Applied Geqruphy (1983), 3, 133-144 133

Improvement of a solid waste collection system: the case of Givatayim, Israel*

Rivka Ronen

The Society jbr the Protection of‘ Nature, Tel-Aviv, lsruel

Aharon Kellerman

Department I$ Geography, The University, Ha{fti 31999, Israel

and Mordecai Lapidot

Environment Protection Service, Ministry of’ Interior, Jerusalem, Israel

Abstract

The increasing quantities of solid waste and the high costs of its collection call for modifications of the collection routes in urban areas, in order to reduce the number of collecting teams and the distances travelled by them. Several mathematical models, aiming at the optimization of route length, are examined in this paper. It is suggested that the solutions derived from these models are only partial and that they cannot fully handle some of the constraints which the collection routing problem involves. The preferred method, therefore, is the heuristic model which is based on manual analysis of the routes system using a set of specified rules. This method is, then, used for an analysis and modification of the waste collection routes of Givatayim, Israel. Implementation of the proposed routes may save the town one out of six collection teams and would reduce the total distance travelled by some 18.7 per cent.

Introduction

The collection of household solid waste is surely one of the most basic services in any urban setting. This service needs close attention, in order to make it more efficient, due to four major factors:

The increase in solid waste produced by modern societies has caused an increase in the financial resources spent on its collection and processing. The massive use of trucks in the collection process makes its cost highly influenced by the increase in energy costs. The high awareness of urbanites to questions of quality of life in general, and to air pollution in particular, requires more frequent and, therefore, more expensive collection of solid waste. The nature of the collection process does not attract enough manpower; thus, an efficient collection system could reduce the demand for manpower.

* This paper is based on an unpublished MA thesis entitled ‘Modification of an urban system for solid waste collection: the case of Givatayim’, by R. Ronen, supervised by A. Kellerman and M. Lapidot, Department of Geography, Bar-Ilan University, Ramat-Gan, 1981 (Hebrew).

0143~ 6228/83/020133-12jSO3.00~ 1983 Butterworth & Co (Publishers) Ltd

One of the means by which to save funds, energy and manpower and to reduce air pollution is to modify the routes of the collecting teams, a task which can be done by a geographer using his training in urban and transportation geography.

The purpose of this paper is to examine the various models which might potentially be used for the modification of the routes of an urban waste collection system, The discussion leads to the conclusion that the heuristic model, originally proposed by Shuster and Schur (1974), is the most suitable model for this purpose. An Israeli case study fohows, specifying the computational procedure and the resulting savings.

Models for optimal routing of waste collection

The optimal routing of collection teams should aim at several objectives simultan- eously. First, the number of teams (and thus the number of workers and trucks) should be reduced, so that expenses on wages, equipment and fuel will be minimized. Second, the routes of the remaining teams should be both efficient, thus saving additional energy costs, and safe, by avoiding the use of main roads, left turns, etc. Third, reducing the urban traffic load by optimal routing of the collection trucks will lower air pollution. These daily savings may be quite large when aggregated annually.

Generally, five models or families of models may be considered for the solution of the optimal routing problem: namely, linear programming, the ‘Chinese postman’ solution, branch and bound methods, hierarchical methods, and heuristic approaches.

Linear programming (by the Simplex method)

The objective function would be to minimize the total length of the collection routes (and by this to minimize as much as possible the collection duration). Thus, the number of times each street should be visited has to be minimized, though it cannot be less than one (because each street needs waste collection). Each street may be assigned a parameter stating the utility of its usage (length, width, traffic load, etc.). The constraints may refer to the maximum number of containers to be handled by each team per shift. Despite these possibilities the linear programming solution is not suitable for use in our problem for a number of reasons. The numbers assigned by a linear solution are real numbers, while the collection problem deals with integers, since it is unreasonable to use a solution that a certain street be served 2.2 times. Also, it is cumbersome to incorporate into linear equations one-way streets which would make each street have at least two parameters. Thirdly, the linear equations are aspatial in nature so that they do not show the preferred collection flow.

Scott (1971b) and Lowe and Moryadas (1975) used the linear model for resource allocation between production and consumption places so that transportation costs will be minimized. The waste collection problem seems quite different, however, since the *production’ takes place in thousands of locations (households), and the ‘consumption’ occurs on just one or two sites (the garbage processing area).

The ‘Chinese postman’s’ solution (or the travelliny salesman’s problem)

This method, proposed and described by Leibman and Saman (1974) and by Reinde (1979), aims at the design of a minimal walking route, which is described by a series of arcs. Each arc is assigned a numerical value which expresses its length. One has to go along each arc at least once and return to the point of origin by the shortest path possible. The routing procedure is assisted by graph theory and by Ewler Loops.

R. Ronen, A. Kellerman and M. Lapidot 135

The use of the ‘Chinese postman’ method for routing of waste collection teams has several disadvantages :

1. The routing procedure requires ample manual work, about four to five times the amount of work needed by the heuristic method. In a large urban area with many junctions all matrix computations have to be done by computer.

2. The method does not consider road characteristics such as one-way streets or steep sharp turns, since the only parameter considered is route length. This stems mainly from the method objective being developed for pedestrians rather than vehicles. The assignment of additional parameters to each street portion makes the matrix calculation even more complicated.

3. The waste collection problem does not require route start and route end at the same point as the method proposes.

Branch and bound methods

The branch and bound method calculates the optimal solution of an objective function through consideration of a limited number of possible solutions which were chosen after other solutions had been deleted. The method is called branch and bound since it is based on a branch-like graph with an upper and lower limit. The procedure attempts to unify these two limits and, thus, to achieve a minimal solution for the objective function (Scott 1971a).

In the case of waste collection routing, the objective function would attempt to minimize the sum of lengths of streets to be travelled through. This will, however, be just a partial solution since it will not provide information on the origin and destination points of the routes. Also, the method does not take into account direction of travel and other limiting factors, such as topography.

Hierarchical methods

The hierarchical methods try to handle complex transportation problems by aggregation or decomposition (Steenbrink 1974). The aggregation procedure calls for the reduction of the number of variables, manually or by computer. Thus, the number of areas may become smaller by arbitrary limits on movement among them. Also, less important routes may be skipped. The decomposition procedure calls for reformul- ation of the objective function and its constraints by defining a few functions with their specific constraints (such as major junctions and routes in one group and secondary ones in another). Here, again, no specific routes are received and real numbers are used, so that its application for waste collection is limited.

Heuristic methods

The complex nature of city structure makes it difficult to use strict mathematical solutions for the waste collection problem. The heuristic method, based on human intelligence, common sense and experience, may be of help where more analytical and elegant methods fail. There are, generally, two possibilities for the application of the heuristic method to the waste collection problem. The deterministic version requires the digitizing of all street junctions and the writing of a computer program which will evaluate all possible solutions and choose the best alternative. On the other hand, however, the general heuristic approach calls for a manual search for a solution of the routing problem. Saving the digitizing cost the method is fast, cheap, flexible and easier

136 A sditl wusft~ ~olllJ~t;~)~i .~ysimz

to apply. These qualities make it easy to routinely modify the routes due to seasonal changes or due to construction of new housing. The general heuristic approach has been proposed by several writers for use for the routing problems (Liebman and Magne 1974; Shuster 1974; Shuster and Schur 1974). The routing procedure using the heuristic method involves three stages.

1. Macro routing. At this early stage data are collected on the size and number of trucks, the size of the collection teams, the number and size of waste containers, the urban transportation system. the locations of the waste processing site and truck parking lot, etc.

2. ~~.str~ft~~~ and bff~~~zcii~~. The city has to be divided into collection areas, either by neighbourhood units or by use of major highways, rivers, etc. These collection areas have to be balanced in order to assure an equal number of containers is collected by each team. This is achieved by use of the route balancing equation.

y=u+h+n(n, +t~+If)-C2+~~-I-,~_t<] (1)

where .V = total collection time for a given team; a=journey time from the truck parking lot to the beginning of the collection

route;

collection time ’ per container

net route x driving speed along length collection route

= total collection time; n =number of collection rounds (depending on truck size, and on waste weight

and quantity); c1 ==driving time from end of route to the waste processing site; c2 = driving time from waste processing site to the beginning of a new round (in

case of multiple rounds); d=time spent at the waste processing site; e=driving time from waste processing site to truck parking lot; /‘= formal breaks; 8= time waste (traffic problems, etc.).

3. Micro routiny. At this stage the exact route for each team is determined. This is achieved by a series of simple rules as follows:

(a)

(h) 6)

(j)

the routes should be compact serving one continuous geographical area without overlaps with other routes; collection time for all teams should be equal; actual collection shoutd start as close as possible to the truck parking lot; collection on main roads should be avoided during rush hours; one-way streets should be served in a loop form; left turns should be minimized; steep streets should be served going downwards (which is safer, faster and cheaper) collecting on both sides at the same time; topographically high neighbourhoods should be served first; when collecting one side of a street, the building blocks should be served in a clockwise direction; when collecting both sides of a street it is recommended to complete a long and straight route before making a turn.

R. Ronen, A. Kellerman and M. Lapidot 137

Givatayim: a case study

The town of Givatayim was chosen for the application of the heuristic model for the modification of the municipal waste collection system. This town, being a suburb in metropolitan Tel-Aviv, has a population of some 50 000 on an area of 3 km’. Since this was the first time that the heuristic model was used in Israel for a waste collection system, it was important to choose a medium-sized town with a well-organized sanitation department willing to cooperate in such a study.

The collection budget

The sums allocated by the municipality of Givatayim for waste collection and processing are substantial and their share in the general budget during 1978-81 is on the rise.

Year Share (%)

1978179 6.87 1979180 8.96 1980/8 1 9.95

Also, during the same period the general budget grew by some 262 per cent while the collection budget increased by 424 per cent! Since the population of Givatayim was steady during this period, the increase in the collection costs can be attributed to larger waste quantities and to higher expenses on fuel and truck spare parts. This trend clearly calls, therefore, for a more rational design of the collection routes in order to save as much as possible in manpower, equipment and energy.

The collection system

The relevant data with regard to the collection system are as follows:

Trucks. There are six (five for regular service and one reserve truck), four of which have a capacity of 11 m3, one of 13 m3 and one with 8 m3.

Collection teams. There are six teams, each of which consists of a driver, plus five collection workers, plus two preparing workers (placing the containers on the street). The collection is performed by a private company, but the drivers are town employees.

Quantities. The daily waste quantity is about 30 tonnes (collected from 9000 small containers of 5&75 1 each, 220 medium-sized containers and carts of -750 1 each, and from 150 large containers of 800-1000 1 each). Each team has a basic daily norm of 800-850 small and medium containers. The large containers are collected in two separate rounds after the regular shift is completed. Each truck is equipped for handling all sizes of the containers.

Times. Each container is served three times a week (which is a fixed service level), so that there are currently 10 routes for small and medium-sized containers, and two for large ones. Collection time per small container is 556 s. For medium-sized containers collection time is 25-28 s (the collection of one medium-sized container is equal to that of 5.5 small ones). For large ones, collection takes 6065 s. Driving speed on a collection route is 13 kmh-‘, while on large container routes the speed is 40 kmh- ‘.

138 A solid waste collection system

.- + c-- l 4

l _--L+_-l-+ I

---_I I

LEGEND:

1

+..+... 2

-.-.-. 3

c-+-t--b- 4

i-s-.+. 5

_._-.._ 6

+.-+.-f. 7

_ _ . 8

---- 9

+-.+..+ 10

Figure 1. Existing waste collection routes in Givatayim, Israel.

Tab

le

1. T

he

exis

ting

was

te

colle

ctio

n ro

utes

in

Giv

atay

im,

Isra

el

Rou

te

Park

ing

lot

Net

ro

ute

Rou

te

end

to

Stay

at

Pr

oces

sing

T

ime

Tot

al

Tot

al

Con

tain

ers

Rou

te

to

rout

e st

art

~ pr

oces

s si

te

proc

essi

ng

site

to

lo

ss

colle

ctio

n ro

ute

per

km

conc

entr

atio

n N

o.

of

km

min

si

te

time

leng

th

(%)

km

min

co

ntai

ners

km

m

in

(min

) pa

;$ng

(m

in)

(min

) (k

m)

(min

)

1.

2.

3.

4.

5.

6.

7.

8.

9.

10.

11.

12.

Mea

n M

D

SD

0.77

1.

15

1166

.5

4.12

13

5.66

1@

72

12.5

8 2@

0 10

.8

15

195.

19

26.4

1

44

15.6

2.

25

3.37

85

3.5

4.73

10

7.18

8.

27

8.65

20

.0

10.8

15

16

5.0

26.0

5 33

18

6 1.

4 2.

1 91

3.5

3.21

10

6.16

8.

92

9.88

20

.0

10.8

15

16

3.94

24

.33

38

13.1

9 3.

0 4.

5 89

3.5

3.22

10

4.21

8.

56

9.34

20

.0

10.8

15

16

3.85

25

.58

35

12.5

9 1.

35

2.02

93

8.0

3.98

11

2.16

8.

7 1

9.56

20

.0

10.8

15

16

9.54

24

.84

33

16.0

2 1.

35

2.02

10

54.0

4.

35

125.

47

8.97

9.

7 2@

0 10

.8

15

182.

99

25.4

7 41

17

.08

1.89

2.

83

1110

.5

5.15

13

4.81

8.

9 9.

6 20

.0

10.8

15

19

3.04

26

.74

42

19.2

6 2.

07

3.1

883.

0 4.

35

108.

37

8.6

9.15

2@

0 10

.8

15

166.

42

25.8

2 34

16

.85

1.17

1.

75

1161

.0

5.46

14

1.3

1@62

12

.43

2@0

10.8

15

20

1.28

28

.05

41

19.4

6 2.

84

4.26

87

8.0

3.82

10

5.43

7.

68

8.02

20

.0

10.8

15

16

3.51

25

.14

35

15.1

9 2.

1 3.

15

756.

0 10

.29

91.0

3 9.

17

10.0

20

.0

10.8

15

14

9.98

32

.36

23

31.8

1.

71

2.56

88

8.0

6.53

98

.59

8.18

8.

52

20.0

10

.8

15

155.

47

27.2

2 33

23

.99

1.82

2.

73

957.

9 4.

93

114.

19

8.94

9.

78

20.0

10

.8

15

172.

51

26.5

36

18

.3

0.53

0.

8 10

9.75

1.

28

13.4

0 0.

61

0.95

13

.73

1.39

4.

3 3.

6 0.

63

1.00

12

6.2

1.84

16

.11

0.86

1.

40

15.8

1

2.02

5.

4 5.

01

140 A solid waste collectior~ system

On urban roads without collection, the mean speed is 40 kmh~.‘, and out of town (on way to and from processing site) 60 kmh- ‘. Each shift is thus of three hours, including the time spent at the processing site.

Analysis of current routes

The map of the current routes was drafted after interviewing all truck drivers and their supervisors (Fig. 1). This map was, then, analysed using data on the number and size of waste containers in each block (Table 1). The analysis revealed the following routing problems.

Routes 3 and 8 are quite dispersed. Besides, the number of containers collected by each team varies between 853 and 1166. which is a large range assuming that the collection load per team should have been equal. Comparing the collection load with the distances travelled for their collection reveals that only four routes (1,6,7,9) collect more than 40 containers per kilometre, while three others do 3540 containers per kilometre and the five remaining routes are inefficient, serving fewer than 35 containers per kilometre. In addition, the mean share of the net routes out of the total route length (route concentration) is just 18.3 per cent. In other words, almost 82 per cent of the travelled distance is spent on travel to and from the parking lot and to and from the processing area. Also, 49 left turns were found to be part of the existing 12 routes. These problems result in a mean total collection time of 172.51 min, or almost three hours, with a mean deviation of 13.73 and a standard deviation of 15.81.

The proposed routes

The purpose of the rerouting procedure would be to reduce the number of collecting teams so that the collecting time of the remaining teams would increase as little as possible, while reducing the standard deviation so that collection time would be as uniform as possible. This was achieved using the heuristic method and its rules. It was found that the following rules were the most helpful in redesigning the collection routes :

1. designing compact collection areas, each covering a continuous residential area, whenever possible;

2. avoiding collection in busy streets during rush hours; 3. reducing the number of left turns; 4. route starts close as possible to the truck parking lot.

The new routes are presented in Fig. 2 and in Table 2. It may well be seen that six out of the 10 routes are compact routes serving just one residential area, while routes 3 and 8 serve more than one neighbourhood. Thus, unneeded travelling is avoided. The mean number of containers to be served by each team is 1088.3, an increase of 13.61 per cent, but with lower mean and standard deviations (61.26 and 73.59 respectively, compared to 109.75 and 126.2 in the existing system), so that change between teams may be flexible. This increase in the number of containers served by each team is accompanied by an increase of just 9 per cent of the mean total collection time per route (from 172.51 min to 188.54 min). The low deviations around the total mean (6.74 mean deviation compared to the former value of 13.73, and a standard deviation of 8.16 compared to the former 15.81) permit flexible rotations of routes among teams (the difference between the longest and the shortest routes is just 25 min). The major saving,

R. Ronen, A. ~eller~an and M. Lapidot 141

LEGEND:

+..+.,+ 1

___.-... 2

+...+... 3

+-+.+- 4

__._..- 5

+.-.+. c

_.-._. 7

_--- 8

_ . . . . . 9

-r-4-++ to

Figure 2. Proposed waste collection routes for Givatayim, Israel.

Tab

le

2. T

he

prop

osed

w

aste

co

llect

ion

rout

es

for

Giv

atay

im,

Isra

el

Rou

te

Park

ing

lot

to

Net

ro

ute

Rou

te

end

to

Stay

at

Pr

oces

sing

T

ime

Tot

al

Tot

al

Con

tain

ers

Rou

te

rout

e st

art

~___

____

~ pr

oces

s si

te

proc

essi

ng

site

to

lo

ss

colle

ctio

n ro

ute

per

km

conc

entr

atio

n __

___

No.

of

km

min

~~

___~

si

te

park

ing

(min

) tim

e le

ngth

(“

J km

m

in

cont

aine

r5

km

min

(m

in)

lot

(min

) (km)

(min

)

1.

2.51

3.

85

2.

2.65

3.

97

3.

1.53

2.

29

4.

1.74

2.

6 1

5 0.

77

I.15

6:

1.

75

262

I.

1.42

2.

13

8.

l-9

2.85

9.

2.6

3.9

IO.

1.35

2.

02

Mea

n 1.

82

2.73

M

D

0.48

0.

72

SD

0.58

0.

92

1122

4.

42

132.

6 7.

00

1053

.5

4.32

12

528

8.31

98

7.5

4.76

12

0.7

1 7.

94

1044

.5

5.17

12

X.0

8 x.

7 10

08

421

120.

23

9.31

11

84.5

5.

12

142.

13

8.62

11

73

5.68

14

4.66

X

.15

1071

SG

il 13

0.17

10

.32

1034

5.

85

130.

4 7.

18

1205

4,

28

140.

25

8.12

10

88.3

4.

87

131.

4.5

8.32

66

.26

0.47

6.

76

0.64

73

.59

0.55

8.

56

0.7

7.00

20

x-

71

20

X.1

6 20

9.

3 20

10

.21

20

9.43

20

8.

72

20

11.7

3 20

7.

27

20

9.58

20

9.

01

20

1.03

I -

3x

IO.8

IO

.8

10.8

10

.8

10.X

IO

.8

10.8

IO

.8

10.8

10

%

10.8

15

15

1s

15

15

15

15

15

15

15

15

189.

25

24.7

9 4s

17

.82

183.

76

26.0

8 40

16

.56

176.

96

25.0

3 39

19

.01

1857

9 26

.36

40

19.4

2 17

7.39

25

.09

40

16.7

7 19

9.98

25

.29

47

20.2

4 20

1.3

1 26

.05

45

21.8

19

0.55

28

.02

38

17.8

4 18

7.37

26

.43

39

22.1

3 19

7.65

25

.15

48

17.0

1 18

8.54

25

.82

42

18.8

6 6.

74

0.76

3.

3 1.

66

8.16

0.

92

3-53

I.

91

R. Ronen, A. Kellerman and M. Lapidot 143

however, is the reduction of the number of teams from 12 to 10 with just a minor addition to the workload of the remaining teams, as described.

Savings can be found in all other route parameters as well. Though the mean net route length increased from 4.39 km to 487 km due to the reduction in the number of routes, its standard deviation decreased by 70.1 per cent. By the same token, the mean distance from the parking lot to route starts remained the same with a lower standard deviation, and the mean distance from route ends to the processing site is now lower by 6.93 per cent with lower standard deviations. The number of containers served per kilometre is high for seven routes compared to three in the old system (with the three others serving a medium number, 3540 containers per kilometre). The concentration ratio increased as well from 183 per cent for 12 routes to 1886 per cent for 10 routes. The number of left turns is now 41 rather than 49 in the existing system.

Financial savings

Reducing the number of teams from six to five by reducing the routes from 12 to 10 calls for a major saving. Since the salary of one worker is 50 000 Israel she‘kels annually, then IS300 000 may be saved if only five teams remain. This amounts to some 5.44 per cent of the collection budget. Savings are of special importance due to the difficulties in recruiting collection manpower.

Adding together all the distance savings for all routes amounts to a reduction of some 59.72 km or 18.77 per cent (from 318 km to 258.29). Annually some 93 16.32 km may be saved. Since the cost of 1 km is IS25 then some additional IS23 200 or 0.42 per cent of the collection budget could be saved in 1980/81. Altogether, therefore, IS323 290 or 5.86 per cent of the collection budget could be saved in 1980/81 with the proposed routes.

In addition to these direct budgetary savings some other benefits may be achieved through the implementation of the modified routes. The 20 per cent decrease in the total length of the routes might reduce traffic problems in narrow streets, especially during rush hours. Also, the reduction in the number of left turns adds to the safety of the collection teams. Of less importance is the slight decrease in air pollution due to the shorter routes of the collection trucks.

Conclusion

The application of the heuristic method to the modification of waste collection highlights two important points.

1. Making a system more efficient does not always require large investments in computer hardware and software and other equipment, or very specialized manpower. Manual analysis of a system and its improvement may have its own merits in terms of lower costs, more flexibility and shorter time needed until completion.

2. The basic skills of a geographer, namely careful map analysis and awareness of area characteristics, may be extremely helpful in the solution of problems sometimes considered outside the domain of traditional applied geography.

The implementation of the system in Givatayim now awaits approval by the Mayor and later by the workers themselves. Since no major problems can be seen, its use in towns and cities throughout Israel is expected within the next few years,

144 A solid ~t~ste collection s ystc’m

References

Liebman, J, C. and Magne, W. (1974) Routing o~s~i~~ l+xzste coile~tio}~ vehicles. Appendix B: Optimal routing of solid waste collection vehicles. Chicago: Illinois University.

Liebman, J. C. and Saman, H. (1974) Rouring ofsolid was& collection vehicles. Appendix A: A linear programming approach for the travelling salesman problem. Chicago: Illinois Ilniversity.

Lowe, J. C. and Moryadas, S. (1975) The geography oj‘movement. Boston: Houghton Mifflin. Reinde, J. (1979) Routing by the ‘Chinese postman’ method helps minimize backtracking. Solid

Waste M~n~gernei~t 7, 72-74. Scott, A. J. (197la) ~ombinutoria~ programming, spatial analysis und planning. London: Methuen. Scott, A. J. (197lb) An introduction io sputiui docation ana&sis. Washington, DC: The

Association of American Geographers, Resource paper No. 9. Shuster, K. A. (1974) A ,jve stage improvement process ,br solid waste collection systems.

Washington, DC: US Environmental Protection Agency, SW-131. Shuster, K. A. and Schur, D. A. (1974) Heuristic routing ,jbr solid ssaste collection cc~hicl~s.

Washington, DC: US environmental Protection Agency, SW-I 13. Steenbrink, P. A. (1974) ~~~irnizaf~#n qf transport ?7et~~ork. New York: Wiley.

(Revised manuscript received 10 June 1982)