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The United States spends more
than $4.5 billion annually on
solid waste management—and
more than 80 percent of that
goes for collection. An effi-
cient collection system is thus crucial
to the overall success of a solid waste
management system. Cutting col-
lection costs can be approached in a
number of ways. Wastes could be
eliminated before they require col-
lection, or wastes difficult or expen-
sive to collect might be replaced by
those which are not. Manpower re-
quirements could be reduced or better
collection vehicles developed.
Still another approach is operations
research models, which can be helpful
in planning and managing any col-
lection system. It is relatively easy to
apply such models to systems with
well-defined objectives and restrictions
and readily measured effectiveness. A
fleet of laundry trucks, for example,
must be routed so that the customer is
satisfied with the frequency of service
and costs are kept to a minimum.
In applying operations research
models to systems like those collecting
solid waste, however, many stumbling
blocks are encountered. The objectives
of a solid waste collection system may
be vague and difficult to express.
Restrictions (especially the political
and social) may be difficult to
measure. The political implications of
who controls a system and who pays
for which service may mean that a
seemingly efficient scheme is thrown
out. Since large amounts of money
may already have been invested in the
system, the operations research analyst
must often work around the blunders
of the past. But the biggest problem in
analyzing solid waste collection is in
measuring its effectiveness. Frequency
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of collection, types of wastes col-
lected, locations from which wastes
are collected, and general customer
satisfaction—all are involved, but it is
almost impossible to evaluate them in
concrete terms.
All this does not mean that opera-
tions research models and tools should
not be applied to solid waste pro-
blems. But as with all models, they
must be used carefully with an appre-
ciation of the factors that the models
cannot consider directly. A model
does not replace a decision maker, it
helps him. But it helps him only if he
continues to use his own judgment and
does not follow the model blindly.
Decision makers may get some help
from a study by David H. Marks and
Jon C. Liebman of Johns Hopkins
University's Department of Geography
and Environmental Engineering. Work-
ing under a research grant from the
solid waste management program of
the U.S. Environmental Protection
Agency, they developed a number of
solid waste collection models. The first
involves determining the location of
intermediate stations where solid
wastes can be transferred from col-
lection vehicles to vehicles (such as
large trucks or trains) more suited to
long-haul transportation to disposal
sites. The second model analyzes the
best way of routing the wastes to the
transfer facility, assuming first that all
wastes are collected together, then
that a number of different kinds are
collected separately. The third model
concerns scheduling routes for in-
dividual trucks.
The Hopkins engineers then applied
one of the models to the solid waste
collection system of nearby Baltimore,
Maryland. They concluded that the
models, although limited to part of the
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location of
transfer stations
total collection system, can still pro-
vide a great deal of insight into the
system. Application of operations
research to those parts of the col-
lection system amenable to such
analysis can, they feel, yield a wealth
of information to the decision maker
charged with planning and managing a
large-scale solid waste collection
system.
The fundamental questions regarding
transfer stations involve their desirabil-
ity, number, location, and capacity, as
well as the specific functions they
should perform. The answers involve a
trade-off between the cost of building
the station and the cost of trans-
portation. Two points are clear:
• This is a general problem of locat-
ing facilities, so that other studies
may provide valuable information.
• Assuming that facility and trans-
portation costs can be defined, it is
possible that the problem can be
defined in mathematical terms.
A literature search revealed that
mathematical procedures had indeed
been formulated, particularly for the
large-scale "flow of goods," in which
the concern is with selecting paths
over which materials move between
collection areas and central facilities.
When the materials flow from the
facility to supply demand in the sur-
rounding regions, it is called a "ware-
housing" problem; when they flow
from the surrounding regions to a
central producing facility, it is a "plant
location" problem. In either case, the
transporting vehicles are assumed to be
smaller than the quantity of material
to be transported, so the vehicle does
not have to be routed to pick up a full
-------
load; this assumption simplifies the
mathematical procedures.
Operations research analysts work-
ing on this problem have faced two
basic questions:
• Is demand spread, uniformly or
otherwise, continuously across the
entire area to be served, or is it
located at discrete points?
• Is the number of potential facility
sites infinite, or is it limited?
If both demand and potential sites
are assumed to be infinite, the pro-
blem becomes very difficult to solve.
Fortunately, there is not an infinite
number of sites in a city where solid
waste facilities can be located; rather,
there is a finite and very small number
based on available land, zoning, con-
centrations of people, and the location
of existing structures. Demand does
tend to cluster, and in most cases it is
reasonable to subdivide a region into
areas with demand centered at a point.
The problem then is to determine on
which of the potential sites the facili-
ties should be built and which demand
areas each facility should serve. The
objective is to minimize the total
cost—that is, the cost of transporting
the wastes and of building the
facilities.
Marks and Liebman found that the
problem in solid waste management
had added dimensions over a simple
warehousing or plant location pro-
blem.
Earlier work had placed no restric-
tions on the flow of materials through
the facilities, when in fact transfer
facilities do have capacities, which
must be observed in models. Further-
more, since the wastes might be
processed at the station (sorted, com-
pacted, or incinerated, for example) a
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minimum through-put may be neces-
sary to keep the process operating.
Two transportation costs are in-
volved, since the facilities are inter-
mediate points between where the
wastes are generated and where they
are disposed.
Thus, Marks and Liebman were
seeking to solve a special problem,
which they called "the capacitated
trans-shipment facility location pro-
blem," They solved it by means of a
network flow algorithm combined
with a branch-and-bound technique.
The model that they developed,
when programmed for the computer,
could handle a very large and complex
solid waste collection system and find
the best solution quickly. A short
solution time is very important, since
the value of models is their ability to
make repeated runs and determine the
effects of changing various conditions
in the system.
other models
The other models developed in the
study were not so successful. The
second model considers the best way
for wastes to flow through the net-
work when the transfer sites have been
chosen; again, the small-scale routing
of individual coHection vehicles is
ignored. Marks and Liebman con-
sidered two cases of routing a fleet of
vehicles between points in the net-
work. In one case, all wastes were
collected together. In the other, a
number were collected separately.
Residential, industrial, and construc-
tion wastes, salvageable materials,
ashes, leaves, and even Christmas trees
are sometimes collected separately.
Although the model can find solutions
quickly, the size of the networks is so
small that it can't be used on solid
waste collection systems.
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network with
potential transfer
stations
Locating stations where solid wastes will be trans-
ferred from collection trucks to long-haul vehicles
is essentially a problem of large-scale flow of goods
in which the goal is to minimize the distances trav-
eled in the network of collection areas, transfer sta-
tions, and disposal areas. This simplified example
considers just two collection areas, three transfer
station sites, and two disposal points. The actual
Baltimore analysis considered 40 collection areas,
7 transfer station sites, and 1 disposal point.
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The third model assigns collection
stops to individual trucks. Many public
and private agencies share this problem
of scheduling vehicles to and from
given locations, so it has received a
great deal of attention from operations
research analysts. Vehicle scheduling
problems can be classified according to
a number of criteria, including:
• Is demand discrete or continuous?
• Is it uniform or nonuniform?
Discrete demand implies demand is
located at specific points of a network,
with travel between the points taking
place along arcs. An example is routing
petroleum products to service stations.
Continuous demand is illustrated by
snow plowing; this is also an example
of uniform demand, while service
stations are a case of nonuniform
demand.
Marks and Liebman classified solid
waste collection as discrete but uni-
form demand, and stated the problem
in the form of the well-known "travel-
ing salesman" problem. The salesman's
route calls for him to visit all required
cities once and return to the starting
point, while traveling the minimum
distance. The size and complexity of
solid waste collection systems require
many "salemen," and this multiroute
problem has not been studied in great
detail. Marks and Liebman were able
to develop a solution method for the
multiroute problem, although it is not
yet practical in the solid waste col-
lection context. The reason is that the
total number of "cities" (representing
households or block-faces) which can
be handled in reasonable computer
time is quite small. In test cases,
12-city problems took 30 seconds on
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an IBM 7094 computer, while 16-city
problems took as much as 2 minutes.
This exponential relationship between
problem size and computer time
would make practical-sized collection
systems impossible to solve using the
present model.
Others working with vehicle sched-
uling models have encountered the
same difficulty, and Marks and
Liebman believe that, in the interest of
solving real-world problems, it might
be profitable to stop pursuing the
mathematics through to completion to
determine the best solution. Rather,
the emphasis should shift to using a set
of rules that ensures finding a good
solution. To date, no one has investi-
gated the difference between a good
solution and the best solution in
vehicle routing to determine if the
search for the best is worthwhile.
Meanwhile, comparisons of alternative
solutions based on procedures seeking
a good solution should be viewed with
caution.
Vehicle scheduling models might
also be improved if demand were
thought of as being continuously dis-
tributed along the arcs of a network,
according to Marks and Liebman. This
is the so-called "Chinese postman"
problem, which can be remarkably
easy and quick to solve. The problem
is to find a continuous route for one
vehicle that travels all arcs while travel-
ing the minimum distance. The Johns
Hopkins investigators believe it is
possible to extend these techniques to
more than one vehicle and develop
practical computer programs that can
ensure finding good solutions to the
problems of routing a fleet of collec-
tion vehicles.
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ANALYSIS OF BALTIMORE'S
SOLID WASTE COLLECTION SYSTEM
Using the transfer facility location
model, Marks and Liebman turned to
analyzing Baltimore's solid waste col-
lection system. Baltimore is a good
example of a large city with extensive
investment in a public system. In fiscal
year 1971, the city budgeted $7.4
million to collect and dispose of mixed
municipal wastes. Baltimore was a
good choice for another reason: a
great deal of data has been collected
on operation of the system.
The Hopkins study, which consi-
dered only the short-range picture,
asked these main questions:
• Are transfer stations feasible within
the city? If so, where should they
be located? What size should they
be?
• What are the costs and effects of
increasing collections from two to
three times a week?
• Under what conditions and at what
price would rail haul become a
feasible alternative for the city?
Subordinate to these questions, but
still of great interest, are three addi-
tional questions:
• How sensitive are the solutions
found to changes in conditions and
cost estimates?
• What are the effects of political and
aesthetic restrictions that might
force a change from the solution
suggested by economic and engi-
neering considerations to one
perhaps more acceptable to seg-
ments of the community?
• Are there advantages to cooper-
-------
the study area
ation between governmental units
within a region where such cooper-
ation does not now exist?
Marks and Liebman chose as the study
area Baltimore's Northwestern Div-
ision, one of the city's five autono-
mous districts. It is inhabited by about
225,000 people. It can be subdivided
into 40 census tracts for which exact
population, location, number of
household units, and housing unit den-
sity are known. The density is impor-
tant because it gives some indication
of the speed of collection. In the study
area, significantly greater weight can
be collected each hour in neighbor-
hoods having more than 10 housing
units per acre than in those having less
than 10.
The speed of collection also
depends on the number of days since
the last collection. Mixed refuse is
picked up twice weekly from resi-
dential and noncommercial sites in the
study area. The collection in the early
part of the week is generally larger
since it picks up four days of solid
waste accumulation. Normally, the
crews for the larger collections consist
of a driver plus three laborers; there
are two laborers for the smaller col-
lections.
As transfer sites, Marks and
Liebman chose seven possibilities.
Five, including one for rail haul, are
within the Northwestern Division.
Four are already publicly owned. As
a disposal site, they picked the Pulaski
incinerator, the newest of Baltimore's
two incinerators. It is closer to the
study area, and its unit costs are
somewhat lower than Baltimore's
older incinerator. Wastes would move
to the incinerator via 75-cubic yard
tractor trailers with a capacity of
35,000 pounds. Not all wastes, how-
ever, would go to transfer stations. It
would be more economical for areas
close to the incinerator to send their
wastes there directly. For rail haul, the
wastes would go to abandoned coal
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MOUSING UNITS
PER ACRE
| | LESS THAN 10
| I MORE THAN1O
location of
proposed transfer sites
and present incinerator sites,
Baltimore, Maryland
-------
mines in western Pennsylvania.
In all, 60 computer runs were made
on the facilities location model. Using
the IBM 7094, these runs took a total
of 45 minutes of computer time—or
about $375 at commercial rates. A
number of factors and conditions were
varied in the runs. Stations of various
sizes were assumed at the potential
sites. Collection frequencies of two
and three times weekly were con-
sidered. Haul distances to final dis-
posal, waste loads, and collection rates
were varied.
One of the runs duplicated the
present system, which was to serve as a
benchmark against which changes
must be evaluated. This system of two
collections a week in the study area
costs $12,666 per week, based on
1965 cost figures; this covers the costs
of collecting 1,428 tons of wastes and
transporting them to the incinerator,
plus incineration costs. Systems using
transfer stations have two additional
costs—those of the station itself and of
transferring the wastes from the
station.
The run on the present system also
served to check the validity of the
model. Using 1960 population figures,
the model reported the present
system's annual cost at $688,632, or
4.5 percent below the $722,000 the
city reported for the year 1965. Since
the study area is gaining in population,
the model estimates would be ex-
pected to be lower than the actual
1965 expenditures.
feasibility of
transfer stations
A series of computer runs was
carried out with different capacity
transfer stations to determine if
stations lower the cost of the solid
waste collection system. In every case
they did. The savings is 7 percent of
-------
17000
M:
(B)
larger transfer
stations are
more economical
to operate
15000
600 900 1200
TRANSFER STATION CAPACITY IN TONS PER WEEK
1500
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the present cost and would be ex-
pected to increase in the future as the
system expands. The dollar difference
between the transfer and nontransfer
solution is a rough measure of how
much money should be invested in
stations.
The model indicated that one trans-
fer station should be built in the
Northwestern Division. Site B is usual-
ly the best site, even when conditions
in the system are changed drastically.
If for some reason, B could not be
used, site C, then A, could be selected
at little extra charge.
The size of the transfer stations
considered varied from 600 to 1500
tons per week. For the smaller sta-
tions, site A, or A and C as alterna-
tives, were chosen. For the larger
stations, B was chosen. In all cases, the
model assigns some wastes directly to
disposal without transfer. Both the
1200- and 1500-ton stations were used
at less than capacity, with about 40
percent of the wastes going directly to
disposal. The total system cost stays
about the same once the station
reaches a capacity of 900 tons. The
1,500 ton size, therefore, was picked as
the best size, since, at no extra cost, it
allows for the large loads arriving early
in the week, as well as for future
growth of the system.
increasing
collection
to three times
weekly
The extra costs involved in increas-
ing collection frequency to three times
per week were studied in a number of
computer runs. For the present
system, the cost would increase by 4.6
percent. There are, however, several
assumptions buried in the calculation
-------
that should be kept in mind. First, the
routes would have to be redesigned to
ensure that the trucks are close to
capacity before they go to the transfer
or disposal points. The average truck
load for two times a week is 9,000
pounds. Since less waste would be
collected from each stop on the three
times a week schedule, the truck
would have to service more stops to
get a complete load. Should the
average truck load for three times a
week drop, by 10 percent for example,
because routes are no longer of the
best design, the added cost would rise
to 8 percent; a 25 percent drop in load
would mean a 14 percent difference in
cost.
Time is another factor that must be
watched in designing routes. Many
systems forbid overtime, which means
trucks return at a given time regardless
of the load collected. Because travel
times are longer with three collections
a week, the time a route takes must be
watched carefully. A good routing
model could help in designing routes
properly.
The second assumption is that the
weekly waste load is the same,
whether the load is picked up in two
collections or three. Studies in Chicago
indicate that waste loads increased
from 30 to 50 percent when col-
lections were increased from once to
twice a week. In several of the Balti-
more runs waste loads were assumed
to increase; the results indicate that
the cost difference is very sensitive to
increased loads, so the question of
waste load should be studied before
collection frequency is increased.
The present haul distance from the
Northwestern Division to the Pulaski
incinerator averages 8 miles one way.
This distance will probably increase as
the city expands, since the tendency is
to move waste disposal farther out to
avoid complaints from nearby com-
increasing
haul distances
-------
munities; also, it becomes increasingly
difficult to find enough suitable sites
near the city.
Computer runs were made assuming
haul distances of 10, 12, 14, and 16
miles, with and without transfer
stations. With rail haul the distance
was assumed to be 200 miles. The
results indicate that as haul distance
increases, both transfer and rail haul
become more attractive.
With twice-a-week collection, rail
haul costs become competitive with
the present system at 11.5 miles; with
transfer stations rail haul becomes
competitive when distances reach 22.5
miles.
Under present conditions, rail haul
is not an attractive alternative. It
would cost $18,791 a week, or 12.8
percent more than the present system
and 19.7 percent more than the pres-
ent system would cost if it used
transfer.
sensitivity to
other (actors
Other computer runs were made to
show how sensitive the system is to
some additional factors:
Waste Loads. As waste loads in-
crease, total system costs increase pro-
portionately. B was always the best
site in the test cases. Even when waste
loads almost doubled, a second station
at a different site was not the cheapest
answer, unless the capacity was re-
stricted to 600 tons per week.
Speed of Transfer Vehicle. The
large tractor trailers carrying wastes
from transfer station to disposal would
travel at 16 miles per hour, the same
average speed collection vehicles now
make. If speed could be increased to
30 miles per hour, costs would drop
by 7.5 percent. Such an increase seems
unlikely, however.
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19000
ui
ui
a
UI
18000
- 17000
2
UJ
> 16000
15000
2 COLLECTIONS PER WEEK
use of transfer
stations reduces
solid waste
management costs
8 10 12 14 16 18 20 22 24 26 28 30
AVERAGE ONE-WAY HAUL DISTANCE IN MILES
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political, aesthetic,
and regional
restrictions
Collection Rates. Increasing or
decreasing the collection rate by 10
percent leads to a 5 percent change in
total system cost. Thus, care should be
taken in estimating these rates. Fur-
ther, inexpensive time-saving devices
or changes in work rules should be
investigated.
Station Cost. Fixed costs of the
stations were increased from 25 to 100
percent. At about 75 percent, transfer
stations are no longer feasible, but up
to that point the same station was
chosen every time.
Limitations sometimes develop that
preclude use of what appears to be the
best alternative. For example, a site
suitable for a solid waste facility might
be better used as a school site. The
surrounding neighborhood might
strongly oppose a solid waste facility.
Or cooperation between political sub-
divisions might be impossible. Two
computer runs in which site B was
excluded from consideration showed
that using site A would add only $60
to the total system cost. Thus, the
decision maker may have considerable
leeway in choosing between alter-
natives when he must also consider
intangible criteria. The model also
helps the decision maker put a dollar
value on these criteria. If the first
alternative costs $100,000 and the
second $150,000, are intangibles
worth $50,000 to the community?
Regionalization was considered in
the study by dividing the North-
western Division into two non-
cooperating regions. The northern
regions were to use only transfer sites
A,D, and E; the southern areas only
sites B,C, and F. In this case, transfer
is still feasible, but just barely. Marks
and Liebman believe that analysis of
the entire Baltimore area would show
even greater advantages to the use of
transfer stations than those shown in
the Northwestern Division.
-------
The Pulaski incinerator was designated as the dis-
posal site in the study of Baltimore's solid waste
collection system. It was chosen over the City's
other incinerator because it is closer to the study
area and its unit costs are lower
-------
For several years Denver, Colorado used this trans-
fer station in its solid waste management system.
Packer truck (upper left) transfers its load to the
trailer (bottom right) for the 12-mile trip to
Lowry Air Base Bombing Range. Station is
now temporarily closed
-------
The location model developed in the
Hopkins study may be used by any
community to evaluate alternative
sites for transfer stations. Data needed
would include:
• Location of each potential site
• Location of each collection area
• Population density of each col-
lection area
• Waste generation rate of each col-
lection area
• Costs of vehicles, labor, and facil-
ities
• Location of each disposal facility
The model requires a medium-sized
computer to run studies of any large
city. Present computer codes are writ-
ten in Fortran IV for an IBM 7094
computer (32K memory), although it
is likely that a 16K machine could be
used if the program were modified.
Obviously, there are some simplifi-
cations in a model such as this one.
Since the model only chooses between
alternatives, it may reasonably be
assumed that the details left out would
affect each alternative equally, so that
the relative choice would still remain
the same. However, the costs estim-
ated by the model may be in error
because these details are lacking. A
simulation model developed earlier by
the Hopkins group can be used to
examine in more detail the cost of
operation of a particular alternative
selected by the location model. The
simulation model requires much more
data, however, and is likely to need
some program modification to reflect
accurately the conditions in a given
city. The development and use of this
model are reported in Mathematical
Modeling of Solid Waste Collection
Policies.
application
to other solid
waste systems
-------
Baltimore Data Used in Mathematical Model
The mathematical model calculates as many as five separate costs for each of 40 subregions to arrive
at total cost for the various solid waste collection systems proposed for Baltimore's Northwestern Division.
Figures represent Baltimore costs in 1965-66.
COLLECTION COSTS
equipment costs
labor costs
waste loads
$4.40 per hour for 20-cubic-yard vehicle
$20 per day for drivers, $18 for laborers; assuming 6
hours are spent productively yields hourly rates of
$3.33 for drivers, $3.00 for laborers
1 .95 pounds per person per day
COSTS OF TRANSPORTING WASTES
TO TRANSFER STATION OR DISPOSAL POINT
equipment and
labor costs
distances traveled
vehicle speed
vehicle load
same as above
calculated for each subregion
16 miles per hour
9,000 pounds
TRANSFER STATION COSTS
land costs
$40,000 for below 200 tons per day capacity, plus
$200 per additional ton. Yearly cost is based on
interest on investment; land is assumed not to de-
preciate; no taxes are lost, since most sites are
publicly owned
labor costs three men at $20 per day each for station of less
than 200 tons per day; four men for greater capacity
capital costs of $125,000 for below 100 tons per day capacity, plus
structures $500 per additional ton. Yearly cost has been pro-
duced through discounting, assuming 30-year life and
10 percent interest rate
maximum daily 306 tons per day
load
COSTS OF TRANSPORTING WASTES
FROM TRANSFER STATION TO DISPOSAL
equipment costs $1 1 .00 per hour for 75-cubic-yard tractor trailer
labor costs $3.33 per hour for driver
distances traveled calculated for each subregion
vehicle load 35,000 pounds
Rail haul transport and disposal costs are calculated together at $5.40 per ton,
the price Philadelphia was to pay for shipping and disposal in abandoned coal
mines in western Pennsylvania
DISPOSAL COSTS
$2.80 per ton at Pulaski incinerator
yo571
U.S. GOVERNMENT PRINTING OFFICE: 1972 O-468-193
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