the exogenous var-
iables ht may also be of interest to the
policymaker, but since they are beyonc
-------
his control, there is no need to include
them explicitly in the objective func-
tion.
The economic policy problem is to
maximize the welfare function subject
to the constraints imposed by the eco-
nomic system characterized by (A-18).
In this general form, this is a non-linear
programming problem with stochastic
constraints which is a rather intractable
problem. Hence, it is necessary to
simplify the problem in order to obtain
a problem that it is feasible to solve.
A simplification that makes the prob-
lem somewhat more tractable is the in-
troduction of a quadratic, separable
welfare function of the form
(A-29)
In this formulation, yt* and gt* denote
optimal values of the endogenous and
control variables and K,.1 and Kt2 are
symmetric positive semideflnite matrices
which assign costs to deviations of yt
and gt from the optimal values. For
example, if Ktr is a diagonal matrix
with diagonal elements kt«, then the
contribution of yt to the welfare func-
tion is
If the diagonal elements were all equal,
then the squared deviations (yjt — yjt*)2
would all have equal weight in the
objective function.
If this welfare function is combined
with the linear model (A-14), a solu-
tion can be obtained without a great
deal of difficulty. This type of economic
control problem has been discussed by
Chow [2], Pyndick [23], and others. If
the econometric model is not linear, the
usual procedure is to employ a linear
approximation in the neighborhood of
the control solution. An iterative solu-
tion process based on such a linear
approximation is discussed in a recent
paper by Holbrook [13].
It is readily apparent that one of the
major difficulties with this approach to
the design of economic policy is the
specification of the objective function.
To the extent that the policies derived
from the optimization procedure are
sensitive to small changes in the objec-
tive function, the policymaker may be
reluctant to implement the policies. If
optimal economic policies are this sen-
sitive, an awareness of the sensitivity
seems desirable.
Optimal economic control with an
econometric model is still in its infancy.
Much remains to be done before opti-
mal control methods can be applied
with any degree of confidence. Even so,
it is desirable for policymakers to be
aware of these developments so that
they will be prepared to describe their
preferences in the coherent and rigor-
ous manner that is required by the
control-theoretic approach to policy-
making.
tVUS. GOVERNMENT PRINTING OFFICE: 1974 O—535-365
415
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