Capacitated location of collection sites in an urban waste management system

Abstract

Urban waste management is becoming an increasingly complex task, absorbing a huge amount of resources, and having a major environmental impact. The design of a waste management system consists in various activities, and one of these is related to the location of waste collection sites. In this paper, we propose an integer programming model that helps decision makers in choosing the sites where to locate the unsorted waste collection bins in a residential town, as well as the capacities of the bins to be located at each collection site. This model helps in assessing tactical decisions through constraints that force each collection area to be capacitated enough to fit the expected waste to be directed to that area, while taking into account Quality of Service constraints from the citizens’ point of view. Moreover, we propose an effective constructive heuristic approach whose aim is to provide a good solution quality in an extremely reduced computational time. Computational results on data related to the city of Nardò, in the south of Italy, show that both exact and heuristic approaches provide consistently better solutions than that currently implemented, resulting in a lower number of activated collection sites, and a lower number of bins to be used.

Introduction

Urban Waste Management (UWM) is becoming one of the most relevant issues for modern society municipalities because of its social, political, and economical impact. Its social relevance is mainly due to the growing public concern for environmental preservation and pollution aversion. The political importance of this problem is evident not only from citizens’ point of view, who give a lot of awareness to UWM when choosing their representatives, but also from institutions’ point of view. The economical importance of this problem is shown from the huge resources put in play behind UWM, and from the number of actors involved in this process. From one side, municipalities that allocate an important portion of their own budgets to deal with this task, as well as citizens who support this service by paying taxes. From the other side, private companies that are interested either in performing direct UWM activities or taking advantage from many spin-off businesses, such as material recycling and waste-to-energy production.

Nowadays, municipalities generate huge quantities of wastes, both in industrialized and developing countries. For instance, the average per-capita residential waste generation (in kg/day) is about 0.51 in India (Esakku et al., 2007) and 1.03 in Canada (Statistics Canada, 2010). Moreover, the per-capita waste production is rapidly increasing, with values ranging from 8% in North America to 14% in the EU during a period of 11 years, from 1995 to 2006. Table 1 reports the total and per-capita waste generation increase between the years 1995 and 2006 in North America, the EU, and Italy (OECD, 2008).

UWM consists in various activities that can be clustered into four stages of the waste life-cycle: generation, collection, transformation, and disposal. The efficient execution of each of these stages requires taking many decisions at the strategic, tactical, and operational levels. Examples of decisions involved in these processes are: the selection of wastes treatment technologies, the location of wastes treatment sites and landfills, the future capacity expansion strategies of the sites, waste flow allocation for transformation facilities and landfills, service territory zoning into districts, collection days selection for each zone and for each waste type, fleet composition determination, and collection vehicles’ routing and scheduling. A detailed description of these problems is beyond the scope of this paper. Interested readers may refer, for instance, to Pichtel (2005) who describes the main issues related to UWM.

This study focuses on the second stage of the waste life-cycle: the collection stage. Specifically, we face the problem of locating unsorted waste collection sites in a residential town. This problem concerns countries like Italy, where the households bring their waste to collection points, contrary to several European countries with a door-to-door collection. We propose an integer programming model, whose aim is to help decision makers in choosing where to locate the garbage collection bins, as well as defining the capacities of the bins to be allocated to each collection site. Our approach is tested on real data related to the city of Nardò, in the south of Italy, which represents a good sample of medium-sized urban area, with its 30,000 inhabitants.

A huge amount of research has been produced about location problems and modeling approaches (see ReVelle and Eiselt (2005) for a survey on a number of important problems in facility location). However, contrarily to other location problems in the context of UWM, the problem we are studying has received little attention in the literature, despite its considerable impact on both individual citizens and the whole community. In addition, this is recognized to be a semi-obnoxious problem. In fact, typically, a citizen prefers having a waste collection site as close as possible to his/her home, but, at the same time, he/she aims at paying as less taxes as possible to have this service guaranteed. On the other hand, the community is interested not only in reducing the expenses related to the collection stage, but also in limiting the visual impact due to the presence of the collection bins close to the residential sites. Given that both these factors depend on the number of collection sites, ensuring a good service with the least number of collection sites represents a key objective.

We are aware of only a limited number of works on this topic. Bautista et al. (2006) propose two mathematical formulations for locating waste collection areas. In the first formulation, the problem is modeled as a set covering problem and solved by using a genetic algorithm. The second formulation models the problem as a Max-Sat problem for which the authors propose a GRASP approach. Both algorithms are tested on a real world instance representing a city in the metropolitan area of Barcelona. Badran and El-Haggar (2006) present a model for municipal solid waste management in Port Said (Egypt). The proposed model aims at minimizing the municipal waste management cost, determining the best location for collection sites among a given set of candidate locations. Erkut et al. (2008) present a mixed-integer multiple objective linear programming model, to solve the location–allocation problem of municipal solid waste management facilities in the Central Macedonia region in North Greece. Recently, Tralhão et al. (2010) propose a mixed-integer, multiobjective programming approach to identify the locations and capacities of multi-compartment sorted waste containers. The model aims at determining the number of facilities to be opened, as well as the respective container capacities, their locations, their respective shares of the total waste of each type to be collected, and the dwellings assigned to each facility. The approach is tested on a case study represented by Coimbra city (Portugal).

The main contribution of this paper is twofold. First, we solve a capacitated version of the location problem. Indeed, our model includes constraints that force each collection site to be capacitated enough to fit the expected waste to be directed to that site. Second, we include additional constraints that ensure the Quality of Service (QoS) from the citizens’ point of view. This QoS requirement ensures that each citizen is served by the waste collection site closest to his/her home, rather than just any close site.

The remainder of the paper is organized as follows. Our optimization model is presented in Section 2. A heuristic solution approach is then described in Section 3. The computational results on a real-life application are reported in Section 4, and finally, concluding remarks follow in Section 5.