application method for optimization in solid waste

FACTA UNIVERSITATIS Series: Mechanical Engineering Vol. 8, No 1, 2010, pp. 63 - 76

APPLICATION METHOD FOR OPTIMIZATION IN SOLID WASTE MANAGEMENT SYSTEM IN THE CITY OF NIŠ

UDC 514.863:351.777.61

Danijel Marković, Dragoslav Janošević, Miomir Jovanović, Vesna Nikolić

Mechanical Engineering Faculty, University of Niš, A. Medvedeva 14, 18000 Niš, Serbia, E-mail: [email protected]

Abstract. The paper shows the procedure for selecting an optimal solid waste management system in the city core of Niš. The following objectives are to be achieved by the system optimization: maximal system efficiency and maximal satisfaction of system services users. For the selection of the waste management system, due to its complexity and possibility of variable performance, the multi-criteria method of optimization and decision making, Analytic Hierarchy Process, is used. In the optimization procedure, the detailed measurement and analysis of the existing waste management system parameters are first conducted on the site. Then, three possible system variants are defined. As the first system variant, the existing solution for the waste management system whose parameters are determined upon the evaluation and experience without using a mathematical model of the system is adopted. The other two system variants are defined upon a developed mathematical model of the system by using the Clarke-Wright savings algorithm and the Geographical Information System. Upon the selection of the optimal waste management system variant, from a cluster of the previously defined possible variant solutions, we form a set of five criteria. By the eventually conducted optimization procedure, the optimal solution is selected with new system parameters that can correct the existing solid waste management system in the city core of Niš in order to improve its efficiency.

Key Words: Solid Waste Management, Routing, Optimization

1. INTRODUCTION

In the last decade, several analyses of the environment condition have been carried out on the territory of the Republic of Serbia (RS). The analyses were made by many state institutions of the RS (Department of Environmental Protection – Ministry of Health and Environmental Protection (2001), Ministry of Natural Resources and Environmental Protec-tion (2002-2003)) as well as by some international organizations (World Bank (2002), United Nations Economic Commission for Europe (2002)). The conducted analyses show that one of the major ecological problems in the RS is the inadequate waste management.

Received January 16, 2010

64 D. MARKOVIĆ, D. JANOŠEVIĆ, M. JOVANOVIĆ, V. NIKOLIĆ

With the aim of dealing with the existing and future ecological problems in a planned and adequate manner, the RS adopted in 2003 the National Strategy for Waste Manage-ment (NSWM) with the European Union (EU) convergence program [1].

Municipal services and waste management functions in the city of Niš are conducted by the Municipal Services Company "Mediana" (MSCM). The waste management system encompasses around 72.000 households and around 1.800 enterprises that generate mu-nicipal waste [2]. Based upon the conducted analyses, the morphological composition of waste generated by an average citizen of Niš is determined. The analysis show that the largest part of waste is organic in origin (food remains) (73,29%), while the inorganic part of waste is mostly composed of plastic (8,62%), paper (6,70%) and glass (3,83%) [3].

Due to the complexity of the waste management systems, the optimization procedure is divided into three levels [14]: (1) waste management system optimization through the selection of waste handling technology, (2) waste management system optimization through the selection of transfer stations, (3) waste management system optimization through the selection of waste collection and transportation routes.

There are many studies and methods for the determination of the optimal vehicle routing for solid waste collection that appeared in the middle of the twentieth century [4]. Depending on the complexity of the model, exact and heuristic methods have been devel-oped. The application of exact methods of problem solving is limited to simple models, while more complex models can only be solved by applying heuristic methods. Some-times, in order to avoid using heuristic algorithms, the problems are rather simplified by being solved in several phases. The techniques that were used are linear programming, mixed integer programming, genetic algorithms, inexact quadratic programming, non-lin-ear multi-objective integer programming, Geographical Information Systems (GIS) and network analysis [5,13].

2. MATHEMATICAL MODELS

In this paper, the method Analytic Hierarchy Process (AHP) [6] is used for the selection of optimal solid waste management system solution in Zone 107 of the city core of Niš, and the Clark Wright savings algorithm is used for the routing vehicle [11].

2.1 Clark Wright Savings algorithm

By far the best-known approach to the Vehicle routing (VRP) problem is the "sav-ings" algorithm of Clarke and Wright. Its ba-sic idea is very simple. Consider a depot D and n demand points. Suppose that initially the solution to the VRP consists of using n vehicles and dispatching one vehicle to each one of the n demand points. Now if we use a single vehicle to serve two points, say i and j, on a single trip, the total distance traveled is reduced by the amount (Fig. 1).

[ ]( , ) 2 ( , ) 2 ( , ) ( , ) ( , ) ( , )

( , ) ( , ) ( , )i js d D i d D j d D i d i j d D j

d D i d D j d i j

= + − + + =

= + − (1)

Fig. 1 Graphic view savings

Application Method for Optimization in Solid Waste Management Systemin The City of Niš 65

Quantity s(i, j) is known as the "savings" resulting from combining points i and j into a single tour. The larger s(i, j) is, the more desirable it becomes to combine i and j in a single tour. However, i and j cannot be combined if in doing so the resulting tour violates one or more of the constraints of the VRP.

The algorithm can now be described as follows. STEP 1: Calculate savings s (i, j) = d(D, i) + d(D, j) − d(i, j) for every pair (i, j) of

demand points. STEP 2: Rank savings s(i, j) and list them in a descending order of magnitude. This

creates the "savings list." Process the savings list beginning with the topmost entry in the list (the largest s(i, j)).

STEP 3: For savings s(i, j) under consideration, include link (i, j) in a route if no route constraints will be violated through the inclusion of (i, j) in a route, and if: a. Either, neither i nor j have already been assigned to a route, in which case

a new route is initiated including both i and j. b. Or, exactly one of the two points (i or j) has already been included in an

existing route and that point is not interior to that route (a point is interior to a route if it is not adjacent to the depot D in the order of traversal of points), in which case link (i, j) is added to that same route.

c. Or, both i and j have already been included in two different existing routes and neither point is interior to its route, in which case the two routes are merged.

STEP 4: If savings list s(i, j) has not been exhausted, return to Step 3, processing the next entry in the list; otherwise, stop: the solution to the VRP consists of the routes created during Step 3. (Any points that have not been assigned to a route during Step 3 must each be served by a vehicle route that begins at the depot D visits the unassigned point and returns to D.)

2.2 Optimization Method

The activities of the municipal solid waste management system can be categorized as six functional elements which are: (1) waste generation; (2) handling, separation, storage, and processing at the source; (3) collection; (4) transfer and transport; (5) separation, processing and transformation; and (6) disposal (8). As the structural bearers of the aforementioned partial functions of waste management, very complex structural systems emerge. Apart from its complexity, it is characteristic that one and the same partial function can be structurally realized in different variant solutions.

Due to their complexity and possibility of variant solutions, it is necessary to use multi-criteria methods of optimization and decision making when developing and designing waste management systems [7]. In this paper, the method Analytic Hierarchy Process (AHP) [6] is used for the selection of optimal solid waste management system solution in Zone 107 of the city core of Niš.

The AHP Method is one the most known and lately most used procedures for the multi-criteria decision making on the selection of the optimal solutions to complex systems [8,9].

The fundamental elements of the AHP method are: (1) a set of defined goals of optimization, (2) a set of possible variant solutions of system E:


{ } 1, 2,3,....,iE E i n= = (2)

and (3) a set of optimization criteria C: { } 1, 2,3,....,jC C j m= = (3)

where Ei is a possible variant system solution, n is the number of variant system solutions, Cj is the optimization criterion, and m is the number of optimization criteria. The optimal solution of system Eo is abstracted from the set of possible variant solutions E, according to maximal solution validity index umax : max max { } 1, 2,3,....,iu u i n= = (4)

where ui is variant solution validity index Ei. Validity index ui of variant solution Ei is determined by equation:

∑=

⋅=m

1jjiji cpu (5)

where pij is the priority factor of variant solution Ei, according to criterion Cj, cj is the factor of optimization criterion importance Cj.

The variant solutions priorities of system pij and the factors of optimization criterion importance cj are determined by the appropriate mathematical procedure based on the comparison of variant system solution pairs and the comparison of optimization criteria pairs using the Saaty scale in Table 1 [9].

Table 1 Saaty Scale

Verbal judgment Degree of importance Extremely more important 9 Very strongly more important 7 Strongly more important 5 Moderately more important 3 Equally important 1 Intermediate values 2, 4, 6, 8 Inverse comparisons Reciprocals

3. ANALYSIS

In the procedure for selecting the optimal waste management system in Zone 107 of the city core of Niš, a detailed analysis of the existing system was first conducted. The analysis was conducted upon the data of technology of work and available resources of MSCM [2] and measured system parameters.

Measurements with system parameters were done directly on a site by following a solid waste collection vehicle along the entire movement route. Upon the defined pro-gram, the measurements were done by the Department of Transport Engineering and Lo-gistics of the Faculty of Mechanical Engineering at the University of Niš in cooperation with MSCM. The measurements were done twice, in October 2005 and October 2008.


The following parameters of the existing system were measured, monitored, assessed and marked in Table 2: (1) the number and position of location of waste containers where waste generators (service users) dispose of waste; (2) the assessment of waste containers location accessibility (expressed in attributes good or bad); (3) the assessment of the in-fluence of waste containers location on the urban city space (expressed in attributes good or bad); (4) the number of waste containers on location; (5) the assessment of container volume fullness with waste on location (expressed in the container fullness coefficient); (6) the retention time of waste collecting vehicle on location during container unloading; (7) traffic signals density along route sections between locations (expressed in traffic lights number); (8) traffic frequency along route sections between adjacent locations (ex-pressed in attributes small or large); (9) terrain configuration along route sections be-tween adjacent locations (expressed in attributes even or uneven).

The assessment of location accessibility represents: (1) the assessment of location distance from waste generators and (2) the assessment of available area on location for manipulation with containers upon their unloading and returning back on location.

The assessment of container fullness with waste on location is expressed with the container fullness coefficient. Based on the fullness coefficient, the total volume of waste on location is determined:

kikikiwi kVnV ⋅⋅= (6)

where Vwi is the total volume of waste on location, nki is the number of containers on location, Vki is the declared volume of containers on location, kki is the container fullness coefficient on location. The assessment of location influence on the urban city space represents the assessment of container location influence on the aesthetics of urban space and the architecture of the ambient where it is situated. This assessment is necessary, since we are dealing with the waste collection system in the city core.

The analysis of the researched parameters of the existing waste management system in Zone 107 of the city core of Niš shows that the primary waste generators are: households in housing blocks, trade, hotel and business centers, administrative institutions and school, cultural and health organizations. Waste is collected every day with one vehicle operated by a driver and three workers. Vehicle movement route for waste collection is situated on the traffic network of the observed zone on even terrain configuration. Vehicle route passes the main and side streets with different traffic frequencies.

The fundamental parameters of the existing system: the position and number of con-tainer locations, the number of containers on location and the vehicle movement route for waste collection are determined upon the assessment and experience of MSCM, without using any mathematical model.

There are standard waste containers with same volume on all locations. The values of waste container fullness coefficients point to the fact that there are inadequate numbers of containers in some collecting spots (Table 2).


Table 2 Solid waste management system parameters in Zone 107 of the city core of Niš measured in October 2005 and October 2008

2005 2008 Location number

I

Number of containers on

location nki

Container fullness

coefficient kki

Waste volume on

location Vwi [m3]

Number of containers on

location nki

Container fullness

coefficient kki

Waste volume on

location Vwi [m3]

1 5 0,7 3,85 5 0,8 4,4 2 12 0,7 9,24 12 0,6 7,92 3 5 0,9 4,95 5 0,9 4,95 4 4 0,3 1,3 4 0,4 1,76 5 2 1 2,2 2 1,1 2,22 6 5 0,7 3,85 5 0,8 4,4 7 5 1 5,5 5 1 5,5 8 3 1,2 3,96 3 1,2 3,96 9 3 0,3 0,99 2 0,5 0,99

10 4 1,3 5,72 4 1,3 5,72 11 4 0,5 2,2 4 0,4 1,76 12 5 0,7 3,85 5 0,7 3,85 13 5 0,6 3,3 5 0,6 3,3 14 3 1 3,3 3 1 3,3 15 14 0,8 12,32 14 0,8 12,32 16 5 0,5 2,75 5 0,6 3,3 17 5 0,7 3,85 5 0,8 4,4 18 4 0,5 2,2 4 0,6 2,64 19 4 0,7 3,08 4 0,7 3,08 20 6 0,8 5,28 6 0,9 5,94 21 26 0,8 22,88 26 0,8 22,88 22 5 1 5,5 5 1 5,5 23 3 0,8 2,64 3 0,8 2,64 24 2 1,1 2,42 2 1,1 2,42 25 7 1,1 8,47 7 1,1 8,47 26 3 0,8 2,64 3 0,8 2,64 27 1 0,9 0,99 1 0,9 0,99 28 4 0,7 3,08 4 0,7 3,08 29 5 0,9 4,95 5 0,8 4,4 30 23 0,9 22 1 1 1,1 31 7 1 7,7 32 7 0,9 6,93 33 8 0,7 6,16


4. OPTIMIZATION

4.1 Waste Management System Variants

Based on the performed analysis of the measured parameters of the existing waste management system, the following is determined: area, restrictions and system optimiza-tion criteria.

The variable system parameters belong to the system optimization area: (1) container location position; (2) number of locations; (3) number of containers on collecting location and (4) vehicle movement route for waste collection.

System optimization restrictions represent the characteristics of MSCM available resources: (1) waste collecting vehicle body working volume Vv=15 m3, (2) declared waste compaction degree in vehicle body kc=5, (3) waste collection container volume Vk=1,1 m3 and (4) the demand for daily waste collection in the observed city zone.

With the introduced optimization restrictions and by changing the system parameters in optimization area, set E of three possible variant system solutions is defined for waste management in Zone 107 of the city core of Niš (Table 3):

1 2 3{ , , } E E E E= (7)

First system variant E1: The existing waste management system which is applied in Zone 107 of the city core of Niš is adopted for the first system variant solution E1. The parameters of adopted variant E1 of the waste management system correspond to the measured and assessed parameters researched in the field in 2008 (Table 2). The pa-rameters of the adopted system variant: position and number of locations, number of containers in situ and vehicle movement route are designed upon the experience and practice of MSCM without developing a mathematical model of the system.

Table 3 Parameters of possible waste management variant solutions in Zone 107 of the city core of Niš

System variant

Route length [km]

Number of

locations

Number of

containers

Number of locations

with good/bad

accessibility

Number of route

sections with small/large

traffic frequency

Number of locations

with good/bad influence on urban

environment Variant E1 21,54 33 182 17/15 13/19 14/18 Variant E2 18,67 33 182 17/15 17/15 14/18 Variant E3 17,83 29 179 20/8 15/13 17/12

By monitoring the vehicle using GPS, the system variant E1 route l1=21,54 km in length is determined.


Within this variant, the vehicle makes three rounds during the day collecting waste in the observed city zone along the projected route. During one of the rounds, the vehicle starts empty from the landfill and covers a section of the route until it is fully loaded with waste, after which it returns to the landfill. The included container locations and some of the daily rounds' routes of the first system variant E1 are given in Figs. 2a, 3a, 4a.

Second system variant E2: The second possible system variant E2 differs from the first variant solution E1 only in vehicle movement route. The other system parameters: position and number of locations and number of containers on location are the same. However, within the second variant E2 the vehicle movement route is designed upon a developed mathematical model of the system based on the Clarke-Wright savings algorithm [11]. The authors have developed software for optimal vehicle movement route determination based on the mathematical model of the system. The following information is given as input software data: (1) the database on waste volume on each location, (2) the database on the distance between container locations (including the waste disposal landfill) and (3) vehicle body volume restriction.

For system variant E2 the database on waste volumes on each location is determined upon the data from the 2008 measurements (Table 2), while the database on the distance between locations (including the landfill) is defined by using GIS [10].

Fig. 2 Vehicle Movement Routes in the First Waste Collection Round:

a) First System Variant E1, b) Second System Variant E2

Using the developed software and defined databases, a vehicle movement route l2=18,67 km in length is determined for system variant E2.

7 4 6 3

5 8

9 12

1210

11D

D

3

811 2

116

26

17 18 19

1415

13

a) b)


Due to the introduced restriction in system variant E2, the vehicle also has to make three rounds to the landfill where waste is disposed while collecting it in the entire city zone along the projected route. The included container locations and some of the daily rounds' routes of the second system variant E2 are given in Figs. 2b, 3b, 4b.

Third system variant E3: The third possible system variant E3 differs, from previous E1 and E2 variants, in position change and reduction in numbers of locations and in contain-ers number reduction. By position change and location number reduction leads to de-crease in influence of some locations on the urban space and city core architecture. Apart from that, the introduced changes correct the inadequate container fullness with waste on some locations based on the field measurements conducted in 2005 and 2008.

Using the developed software and defined input databases, a vehicle movement route l3=17,83 km in length is determined for system variant E3.

In system variant E3 also, the vehicle has to make three rounds to the landfill where waste is disposed while collecting it in the entire city zone along the projected route.

Fig. 3 Vehicle Movement Routes in the Second Waste Collection Round:

a) First System Variant E1, b) Second System Variant E2

28 29

22

20

25

27

29

D D

28

10

27

25

9

7

33

3132

30

30

a) b)


Fig. 4 Vehicle Movement Routes in the Third Waste Collection Round: A) First System Variant E1, B) Second System Variant E2

4.2 System Optimization Criteria

Upon selecting the optimal waste management system variant, from set E of previously defined possible variant solutions, a five-criterion set C is formed:

{ } C,C,C,C,C C 54321= (8) where individual criteria relate to: (1) C1 – length of vehicle movement route for waste collection; (2) C2 - number of container locations; (3) C3 - container location accessibility to waste generators; (4) C4 - traffic frequency in route sections; (5) C5 - container location influence on urban city space. The selected criteria significantly determine the fundamental parameters and set goals for waste management system optimization.

Using the adopted decision making model AHP, and upon the Saaty scale, a criteria relation matrix is defined:

C1 C2 C3 C4 C5 C1 1 5 2 3 2 C2 1/5 1 1/3 1 1/2 C3 1/2 3 1 2 1 C4 1/3 1 1/2 1 ½ C5 1/2 2 1 2 1

The comparison of optimization criteria pairs shows how many times one criterion is more important than some other for reaching the given optimization goal.

(9)

D

23 21

1716 15

14 18 1913 24

D24

2221

1220

23

564

a) b)


Upon the criteria relation matrix, and by using the software Expert Choice [12], the values of importance factors cj of the set criteria are determined (Table 4).

Table 4 Importance factors cj of optimization criteria Cj

Criterion Cj

Criterion importance factor cj

C1 0,325 C2 0,101 C3 0,326 C4 0,125 C5 0,123

The largest importance factor c3 has criterion C3 that relates to container location accessibil-ity where the satisfaction of users/waste generators is addressed upon the system variant selec-tion. The second in importance is criterion C1 which relates to route length, since it has a signifi-cant influence on the efficiency and costs of waste management systems.

4.3 Priorities of Variant System Solutions

Using the Saaty scale, possible variant system solution relation matrices upon each optimization criteria are defined (Table 4). Upon the definition of possible variant system solution relation matrices, it is assessed, according to the observed criterion, how many advantages one system variant has in relation to another. Variant solution relation matrices Ei upon each criterion Cj are given in Table 5:

Table 5 Variant solution relation matrices Ei upon each criterion Cj

Criterion Ci

Possible variant solution relation matrices

Criterion Ci Possible variant solution

relation matrices

Criterion C1

E1 E2 E3 E1 1 1/5 1/6 E2 5 1 1/2 E3 6 2 1

Criterion C4

E1 E2 E3 E1 1 2 3 E2 1/2 1 5 E3 1/3 1/5 1

Criterion C2

E1 E2 E3 E1 1 1 1/2 E2 1 1 1/2 E3 2 2 1

Criterion C5

E1 E2 E3 E1 1 2 3 E2 1/2 1 5 E3 1/3 1/5 1

Criterion C3

E1 E2 E3 E1 1 1/2 4 E2 1/2 1 4 E3 1/4 1/4 1


Upon the variant system solution relation matrices, and by using the software Expert Choice, priority factors pij of variant solutions Ei upon each criterion Cj are determined (Table 6).

Table 6 Priority factors pij of variant solutions Ei upon criteria Cj

Priority factors of variant solutions pij

Variant solutions Ei pi1 pi2 pi3 pi4 pi5 E1 0,081 0,250 0,344 0,508 0,250 E2 0,342 0,250 0,547 0,379 0,250 E3 0,577 0,500 0,109 0,113 0,500

Based on the calculated optimization criteria importance factors and variant solution

priority factors, the validity index for each waste management system variant (Table 7) is determined using the equation:

55i44i33i22i11ii cpcpcpcpcpu ++++= (10)

Table 7 Validity indices ui of variant system solutions Ei

Variant solutions Ei

Solution validity indices ui

E1 0,263 E2 0,391 E3 0,346

5. CONCLUSION

Based on the applied optimization procedure it can be concluded that the second possible system variant E2 has the largest total validity index ui=0,391 (Table 9), thus it represents, with respect to the given criteria, the optimal waste management system solution for Zone 107 of the city core of Niš. In relation to the existing system, that is, variant E1, optimal system variant E2 has a shorter daily vehicle movement route for waste collection by 2,87 km, which, on the annual level, amounts to a reduction in route length of up to 1000 km. The route reduction also implies the reduction of: all accompanying vehicle movement costs, the ecological effect of vehicle movement on city environment and route duration time. The third system variant E3 has the shortest route and the reduced number of waste containers locations. By reducing the number of locations, the accessibility of the system is also reduced, since the distance between users/waste generators and waste containers is increased in some locations. Due to these reasons, the third variant E3 has a smaller total validity index than the adopted optimal system solution. Further research envisions analysis and waste management system optimization in all of the other zones of the city of Niš. The aim is to provide the complete research results to MSCM for consideration and use for the correction of the existing waste management system.


Acknowledgement. Paper is done within the research project “Development of the Model and Technologies of Logistics of the Communal Waste Transport” from the Program of Technological Development, No. 14068, financed by the Ministry of Science of the Republic of Serbia.

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PRIMENA OPTIMIZACIONIH METODA PRI UPRAVLJANJU ČVRSTIM OTPADOM U GRADU NIŠU

Danijel Marković, Dragoslav Janošević, Miomir Jovanović, Vesna Nikolić

U radu je dat postupak izbora optimalnog sistema upravljanja čvrstim otpadom u gradskom jezgru grada Niša. Pri optimizaciji sistema postavljeni su sledeći ciljevi: maksimalna efikasnost sistema i maksimalno zadovoljenje korisnika usluga sistema. Za izbor sistema upravljanja otpadom, zbog njegove složenosti i mogućnosti varijantnog izvođenja, korišćen je višekriterijumski metod optimizacije i odlučivanja Analitic Hierarchy Process. Postupkom optimizacije prvo je izvršeno detaljno merenje i analiza parametara postojećeg sistema upravljanja otpada na terenu. Zatim su definisane tri moguće varijante sistema. Kao prva varijanta sistema usvojeno je postojeće rešenje sistema upravljanja otpadom čiji su parametri određeni na osnovu procene i ikustva bez korišćenja matematičkog modela sistema. Druge dve varijante sistema su definisane na osnovu razvijenog matematičkog modela sistema korišćenjem Clark-Wright-ovog algoritma uštede i geografskog informacionog sistema. Pri izboru

76 D. MARKOVIĆ, D. JANOŠEVIĆ, M. JOVANOVIĆ, V. NIKOLIĆ optimalne varijante sistema upravljanja otpadom, iz skupa prethodno definisanih mogućih varijantnih rešenja, postavljen je skup od pet kriterijuma. Na kraju sprovedenim postupkom optimizacije, izabrano je optimalno rešenje sa novim parametrima sistema kojima se postojeći sistema upravljanja čvrstim otpadom u gradskom jezgru grada Niša može korigovati u cilju veće efikasnosti.

Ključne reči: Upravljanje komunalnim otpadom, rutiranje, optimizacija

application method for optimization in solid waste

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