A Heuristic Model for Municipal Solid Waste Collection Vehicle Routing

Appropriate vehicle routing is critical for collecting municipal solid waste (MSW) efficiently. Conventional empirical routing is not easily altered in response to rapidly changing waste management plans and generation. An enhanced model is proposed herein to solve a MSW collection routing problem involving a homogenous fleet. A minimum cost flow method is applied to pre-process the original collection network for vehicle flow balance. Collection of MSW along a street segment is transformed into a node expression. With this arc-node transformation and the property of trichotomy, the sub-tour problem can be practically resolved. A mixed-integer programming model is established for the transformed network. In addition to reducing the collection time, the model also considers the workload balance among vehicles and vehicle turning suitability. The proposal model has been applied to the eastern district of Hsinchu City, Taiwan. Results obtained from the case study demonstrate the effectiveness of the proposed model in reducing the collection time, deviation of workloads, inappropriate turns, and redundant routes. Corresponding author Email: [email protected] INTRODUCTION Municipal solid waste (MSW) collection is an important part of waste management. Regional population growth significantly alters the frequency, equipment use, and manpower requirement of a collection system. Privatization of MSW collection is currently promoted in several cities in Taiwan, R.O.C. During this initial privatization stage, collection routing for both public and private collectors will change frequently. Given such changes, a collection system must be continuously adjusted to remain applicable and efficient. The conventional collection routing approach based on a trial-and-error adjustment is impractical in response to frequently changing situations. Hence, this study explores a planning model capable of developing appropriate routes. A municipal collection routing network is generally a mixture of directed and undirected streets. An undirected street can be traversed in both directions, but only a single sweep is necessary to collect MSW on both sides of the street (in this study, a wide street with both sides being collected separately is treated as two directed streets). Papadimitriou [1] indicated that, excluding some special cases, a mixed network problem is an NP-Complete problem that is difficult to solve. Another difficulty in solving a collection vehicle routing problem with a mathematical programming model is the sub-tour problem [2]. In a MSW collection routing problem, a collection vehicle may pass through an intersection several times. Such multiple vehicle entries and exits can cause mathematical ambiguity and computational problems for determining their exact sequences. Although algorithms exist (e.g., [3]) to solve this sub-tour problem, the number of constraints required is significantly large, making the problem difficult to solve, particularly for a real city-scale problem. To overcome above difficulties, various optimization and heuristic approaches have been developed. Bodin et al. [4] provided a detail description for both optimization and heuristic approaches for various routing and scheduling problems. Although models are available for a mixed network problem, the computational time required to solve these models is often exponentially proportional to network size, making them impractical for real world problems. A heuristic approach (e.g., [5-8]) is thus generally employed. However, a major drawback for a heuristic approach is that the difference of the obtained solution to its 58 Journal of the Chinese Institute of Environmental Engineering, Vol. 16, No. 1 (2006) true optimum is uncertain. Although this study proposes a heuristic approach, the heuristic portion of the approach is minimized to improve optimality. This study applies the vehicle flow balance concept reported by others [9,10] and the Minimal-Cost Flow (MCF) method [11], a total shortest path method, to pre-process a street network into a network with vehicle serving flow balanced on each node of the network. This is the only heuristic step of the approach and the rest implements a true optimization. An arc-node transformation resembling the one proposed by Laporte [12] is applied to transform an arc-capacitated network into an equivalence node-capacitated network. Constrains based on the property of trichotomy are developed with a mixed-integer programming model for resolving the sub-tour problem. The number of constraints needed to solve the sub-tour problem is significantly reduced to be linearly proportional to the number of streets. In this study, we focus on solving a MSW collection routing problem with a homogenous fleet, of which all vehicles are of the same type. Therefore, other generally observed difficulties for a MSW collection routing problem such as crew assignment are not considered herein. Most waste collection routing studies focused primarily on minimizing total time or cost [13-16]. Bodin [8] indicated that working hours and quantity of collected MSW for each worker are often neglected. Workload equity among collection vehicles is also a pertinent issue for a good collection routing. Although few equity-related studies (e.g., [17-18]) have been reported for other waste management issues, the equity of collection vehicle workload is rarely addressed. In addition to reducing collection time, the proposed model can also evaluate the workload equity for each vehicle based on total collection time, total quantity of collected MSW, or a weighted sum of the previous two factors. In addition to time reduction and vehicle workload fairness, traveling safety requires further consideration. Collection vehicles must drive along the shoulder of a road in the slow traffic lane to ensure easy MSW collection. Besides, a MSW collection vehicle is generally bulky. Excessive U-turns or left turns on a collection route may incur safety problems and may affect the traffic. The turn penalty suggested by Bodin and Kursh [19] is thus applied in this study to reduce unnecessary turns in planned collection routes. The proposed model applies an arc-node transformation. Such a transformation makes it easy to evaluate the turning suitability. The study area is the eastern district of Hsinchu City, Taiwan, R.O.C. A mathematical model is established. In the following description, pre-processing of the original route network and model development are explained, with workload equity and adequate vehicle turning being defined. Afterwards, the application of d a a