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Weekly UpdatesABSTRACT
Privatization of municipal solid waste (MSW) collection can improve service quality and reduce cost. To reduce the risk of an incapable company serving an entire collection area and to establish a competitive market, a large collection area should be divided into two or more subregions, with each subregion served by a different company. The MSW subregion districting is generally done manually, based on the planner's intuition. Major drawbacks of a manual approach include the creation of a districting plan with poor road network integrity for which it is difficult to design an efficient collection route. The other drawbacks are difficulty in finding the optimal districting plan and the lack of a way to consistently measure the differences among subregions to avoid unfair competition. To determine an MSW collection subregion districting plan, this study presents a mixed-integer optimization model that incorporates factors such as compactness, road network integrity, collection cost, and regional proximity. Two cases are presented to demonstrate the applicability of the proposed model. In both cases, districting plans with good road network integrity and regional proximity have been generated successfully.
INTRODUCTION
Privatization of municipal solid waste (MSW) collection has become a major environmental policy for years in many countries. In 1990, more than 80% of waste collection in the United States (1) and the United Kingdom (2) was done by private companies. Similar MSW collection privatization can be observed in other countries. (3) As Fleming (4) indicated, privatization of waste services is nothing new and competition exists among private sectors and between the public and private sectors in some cases. McDavid, (5) after comparing public and private waste collection services for 327 local governments in Canada, stated that contracting-out MSW services is an effective way to reduce cost, especially for communities that use more than one contractor. Steel and Long (6) also pointed out that having fewer bids could result in less competitive outcomes. A proper districting plan that divides the entire area into several subregions is thus essential for promoting privatization of the MSW collection. Dividing a large area into several subregions and allowing more contractors to bid can reduce the investment risk and make it more attractive for companies to bid. Also, a proper districting plan can prevent the domination of the MSW collection market by one large company and can be effective in promoting competition among MSW collection contractors. An approach like this has been reported to be successful in Phoenix, (4) Charlotte, (4) and Seattle. (1) For example, in Phoenix, an area with approximately 60,000 residents was split into six subregions.
The MSW subregion districting is generally done manually, based on the planner's intuition. This manual approach, however, has three major problems. First, a districting plan with poor road network integrity may be generated and that could make the planning of an efficient collection route difficult. Also, many different districting plans are available and it is difficult for the planner to evaluate all of them to find the optimal one. Finally, in the absence of a quantitative procedure, an inappropriate districting plan may be selected and that would make the competition unfair. Thus, a quantitative tool to overcome these problems is explored in this study.
To our knowledge, after a wide search for related literature, no subregion districting model is specifically made available for MSW collection. Most subregion districting models have been constructed for developing voting districts or sales territories. (7-12) Among these studies, compactness was a primary factor to evaluate. Compactness ensures the integrity of each subregion and eliminates impractical districting plans, such as ring-like or wiggled-band districting. In general, the shape of a compact subregion is close to a square or circle. (10) Districting problems considering compactness are often analyzed with optimization models (9,10,13-15) that require significant computational effort. Compactness can be used also to screen out many inappropriate solutions during the problem-solving process. However, previous definitions of compactness typically evaluated only subregion shapes and are not applicable for a MSW collection problem because MSW collection activities occur along collection routes instead of over the entire region. A new definition for the integrity of a road network in a subregion is thus proposed in this study to overcome this problem.
In addition to compactness and road network integrity, factors such as waste generation, workload, and total length of routes can significantly affect the cost of an MSW collection service. Three factors are thus adopted when evaluating the appropriateness of a MSW collection-districting plan. Similar to previous studies, (13,14) individual values for these factors for all geographical units of a subregion are accumulated to evaluate the suitability of a subregion districting.
This study presents a procedure and an optimization model for dealing with MSW collection subregion districting problems. The subregions obtained using the proposed model are expected to have acceptable spatial compactness, high road network integrity, low collection cost, and good regional proximity. Although, after an extensive literature search, no model is specifically designed for MSW collection, several mixed integer programming (MIP) models are available for other types of districting problems. For instance, Hess et al. (7) proposed an MIP model, probably the first, for voting districting problems. The model partitions a region into a prespecified number of districts that maximizes the sum of the compactness values for all subregions. Several enhancements, (8,10) including heuristic approaches, for solving the same model were also developed. Benedallah et al. (9) proposed an MIP model, a modified version of the model developed by Wright et al. (15) for siting a single subregion to solve a multiple subregion allocation problem. In our previous work, (13) a MIP model was developed for siting a landfill. In this work, the model was revised for MSW collection districting problems. In the following sections, the factors considered for assessing the suitability of a subregion districting are first discussed and followed by an explanation of the optimization model proposed in this work. Two real MSW collection cases in Taiwan are then demonstrated and discussed.
DISTRICTING PROCEDURE
Figure 1 shows the proposed procedure for MSW collection districting. First, the desired number of subregions to be districted is determined. Then, various districting factors, including subregion compactness, collection cost, and subregion size, are used to evaluate the suitability of candidate districting plans. Finally, the proposed optimization model, which considers road network integrity, is established and applied to resolve a NSW collection districting problem. The procedure is detailed as follows.
Numbers of Subregions
One major goal of MSW collection districting is to promote a competitive market. An entrance barrier of the market will occur when the ability required for serving a subregion is beyond a typical company. Generally, the number of companies bidding for MSW collection contracts is correlated with the degree of market competition. However, total cost and management difficulty would likely be high when an area is divided into too many subregions. Determining an appropriate number of subregions is essential for making a districting plan. The recommended procedure for determining the number of subregions is described as follows. First, information on regional characteristics such as the service ability of the candidate companies, the management capability of the public sector, the quantity of waste, difficulties in collection, and the residents' preferences should be collected and carefully evaluated to determine the capacity of a typical contractor. Thereafter, the total MSW quantity of the entire area is estimated. The expected number of subregions is given by the quotient of the total MSW quantity and the capacity of a typical contractor, rounded to an integer value.
[FIGURE 1 OMITTED]
Districting Factors of MSW Collection
Factors considered for MSW collection subregion districting are compactness, road network integrity, collection cost, and regional proximity. The compactness factor assures that the shapes of divided subregions are as compact as possible. The road network integrity factor ensures the integrity of the interior road network in a subregion. The collection cost factor is evaluated to reduce the cost. The regional proximity factor is examined to reduce the differences among subregions and thereby prompt a competitive market. These factors are explained as follows.
Compactness. The compactness factor assures the spatial integrity of subregions. Without this compactness factor, subregions may be in discrete or irregular shapes. Different definitions are available for compactness, and a discussion of them was provided by Kao and Lin (13) for a landfill siting study. During that landfill siting research, for ease of integration into a landfill siting model, the compactness was defined as the value of the total perimeter over the total landfill site area. This definition is also used for this study to avoid subregions with discrete land parcels.
Road Network Integrity. The compactness factor considers only subregion shape that is insufficient for an MSW collection problem because MSW collection occurs along collection routes instead of over the entire region. A new factor for road network integrity was thus defined for an MSW collection districting problem. The number of boundary crossing points (NBCPs), defined as points that roads pass through a subregion boundary, is used to evaluate road network integrity. From the example illustrated in Figure 2, the NBCPs for the region shown in the figure is five. A subregion with few NBCPs on its boundary implies that the interior road network has good integrity, without too many broken roads or roads connecting adjacent subregions. When too many broken roads exist on the boundary, U-turns or multiple trips are necessary and the associated MSW collection routing plan can be inefficient or impractical. To demonstrate the relationship of NBCPs and road network integrity, a simple case is provided in the Appendix.
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