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This study presents a vehicle routing procedure for solid waste collection in a municipal area. GIS database, which includes road network, road length and permitted travel direction, waste collecting points and waste volume for each point, was first constructed. The proposed routing procedure comprises two main modules: grouping and routing.
An OR method, namely Minimum Spanning Tree Algorithm, is modified for the calculation in the first module, while a GIS software function is employed for the latter. The result shows that the GIS database highly benefits the user by its visualized routes network and its ability to manipulate and store large amount of data. Although the proposed routing procedure has a weakness in computational time, it has a competence for development and application with real world situations. Keywords: Network Problem, Vehicle Routing, Operations Research (OR), Geographic Information Systems (GIS), Solid Waste Collection 1.
Introduction Solid waste collecting is one of the public services that local administrators provide for the quality of life of their citizens. Problems arising in the management of this service may include high operational cost and difficulty in collecting route design. Ineffective collecting routes lead to excessive travel length, fuel consumption, workforce, and vehicles. This means higher direct and indirect operational costs. Since the problem data can be view as spatial data, the use of Geographic Information Systems (GIS) will be advantageous for data organization and can help the route designer works easily.
This study uses a GIS software named ArcView 3.
1. Phitsanulok
Municipality, a case study in this paper, is responsible for garbage collection with more than thousands collecting points through out the city as shown in Fig. 1. There are roughly two types of collecting vehicle: open bin manually loaded and container system trucks. In this study, only the first type will be concerned since their collecting systems are quite different. Each day a fleet of trucks start the waste collecting activities from the Municipality depot to pick up garbage from collecting points along a predetermined route for each truck.
A waste volume at each collecting points is varied depending on the type of provided bins, which includes 240 liter-bin, 140 liter-bin, and blacked-bag with less than 140 liter capacity. The calculation is based on an assumption that all bins contain its full load. When the garbage volume reaches its capacity, the truck will travel to a transfer facility in Tumbon Tha Na Ngarm to unload before return to gather garbage again. Considering number of collecting points, trucks, road sections and route choices, the problem becomes real complex.
This study aims to combine OR techniques with GIS abilities to support routing decision. In the previous practice, the route designer draws a line using a colored-pen on a printed out map to show a route for each truck. Routes are designed by the designer’s experience accompanied with a bulk of raw data. When there are some changes in any route structure, the whole thing must be re-done. Obviously, GIS can play a major role in dealing with massive input data and allows the designer to adjust the routes conveniently. An embedded OR method can make the computation more reliable and flexible.
The rest of this paper is organized as follows. In section 2, some related studies are briefly reviewed, followed by the proposed routing procedure in section 3. Then, in section 4, the validation and computational results are presented. At the end, there is a conclusion and recommendation.
2. Literature
Review Tchobanoglous et al. (1993) defined solid waste as all the wastes occurring from human and animal activities that are generally solid and are unwanted. The collection routes design involves a series of experiments and there is no algorithm that can be used with all cases. Tchobanoglous et al. 1993) provided some heuristic guidelines for route layouts concerning current policies and regulations, crew size and vehicle types, starting and ending points, geographical and physical boundaries, time of a day, and collecting frequency. Most of the studies related to vehicle routing for waste collection use heuristic approaches to solve this NP-hard problem. Amponsah & Salhi (2004) presented a heuristic approach find garbage collecting routes with an emphasis on environment issue. Therefore, the objective was to minimize the total cost and the inconvenience due to smell from the deterioration of garbage.
A heuristic procedures based on the Rural Postman Problem on a mixed graph (MRPP) can be applied with a garbage collection problem (Corberan et al. , 2000). Tung & Pinnoi (2000) proposed a heuristic procedure consisting of construction and improvement phases. The modification of Solomon’s I1 heuristic was applied for the construction initial routes network. Then, the combination of Or-opt and 2-opt heuristic algorithms was used in the second phase, where routes are improved concerning the total cost and the number of vehicles utilized.
This study applies an OR technique, namely Minimum Spanning Tree Algorithm, to indicate a vehicle responsible area. However, the algorithm is adjusted with some constraints to be more appropriate with the problem in this study. The original Minimum Spanning Tree Algorithm is as follows (Taha, 2003). Define N= {1,2,…,n} Set of nodes on a network Ck = Set of nodes that have been connected at iteration k [pic]= Set of nodes that are not yet connected at iteration k Step 0 Set [pic] and [pic] Step 1 Set a start node i arbitrary, select from [pic] and set [pic], [pic]
Then, update k = 2 Step k Select node j* from [pic] that has the shortest length from a node in Ck-1 and set [pic], [pic] If [pic]is empty then stop. Otherwise, update k = k+1 and repeat the step. The Geographic Information Systems (GIS) is used to input, store, retrieve, manipulate, analyze and output geographically referenced data, in order to support decision making about planning and management of land use, natural resources, environment, transportation, urban facilities, logistics and so on. Tarantilis & Kiranoudis (2002) and Tarantilis et al. 2004) presented a decision support system (DSS) that connected GIS and an OR algorithm to solve Open Vehicle Routing Problem (OVRP). The OVRP problem is similar to the problem concerned in this study. The OVRP finds a set of routes for a fleet of capacitated vehicles to deliver goods to customers without returning to the starting point. The GIS software used in both studies was ArcView. Butler et al. (2005) applied GIS and OR in the management of milk collection. The study presented a user-friendly DSS system for a scheduler to effectively plan milk collection routes.
3. Proposed heuristic method
The heuristic method proposed in this study consists of two main modules: Grouping and Routing. The first module assigns collecting points to each truck by using a modified Minimum Spanning Tree algorithm. From section 2 of this paper, the original Minimum Spanning Tree algorithm will be executed repeatedly until all nodes are connected. Since each truck has a limited capacity, the modified version will be repeated until the waste volume reaches or nearly reaches the truck capacity. Then, the assignment of unconnected collecting points will be performed for consecutive trucks until all points have been connected (See Fig. ). This module can be executed under a programming language named Avenue, which is available with ArcView package. An important input for the grouping module, such as lengths along the road network between each pair of collecting points, is prepared by utilizing ArcView. The results from grouping module are used as inputs for the second module. The second module uses ArcView special function, called Find Best Route, to set the shortest route for each truck according to a collection of points determined by the grouping module.
The first and the last collecting points are set to be the points closest to the depot and the transfer facility, respectively. 4. Results and Analysis The grouping module separates the 1,419 waste collecting points into 18 groups. Each group has a different number of collecting points, which can be classified into different bin types. The total waste volume must not exceed the capacity of a vehicle assigned to each group. The fleet of vehicles includes 11 trucks. Therefore, most trucks operate two trips, which means two groups, a day. The details are shown in Table 1.
The results of the routing module for each group are shown in Figures 3-20 and the summary of total distances for each group is in Table 1. The GIS ability allows us to view the resulted route together with its statistics. Users can use GIS typical functions, such as zoom in, zoom out, label and statistics, to have the best visual perception. The comparison between the current practice and the proposed method has been made quantitatively. The overall length, comprising from the sum of the total length of the 18 groups that is 169. 76 km, is compared to the current figure of 315. 9 km. Therefore, the reduction in overall length is 43. 12%.
However, the resulted routes generally have a lot of U-turns, which may not practical in certain roads at a specific period of time of a day. For further studies, penalties may be used to control the number of U-turns. The computational time for running this application was the main obstacle. It increases rapidly with an increase in number of collecting points. Implementing the design of experiment theories within the computational part, may help in improving the computational time. 5. Conclusion This study addresses the application of the Geographic Information Systems (GIS) and the Operations Research techniques to solve real world problem.
The problem concerned in this study is vehicle routing for solid waste collection in municipal areas. The proposed algorithm is a combination of an OR technique called Minimum Spanning Tree and the GIS ability. The objective of the algorithm is minimizing the overall travel length, while satisfying all demand in the network. The results show the 43 % reduction in the overall length. Acknowledgement I would like to thank the research assistants, Mr. Chaimongkol Limpianchob and Mr. Wittaya Jansong, for their help in the construction of the GIS database. References Amponsah, S. K. & Salhi, S. 2004) The Investigation of a Class of Capacitated Arc Routing Problems: The Collection of Garbage in Developing Countries. Waste Management Vol 24 pp. 711-721 [online]. Available from: http://www. sciencedirect. com [accessed 1 December 2005] Corberan, A. & Marti, R. & Romero, A. (2000) Heuristics for the Mixed Rural Postman Problem. Computers & Operations Research Vol 27 pp. 183-203 [online]. Available from: http://www. sciencedirect. com [accessed 1 December 2005] Butler, M. & Herlihy, P. , Keenan, P. B. (2005) Integration Information Technology and Operational Research in the Management of Milk Collection.
Journal of Food Engineering Vol 70 pp. 341-349 [online]. Available from: http://www. sciencedirect. com [accessed 1 December 2005] Division of Public Health and Environment (2003) A Report on Environment Issues in Phitsanulok Municipality 2002. Division of Public Health and Environment. Frederick S. Hiller & Gerald J. Lieberman (1995) Introduction to Operations Research. McGraw-Hill. Taha, H. A. (2003) Operations Research, An Introduction. Prentice-Hall. Tarantilis, C. D. & Kiranoudis, C. T. (2002) Using a Spatial Decision Support System for Solving the Vehicle Routing Problem.
Information & Management Vol 39 pp. 359-375 [online]. Available from: http://www. sciencedirect. com [accessed 1 December 2005] Tarantilis, C. D. & Diakoulaki, D. D. , Kiranoudis, C. T. (2004) Combination of Geographical Information System and Efficient Routing Algorithms for Real Life Distribution Operations. European Journal of Operational Research Vol 152 pp. 437-453 [online]. Available from: http://www. sciencedirect. com [accessed 1 December 2005] Tchobanoglous, G. & Theisen, H. & Vigil, S. (1993) Integrated Solid Waste Management, Engineering Principles and Management Issues. pp. 3, 193-244.
Tung, D. V. & Pinnoi, A. (2000) Vehicle Routing-Scheduling for Waste collection in Hanoi, Case Study. European Journal of Operational Research Vol 125 pp. 449-468 [online]. Available from: http://www. sciencedirect. com [accessed 1 December 2005] [pic] Fig. 1 A GIS database showing 1,419 waste collecting points on the 4,544 road sections throughout the area concerned in the case study (Note: The road network data file was given by Phitsanulok municipality and has been corrected to be able to apply with this study) [pic] Fig. 2 A flow chart of the proposed heuristic method; Grouping module
Table 1 The summary of the result from the proposed heuristics method | |Number of waste bins |Number of |Total daily waste |Operate by truck |Total distance | |Group | |collecting points |volume (m3) |number |(km) | | | | | |(Capacity in m3) | | | |Large |Medium 140 |Small | | | | | | |240 l. |l. |