EPA/530/SW-574
February 1977
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This report was prepared by the Mitre Corporation, Bedford,
Massachusetts, under Contract No. 68-01-2976. '" "4
~"~ 1
An environmental protection publication (SVi*-573| in the solid waste
management series. Mention of commercial products''does not constitute
endorsement by the U.S. Government.
Single copies of this publication are available from Solid Waste
Information, U.S. Environmental Protection Agency, Cincinnati, Ohio
45268.
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WRAP
A MODEL FOR REGIONAL SOLID WASTE MANAGEMENT PLANNING
User's Guide
SVY-574
This report ($i|i|I) was prepared for the Office of Solid Waste
***S|iEdward B. Berman and staff,
under the direction of Donna M. Krabbe
U.S. ENVIRONMENTAL PROTECTION AGENCY
1977
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Table of Contents
CHAPTER 1: THE WRAP MODEL
1
CHAPTER 2: DETAILED MODEL DESCRIPTION 5
Model Background 5
Equation Structure: Static Version 9
Cost Structure: Static Version 13
Equation Structure: Dynamic Version 14
Cost Structure: Dynamic Version 18
CROW-FLY Program 20
Processing Levels 21
Source Designation 22
Site Designation 22
Process Designation 22
Transportation Specification 22
Sizing the Model 23
Advanced Starting Point (or Basis) 27
CHAPTER 3: SPECIFYING THE MODEL INPUT 29
Summary of Input Cards: 29
Control Card 29
Dynamic Control Card 36
Title Card 37
CROW-FLY Card 38
Source Card 39
Site Card 41
The Process File: 44
Process Header #1 45
Process Header #2 47
Process Input Links Card 49
Process Output Links Card 50
Process Cost Card 51
Site Process Card 53
Transportation Card 55
Truck Card 57
Advanced Starting Point (or Basis) 58
CHAPTER 4: INTERPRETING THE MODEL OUTPUTS 69
Algorithm Outputs 69
The WRAP Model Outputs 71
CHAPTER 5: SAMPLE INPUTS AND OUTPUTS 85
N. E. Mass. B-2 Static Case 86
Inputs 86
Outputs 90
ill
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Page
St. Louis G Dynamic Case 92
Inputs 92
Outputs 94
CHAPTER 6: RUNNING TIMES EXPERIENCE 115
CHAPTER 7: GUIDANCE ON USING THE MODEL 117
How to Structure an Application 117
Controlling the Structure of the Solution 121
(Configuration Forcing)
How to Structure the Set of Sources .122
How to Structure the Set of Sites 123
How to Strip Down a Problem for Optimization 123
List of Figures
Figure Number Page
1 Piecewise Linear Approximation of a Concave Function 6
(Representing Economies of Scale)
2 Model Organization 7
3 The Plan Set 119
4 Illumination of Issues 120
List of Tables
table Number Page
1 Model Running Times 116
iv
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CHAPTER 1
THE WRAP MODEL
What to do with the millions of tons of solid waste produced
annually throughout the country creates difficult decisions that must be
addressed at local levels. These decisions, which were once rather
straightforward, are now complicated by the increasing costs of
disposal, new technologies, environmental regulations, and the
unavailability of land for landfill. These factors facing local
decision makers give rise to strong pressures towards the
regionalization of solid waste management functions. However,
regionalization itself creates two fundamental problems: the complexity
of the regional system design; and a problem of political consensus
amongst the participants. Both of these problems have to be addressed
by developing and clearly presenting technical and economic data about
the consequences of various regional approaches.
To assist decision makers who are considering the implementation of
regional solid waste management functions, the, U.S. Environmental Protection
Agency has sponsored the development of a computer model called WRAP
(Waste Resources Allocation Program). Based upon data inputs provided
by the users, WRAP sorts out the various options and indicates a
preferred solution which is the minimum cost regional plan that meets
all the constraints determined by its users. Use of the model enables
officials to study and analyze the costs and implications of all
available alternatives under consideration. By using WRAP, decision
makers can find answers to such questions as: Which technology should
be selected? Where should the facility and subscribing transfer stations
be located? Whom should they serve? How large should they be? What will
a system that meets all the objectives cost? What are good alternatives
and what will they cost? In sum, what is the most economically
preferred regional system design and what are the costs associated with
changing that design?
<\ key capability of WRAP is its ability to balance the economies of
scale .achievable through centralization of processing at one location
against the additional haul costs required for centralization. This
makes it possible to determine what levels of centralization make the
most economic sense.
WRAP consists of a series of equations which consider the sources of
solid waste generation over a given planning region, a set of sites, and
processes to be considered at those sites, as well as various site and
process capacity constraints. The processes can be transfer stations,
resource recovery processes (including the extraction of recoverable
resources to be marketed), secondary processes (which receive the
residue of primary processes as input) and various disposal processes.
WRAP further considers many transportation route alternatives from
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sources of waste generation to sites, and from sites to sites, with due
allowance for site traffic constraints.
Processing costs are input to WRAP so as to reflect the economies of
scale available for each process, and revenues from the marketing of
recovered materials. Haul costs are included, which increase directly
which both tonnage and travel time.
WRAP has three essential components:
structure - which assures that each alternative considered is
feasible in the sense that all wastes generated are entered
into transportation, that all wastes arriving at a site are
processed, that all residues generated are processed at the
site or entered into transportation, that no process exceeds
the indicated tonnage maximums, and that traffic constraints
are observed;
cost - which assures that each alternative is properly costed,
including economies of scale where appropriate; and
procedure - an organized mathematical search which allows those
options which improve the solution to be separated from those
that make it worse, and indicates when the least cost solution
has been identified.
To date, the WRAP model has been used in several locations by
decision makers who are considering regional solid waste management. In
Massachusetts, the model was used to identify the most efficient
regional system design for that state's first regional resource recovery
system. And in St. Louis, Missouri, WRAP was used to determine the
advantages of community participation in a proposed regional solid waste
management plan.
Comprehensive information that describes and documents the use of
the WRAP model is available to potential users. This information
comprises three volumes: A User's Guide; A Programmer's Manual; and a
full documentation of the model applications made for EPA.
This document comprises the User's Guide, which is addressed to the
individual, or group of individuals, who are intending to use the WRAP
model to assist in the decision-making process. The model is fully
described in terms of its makeup and equation structure to familiarize
the users with its capabilities. The guide additionally contains a full
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description of the kinds of data required for its use, as well as how to
prepare and utilize those data and how to interpret outputs. Examples
of prepared data inputs are provided, as well as a guide to the design
and operation of the model.
For further information about the WRAP model, call or write:
Office of Solid Waste Management Programs
ATTN: Systems Management Division (AW-464)
U.S. Environmental Protection Agency
Washington, D.C. 20460
Telephone (202) 755-9125
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CHAPTER 2
DETAILED MODEL DESCRIPTION
Model Background
WRAP is a fixed-charge linear programming model, using as the
optimizer an algorithm developed by Dr. Warren Walker.1
The fixed-charge capability of the model permits the representation
of economies of scale in process costs. Figure 1 illustrates a concave
total cost function, typical of solid waste processing, as represented
by several linear segments. Since the model is cost-minimizing, it will
seek out the lowest cost segment at any level of tonnage. Thus the
capability of treating cost in two parameters (fixed and variable, or
intercept and slope) permits the model to represent economies of scale
at any level of accuracy desired. In the actual model applications,
three-segment representations have been used for nearly all processes.
Model Overview
The model operates in two modes:
A. Static
B. Dynamic
In the dynamic mode, the total planning period is divided into from
two to four model periods. The model periods may each be any integer
number of years which add up to the planning period.
The model has a pre-processor, an optimizer, and a post-processor as
shown in Figure 2. Note that the pre-processor and post-processor
differentiate between the static and dynamic modes; but the optimizer
does not.
1. Walker, W. Adjacent extreme point algorithms for the fixed charge
problem. Technical Report No. 40. Ithaca, N. Y., Cornell
University, College of Engineering, Department of Operations
Research, Jan. 30, 1968. 23 p.
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The optimizer operates in four phases:
• phase 1: linear programming phase 1, generating a feasible
solution (i.e., no negative activity levels).
• phase 2: linear programming phase 2, generating an optimal
solution without consideration of fixed charges.
t phase 3: Walker algorithm without forcing, generating a local
optimum from adjacent extreme points which can improve the
solution; fixed charges are considered.
• phase 4: Walker algorithm with single or double forcing, seeking
a general optimum solution by forcing in one or two
columns at a time and rerunning phase 3. Fixed charges
are considered.
Although all four phases are built into the optimizer, WRAP as presently
configured enters phase 3 in all circumstances, thus bypassing phases 1
and 2. This bypass requires an advanced starting point, or initial
feasible basis. The user may provide a basis, but an advanced starting
point algorithm is built into WRAP and is brought into operation
whenever the user signals that a basis has not been provided.
There are five categories of transportation activities, as follows:
1. Source to ultimate site (i.e., landfill)
2. Source to intermediate site
3. Intermediate site to intermediate site
4. Intermediate site to ultimate site
5. Any of the above which bypass the truck constraints, such as:
t haul between collocated sites
t rail haul
t barge haul.
The transportation activities T will be superscripted as follows:
T15 includes all source to ultimate site transportation
activities whether in category 1 or category 5, but
T1 includes only category 1 transportation activities.
Similarly, T25 and T2
T35 and T3
and T1*5 and T1*.
8
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The T activities without the 5 superscript are used only in
the truck constraints.
Equation Structure: Static Version
There are seven basic equations in the static version as follows:
Source Balance Equations
For each centroid source of waste generation there is a source
balance equation,
Z: T» + E T?| - G,. (1,
where
T15 1s transportation 1n thousand tons per year from source 1
1k
to ultimate site k;
T25 is transportation in thousand tons per year from source i
to intermediate site j;
and
G is thousands of tons per year generated at site 1.
1
This equation assures that all tonnage generated at a source 1s entered
into transportation.
Intermediate and Ultimate Site Processing Constraints
For each intermediate site that is coded "limited" th re 1s a
processing constraint,
< K
p i JH jy -
where
P is processing in thousand tons per year at intermediate
site j, process p, linear segment 1;
K 1s an arbitrarily large number (e.g., 1,000);
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and
a = K/K is the capacitation coefficient for intermediate
JP JP
site j, process p;
where
K is the capacity in thousands of tons per year of process p
JP
at intermediate site j, assuming site j were totally
devoted to process p.
This constraint is omitted for an unlimited intermediate site.
Similarly;
for ultimate site k.
Each ultimate site has one constraint. If the site is coded
unlimited, a land constraint 1s entered:
where
d = dK/L is the land requirement coefficient for ultimate
k k
site k;
d is the land requirement in acre-feet per thousand tons per
year of sanitary landfill;
and
L is the available land at ultimate site k in acre-feet divided
k
by the number of years in the planning period.
An effective density (defined as the weight of refuse divided by the
volume of refuse plus cover, in place in a landfill) of 750 lbs/yd3 is
assumed.
If an ultimate site is coded limited, and if
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(1) either there is only one process at the site, or
(2) if all processes have the same coefficient a
kp
then the tighter of equation 3 and equation 3a will be entered for the
site.
If there are two or more processes at the site with differentiated
coefficients a ,
kp
then a single equation will be formed by selecting for each process the
larger coefficient from equation 3 or from equation 3a.
Intermediate Site Input Balance Equations
For each intermediate site there is an Input balance equation,
where
T35 is transportation in thousand tons per year from intermediate
site i, process p, to intermediate site j.
The total transportation into each intermediate site equals the
total processing at that site. The model is allowed to choose which
process and which linear segment to use for the site, based on cost-
minimization.
Ultimate Site Input Balance Equations
For each ultimate site there is an input balance equation,
where
T45 is transportation in thousand tons per year from
jpk
intermediate site j, process p, to ultimate site k;
and
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c is the density coefficient, or the ratio of the effective
P
density of raw refuse in place in a landfill (750 lbs/yd3) to
the effective density in place of the output of process p,
assuming that that output were to be landfilled without further
processing.
The total transportation into each ultimate site from all sources
and intermediate site/processes, equals the total processing at that
ultimate site, measured in equivalent (in volume) raw refuse tonnage.
Intermediate Facility Output Balance Equations
For each intermediate site/process there is an output balance
equation,
Tj», - bp E P . 0 (6)
1
where
b is the output coefficient for process p, or the tons of
P
non-saleable output per ton input;
and
T35 is the transportation in thousand tons per year from
Jpl
intermediate site j, process p, to intermediate site i.
The total transportation from each intermediate site/process to all
intermediate and ultimate sites equals the total non-saleable output
from processing at the intermediate site/process.
Truck Constraints
For each specified site or group of (up to three) collocated sites
to be subjected to a truck constraint:
^ *Ms (7)
where
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e is the reciprocal of tons per packer truck, as input
P
e is the reciprocal of tons per transfer vehicle, as input
t
^ c
2-.T is the sum of transportation activities of category c,
s
in thousands of tons, which either originate from or arrive
at any of the specified sites of set s;
and
M is the maximum number of trucks, in thousands per year,
s
permitted to service the set of sites s.
Cost Structure; Static Version
The cost for a transportation activity is the cost per ton
transported, defined as the cost per ton-minute times the number of
minutes. The cost per ton-minute is input separately for each source
and for each process; the one-way transit time is input separately for
each origin/destination pair, or generated by a subroutine from
longitude and latitude coordinates and from average speed to be input.
The number of minutes for a source origin is double the one-way transit
time; the number of minutes for an intermediate site origin is double
the one-way transit time plus a standard turn-around time, which is
input.
Costs for processing activities are input as a capital intercept and
slope and operating intercept and slope for each linear segment of each
process, together representing an annual cost function per ton per year.
The capital and operating slopes are added together in the static model,
so that their division within a correct total is arbitrary. The same is
true for capital and operating intercepts in the static model.
Succeeding linear segments of the same process should show increasing
intercepts and declining slopes.
A site-preparation cost, representing an amortized annual cost, is
input separately for each site, and is added to the capital intercept of
each linear segment of each process at that site.
A revenue per input ton is input separately for each site/process,
and is subtracted from the operating slope of each segment of the
site/process.
All other processing costs are input by process.
Each existing facility is identified as a separate process, e.g.:
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process No. 913 Existing Lowell incinerator
process No. 914 Exisitng Salem incinerator.
This separate process identification will permit differentiated costing
for existing facilities. An existing facility might have an intercept
equal to the amortized annual cost of environmental upgrading, and a
slope equal to the operating cost per ton. Sunk capital costs (and
committed costs as well) should not be included in the cost function of
an existing facility. A proper decision can be made by the model, as in
any other decision analysis, only if decisions are related to the costs
that they can affect. Both sunk costs and committed costs (i.e., costs
irrevocably committed, but not yet expended) can only distort the
decisions to be made by the model. They should properly be excluded.
Equation Structure: Dynamic Version
In the dynamic version, the processing activities P are not
segmented, and are free of costs. Additional equations are added which
require that processing activity in a period be less than or equal to
capacity put into place during that period and prior periods as far back
as its useful life or the start of the model, whichever is later. Costs
of capital and full-capacity operation are charged against capital
building activities K from the time of building to the end of the useful
life or the end of the model, whichever is earlier, and these are broken
into linear segments to represent economies of scale. An activity
representing underutilization of capacity is provided, with a refund of
operating cost slope, to permit the process to operate at less than full
capacity in any period desired (cost-minimization will assure that no
process operates at less than full capacity in all periods). This
device of charging capital and full-capacity operating cost, and
providing a refund of operating cost slope for less-than-full-capacity
operation, permits the model to represent the concave cost functions in
processing in a dynamic context, and also permits the model to overbuild
capacity in an early period in order to allow for growth without
incurring the additional intercept cost of a new capital-building
activity. The model may of course elect not to overbuild capacity if
that would lower the cost of the solution. The underutilization
activity also permits the model to abandon capacity before the end of
its useful life, if that will lower the system cost.
The dynamic version consists of nine basic equations as follows:
Source Balance Equations
For each centroid of waste generation in each model period there is
a source balance equation,
- G,. (8)
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where
T15 is transportation in thousand tons per year from
ikt
source i to ultimate site k in model period t;
T25 is transportation in thousand tons per year from
ijt
source i to intermediate site j in model period t;
and
G is thousands of tons per year generated in centroid
it
source i in model period t.
^Intermediate and Ultimate Site Processing Constraints
For each limited intermediate site in each model period there is a
processing constraint,
> a P ^ I/
^ JP JPt ^ K
where
P is processing in thousand tons per year at intermediate
JPt
site j, process p, in model period t.
Similarly; *
for each ultimate limited site k. In the dynamic model, this constraint
is omitted for both unlimited intermediate and unlimited ultimate sites,
since a land constraint is provided in equation 17.
Intermediate Site Input Balance Equations
where
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T35 is transportation 1n thousand tons per year from
ipjt
site i, process p, to site j, in model period t.
Ultimate Site Input Balance Equations
For each ultimate site in each model period there is an input
balance equation,
where
T1*5 is transportation in thousand tons per year from
jpkt
intermediate site j, process p, to ultimate site k, in model period t.
Intermediate Facility Output Balance Equations
For each intermediate site/process in each model period there is an
output balance equation,
- bpPjpt . 0
where
T35 is the transportation in thousand tons per year from
jpit
intermediate site j, process p, to intermediate site i,
in model period t.
Truck Constraints
For each time period and each specified site or group of (up to
three) collocated sites to be subjected to a truck constraint:
ETjt + ET* + e ET3 + LT < H (14)
where
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]CT is the sum of transportation activities of category c
st
in model period t, in thousands of tons, which either
originate from or arrive at any of the specified sites
of set s;
and
M is the maximum number of trucks, in thousands per year,
st
permitted to service the sites of set s in model period t.
Site/Process Capacity Balance Equations
For each intermediate site/process in each model period there is a
site/process capacity balance equation,
"jpt - SE Kjp]m * S.pt - 0 (IS)
where
K is the capacity in thousand tons per year of process p
jplt
at site j, linear segment 1, put into place at the
beginning of model period t;
S is the unused capacity, in thousand tons per year, of
jpt
process p at site j in model period t;
and
s is the earliest model period in which capccity of process p
put into place at site j would continue to be in operation in period
t, or the first model period, whichever is later.
Pkpt - SE K + S- 0 (16)
Similarly;
PI,,,* -
1 m=s
for each ultimate site k, process p, model period t.
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Land Constraints
For each ultimate site, there is a land constraint,
? dt"kPt * H (")
where
L is the available land at ultimate site k in acre-feet;
k
p is the sanitary landfill process;
and
d is the land requirement in acre-feet per thousand tons
t
per year of sanitary landfill, multipled by the number of
years in model period t.
An effective density of 750 lbs/yd3 is assumed.
This equation assures that the total landfill at site k over all
model periods does not exceed the land available at that site.
Cost Structure: Dynamic Version
An annual discount rate and an annual inflation rate are input into
the model (either of these may be bypassed by inputting rates of 1.000
in each case.)
Transportation cost is the sum of the annual discounted and inflated
costs over the years included in the relevant model period for
transporting one ton per year from origin to destination. The
undiscounted and uninflated costs per ton-minute, and the distances,
speeds, and times are obtained as in the static version.
Processing costs are input by process in cost sets. Each cost set
will contain an annual operating cost function of tons per year, defined
as an intercept and a slope, and an annual amortized capital cost
function of tons per year, defined as an intercept and a slope, for each
linear segment in the process. There is one cost set for each process
for each period in which its capacity may be built.
The amortized capital costs should represent the dollar outflow per
year to pay back the capital over the useful life of the process, and to
pay interest at an appropriate rate (e.g., 7% for municipal projects and
10% for private projects), on the unamortized balance. The interest
rate for amortization need not be related to the overall discount rate
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of the model. For amortization purposes, the actual useful life, and
not the remaining time in the model, is relevant. Both capital and
operating costs should be defined in dollars of the first year of the
model, since they are inflated from that point.
The annual amortized cost per dollar of investment is:
(Hi)"
where
i is the interest rate
and
n is the useful life.
A capital lead time is input for each process, representing the
average investment lead time on facilities and equipment prior to first
operational date, rounded to the nearest integer year.
Process costing (and capacities) assume that a process operates from
the beginning of one period to the end of another. Thus the useful life
is defined in whole model periods.
The process operating cost is discounted and inflated and summed
over the years included from the time of first operation to the earlier
of the end of its useful life or the end of the model. Capital costs
are inflated only to the year (start of operation - capital lead time)
and then discounted and summed over the same period as the operating
costs. This differentiation represents the fact that capital costs are
not subject to inflation once the commitment is made to pay them,
whereas operating costs inflate throughout the useful life.
After appropriate inflation and discounting, operating and capital
cost slopes are combined to obtain the slope of the linear segment, and
operating and capital cost intercepts are combined to obtain the
intercept of the linear segment. These costs are applied against
capacity building activities K.
The S activities, representing the refund of operating cost for non-
use of capacity, are costed by selection of the lowest operating cost
slope relevant to the site/process, and inflating, discounting and
summing over years of the relevant model period only.
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Process cost sets are input by process, site preparation costs are
input by site, and revenue per input ton is input by site/process.
Before inflation, discounting, and summing, the site preparation cost is
added to the capital cost intercept, and the revenue per input ton is
subtracted from the operating cost slope. These adjustments relate to
both K and S activities as appropriate.
If a process may be municipally financed at one site and privately
financed at another, it should be input as two separate processes in
order to allow cost differentiation.
It should be understood that the cost set for a period relates to
facilities which begin operations at the beginning of that period.
Thus, in model period t+1, a facility built in model period t would be
costed with the period t cost set, with the one exception of the revenue
per input ton, which relates to the period of operation. Thus, the
revenue per input ton of period t+1, would be subtracted from the slope
of period t operating costs to represent the undiscounted, uninflated
net operating cost per year in period t+1.
CROW-FLY Program
There are three CROW-FLY options:
0: CROW-FLY will not be used
1: CROW-FLY will be used to generate up to ten origin-destination
pairs; where input linkage or output linkage is missing (beyond
ten the model will abort); CROW-FLY will be used to complete
distance, speed, and time estimates as needed.
2: CROW-FLY will be used to generate all possible origin-
destination pairs within a maximum radius, and beyond that
limit where needed to complete input or output linkage; CROW-FLY
will be used to complete distance, speed, and time estimates as
needed.
The CROW-FLY Program, operating from coordinates in longitude and
latitude, generates origin-destination pairs, measures distances, finds
the shortest input linkage for a site, finds the shortest output linkage
for a site, and applies a standard speed, as appropriate. CROW-FLY
outputs can be available as a punched deck suitable for input as
transportation activities, or alternatively can be input directly into
the master program as transportation activities. A standard speed is
input into the model as well as a maximum radius. The standard speed is
used for all generated origin-destination pairs, and for any other pairs
where required to generate one-way transit time in minutes. In CROW-FLY
option 2, the maximum radius is used as a criterion to select generated
pairs. All pairs less than the maximum radius will be selected, plus
the shortest pair greater than the maximum radius where input or output
20
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linkage would otherwise be incomplete. CROW-FLY distances are straight-
line flat-earth distances in nautical miles, but are translated into
statute miles before being output to the CROW-FLY deck or to the master
program. A standard factor of nautical miles per minute of longitude at
approximately the center of the region is entered as input and used to
translate longitude differences into nautical miles.
If CROW-FLY option 1 or 2 is selected, all sources, intermediate
sites, and ultimate sites must be provided with coordinates in longitude
and latitude in degrees, minutes, and lOths of minutes.
Processing Levels
Four processing levels are provided in the model:
A. Transfer Station
Input linkage from sources and level A
Output linkage to levels A, B, and D
B. Primary Processing
Input linkage from sources and level A
Output linkage to levels C and D
C. Secondary Processing
Input linkage from levels B and C
Output linkage to levels C and D
D. Landfill
Input linkage from sources and levels A, B, and C
No output linkage
Levels A, B, and C are intermediate site levels and level D is an
ultimate site level. The A-to-A linkage permits a packer-to-van
transfer to be linked to a truck-to-rail or truck-to-barge transfer.
The C-to-C linkage permits ficticious processes to be established to
generate differentiated revenues for different types of residues to be
processed in the same secondary processing plant.
Fictitious B-level or C-level processes can be used to represent
differentiated landfill costs (e.g., one process for balefill and
another for standard sanitary landfill). If this is used, separate
ficticious sites must be identified for balefill and standard landfill
at the same real site (collocated) in order to achieve separate input
balance, and then a D-level site and a costless D-level process can be
driven by the two or more B or C-level site/processes to generate a
proper land impact. A Category 5 transportation activity (which
bypasses the truck constraint) with negative minutes will translate to a
zero cost transportation activity. An output of 100% should be used for
the B and C-level landfill processes, with the output densities of the
21
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processes preceding D-level being-used to control the land .Impact at D-
level. If differentiated land impact without differentiated cost is
desired, the use of ficticious B or C-level activities is not necessary
since that can be accomplished through the output densities of the
processes preceding landfill.
Source Designation
Sources should be numbered from 100 to 499, and need not be
consecutive.
Site Designation
The model provides a separate input balance and a separate site
processing constraint for each separate site identification number. The
user should use the same site number for collocated processes unless (1)
there is a need to differentiate input, or (2) there is a need to
differentiate land use. The use of the same site number permits the
model to select the process in the course of its search for a minimum
cost solution. It also reduces the required number of linkages. The
need to differentiate input requires the designation of separate site
numbers for collocated primary processing (B-level) and secondary
processing (C-level) since the former processes raw refuse and the
latter processes residue. The need to differentiate land use requires
the designation of separate site numbers for D-level processing
collocated with any other level.
A and B-level processes at the same site can be treated together and
can be assigned the same site number. A and B-level sites should be
numbered from 500 to 599, and need not be consecutive.
C-level processes should not be designated at the same sites where
A, B, or D-level processes are designated. Separate C-level site
numbers should be designated for C-level processes. These should be
numbered from 600 to 699, and need not be consecutive.
D-level processes should not be designated at the same sites where
A, B, or C-level processes are designated. Separate D-level site
numbers should be designated and numbered from 700 to 799, the numbers
need not be consecutive.
Process Designation
Processes should be numbered from 800 to 999, and need not be
consecutive.
Transportation Specification
Transportation links are from source to site or from site/process to
site.
22
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If a zero transportation cost 1s desired, as between two collocated
sites, (for example, primary and secondary processing at the same site)
an input of -0.1 minutes (or any other negative quantity) will be
translated by the model into a zero cost for the transportation
activity. No turnaround time will be added in this case.
An input of zero or blank minutes will be read as a blank in CROW-
FLY option 0 or 1, and as a zero in CROW-FLY option 2. Hence, if zero
minutes are desired in CROW-FLY option 0 or 1 (which will add the
standard turn-around time for a site origin) input a 1 in the last
minutes place; this will be read as 0.1 minutes, and permit the program
to continue. If this is too large, the decimal may be specified in the
minutes field of the transportation card, and a very small (but positive
number of minutes specified for the activity.
Where only one-way distance is provided, speed will be the standard
speed provided as input, if CROW-FLY option 1 or 2 is selected; in CROW-
FLY option 0, the run will abort.
Where none of the entries is provided, CROW-FLY will be-used for
distance, and standard speed will be used, if CROW-FLY option 1 or 2 is
selected; in CROW-FLY option 0, the run will abort.
Where one-way minutes is provided, it will be used whether or not it
is consistent with distance and speed inputs.
The set of transportation activities will be checked to verify that
each source and site/process has output linkage, and that each site has
input linkage. If linkage is missing, the shortest possible link will
be generated through CROW-FLY and entered into the Transportation
Activity File, if CROW-FLY option 1 or 2 is selected (up to 10 in option
1; unlimited in option 2); in CROW-FLY option 0, the run will abort.
If CROW-FLY is to be used only for the standard speed, it will still
be necessary to provide longitudes and latitudes for each source and
site. For this case, these may be input identically as 1 (or any
positive number).
Sizing the Model
Dummy Row and Column
An additional row and column have been added to the matrix as
follows:
Dummy Row: Capacitation, N.E.C. (Not Elsewhere Classified)
The sum of all processing activities which:
a. are at unlimited intermediate sites, and
23
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b. have no output
are less than or equal to a very large number. This equation insures
that there will be no activities other than slacks, which have only a
single coefficient. The presence of such activities has led to cases of
non-invertible bases in phase 1. This row is the last row in the static
model, and precedes the site-process capacity balance equations in the
dynamic model. (Phase 1 is now bypassed.)
Dummy Column: Column Z
An additional column with a minus one in each inequality (that is,
each site capacitation, land constraint, or truck constraint, and in the
capacitation n.e.c.) has been added for use in the automatic advanced
starting point algorithm. This column relieves each constraint by one
unit, and bears a variable cost of $1,000, so it will be easily driven
out of the solution in phase 3 if there is a feasible solution.
Whether column Z is required for an advanced starting point or not,
the program goes to phase 3 (linear programming with consideration of
fixed costs for adjacent extreme points only).
Sizing the Static Model
Rows and Row Order
There will be one source balance equation for each source, sorted in
order of source number. This will be the first set of equations.
There will be one site processing constraint for each limited
intermediate site, and one site processing constraint for each ultimate
site, sorted in order of site number. This will be the second set of
equations.
There will be one input balance equation for each separate site,
sorted by site number. This will be the third set of equations.
There will be one output balance equation for each separate site-
process with positive output. This will be the fourth set of equations.
Within the set, the equations will be sorted by process within site.
There will be a number of truck constraints as specified by the
user, and in the order specified by the user. This will be the fifth
set of equations.
There will be one capacitation, n.e.c., which will be the last
equation.
24
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Columns and Column Order
There will be a column for each separate transportation activity T.
This will be the first set of columns, and will be sorted as follows:
Major: category number (category 1-5)
Next: origin
Source
Source number
Site
Site number
Next: origin process by process number
Next: destination by site number.
There will be a column for each processing activity P, representing
each separate site, process, and linear segment. This will be the
second set of columns and will be sorted by segment within process
within site.
There will be one column Z, following the processing activities.
There will be a number of slacks equal to the number of
inequalities, and a number of artificials equal to the number of rows
minus the number of slacks (i.e., the number of equations). These will
be ordered slacks, and then artificials; within each set, the columns
will be ordered by the row number to which they correspond.
Sizing the Dynamic Model
Rows and Row Order
The static rows and row order exist in the dynamic model as well,
except:
1. a site processing constraint exists for an ultimate site
only if it is coded limited. (There is a separate land
constraint which cuts across model periods).
2. The set of static rows as modified is repeated in each
model period. The sort is:
major: model period
minor: same sort as the static model.
There is one capacitation, n.e.c., which follows the repeated static
rows.
There is a site-process capacity balance equation for each
combination of site, process, and model period which is indicated as
available in the input. The rows are sorted by model period within
25
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process within site. This set of equations follows the capacitation,
n.e.c.
There is one land equation for each ultimate site, sorted by site.
This is the last set of equations.
Columns and Column Order
The static transportation and processing columns exist in the
dynamic model, except:
1. the processing columns are site-process only (no
differentiation by linear segment).
2. the set is repeated in each model period.
The static columns are sorted:
major: model period
minor: same sort as the static columns.
The capacity-building activities (K) follow the repeated static
columns. There is one K activity for each site, process, model period,
and linear segment in which the process is indicated by the input as
available for capacity-building in the model period.
The K activities are sorted by linear segment, within process,
within site, within model period.
There is one underutilization (S) activity for each site, process,
and model period in which a corresponding P activity exists. The S
activities follow the K activities, and are sorted by process, within
site, within model period.
There is one column Z which follows the S activities.
There are slacks and artificials following Column Z defined and
sorted as in the static case.
The number of columns before expansion is the number not including
slacks and artificials.
The number of columns after expansion is the number including slacks
and artificials.
The WRAP object program currently available from the EPA will handle
a problem up to 90 rows by 360 columns (before expansion).
26
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Advanced Starting Point (or Basis)
An advanced starting point may be provided by the users (and that
fact must be indicated on the control card). If none is provided, an
advanced starting point will be selected by a subroutine. In either
case, the advanced starting point will be tested for feasibility. If it
is feasible (i.e., provides a solution to the system of equations with
no negative activity levels) the model will go to phase 3. If the
advanced starting point generates one or more negative activity levels,
the column with the largest negative activity level will be replaced by
column Z (which relieves all constraints) and the advanced starting
point will be tested for feasibility. If there is still a negative
activity level, the program will abort. If there are no negative
activity levels, phase 3 will be entered.
The advanced starting point must specify a number of columns equal
to the number of rows. The columns are specified by sequential column
number.
Advanced Starting Point Subroutine
Static Case
For all inequalities, the slack is selected. These are sequential
column numbers from the number of columns before expansion plus one
through the number of columns before expansion plus the number of
inequalities.
For each source balance equation, one type 2 or type 1
transportation activity is selected in which the source is origin; type
2 takes precedence over type 1; within each, the first available
transportation activity is selected.
For each input balance equation, one processing activity at the site
is selected. First precedence is given to minimum percent output by
weight. For equal percent outputs by weight, the lowest process number
and linear segment number at the site is selected.
For each output balance equation, one type 5 or type 3
transportation activity in which the site-process is origin is selected.
Type 5 takes precedence over type 3; within each, the first available
activity is selected.
Dynamic Case
For the static repeated equations the static rules for activity
selection are followed except:
For input balance equations, a processing activity selected
for a site in an earlier period is given first precedence for the
27
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next succeeding period for the same site 1f 1t is still
available.
For site/process capacity balance equations, the K activity matching
in site, process, and period, first available linear segment, is
selected. If no matching K activity exists, the corresponding S
activity is selected.
28
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CHAPTER 3
SPECIFYING THE MODEL INPUT
Summary of Input Cards
There are fourteen input card types as follows:
Card
ID Code Number Required
Control CONTRL
Dynamic Control CNTR2
Title TITLE
CROW-FLY CRWFLY
Source SOURCE
Site SITE
Process Header #1 PRC1
Process Header #2 PRC2
Process Input Links LNKI
Process Output Links LNKO
Process Cost PRCOST
Site Process SIPROC
Transportation TRANS
Truck TRUCK
one
one for dynamic run only
one
one if CROW-FLY option (control
card, col. 23) is 1 or 2
At least one (one per source)
At least one (one per site)
At least one (one per process)
At least one (one per process)
At least one (one or two per process)
One or two per process with output
One per process per linear segment per
model period
One for each process at each site
One per user-provided transportation
activity
one per truck constraint
The model input is here described in detail for each data field of
each of the different types of data input cards with annotations
following the description. A complete input listing for one static run
(Northeast Massachusetts Run B-2) and for one dynamic run (St. Louis G)
is provided in Chapter 5.
Each card starts with an identification, or ID code.
One always required.
ID Code; "CONTRL"
Mode of Execution
1 = static
2 = dynamic
Control Card
Columns
1-6
9
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Columns
Last Phase of Execution (3 or 4) T1
It is suggested that the user proceed with caution in
using phase 4 beyond a size of 70 rows by 200 columns. The
running time tends to increase enormously.
Forcing for Phase 4 Only 13
1 = single
2 = double
Single forcing is suggested for all but very small
problems. In single forcing, each column outside the basis
is forced in and a phase 3 [adjacent extreme point optimiza-.
tion) is performed. If the solution is improved, the column
is kept; otherwise the model reverts to the previous best
solution.
In double forcing, each column outside the basis is
forced in, and while it is held in, each other column
outside the basis is forced in and a phase 3 is performed.
While single forcing may miss the optimum solution, double-
forcing runs can be costly. A viable alternative is a
technique known as configuration forcing, in which the model
is made to look at a different solution structure, either by
making an option unavailable, or by raising the cost of an
option, or by a controlled advanced starting point. Several
single forcing runs, using configuration forcing, are much
less expensive than one double forcing run.
Output Printing Options 15
1 = complete [Rows (right-hand sides); columns
(costs); matrix; intermediate and final output]
2=1-0 summary and final output (number of rows and
columns; number of non-zero coefficients; last-
phase output only
3 = 1-0 summary and all output (intermediate-phase
output is provided).
®o
These refgr to Walker algorithm outputs only. WRAP
inputs and post' processor outputs are always provided.
Steepest Descent Request 17
1 = No
2 = Yes
Without steepest descent, the first column which is
discovered to improve the solution is selected for
30
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introduction. With steepest descent, all columns outside
of the basis are evaluated, and that column which makes the
greatest improvement in the solution is introduced.
2 is recommended for all applications.
Columns
Starting Basis Available 19
1 = No
2 = Yes
An advanced starting point can be used as a primary
control in configuration forcing. If 1 (no) is selected,
the advanced starting point subroutine will generate a
starting basis. If 2 is selected, a starting basis must be
provided at the end of the input.
Punch Final Basis 21
1 = No
2 = Yes
An entry of 2 will generate the model solution in the
form of a starting basis. This is useful if and only if a
succeeding run retains the same row and column structure,
which means that costs can be freely changed and the generated
starting basis used. Right-hand sides and flow coefficients
can also be changed, but with a risk of the basis becoming
infeasible, which would cause the run to abort.
CROW-FLY Option 23
0 = No
1 = Limited
2 = Maximum radius
Option 0
The program will abort if (1) there is any site without
input linkage (i.e., through transportation activities
input on transportation cards; or (2) any source, or site-
process with positive percent output by weight, is without
output linkage. Each transportation activity must have
positive minutes, or otherwise the run will abort. If zero
minutes is desired, specify a very small value in the minutes
field.
31
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Option 1
Any missing linkage will be provided with the shortest
distance link, for up to ten separate omissions, (i.e.,
transportation activities will be generated). Beyond ten
omissions, the program will abort. Speed and/or distance
will be provided without limit for identified transportation
activities which lack such measures. A zero or a blank will
be read as a blank for minutes, distance, or speed. If zero
minutes is to be stipulated, a very small positive value
should be inserted in the minutes field; although equal
longitude and latitude will generate zero minutes in any case.
Option 2
All legal links will be defined up to a maximum radius,
plus the shortest legal link 1f the maximus radius does not
complete linkage.
If option 1 or 2 is selected, longitude and latitude must
be provided for all sources and sites, but these may be
dummied in (e.g., all 1's) if only speed is to be provided
by CROW-FLY.
In CROW-FLY Options 1 and 2, the following priority
system exists:
1. A transportation activity provided by the user (on
a transportation card) for a link will prevent Crow-
Fly from generating a transportation activity for
that link.
2. Any of speed, distance, or time estimates provided
by the user (on a transportation card) for a link
will prevent CROW-FLY from generating corresponding
estimates for that link. If distance only is provided
by the user, CROW-FLY will use the standard speed and
the user-provided distance to estimate one-way time
in minutes; if speed only is provided by the user,
CROW-FLY will generate distance, and then use that
and the user-provided speed to estimate one-way minutes.
If a transportation card is used to provide a link,
but all of the distance, speed, and time fields are
left blank, CROW-FLY will estimate distance, and use
the standard speed to estimate one-way time in minutes.
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If one-way minutes are provided by the user on a
transportation card, that will be used by the model
whether or not distance and speed are also provided.
If all three are provided, the consistency will not be
checked.
Columns
Punch Transportation Results 25
0 = No; continue
1 = Yes and stop
2 = Yes and continue
Transportation activities generated by CROW-FLY may be
punched out, inspected, and reinserted as a provided trans-
portation file. These cards may be obtained with a program
stop (select 1) or with a continuation (select 2). The cards
will be formatted as Transportation Cards.
Punch Out Prepared Algorithm Input 27
0 = No; continue
1 = Yes; stop
2 = Yes; continue
The preprocessor results may be punched out as a matrix,
costs, and right-hand sides, in a form suitable for input
into a separate Walker Algorithm. This algorithm is avail-
able as proprietary software known as FCSS from Compuvisor,
Inc. This output cannot be used with the WRAP model.
Truck Constraint Option 29
1 = No
2 = Yes
If 1 is selected, columns 51 and 52 should be left blank.
If 2 is selected, the number of truck constraints (i.e.,
number of Truck Cards) should be provided in columns 51 and 52.
Number of Modeling Periods 31
1 if static
2-4 if dynamic
Number of Sources 33-35
This must be equal to the number of source cards submitted.
Number of Intermediate and Ultimate Sites 38-39
33
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This must be equal to the number of site cards submitted.
Columns
Number of Processes 40-41
This must be equal to the number of Process Header #1 and
#2 cards submitted.
Number of Site-Processes 43-45
This must be equal to the number of site process cards
submitted.
Number of Transportation Activities 47-49
This must be equal to the number of transportation cards
submitted.
Number of Truck Constraints 51-52
This must be equal to the number of truck cards submitted.
There should be a zero here if there is a 1 in column 29.
Standard Turn-Around Time 55-58
in minutes decimal: 58.59
added to 2-way minutes for transportation originating at
a site.
This turnaround time represents the time to load a
transfer van at a transfer station, the time to unload it
at the destination, and the maneuver time at both locations.
If it is necessary to differentiate turnaround time from site
to site, enter the least turnaround time as the standard
turnaround time in columns 55-58, and then add additional
time as needed for a site to the one-way minutes field on
each of the transportation cards originating at that site.
The amount to be added should be one-half the difference
between the site turnaround time and the standard turnaround
time, since the one-way minutes entry is later doubled in
estimating haul cost.
34
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No turnaround time is included for packer haul (i.e.,
haul originating at a source) since that would merely generate
a constant cost in the model, independent of anything the
model did. In a sense, the packer unloading time is generated
by the loading of the packer, and not controlled by the model.
The model charges itself for incremental time incurred on the
packer trucks as a function of the model's choice of offload
points for the packers.
Columns
Number of Years in Total Planning Period 60-61
Number of Years in Each Model Period
1st period 63-64
Any integer 2nd period 66-67
number 3rd period 69-70
4th period 72-73
Fill in 1st period only for a static run; leave blank for
any period which does not apply.
Capacity of Packer Vehicles 75-76
Average tons per truck; used for truck constraint
coefficients.
Capacity of Transfer Vehicles 78-79
Average tons per truck; used for truck constraint
coefficients.
35
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Dynamic Control Card
One required for Dynamic Run only.
Columns
ID Code; "CNTR2" 1-5
Inflation Rate (annual) 7-10
decimal: 7.8
The rate should be greater than or equal to 1.0.
A rate of 1.0 avoids the use of an inflator.
Discount Rate (annual) 12-15
decimal: 12.13
The rate should be less than or equal to 1.0; for a
discount rate of i,
1
1+1
should be entered as the discount rate. A rate of 1.0
avoids discounting.
In a dynamic run, the inflation rate and discount rate
are used to inflate and discount all costs and revenues,
except capital costs between the years in which they occur
and the first year of the model.
Amortized capital costs are inflated only to the year
in which the capacity first becomes available minus the
number of years in the capital lead time (provided on the
process header #1, column 74). These costs are however-
discounted from the years in which they occur to the first
year of the model.
The amortized capital costs should represent the dollar
outflows per year to pay back the capital over the useful life
of the process, and to pay interest at an appropriate rate
(e.g., 7% for municipal projects and 10% for private projects)
on the unamortized balance. The interest rate for amortization
need not be related to the overall discount rate which is
entered on the Dynamic Control Card. It is the dollar outflow
per year, defined as above, and established through a project
interest rate, that is inflated and discounted, using the
model discount rate.
36
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Title Card
One always required.
Columns
ID Code: "TITLE" 1-5
Title Information 7-80
37
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CROW-FLY card
One required only if CROW-FLY option (Control Card,
Column 23) is 1 or 2.
Columns
ID Code: "CRWFLY" 1-6
Maximum Radius (miles) 9-11
(From 001 to 700)
Criterion for selection in CROW-FLY Option 2.
Nautical Miles Per Minute of Longitude 13-16
decimal: 13.14
This should be estimated for the center of the region.
It is 1.0 at the equator, and less elsewhere.
Standard Speed 18-19
In integer miles per hour, averaged for the region over
all roads and truck types. This speed is used for a link
where neither one-way minutes nor speed has been provided by
the user for that link; and where the CROW-FLY option is 1 or 2.
38
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Source Card
One card for each source. The number of source cards
supplied must equal the Number of Sources control variable
(control card, columns 33-35). All source cards must be
submitted in one group, but may be in any order within the
group.
At least one source card is required.
Columns
ID Code: "SOURCE" 1-6
Source Identification Number 7-9
A three digit number from 100 to 499.
Numbers need not be consecutive.
Source Name 10-29
Source Longitude
Degrees 30-31
Minutes 32-34
decimal: 33.34
Source Latitude
Degrees 35-36
Minutes 37-39
decimal: 38.39
Longitude and latitude need not be entered if the
CROW-FLY option is 0 (control card, column 23). If Crow-
Fly option is 1 or 2, longitude and latitude must be
entered. If CROW-FLY is to be used only for standard
speed, any arbitrary positive numbers may be filled in.
If necessary, a constant should be added to or subtracted
from all longitudes or latitudes to make all of the entries
for the region fit within the available field. For example,
in Los Angeles, the user might subtract 100 degrees from all
longitudes.
Source Tons in Thousands of Tons Per Year
1st period 40-44
decimal: 43.44
2nd period 45-49
decimal: 48.49
39
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3rd period
4th period
decimal:
decimal:
Columns
50-54
53.54
55-59
58.59
For the static mode, use columns 40-44 only. Leave
blank fields that do not apply (i.e., 3rd and 4th periods
for a 2-period run). This should be consistent with number
of periods in column 31 of the control card.
Source Haul Cost per Ton-Minute
1st period
2nd period
3rd period
4th period
This should be the cost per packer truck per minute of
operation divided by an average load in tons.
Fill in only those fields appropriate to the run. This
should be consistent with the number of periods in column
31 of the control card.
decimal :
decimal :
decimal:
decimal :
60-64
(59). 60
65-69
(64). 65
70-74
(69). 70
75-79
(74). 75
40
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Site Card
One card for each site. The number of site cards
supplied must equal the Number of Sites control variable
(control card, columns 38-39). All site cards must be
submitted in one group but may be in any order within the
group.
Columns
ID Code: "SITE" 1-4
Site Identification Number 6-8
This is a primary control in the design of an application.
500-599 for A level (transportation) and B level (primary
processing)
600-699 for C level (secondary processing)
700-799 for D level (landfill)
Note: The model provides a separate input balance and a
separate site processing constraint for each separate
site identification number. The user should use the
same site number for collocated processes unless (1)
there is a need to differentiate input, or (2) there
is a need to differentiate land use. The use of the
same site number permits the model to select the process
in the course of its search for a minimum cost solution.
It also reduces the required number of linkages. The
need to differentiate input requires the designation of
separate site numbers for collocated primary processing
(B-level) and secondary processing (C-level), since the
former processes raw refuse and the latter processes
residue. The need to differentiate land use requires
the designation of separate site numbers for D-level
processing collocated with any other level.
Identical second and third digits can be used as a mnemonic
for cases of A/B-level and C-level collocation. This number
assignment has no model control function. Collocation is
accomplished by:
1. providing a category 5 transportation activity
with zero cost (negative quantity in the minutes
field of that TRANS card); and
2. if there is a truck constraint, listing the
collocated site numbers on the TRUCK card.
Site Name 10-29
41
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Columns
Site Type 32
1 = unlimited - there is no tonnage constraint, but
there may still be a truck constraint.
2 = limited - tonnage capacities should be provided
on the SITE-PROCESS card.
Site Longitude
Degrees 34-35
Minutes 36-38
decimal: 37.38
Site Latitude
Degrees 40-41
Minutes 42-44
decimal: 43.44
All of the comments on Source longitude and latitude
apply here exactly.
Number of Processes Proposed at this Site 46
Site Preparation Cost 48-53
decimal: 51.52
In thousands of dollars per year, amortized, representing
those costs that pertain to the site, rather than the process.
This cost includes building access to the site, grading,
blasting, etc., as necessary, to prepare the site to receive
the processes proposed for it. If the user wishes, he may
include the cost of the land also.
This cost is added to the capital intercept cost for each
segment of each process at the site. A negative site
preparation cost was used in the Massachusetts Exercise Series
to represent the annual amortized value of an EPA grant at
site 607, Lowell secondary processing, which could be retained
in fact only if the particular process (Bureau of Mines incin-
erator residue process, process number 906) were retained in
Lowell. This device could not have been used if there were a
second process at the site. If that were the case, it would
have been necessary to identify secondary processing at Lowell
as a separate process, and to represent the value of the EPA
grant as a reduced capital intercept on the process cost card.
42
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The formula
C. =
1 (Hi)"
(Hi)" - 1
where
C is the annual payback factor
a
i is the interest rate per year
and
n is the useful life in years
should be used to determine all amortized costs. The
interest rate and useful life for the site preparation cost
should be consistent with those of the capital intercept and
slope of the process cost card.
If for any reason it is not possible to apply the same
site preparation cost to all processes at a site, it will be
necessary to identify separate process numbers for that site,
and apply the appropriate site preparation cost to the capital
intercept cost on the process card.
Columns
Land Available in acre-feet 55-60
decimal: 60.(61)
Enter only for a D-level (i.e., sanitary landfill) site.
43
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The Process File
There are five different process cards, Process Header #1
(PRC1), Process Header #2 (PRC2), Process Input Links Card (LNKI),
Process Output Links Card (LNKO), and Process Cost Card(PRCOST).
It is essential that these cards should be entered into the
model in the following order for each process:
PRC1,
PRC2,
LNKI,
LNKO,
PRCOST
by model period
by linear segment within model period.
The process identification number is entered into
columns 78-80 of each card in the process file except the
PRC1 card, in which that number is entered in columns 9-11.
Processes need not be input in order of process
identification number.
A single process may be offered at only one site if the
process existence code (Process Header #1, column 38) is 1
(existing) but may be offered at many sites if the process
existence code is 2 (new). If a process is offered at more
than one site, the user must make certain that all of the
information provided for the process applies at all sites at
which it is offered. If any information must be differ-
entiated, it will be necessary to designate different process
numbers, and to set up different processes in the file.
The assignment of processes to sites is made on the site
process card.
44
-------
Process Header #1
One per process (the total number must be equal to the
number of processes on the control card, columns 40 and 41.)
Columns
ID Code: "PRC1" 1-4
Process Identification Number 9-11
A different number from 800 to 999, should be assigned
whenever it is necessary to differentiate any entry on any
card in the process file.
Process Name 13-32
Process Level Code 36
A = transfer
B = primary processing
C = secondary processing
D = landfill
Process Existence Code 38
1 - existing
2 = new
An existing process can be assigned at only one site
(and that is edit checked).
Percent (non-saleable) Output by Weight 39-43
decimal: 41.42
Should be left blank if there is no non-saleable output.
Output Density 45-48
in pounds per cubic yard decimal: 48.(49)
This is the effective density of the non-saleable output
of this process if put in a quality landfill, assuming that no
further processing intervenes. Effective density is the weight
of the waste in place divided by the volume of the waste plus
cover (if applicable). The output density must be provided if
percent output by weight is positive, and should be left blank
if percent output be weight is zero. The output density con-
trols the cost and land impact of sanitary landfill. For
example, an output density of 1500 pounds per cubic yard, twice
that of raw-refuse landfill, would generate only half as much
processing cost and land use per ton as would raw refuse.
45
-------
The effective density of raw refuse landfill is built
into the model at 750 pounds per cubic yard.
A transfer station process should use an output density
of 750.
Haul Cost per Ton-Minute
Columns
1st period 50-54
decimal: (49).50
2nd period 56-60
decimal: (55).56
3rd period 62-66
decimal: (61).62
4th period 68-72
decimal: (67).68
This cost is the cost of a suitable truck per minute
divided by the number of tons in an average load.
This should be left blank if the percent non-saleable
output by weight is zero. With positive percent output by
weight, data for a number of periods should be entered con-
sistent with the number of periods in column 31 of the con-
trol card.
Capital Lead Time (in integer years) 74
The average lead time between commitment of capital and
initial operating capability of the plant.
This field should be left blank in a static application.
In a dynamic application, the capital lead time controls
the end of inflation for capital costs.
46
-------
Process Header #2
One is required for each process.
Columns
ID Code: "PRC2" 1-4
Process Avail ability to be Built
Period 1 7
Period 2 9
Period 3 11
Period 4 13
1 = not available for building in that period
2 = available for building in that period.
In static applications, enter a 2 in column 7 and leave-
others blank. In a dynamic application, fill in a number of
fields consistent with the number of periods in column 31 of
the control card.
A process may not be available in an earlier period
because it is not yet developed; a process may not be avail-
able in a later period because of tightening environmental
constraints.
Final Period of Availability of a Facility Built in:
Period 1 15
Period 2 17
Period 3 19
PerTod 4 21
For each model period enter a number 1 through 4 as
appropriate to indicate the last model period during which
the process would be available if the facility were con-
structed during this period. For example, if each model
period is five years and this type of process facility
normally has a ten year life, then if the facility were
constructed in period 1, it would be available through period
2 (these two periods together being ten years) and you would
put a "2" in column 15. The number entered cannot be less
than the period. Enter data for a number of periods equal to
the number of model periods entered in'column 31 of the con-
trol card.
For static applications, enter a 1 in column 15, and
leave the others blank.
47
-------
Columns
Number of Segments 31
Enter 1, 2, or 3 to indicate the number of linear segments
which will be used to represent the cost functions for this
process.
Process Identification Number 78-80
48
-------
Process Input Links Card
At least one process input links card is required
per process. This card identifies as "links" those processes
the outputs of which may be input into the subject process.
The first link field is used to indicate whether the subject
process can receive directly from sources. There must be at
least one positive link for each process (i.e., if the process
cannot receive from source, it must receive outputs from at
least one other process).
Up to 18 links may be supplied per card. Thirty-five (35)
is the maximum total links possible. A zero or blank must be
supplied in the link field following the last link. (If the
last link is at the end of a card, a dummy link card with zero
or blank in the first link field must follow.)
Columns
ID Code; "LNKI" 1-4
Link 1 9
'(1st link on 1st LNKI card is used to indicate if the
process can receive directly from sources.)
1 = no source link
2 = source link
(on 2nd LNKI card, the first link field is in
columns 7-9).
Other Link Fields 11-13
Fill in process identification numbers of 15-17
processes, the outputs of which may be input 19-21
into the subject process. List in increasing order 23-25
of process identification number. 27-29
31-33
35-37
39-41
43-45
47-49
51-53
55-57
59-61
63-65
67-69
71-73
75-77
Process Identification Number 78-80
49
-------
Process Output Links Card
A process output links card Is required if and only if
Percent Non-Saleable Output by Weight on Process Header #1
is greater than zero. Otherwise omit. This card identifies
as "links" those other processes which can receive the outputs
of the subject process. Up to 18 links may be supplied per
card. Thirty-six (36) is the maximum total number of links.
A zero or blank must be supplied in the link position
following the last link supplied. (If the last link is at the
end of a card a dummy output links card with a zero or blank
in the first link position must follow.)
Columns
ID Code; "LNKQ" 1-4
1st Link Field 7-9
Other Link Fields 11-13
Fill in process identification numbers of processes 15-17
which may receive the non-saleable or residue outputs of 19-21
the subject process, in increasing order of process Identi- 23-25
fication number. 27-29
31-33
35-37
39-41
43-45
47-49
51-53
55-57
59-61
63-65
67-69
71-73
75-77
Process Identification Number 78-80
50
-------
Process Cost Card
There must be one process card per linear segment per
model period. For example, for 3 linear segments, 4 model
periods, there must be 12 process cost cards. Do not submit
cost cards for model periods in which the process is coded
as non-available for building (PRC2, columns 7, 9, 11, and 13).
This card is the primary method for inputting cost data.
A capital cost slope and intercept and operating cost slope
and intercept are submitted on this card for the process
wherever located. In addition, a site preparation cost, sub-
mitted on the SITE card, is added to each capital intercept
of each process at the site. A third component of cost,
revenue per input ton, is submitted on the SITE PROCESS Card
(SIPROC). The revenue is subtracted from the operating
cost slope for each segment of the site-process. Submitting
the revenue by site process permits the revenue to be differ-
entiated by site, representing more or less favorable location
vis-a-vis markets.
In static applications, the differentiation between
capital and operating costs is arbitrary, since they are
merely added together to obtain a combined slope and a
combined intercept.
One good way to prepare cost information is to perform
all process cost analyses on log/log graph paper, thus
obtaining a best fit curve in the form of one or more log-
linear segments for cost versus scale. The cost estimate
would then be transferred to straight graph paper on which
from one to three linear segments can be fitted to the curve.
Where capital and operating costs exhibit substantially dif-
ferent scale effects, capital and operating costs should be
estimated independently. Where the slopes are similar, it is
possible to estimate the total cost and the capital cost, and
to treat the operating cost as a residual (that is, the dif-
ference between total and capital costs).
Columns
ID Code: "PRCOST" 1-6
Model Period (1. 2. 3, or 4) 8
Segment Identifier (1. 2, or 3, segment 1 being 9
leftmost on the graph)
Capital Slope (thousands of dollars per thousand tons) 11-19
decimal: 13.14
51
-------
Columns
Capital Intercept (thousands of dollars per year 21-29
decimal: 26.27
Operating Slope (thousands of dollars per thousand tons) 31-39
decimal: 33.34
Operating Intercept (thousands of dollars per year) 41-49
decimal: 46.47
Process Identification Number 78-80
All capital costs should be amortized annual costs using
the following formula to estimate the payback factor:
C. =
(Hi)" - 1
where
C is capital payback factor
a
i is the interest rate per year
and
n is the number of years in the useful life.
The interest rate should be appropriate to the process,
and need not be the same as the discount rate used for the
model as a whole.
If the process can exist at one site under municipal
financing, and another under private financing, two different
process identification numbers should be assigned in order to
differentiate the capital payback factor.
The process interest rates are used to establish annual
amortized costs which in turn are discounted in a dynamic
run using the model discount rate input on the dynamic card.
There is no discounting in a static run.
52
-------
Site Process Card
One is required for each process at each site.
Columns
ID Code: "SIPROC" ~1^6
Site Identification Number 8-10
Process Identification Number 12-14
Segments 18-19
Identify which segments of the process cost represent
facility sizes which might be built at a particular site
by the following:
01 = 1st only
02 = 2nd only
03 = 3rd only
12 = 1st and 2nd
23 = 2nd and 3rd
13 = all three of three.
Capacity (in thousands of tons per year) 21-24
decimal: 24.(25)
This is to be entered only for a site coded "limited"
on the site card, column 32.
It is the maximum tonnage at the site assuming the
subject process and only the subject process is selected at
that site.
Revenue Per Input Ton
Net revenue (less cost of haul to market)
1st period 26-31
decimal: 28.29
2nd period 33-38
decimal: 35.36
3rd period 40-45
decimal: 42.43
53
-------
Col Limns
4th period 77^51
decimal: 49.50
Process Level (A, B. C. or D) 54
(Must be same as on PRC1, column 36)
54
-------
Transportation Card
Each transportation card sets up a single transportation
activity. Additional transportation activities may be estab-
lished in CROW-FLY if CROW-FLY option 1 or 2 is selected. The
number of transportation cards must equal the number entered on
the control card, columns 47-49, representing the number of
transportation activities provided by the user.
If the CROW-FLY option is 0 (column 23 of the control
card), then transportation activities (i.e., transportation
cards) must be provided sufficient so that each source, and
each site-process with positive output, will have at least
one outgoing transportation activity, and so that each site
will have at least one incoming transportation activity.
The input is edit-checked for linkage sufficiency in the
above sense, and if the test fails, the run will abort.
If the CROW-FLY option is 1, up to ten transportation
activities will be created to complete linkage, using a
minimum distance criterion for selecting one activity for
each case of incomplete linkage; but beyond that the run
will abort.
If CROW-FLY 2 is selected, transportation activities
will be generated for all legal linkage (the LNKI and LNKO
data being the criteria of legality) up to a maximum radius
provided on the CROW-FLY card. In cases of incomplete linkage
(i.e., there is no linkage that can be made within the maximum
radius), one additional transportation activity will be pro-
vided beyond the maximum radius criterion for each case of
incomplete linkage. In CROW-FLY option 2, an activity
provided by the user on a transportation card will supersede
a generated activity.
Every transportation card must have entries for activity
type, activity origin by ID number, and activity destination.
If the CROW-FLY option is 0, activity origin process by
number and one-way time in minutes must also be provided. In
CROW-FLY option 1 or 2, one-way distance and speed in mph,
if provided by the user, will be used to calculate one-way
time in minutes, unless one-way time in minutes has also been
provided by the user. One-way time in minutes will dominate
if provided, and will not be checked for consistency with
distance and speed if all three are provided.
In any CROW-FLY option, a negative quantity in the one-
way time in minutes field will generate a zero cost transpor-
tation activity; i.e., even turnaround time will not be added.
55
-------
In CROW-FLY 2, a zero entry or a blank in the one-way
minutes field will be read as zero minutes. Turnaround time
will be added if appropriate. In CROW-FLY 0 and 1, a blank
or a zero in the one-way time in minutes field will be read
as a blank. In CROW-FLY 0, the run will abort if a blank is
read in minutes; in CROW-FLY 1, the blank will lead to a
measurement of the distance and speed as appropriate. The
user should thus enter a very small positive quantity in the
one-way time in minutes fields if he wishes a zero read in
either CROW-FLY option 0 or 1. In this way, the turnaround
time will be added. Note that only a negative quantity in
the minutes field will avoid the addition of the turnaround
time.
Columns
Id Code; "TRANS" 1-5
Activity Type* 7
1 = source to ultimate site
2 = source to intermediate site
3 = intermediate to intermediate site
4 = intermediate to ultimate site
5 = any of the above that is to avoid any truck
constraints placed on the origin and destination
sites
Activity Origin Site or Source ID Number* 9-11
Activity Origin Process ID Number* 13-15
If source origin, repeat source ID number
Activity Destination Site ID Number* 17-19
One-way Time in Minutes* 24-28
decimal: 27.28
One-way Distance in Miles 30-33
(statute miles) decimal: 32.33
Speed in Miles Per Hour 35-37
decimal: 36.37
*Required for any CROW-FLY option.
+Required for CROW-FLY option 0.
56
-------
Truck Card
One card must be provided per truck constraint. The
number of truck cards must be equal to the number indicated
on the control card, columns 51-52.
Columns
ID Code: "TRUCK" 1-5
Site Numbers (up to three) 7-9
The indicated sites are jointly subjected to a 11-13
single truck constraint for all outgoing and incoming 15-17
trucks, except for type 5 transportation activities.
Maximum Number Per Year (in thousands of trucks)
Fill in for a number of periods equal to the number of
model periods (control card, column 31).
1st period 19-23
decimal: 22.23
2nd period 25-29
decimal: 28.29
3rd period 31-35
decimal: 34.35
4th period 37-4]
decimal: 40.41
57
-------
Advanced Starting Point (or Basis)
Enter a number of column index numbers equal to the number of
equations. Enter 16 columns per card, using columns 2-4 7-9 12-14
77-79.
One source of an advanced starting basis would be the final basis
(or optional card output) of a previous WRAP execution, obtained by
entering 2 on the control card, column 21. This can be used only if the
same row and column structure is maintained for both runs. This
limitation permits costs to be modified freely. Right-hand sides and
flow coefficients may also be modified with care to ensure that the
basis does not become infeasible. If that were to happen, the run would
abort.
58
-------
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-------
CHAPTER 4
INTERPRETING THE MODEL OUTPUTS
Algorithm Outputs
The SWAP program, the subroutine of WRAP which contains the fixed-
charge linear programming algorithm, has outputs controlled by the entry
in column 15 of the (WRAP) control card. This chapter will discuss the
complete output printing option (obtained by entering 1 in column 15 of
the control card). An entry of 2 provides only a summary of the size of
the matrix (number of rows, number of columns, number of non-zero
coefficients including slacks and artificials) and the output of the
last phase (i.e., phase 3 outputs are suppressed if phase 4 is last-
phase). An entry of 3 provides the same information as an entry of 2,
except that intermediate phase outputs (i.e., phase 3 if phase 4 is
last-phase) are not suppressed.
It should be noted that the static and dynamic modes-are not
differentiated in SWAP, but only in the structure of the matrix, right
hand sides, and costs that are presented to SWAP. Thus, there is no
mention of whether the mode is static or dynamic in SWAP outputs.
SWAP Summary
A summary is provided which indicates
1. last phase
2. (if last-phase is 4) whether single or double forcing
3. whether steepest descent was selected.
SWAP summaries are shown for N. E. Mass. B-2, representing the last-
phase = 4 format, and for St. Louis G, representing the last-phase = 3
format. Note that N. E. Mass. B-2 was a static run, and St. Louis G was
a dynamic run, but that differentiation does not appear in the summary.
Row Data (Right-hand Sides)
These data indicate the number of rows. For each, the row number,
type, and right-hand side are shown. Type 0 is an equation and type 1
is a less-than-or-equal constraint. Type 2, which never appears in
WRAP, is a greater-than-or equal constraint.
Row data are displayed for N. E. Mass. B-2 and St. Louis G.
69
-------
The asterisks in row 60 of N. E. Mass. B-2 and row 77 of St. Louis G
represent a very large right-hand side for the capacitation, n.e.c.,
constraint.
In the N. E. Mass, run B-2 row data, the first 14 rows are source
balance equations; rows 15-17 are site processing constraints; rows 18-
56 are input and output balance equations; rows 57-59 are truck
constraints.
In St. Louis G row data, rows 1-8, 20-27, 39-46 and 58-65 are source
balance equations; rows 9-19, 28-38, 47-57 and 66-76 are input and
output balance equations; rows 78-114 are site/process capacity balance
equations, and row 115 is a land constraint.
Column Data (costs)
These data indicate the number of columns. For each, an index, a
column number, a variable cost, and a fixed cost are shown. The index
is the sequential number of the column. The column number is equal to
the index except for slacks and artificials. For slacks (one for each
type 1 row -- i.e., less-than-or-equal constraint) the column number is
3000 plus the number of the type 1 row to which the slack corresponds.
Artificials (one for each type 0 row — i.e., equation) exist only for
purposes of phase 1, which, along with phase 2, is bypassed by WRAP.
For these columns, the column number is 2000 plus the number of the type
0 row to which the artificial corresponds.
The full set of column data of N. E. Mass, run B-2 follows.
The first 98 columns are transportation activities with only
variable costs. Of these, the last 11 are type 5 transportation
activities representing dummy shipments for collocated sites. These
show zero variable and fixed costs. Columns 99 through 148 are
processing activities which potentially may have both variable and fixed
costs. Of these, the last 6 are dummy activities which differentiate
the appropriate heavy end and incinerator residue revenues in secondary
processing. The variable cost here is the negative of the appropriate
revenue, and the fixed cost is zero. Index 149-155 is the set of
slacks, and index 156-208 is the set of artificials.
Matrix
The A matrix is the set of equations for the model in coefficient
form. A row is an equation, a column is an unknown, a right-hand side
is the information to the right of the equals sign.
The A matrix is presented in row within column sort. This matrix
includes slacks, but not artificials. The index, row number, column
number, and value are shown. The index is the sequential number of the
coefficient. The column number is the index (i.e., sequential number of
70
-------
the column) of the column data set. The value is the coefficient. The
number of non-zero elements of the A matrix (including slacks but not
artificials) is inserted at the head of the matrix.
The first page of the matrix of N. E. Mass. Run B-2 is shown.
User-Supplied Initial Basis
Despite the title, this set of data includes the initial basis
whether supplied by the user or generated in the WRAP advanced starting
point algorithm. The basis lists column numbers only, and uses the
column number form of identification (i.e., slacks are 3000 plus the
corresponding row number).
The initial basis from N. E. Mass. B-2 follows. (This basis was
hand-generated and differs slightly from what would have been generated
from the sample input if the automatic starting point algorithm had been
used.)
Intermediate and Final Solutions
Intermediate and final solutions show a phase number, an objective
value (in thousands of dollars per year in the static mode — in
thousands of dollars over the total planning period, discounted to the
present, in the dynamic mode), and the solution. The solution lists
column numbers of activities which are in the basis (i.e., slacks are
3000 plus the corresponding row number) and (activity) levels. The
(activity) levels are thousands of tons per year in both the static mode
and the dynamic mode except truck constraint slacks, which are in
thousands of trucks per year, and land constraint slacks, which are in
acre-feet. It should be noted that the solution as it is output from
the algorithm is unsorted.
The phase 3 and phase 4 solutions of N. E. Mass. Run B-2 follow.
The WRAP Model Outputs
WRAP sorts and interprets the final solution and prints outputs
which may not be varied by the user.
In the static mode, a single presentation is made, sorted in the
order of sequential column number. The columns are grouped as follows:
1) type 1 transportation (source to ultimate)
2) type 2 transportation (source to intermediate)
71
-------
3) type 3 transportation (intermediate to intermediate)
4) type 4 transportation (intermediate to ultimate)
5) type 5 transportation (activities which bypass the truck
constraints such as rail haul and transportation between
collocated sites)
6) processing activities.
The display is headed by a total system cost (in thousands of dollars
per year) and by a system cost per ton, (in dollars per ton).
The full WRAP output of N. E. Mass, (static) run B-2 is presented
below in Chapter 7.
In the dynamic mode, two sorts are presented, neither of which is
sequential column order:
model period major sort and model period inner sort.
In the former, within model period, activities are sorted in sequential
column order, and are grouped as follows:
1) type 1 transportation (source to ultimate)
2) type 2 transportation (source to intermediate)
3) type 3 transportation (intermediate to intermediate)
4) type 4 transportation (intermediate to ultimate)
5) type 5 transportation (activities which bypass the truck
constraints such as rail haul and transportation between
collocated sites)
6) processing activities
7) capacity building activity levels
8) capacity underutilization activity levels
after the presentation of all model periods:
9) land constraint slack activity levels (in acre-feet) (This
displays land remaining at each site at the end of the planning
period.)
72
-------
The model period major sort presentation is preceded by an objective
function value measuring the discounted system cost over the planning
period in thousands of dollars.
In the model period inner sort, the nine groupings of activity
levels become the major sort, and model period is the innermost sort
within each group (except land remaining). The sequential column order
is the intermediate sort.
The model period inner sort is preceded by a repetition of the
objective function value, as in the model period major sort.
The full WRAP output of St. Louis (dynamic) run G is presented below
in Chapter 7.
All activity levels, in both static and dynamic modes, are in
thousands of tons per year except land remaining, which is in acre-feet.
In the WRAP output, slacks are suppressed except for the land
constraint slack in the dynamic mode. In the Chapter 7 WRAP outputs,
basic activities with zero activity levels are included; however, in the
final version of WRAP, printout of such activities has been suppressed.
Maps
The use of maps to interpret and display WRAP outputs is essential.
One method which can be used effectively utilizes a pair of maps to
display each static run and each model period of a dynamic run. The
first map in the pair displays flows from source to initial offload
point. Each district centroid is shown, and is connected to its initial
offload point by an arrow. The second map in the pair shows the
location of active transfer, primary, secondary, and landfill sites, and
differentiates the following kinds of flows:
t truck transfer flows
• rail transfer flows
• flows from primary processing to secondary processing
t fuel flows.
Transfer locations are coded T; primary processing locations are coded
P; secondary processing locations are coded S; and landfill locations
are coded L.
A full set of maps is included below in Chapter 5 for static run N.
E. Mass. B-2 (2 maps) and for dynamic run St. Louis G (8 maps). Note
that fuel flows are undefined in the Massachusetts runs.
73
-------
N. E. Mass. B-2 Static
SWAP PROCESSING WILL BE TERMINATED AFTER °HASE '4
1 COIUMN(S) '-i1. j_ BE FOPcr.p INTO ~y.s r-v-;? our-P.? U,VH r.usE
STEEFf-ST DESCf.N'T WILL BE USEL IN E.ACi' PHASE
St. Louis Dynamic
SWAP PROCESSING WILL BE TERMINATED AFTER PHASE 3
STEEPEST DESCENT WILL BE USED IN EACH PHASE
N. E. Mass. B-2 Row Data
DATA FOR THE 60
t TYPE RIGHT HAND SIDE
1 0 9^.900
2 0 73.900
3 0 27.900
4 0 21.700
5 0 6.000
6 0 22.9CO
7 0 64.600
R 0 19.200
" 0 26.700
10 0 'J4.COO
11 0 S7.600
12 0 93.000
13 0 5.700
14 0 36.300
15 1 1000.000
16 1 1000.000
17 1 1COO.OOO
18 0 0.0
19 0 0.0
20 0 0.0
21 0 0.0
22 0 0.0
27 0 0.0
2^ 0 0.0
25 0 0.0
26 0 0.0
27 0 0.0
28 0 0.0
29 0 0.0
30 0 0.0
31 0 C.O
32 0 0.0
33 0 0.0
34 0 0.0
35 0 0.0
36 0 0.0
37 0 0.0
3B 0 0.0
39 0 0.0
40 0 0.0
41 0 0.0
74
-------
N. E. Mass. B-2 Row Data (concluded)
TYPE
RIGHT HAND SIDE
42
43
44
45
46
4?
4S
49
50
51
52
53
54
55
56
57
58
59
60
0
0
C
0
0
£
0
0
0
0
0
0
0
0
0
1
1
1
1
St. Louis
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
390.0 CO
390.000
390.000
A** *******
G Row Data
DATA FOR THE 115 ROWS
ROW NUMBER
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
2B
29
30
31
32
33
34
35
36
37
38
39
TYPE
RIGHT HAND SIDE
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
39.100
65.500
280.100
10.200
79.300
358.200
795.300
838.700
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
50.800
90.600
361.700
14.800
114.600
449.100
895.600
Z075.300
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
75.900
-------
St. Louis G Row Data (continued)
ROW NUMBER TYPE RIGHT HAND SIDE
40
41
42
43
44
45
46
47
43
49
50
51
52
53
54
C.C.
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
31
82
83
84
85
86
37
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
n
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
148.500
539.800
25.100
195.300
636.100
1070.300
1582.200
0.0
0.0
0.0
0.0
0.0
0.0
.0.0
0.0
n .n
0.0
0.0
98.800
202.400
702.300
34.800
271.000
803.400
1205.400
2042.200
0.0
0.0
0.0
0.0
c.o
0.0
0.0
O.D
0.0
0.0
0.0
**********
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
76
-------
St. Louis G Row Data (concluded)
ROW NUMBER
106
107
108
109
110
111
112
113
TYPE
RIGHT HAND SIDE
115
0
0
0
0
0
0
0
0
0
1
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
20000.000
Co_l_umn__Data for Mass. B-2
INDEX
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
If,
17
18
1"
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
DATA FOR THS 203
COLUMN NL'M3£H VARIABLE COST FIXCD COST
1
2
3
4
5
6
7
S
9
10
11
12
13
14
15
1ft
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
0.316
4.226
1.356
7.571
3.M3
2.531
T.32..'
5.921
0.402
5.627
9.3r><>
5-bfi?
4.678
5. 099
14.323
11.639
1.695
7.006
4.610
5.74C
1.966
6.757
1.514
10.690
6.757
2.757
3.797
7.187
3.955
5.085
0.452
5.605
5.786
5.853
8.565
4.520
4.995
5.514
2.328
8.49R
10.848
0.972
3.302
0.0
0.0
G.O
0.0
r .0
o.o
o.o
o.o
0.0
o.o
0.0
0.0
0.0
0.0
c.o
0 .0
0.0
0.0
0.0
o.o
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
77
-------
Column Data for Mass. B-2 (continued)
INOEX COLUMN NUMBER VARIABLE COST FIXED COST
46 46
47 47
43 48
49 49
50 50
SI 51
52 52
*3 51
54 54
55 55
56 56
57 57
50 50
59 59
63 63
64 64
65 65
66 66
67 67
68 63
69 69
70 70
71 71
72 72
73 73
74 74
75 75
76 76
77 77
73 78
79 79
80 80
81 81
82 82
83 83
84 84
85 85
86 86
87 87
83 83
89 89
90 90
91 91
92 92
93 93
94 94
95 95
96 96
97 97
98 98
99 99
100 100
101 101
102 102
103 103
104 104
105 105
106 \06
107 .,07
103 108
109 109
HO 110
78
2.215
3.333
1.570
0.946
2.030
1.732
2.096
2.356
1.99?
?.356
1.992
1.082
2.912
3.130
1.815
1.882
1.815
3.130
3.531
2.912
3.432
1.794
3.531
1.794
3.432
1.992
3.130
2.704
1.99?
2.704
1.690
1.734
1.810
3.271
1.721
3.203
2.356
2.704
2.356
'.704
..356
2.704
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.702
0.409
0.702
0.409
•3.027
-3.862
•1.243
-3.910
•0.547
1.442
0.702
0.241
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
c.o
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
" 0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
).0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
78.000
121.000
73.000
121.000
938.000
1808.000
1829.000
3224.000
624.000
36.000
73.000
387.000
-------
Column Data for Mass. B-2 (continued)
INDEX
111
112
113
114
115
1 16
117
110
119
120
121
122
123
COLUMN NUMBER VARIAOLE COST FIXED COST
111
112
113
125
\2f>
127
129
129
130
131
132
133
136
137
139
139
140
141
142
143
144
145
146
147
140
149
150
151
152
153
154
155
156
157
153
159
160
161
162
163
164
165
166
167
169
169
170
171
172
173
174
115
116
117
118
119
120
121
122
123
124
126
127
123
129
130
131
132
133
134
135
136
137
133
139
140
141
142
143
144
145
146
147
148
3015
3016
3017
3007
3059
3059
3060
2001
2002
2003
2004
2005
2006
2007
200S
2009
2010
2011
2012
2013
2014
2018
2019
2020
2021
2022
-3.027
-8.100
1.442
0.702
0.241
-3.027
-0.10C
0.702
0.'tC9
-3.027
-3.36?
-0.547
0.702
0.409
5.271
2.760
0.702
0.409
-3.027
-3.862
-1.243
-3.910
-0.547
4.360
2.150
1.200
4.360
2.150
1.200
4.360
2.150
1.200
-19.345
-19.345
-19.345
-30.077
-30.077
-30.077
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
988.000
1092.290
36.000
70.000
307.000
vna.ooo
1092.290
70.000
l.?l .000
938.000
1008.000
624.000
78.000
121.000
265.000
950.000
78.000
121.000
980.000
1808.000
1629.000
3224.000
624.000
331.700
573.500
917.600
135.130
376.930
721.030
331.700
573.500
917.600
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
79
-------
Column Data for Mass. B-2 (continued)
INDEX COLUMN NUMBER VARIABLE COST FIXED cosr
175 2023 o.o o.o
176 2024 0.0 0.0
J77 ?0?5 0.0 o.O
170 2026 0.0 o.O
179 2027 0.0 0.0
lfln 2028 0.0 0.0
181 2029 0.0 0.0
1*2 2030 0.0 0.0
2031 0.0 o.O
2032 0.0 0.0
2033 0.0 0.0
1*6 2034 0.0 0.0
107 2035 0.0 0.0
183 2036 0.0 0.0
189 2037 0.0 0.0
190 2033 0.0 0.0
191 2039 0.0 0.0
192 2040 0.0 0.0
193 2041 0,0 0.0
194 2042 0.0 0.0
195 2043 0.0 0.0
196 2044 0.0 0.0
197 2045 0.0 0.0
198 2046 0.0 0.0
199 2047 0.0 0.0
200 2048 0.0 0.0
201 2049 0.0 0.0
202 2000 0.0 0.0
203 2051 0.0 0.0
204 2052 0.0 0.0
205 2053 0.0 0.0
206 2054 0.0 0.0
207 2055 0.0 0.0
208 2056 0.0 0.0
80
-------
Matrix
THF 3<»4 NON-Z?RO ELEMENTS DF THE A-MATRIX
INDEX RHWNO. COLUMNNO. VALUE
1 1 1 l.CO
2 18 1 1.00
3 1 2 1.00
4 26 2 1.00
5 59 2 0.20
623 1.00
7 19 3 1.00
824 1.00
9 20 4 1.00
10 57 4 0.20
11 2 5 1.00
12 26 5 1.00
13 59 5 0.20
14 3 6 1.00
15 19 6 1.00
16 3 7 1.00
17 20 7 1.00
18 57 7 0.20
19 3 8 1.00
20 26 8 1.00
21 59 8 0.20
22 4 9 1.00
23 20 9 1.00
24 57 9 0.20
25 4 10 1.00
26 21 10 1.00
27 4 11 1.00
28 26 11 1.00
29 59 11 0.20
30 5 12 1.00
31 20 12 1.00
32 57 12 0.20
33 5 13 1.00
34 21 13 l.CO
35 5 14 1.00
36 2? 14 1.00
37 5 15 1.00
^8 26 15 1.00
39 59 15 0.20
40 6 16 1.00
-VI 20 16 1.00
42 57 16 0.20
43 6 17 1.00
44 21 17 1.00
45 6 16 1.00
46 22 18 1.00
47 6 19 1.00
43 26 19 1.00
49 59 19 0.20
50 7 20 1.00
51 19 20 1.00
52 7 21 1.00
53 20 21 1.00
54 57 21 0.20
55 7 ?2 1.00
56 23 ."'2 1.00
57 58 22 0.2C
5R C 23 1.00
59 20 23 1.00
60 57 23 0.20
61 8 24 1.00
-------
User-Supplied Initial Basis of Mass. B-2
THE USER-SUPPLIED INITIAL BASIS CHNSISTS OF THE FOLLOWING
1
4
7
10
13
18
22
24
27
32
35
37
41
44
3015
3016
3017
100
101
104
log
113
119
123
125
128
135
137
140
143
145
146
147
148
45
49
88
89
57
61
64
68
71
74
76
79
82
84
86
93
94
95
96
97
98
3057
3058
3059
3060
The Phase 3 Solution
THE OBJECTIVE VALUE IS
1512.8721
1
4
7
10
13
18
??
24
27
32
35
37
41
44
3015
3016
3017
99
101
103
108
113
118
123
125
127
134
137
IS
IS
IS
IS
IS
IS
IS
IS
IS
IS
IS
IS
IS
IS
IS
IS
IS
IS
IS
IS
IS
IS
IS
IS
IS
IS
IS
IS
BASIC
BASIC
BASIC
BASIC
BASIC
BASIC
BASIC
BASIC
BASIC
BASIC
BASIC
BASIC
BASIC
BASIC
BASIC
BASIC
BASIC
BASIC
BASIC
BASIC
BASIC
BASIC
BASIC
BASIC
BASIC
BASIC
BASIC
BASIC
AT
AT
AT
AT
AT
AT
AT
AT
AT
AT
AT
AT
AT
AT
AT
AT
AT
AT
AT
AT
AT
AT
AT
AT
AT
AT
AT
AT
LEVEL
LEVEL
LEVEL
L^VEL
Lt-VEL
LEVEL
LEVEL
LEVEL
LEVEL
LEVEL
LEVEL
LEVEL
LEVEL
LEVEL
LFVEL
LEVEL
LEVEL
LEVEL
LEVEL
LEVEL
LFVtL
LEVEL
LEVEL
LEVEL
LEVEL
LEVEL
LEVEL
LEVEL
94.9000
78.9000
27.9000
21 .7000
6.0000
22.9000
64 .(SOOO
19.2000
26.7000
54.0000
57.6000
93.0000
5.7000
36.3000
977.6611
931 .5322
000.0000
94.9000
0.0
516.3992
27.7000
22.900C
110.5000
54.0000
93.0000
42.0000
90.3819
0.0
82
-------
The Phase 3 Solution (concluded)
140 IS BASIC AT LEVEL
14^ IS 1ASTC AT LFVEL
144 IS BASIC AT LEVEL
145 IS BASIC AT LEVEL
146 IS 3ASIC AT LEVEL
147 IS BASIC AT LeVFL
148 IS BASIC AT LEVEL
45 IS BASIC AT LEVEL
49 IS BASIC AT LEVEL
T8 IS BASIC AT LEVEL
89 IS HASIC AT LFVEL
57 IS BASIC AT LEVEL
61 IS BASIC AT LEVEL
64 IS BASIC AT LEVEL
63 IS BASIC AT LFVEL
71 IS BASIC AT LEVEL
74 IS BASIC AT LEVEL
76 IS BASIC AT LEVEL
79 IS BASIC AT LEVEL
6?. IS BASIC AT LEVEL
84 IS 3ASIC AT LEVEL
36 IS BASIC AT LEVEL
93 IS BASIC AT LEVEL
94 IS BASIC AT LEVEL
95 IS BASIC AT LEVEL
96 IS BASIC AT LEVEL
97 IS BASIC AT LEVEL
93 IS BASIC AT LEVEL
.1057 IS BASIC AT LEVEL
?050 IS BASIC AT LEVEL
3059 IS BASIC AT LEVEL
3060 IS BASIC AT LEVEL
0.0
23.2500
0.0
0.0
67.1319
0.0
0.0
94.9000
0.0
67 . 1 3 1 9
0.0
27.7000
C.O
22.9000
0.0
110.5000
0.0
54.0000
23.2500
42.0000
0.0
0.0
23.2500
0.0
0.0
67.1319
0.0
0.0
335.0457
361 .3997
379.1292
89999824.0000
The Phase 4 Solution
THE OBJECTIVE VALUE IS
1448.4475
1
4
7
10
13
13
22
24
27
32
35
37
4!
44
2"15
3016
3017
99
101
103
103
113
118
123
125
127
81
IS
IS
IS
IS
IS
IS
IS
IS
IS
IS
IS
IS
IS
IS
IS
IS
IS
IS
IS
IS
IS
IS
IS
IS
IS
IS
IS
BASIC
BASIC
BASIC
BASIC
BASIC
BASIC
BASIC
BASIC
BASIC
BASIC
BASIC
BASIC
BASIC
BASIC
BASIC
BASIC
BASIC
BASIC
BASIC
BASIC
BASIC
BASIC
BASIC
BASIC
BASIC
BASIC
BASIC
AT
AT
AT
AT
AT
AT
AT
AT
AT
AT
AT
AT
AT
AT
AT
AT
AT
AT
AT
AT
AT
AT
AT
AT
AT
AT
AT
LEVEL,
LEVEL
LEVEL
LEVEL
L^VEL
LEVEL
LCVEL
LEVEL
LTVEL
LEVEL
LEVEL
LFVEL
LCVr.L
LFVEL
LCVEL
LFVEL
LpVEL
LFVEL
LFVEL
LF.VEL
LFVEL
LEVEL
LCVEL
LEVEL
LEVEL
LSVEL
LEVEL
94.9000
78 .9000
27.9000
21.7000
6.0000
22.9000
64.6000
19.2000
26.7000
54.0CIOO
57.6000
93 .0000
5.7000
36 .3000
977.6611
9,2?
PCO.OOOO
94.9000
0.0
516.3992
27.7000
22.9000
110.5000
54.0000
93.0000
42.0000
23.2500
83
-------
The Phase 4 Solution (concluded)
137
140
14?
144
145
SA
147
148
45
49
88
39
57
61
64
69
71
74
76
79
32
84
86
93
94
95
9S
97
93
3057
3058
3059
3060
IS
IS
IS
IS
IS
I?
IS
IS
IS
IS
IS
IS
IS
IS
IS
IS
IS
IS
IS
IS
IS
IS
IS
IS
IS
IS
IS
IS
IS
IS
IS
IS
IS
BASIC
BASIC
BASIC
BASIC
BASIC
R \ S T C
BASIC
BASIC
BASIC
BASIC
BASIC
BASIC
BASIC
BASIC
3ASIC
BASIC
BASIC
9ASIC
BASIC
BASIC
BASIC
BASIC
BASIC
BASIC
BASIC
BASIC
BASIC
BASIC
RASIC
BASIC
BASIC
BASIC
BASIC
AT
AT
AT
AT
AT
AT
AT
AT
AT
AT
AT
AT
AT
AT
AT
AT
AT
AT
AT
AT
AT
AT
AT
AT
AT
AT
AT
AT
AT
AT
AT
AT
AT
LEVEL
LEVEL
LFVEL
L'VFL
LrvrL
LEVFrL
LTVCL
LFVEL
LFVrL
LCVCL
LEVEL
LEVEL
LEVEL
LFVEL
LEVEL
LEVEL
LEVEL
LEVEL
LEVEL
LEVEL
LfVEL
LEVEL
LEVEL
LEVEL
LEVEL
LEVEL
LSVEL
LEVEL
LEVEL
LEVSL
LfVEL
LFVEL
LEVEL
90
0
0
0
2?
67
0
67
94
0
0
0
27
0
27.
0
110
0
54
0
42
0
0
0
0
23
r\
0
67
332
356
379
89999824
.3319
.0
.0
.0
.1319
.0
.1319
.9000
.0
.0
.0
.7000
.0
.9000
.0
.5000
.0
.0000
.0
.0000
.0
.0
.0
.0
.2500
.0
.0
.1319
.4641
.08^0
.1292
.0000
84
-------
CHAPTER 5
SAMPLE INPUTS AND OUTPUTS
Full listings of inputs and outputs are presented below for N. E.
Massachusetts B-2, representing a static case, and St. Louis G,
representing a dynamic case. The outputs display activities which were
in the solution with a zero activity level. Such activities are
suppressed in the final version of WRAP.
85
-------
E. Mass. B-2 Static Case
Inputs
CONTPL 1411222003
TITLE NE MASSACHUSETTS CASE
SOURCE101 SOUTH ESSEX OUTER
LAWRENCE
HAVERHILL
NEWRURYPORT
E CENTRAL ESSEX
GLOUCESTER
LOUf-CLL EAST
LOWELL WEST
LOWELL SOUTH
EAST MIDDLESEX
SOURCE: 02
SOURCE103
SOURCE I 04
SOURCK105
SOURCE 106
SOURCEJC7
SOURCE 1 08
SOURCE 10<3
SOURCE! 10
SOU«CF1I1
SOURCE11?
SOURCE113
SOURCE! 14
SIT- SOI
SITc '302
SITC ^03
2 t 14
6-2 - -
705^64^299
71 10042421
7104542465
16
71 1*24^380
712'»3474
71 17042325
7 10l> 342340
71 19042510
HESCO COMMUNITIES
S W CENTRAL ESSEX
SOUTH ESSEIX INNSM
SAL';M TMCTNFlUT-T43
647
EA MinOLF
KtSCO PKrl
SJ c'SSt'X
HAVTKHILL
LOWELL FA
SO F.SX IN
HAV DUMMY
SO FX niJMVY
LiVL DUMMY T
i-iAV DUMMY li
Si) f-X
X TRANS
'"COY -{" ~ 0 V
SCDY RECOV
SCf)Y R£CV
INC IN RFS
INCIN RS
CIM RES
ftVY FNl)
LNKI
FXC1
HEAVY L\l)
i ( r A V Y ,- M 3
TRANS^A STATION
1
0
15 9?'> 935 0
77,1,«5 14
71083
71073
70549
70433
71214
7 1 0 ) '.i
7 n *> 8 ft
71073
71214
70537
71073
712 14
71073
42 4,'8
42457
42492
42371
42377
4J Vt'b
4,'2 69
42376
42457
H2377
42336
42457
-19657
71214
42577
42457
42336
4Z377
1211S
542
A 2100
6634(1
342^
2370
32 13
i
i
i
i
750
02S
901
1000 026
LNK! 2
l.W> 946
PRCUST 11
P'KOST 12
PR COST 13
90) 0
0
2980049
90MOH4
441506
317
66/t
109r
PKC1 9C6 StCGMUARY R6CCVI:RY
PRC2 2
LNKI 1
PR COST 11
PRCCST 12
PRCOST 13
1
936 946 0
126
75
12
3
1767
2015
44485
PRC1 915 RESCO PROCESS
PRC2 Z
LNKI 2
LNKO 936
PRCOST 11
PRCnST 12
1
901 "6
0
0
0
2
0
0
PRC1 925 DRIED SHREDDED FUEL
PRC2 2.
LNKI 2
LNKO 946
PRCOST 11
PRCOST 12
PKCOST 13
1
901 0
0
45
22
115
3
234
58125
10261
3070175
1374693
150641
C 2
31
14
108
0 1 25
5271
276
B 2 13
935
446667
285
70
320
710
155
372
47275
1200 026
265
950
1000 026
306
1?4775
21979
901
VC1
901
90 1
905
905
905
905
905
905
906
9C6
906
906
906
915
915
915
915
915
925
925
r;25
925
925
925
86
-------
N. E. Mass. B-2 Static Case (continued)
Inputs^
PRCl 935 GAS PYROLYSIS B 2
PRC2 2 1 2
LNKI 2 901 0
PRCOST 11 0 38683 0
PRCOST 1? 221333 2496 533967
PRCl 936 DUMMY INCIN RESIDUE C 2100
PRC2 2 1 1
LNKI 1 915 0
LNXO 90', 0
PRCOST 11 0 0 0
PXCl 946 DUMMY HEAVY <=ND C 2100
PRC2 2 1 1
LNKI 1 905 925 0
LNKO 906 0
PRCOST 11 0. 0. 0.
SIPKOC 501 901 23
SIPROC 502 901 23
SIPROC 5C3 905 23 581
SIPROC 503 925 23 791
SIPROC 503 935 02 810
SIPKOC 504 901 12 1240
SIPKOC 504 905 12 124C 581
SIPROC 504 935 01 62 810
SIPROC 50o 901 12 1240
SIPKOC S06 905 12 1240 581
SIPROC 506 935 01 62 010
SIPRJC 507 901 23
SIPROC 507 905 23 531
SIPROC 507 935 02 810
SIPROC 510 901 23
r.IPRUC 51?. 9lr. \Z 465 0
STPrtOC r>14 901 23
SIPROC 514 905 23 5fl 1
SIPROC 514 925 23 791
SIPROC 514 935 02 010
SIPROC 603 906 13
SIPROC 607 906 13
SIPROC 614 906 13
SIPROC 633 926 01 19345
SIPROC 634 936 01 19345
SIPKOC 637 936 01 19345
SIPROC 643 946 01 30077
SIPRUC 644 946 01 30077
SIPROC 647 946 01 30077
TRANS 2 101 101 501 14
TRANS 2 101 101 514 137
TRAVS 2 102 102 50? 6
TRANS 2 102 102 503 13
TRANS 2 102 102 514 335
TRANS 2 103 103 502 151
TRANS 2 103 103 503 112
TKANS 2 103 103 514 324
TRANS 2 104 104 503 262
TRANS 2 104 104 504 2
TRANS 2 104 104 514 249
TRANS ? 105 105 503 414
TRANS 2 105 105 504 247
TRAMS 2 105 105 506 207
TI1ANS 2 105 105 514 2bl
TRANS 2 106 106 504 515
TRANS 2 106 106 506 75
TRANS 2 106 106 503 634
TRANS 2 106 105 514 31
TRANS 2 107 107 502 204
TRANS 2 107 107 503 254
TRANS 2 107 107 507 87
TRANS 2 103 108 503 299
TRANS 2 108 108 507 67 at
70546
3744
1200 026
0
1000 026
0.
A
A
B
B
B
A
0
8
A
B
6
A
6
B
A
U
A
B
B
n
C
C
C
C
C
C
C
C
C
935
935
935
935
936
936
936
936
946
946
946
946
-------
N. E. Mass. B-2 Static Case
TRAMS
TKANS
HUNT,
TKANS
TRANS
Ti^ANS
TRANS
TKANS
TRANS
TKANS
TRANS
TiUNS
TRANS
TRANS
TRANS
TRANS
TRANS
TRANS
TRANS
TRANS
TRANS
TRANS
TRANS
TRAMS
TRANS
TRANS
TRANS
TRANS
TRANS
TRANS
TRANS
TKANS
TKANS
TRANS
TRANS
TRANS
TRANS
TRANS
TRANS
TRANS
TRANS
TRANS
TRANS
TRANS
TRANS
TRANS
TRANS
TRANS
TRANS
TRAMS
TRANS
TRANS
TRANS
TRANS
TRANS
T-vAMS
TR^NS
T-U ,15
T^NS
• ; *\ \
1 i<*\S
TRt\S
TRANS
TRANS
TRANS
TRANS
•>
•t
t
•3
?
2
2
2
2
2
2
2
2
2
2
2
2
2
2
?.
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
?
•»
3
3
3
3
}
1
-.
•>
5
5
5
5
103
10<7
10->
109
10V
110
110
110
110
111
111
111
112
113
113
113
113
IK
114
1U
501
501
501
501
502
502
502
502
503
503
S03
503
so*
•iO14
M*
N • *
M-
514
503
503
507
514
10d
109
10'J
10')
109
no
110
110
110
111
111
111
11?
11?,
113
113
113
114
114
114
901
901
901
•901
901
901
901
901
905
>?05
v;_'5
925
901
901
voi
901
905
505
«05
901
901
901
901
905
905
905
901
901
901
905
^O'j
SOI
901
901
915
01 S
91 '5
401
oci
^ vx ~
•».">
•^•>
90 ^
925
905
905
514
',01
'.07
•>10
514
50?
503
5 ID
r>14
502
503
507
512
503
504
506
514
503
507
514
503
506
507
514
503
504
507
514
644
647
644
o<,7
503
50s
507
514
643
644
647
S03
504
507
514
643
644
647
503
504
514
643
644
503
507
514
633
634
S37
503
507
:>-»5
6*7
643
643
647
644
Inputs
473
2»9
122
u.u
310
175
2, ''5
..'
;*4a
256
259
379
20
393
221
244
103
376
48
43
535
326
638
?02
82
30
233
503
353
2fi3
353
2U3
262
46
502
249
T6?.
249
502
579
46
56
245
579
245
56
203
502
42
233
42
2. '5
243
248
529
231
516
353
c;
•2 i T
.* ^ J
353
41
-1
-1
-1
-1
88
-------
N. E. Mass. B-2 Static Case (concluded)
Inputs
TRANS 5 514 9i5 c>44
TRANS 5 633 936 60?
TRANS 5 63-V 936 o 14
TRANS 5 637 936 607
TSAN'S 5 643 946 603
TKANS 5 644 946 614
TRANS 5 647 946 607
TRUCK 503 633 643 390
TRUCK 507 637 647 390
TRUCK 514 634 644 390
I 4 7 10 13
104 I OS 113 1 1<> I.2J
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St. Louis G Dynamic Case
Inputs
2120 214
SITE
SITE
CONTRL 2411
CNTR2 10*-, 943
TITLE ST. LOUIS DYNAMIC RUN
SOURCE 1OlFRANKLIN COUNTY
SOURCE102J~FFFRSON COUNTY
SCURCri03VAD1SON COUNTY
SOURCE10»MONROE COUNTY
SOURCE105ST. CHARLES COUNTY
SOURCE1C6ST. CLAIR COUNTY
SOURCE107ST. LOUIS CITY
SOURCE103ST. UOU1S COUNTY
SITE 501 Ml TRANS
SITE 506 M6 PROCESSING
507 M7 TRANS/PYROLYSIS
509 M9 TRANS
510 v,lO TRANS/PYROUYSIS
514 Ul MKT/PROCESSING
711 A 19 VIGUS OUARHY
901 TRANSFER P«R TO VAN
22223444 3
0 " "
935 955 0
77885 14
35962 275
12115 542
77335 14
35962 275
12115 542
77885 14
35962 275
12115 542
77885 1 4
35962 275 ~
12115 542
3
7 4
10 30
O 20 25 3 10
759
14d5
5393
251
1953
6361
12
13
SITE
SITE
PRCI
PRC2
LNKt " 2
|_NKO 907
PPCOST 1 1
PKCOST
PRCOST
PRCOST
PRCOST
PRCOST
PRCOST
PRCOST
PRCOST
PRCOST
PRCOST
PRCOST
PRC1
PRC2
LNK1
PRCOST
PRCOST
PRCOST
PRCOST
PRCOST
PRCOST
PRCOST
PRCOST
PRCOST
PRCOST
PRCOST
PRCOST
CASE G " •
9056233255 391 508
902(3133193 655 906
9003133497 2BOI 3617
9309833211 102 148
9032736471 793 1146
8959533334 3582 4491
9014633J72 7953
90214334O1
1 91011
I 90167 38349
1 90388 38377
1 90422 38497
1 90306 38308 2.
\ 90194 38260 1
1 90289 38447 1
A 210 750 O26
9d«l13
£0d'il 13
7023113
343113
2710113
BOJ41 13
89561O7031 2O541 13
83671O753158222104^2113
38368 1
2
2
1 ~
1 13
1 13
1 13
1 13
1 13
1 13
1 13
1 13
1 13
1 13
1 13
1 13
113
113
1 13
113
5 17
13
13
13
13
13
13
13
13
20000
O26
O26
O26
22
23
31
32
33
41
42
43
907 SANITARY LANDFILL
22222344
66346
3423
2875
66346
-3423
2875
66346
3423
2875
66346
3423
2875
0 2.
22
505
668
22
505
663
2H
505
668
22
505
660
2 901 0
11 546875 8525 1640625 76725
12 36 — 1395 -- 108 1 2555O
13
21
22
23
31
32
33
41
42
43
2115 25575 6345
546B75 8525 164O625
36 1395 103
2115 25575 6345
546875 8525 1640625
36 ' - - 1395 — 108 - -
2115 25575 6345
546875 8525 1640625
36 1395 1 OS
2115 25575 6345
PRCI 935 GAS PYROLYS1S B 2
PRC2 1222 444 1
LNKI 2 901 0
PRCOST 11 221333 2496 533967
PRCOST 21 22-1333 2496 533967
PRCOST 31 221333 2496 533967
PRCOST 41 221333 ~ 2496 533967
PRCI 955 SHREDDED FUEL/SEC RC 32
PRC2 22223444 -3
LNKI 2 901 0
PRCOST 11 3145 4937 3473
PRCOST 12 1072 Q447 2278
P'JCOST 13 54 12995 " 1633
PRCOST 21 3145 4937 3473
23O175
76725
125550
230175
76725
125530
230 1^5
76725
125550
230175
3744
3744
3744
3744
901
901
901
9O1
901
9O1
9O1
901
9O1
901
901
901
901
9O1
9OI
9O7
907
907
9O7-
VO7
907
9O7
9O7
9O7
-907
907
9O7
907
907
225
475
1082
225
935
935
935
935
935
935 '
955
955
955
955
955
955
92
-------
St. Loin's G Dynamic Case (concluded)
PRCOST 22 1072
PRCOST 23 54
PRCOST 31 3145
PRCOST 32 1O72
PRCOST 33 54
PRCOST 41 3145
PRCOST 42 1072
PRCOST 43 54
SIPROC 5,01 901 13
SIPROC 506 935 01
SIPROC 506 955 13
SIPROC 507 9O1 13
SIDROC 507 935 01
SIPROC 509 901 13
SIPROC 510 9O1 13
SIPROC 51O 935 Ol
SIPROC 514 955 13
SIPROC 711 907 13
TRANS 1 103 103 711
TRANS 1 1 05 105 71 1
TRANS 1 103 108 71 1
TRANS 2 1O1 101 501
TRANS 2 102 102 506
TRANS 2 102 1O2 51O
TRANS 2 102 102 514
TRANS J> 103 103 506
TRANS 2 103 103 507
TRANS 2 104 lo4 506
TRANS 2 104 lr>4 507
TRANS 2 105 1 O5 506
TRANS 2 105 105 509
TPANS 2 1O5 105 510
TRANS 2 106 106 506
TRANS 2 106 !o6 507
TRANS 2 107 IO7 506
TRANS 2 108 loa 506
TRANS 2 !08 1O8 510
TRANS 3 501 9ol 506
TRANS 3 501 901 510
TRANS 3 5O7 9O1 506
TRANS 3 507 9O1 510
TRANS 3 507 9O 1 514
TRANS 3 509 9O 1 506
TRANS 3 509 90 1 510
TRANS 3 510 9O1 506
TRANS 3 510 901 514
TRANS 4 509 901 711
TRANS 4 510 9O1 711
Inputs
3447 2278 475
12995 1688 1082
4937 3473 225
8447 2273 475
12995 1638 1 O82
4937 3473 225
8447 2278 475
12995 1688 1 O82
A
1554 1554 Ib54 O
6732 6732 6732 6732 B
A
1554 1554 1554 B
A
A
1554 1554 1554 B
8447 8447 8447 8447 B -- - -
D
48
143
25
60
-^45 " ----- —
52
25
472
43
28
29
518
ia
412
4O
•JO ' '
120
239
239
92
60
36
479
. 60
522
32
36
255
342
955
955
955
95b
955
955
953
955
93
-------
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CHAPTER 6
RUNNING TIME'S EXPERIENCE
Table I displays, without comment, the sizes and running times of
all the runs of the St. Louis Operational Test and the Massachusetts
Exercise Program, together with information on whether a WRAP output was
included and whether WRAP generated the starting basis. The running
time was not available for N. E. Massachusetts run A.
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CHAPTER 7
GUIDANCE ON USING THE MODEL
In this chapter, the reader is asked to take a few steps backward
and view the model from a somewhat broader context. The focus of the
discussion here is not so much how to operate the model on a defined
problem, but rather on how to define the problem itself. As a
consequence the guidance to be provided is broader, less specific,
relying more on the good judgement of the person using the model.
How to Structure An Application
An application is a set of runs designed to illuminate issues for
the decision maker.
For a broader view of alternative mathematical structures, the
reader is referred to the report of the original MITRE-sponsored design
study, in which eighteen alternative model modes were presented.2 All of
these modes were designed to use the Walker Algorithm;3 nine modes were
static and nine were dynamic; and twelve had some capability of
representing market saturation.
The reader might also gain insight from reviewing earlier model
applications. In 1974, a basic static mode of the model (then called
SWAMP, Solid WAste Management Planning) was used for a program of
operational runs in support of regional design analysis for the
Commonwealth of Massachusetts.1* In these runs, the inputs to the
algorithm were generated manually, and the outputs were interpreted
manually.
The WRAP operational test in the St. Louis area and the Northeastern
Massachusetts parametric exercise program have been fully reported in E.
B. Berman, WRAP -A Model for Regional Solid Waste Management Planning:
Documentation of Operational artd Exercise Runs. MTR-3219. April 1976.
which is available on request from The Environmental Protection Agency,
2. Berman, E. B. A model for selecting, sizing, and locating regional
solid waste processing and disposal facilities. M73-111. Bedford,
Mass., The MITRE Corporation, Oct. 1973. 61 p.
3. Walker, W. Op. Cit.
4. Berman, E. B., and H. J. Yaffe. Region design analysis for regional
resource recovery system for northeastern Massachusetts. MITRE
Technical Report MTR-2945. Bedford, Mass., The MITRE Corporation,
Nov. 1974. 39 p.
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Office of Solid Waste Management Programs, Systems Management Division,
or from The MITRE Corporation.
In designing an application two things are important
• the modeling person should have a good understanding
of how to put the model through its paces (note the
subsection which follows, Controlling the Structure
of the Solution)
• the model person should not attempt to design the
complete application in advance. Some questions will
arise from the solutions themselves. Time and budget
should be allowed to answer them.
Illuminating Political and Technical Issues
An application, which is a set of runs, is designed to illuminate
political and technical issues.
Each run in the set will:
• handle all wastes
• meet all environmental standards (for only processes which
do meet relevant standards should be offered)
• provide the lowest cost solution for its "case".
The "case" is a defined state of political/technical feasibility. The
case will define such things as:
which sites are available
which processes are available
which transportation activities are available (e.g., can these
cross county or state lines), etc.
The model will generate a plan for each case, and a system cost for each
case. This illuminates the incremental costs of moving from case to
case, and in particular the costs of moving from less political
acceptability to greater political acceptability. Figure 7 illustrates
a hypothetical plan set. Figure 8 summarizes issues which have been
examined in Massachusetts and in the St. Louis area.
118
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Figure 4
ILLUMINATION OF ISSUES
I REGION SIZE
MASS:: LARGE REGION: HOW DOES IT BREAK DOW
ST, UDUIS: REGION VS STATE - BY - STATE
C PROCESS AVAILABILITY
POLITICAL
LMFILJL IN m$S, & ST, LJ3UIS
THMCAL
GAS FYROLYSIS IN MASS,
ft SITE AVAILABILITY
ST, UDUIS - PROCESSING AT PUNT
MASS, - SOUTH ESSEX SITE
© MARKET AVAILABILITY
ST, UDUIS - ILLINOIS POWER CO,
8 SENSITIVITY
TOWAGE, MARKET PRICES, PROCESS COSTS
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Which Issues?
It is important that the modeling person communicate with the
relevant decision-making group to learn what political and technical
issues are important to them. It is essential for an interchange to be
maintained between modeler and decision-maker as solutions are
generated, as some issues are clarified, and as others are newly
generated.
Controlling the Structure of the Solution (Configuration Forcing)
There are two general approaches to controlling the structure of the
solution: (1) forcing the model to consider a structure or structural
element (e.g., a site/process); and (2) forcing the model not to
consider a structure or structural element. In the final analysis, the
model can be made to consider a structure by forcing it not to consider
all other structures.
The most direct way to get the model to consider a -structure is to
use that structure as an advanced starting point. If a costing of that
structure is desired, the advanced starting point technique may not be
sufficient since the model will move away from that structure if a
better (i.e., lower cost) one can be found. For purposes of
configuration forcing, however, it is important only that the model
consider the structure, and the advanced starting point method is
sufficient.
If the cost of a particular structure is desired, it would be more
straightforward to eliminate enough other options to assure that the
desired structure will be the solution.
The model can be made not to consider a structural element either by
removing the structural element or by attaching an artifically high cost
to it.
In the first series of Massachusetts runs, inputs were manually
processed. It was simpler to attach an artificially high cost to
processing activities which were not wanted in the solution, since in
this way the matrix could be left unchanged. However, with WRAP, with
its preprocessor, the cost vectors are less accessible, and at the same
time, there is no disadvantage in needing a new matrix. Thus, for the
St. Louis operational test and the Massachusetts exercise program,
undesired structural elements were merely removed from the input.
The definition of region in the St. Louis series was controlled by
the selection of transportation activities. Thus, run C of that series
represented the case of no interstate flows (of raw refuse or heavy end
residue). To accomplish this, the transportation file was screened, and
all interstate activities were removed. Since each transportation
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activity is a single card in the transportation file, removal of such
unwanted structural elements is easily accomplished.
The removal of a process at a site requires removal of the
appropriate SIPROC card, and readjustment of the number of processes on
the SITE card.
The user should be careful to readjust the appropriate count on the
control card after removal of any structural element.
It should be noted that it is possible to remove a process from each
site where it was offered without changing the process file, since there
is no preprocessor check on whether a process in the file appears on a
SIPROC card (indicating it is offered at a site). On the other hand,
since linkage is checked, it is important in removing transportation
activities to make sure that every site has at least one remaining input
link and that every source and every site/process with positive percent
output by weight has at least one remaining output link. If in doubt,
CROW-FLY option 1 or 2 might be used.
How to Structure the Set of Sources
Ideally one would like to define a region into subregions (or zones,
or districts) such that each had one and only one concentration of
population (and hence waste generation) and such that there was a space
of low population between the concentration and the subregion
boundaries. Then the centroid of waste generation would be defined in
the center of the concentration of population and would accurately
represent the geographical impact of the waste generated in that
subregion.
In real applications, we must compromise the ideal with what we find
in the real world:
1. it is important to keep the size of the model small.
Twenty-nine "districts" were defined for the static
runs of the St. Louis Operational Test. We should
not want to go much beyond that, and would prefer
fewer. Fourteen "zones" were used for Massachusetts
2. inevitably, there are multiple concentrations of
population in a subregion
3. inevitably, a concentration of population will spill
over a subregional boundary.
It is suggested that the centroid of waste generation be defined for
a subregion so as to represent the locational weight of population, and
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at the same time, if possible, to be at a major intersection past which
a large volume of waste would tend to flow.
How to Structure the Set of Sites
Ideally, the set of sites would be:
1. real sites which are actually available to the solid
waste planner
2. sufficient in number and sufficiently well spaced to
allow the model to trade off freely between the
economies of scale of centralization and the costs of
haul required to support it.
In the real world, not enough sites will be nominated, and those
will not be well spaced. It is recommended that additional sites be
added by the user at key intersections in at least one run of the series
to indicate how much additional system cost is implied by limiting the
solution to sites actually available to the planner.
How to Sitrip Down a Problem for Optimization
It is desirable to make a large range of options available to the
WRAP model so that a good solution can be found. However, it is also
desirable to keep computer time and cost down to reasonable levels.
It is good practice to begin an application with one or more
relatively large problems (in terms of the number of rows and columns)
run through phase 3 in order to get some insight into the structure of
the solution. The problem should then be stripped down to a smaller
problem, with fewer rows and columns, which can then be run through
phase 4 for full optimization. This smaller version can also be useful
in reducing the size of subsequent configuration forcing runs. Note in
Chapter 6 above the contrast in size been St. Louis A and B, and St.
Louis A-l, which was the first run in the St. Louis series operated
through phase 4. Similarly, in the Massachusetts exercise series, N. E.
Mass. A was a large problem, operated through phase 3 only, and run A-2
was a stripped-down problem operated through phase 4. (Runs A-3 and A-4
were configuration forcing runs controlled by way of the advanced
starting point, but operated only through phase 3.)
It should be noted that the time required to run using phase 4 is
very sensitive to the number of columns since each additional column
generates an additional forced solution and an additional phase 3
process. Thus it is important to strip out both columns and rows.
Columns can be stripped by reducing the number of linear segments
offered on the SIPROC; by removing many of the transportation
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activities; by removing some processes from some sites, and by removing
some sites altogether. The latter two steps reduce the number of rows
also. The number of rows can also be reduced by combining sources and
by changing sites from limited to unlimited. All of these removals
should be under the guidance of the phase 3 solution of the larger runs,
but much care and thought is required to keep from constraining the
model so much by the removal of options that it cannot find the best
solution.
In one case, in the St. Louis series, two smaller runs were used to
replace one larger run. Thus, St. Louis A offered primary processing in
and near the central city (sites M5, M6, M7, and M10) and also at the
utility sites (Ul and U2). Run A-l offered only off-utility site
processing (M5, M6, M7, and M10) and runs F and F-l offered only on-
utility site processing (111 and U2). Thus the full range of options was
preserved for locating primary processing, but not all in the same run.
Study of earlier applications of the model, as referenced at the
beginning of this chapter, is recommended as a source of further insight
into the operation of the model.
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