LOCATION-ALLOCATION-ROUTING APPROACH TO SOLID WASTE COLLECTION AND DISPOSAL

Various studies have indicated that the collection phase of solid wastes, which comprises of the initial col- lection at the source of generation and the transportation to the disposal sites, is by far the most expensive. Two fundamental issues of concern in solid waste collection are the locations of initial collection and the period of collection by the dedicated vehicles. However, considering the prevailing conditions of adhoc lo- cation of waste containers and the faulty roads in many developing countries, this research was conducted to develop two e�ective models for solid waste collection and disposal such that new parameters measuring the capacity of waste ow from each source unit and road accessibility were introduced and incorporated in the mathematical formulations of the models. To formulate the problems, two classes of integer pro- gramming problems namely, Facility Location Problem (FLP) and the Vehicle Routing Problem (VRP), were used for the collection and disposal respectively. The clustering process involved in the model for the collection phase was based on the Euclidean distance relationship among the various entities within the study area. In this model, the study area was considered as a universal set and simply partitioned with each element representing a cluster. At this stage, a threshold distance was de�ned as the maximum allowable distance between a cluster and the potential collection sites. In the VRP formulation of the disposal model, two new parameters, called the accessibility ratio and road attribute, were introduced and included in the formulation. The inclusion of these parameters ensure that a waste collection vehicle uses only roads with high attributes. The solution to the model on the collection phase was based on the Lagrangian re- laxation of the set of constraints where decision variables are linked, while in the model on waste vehicle routing, the assignment constraints were relaxed. Both resulting Lagrangian dual problems were solved using sub-gradient optimization algorithm. It was shown that the resulting Lagrangian dual functions were non-di�erentiable concave functions and thus the application of the sub-gradient optimization method was justi�ed. By applying these techniques, strong lower bounds on the optimal values of the decision variables were obtained. All model implementations were based on randomly generated data that mimic real-life experience of the study area (Eti-Osa Local Government Area of Lagos State, Nigeria), as well as large-scale standard benchmark data instances in literature. These computational experiments were carried out using the CPLEX and MINOS optimization solvers on AIMMS and AMPL modeling environments. Results from the computational experiments revealed that the models are capable of addressing the challenge of solid waste collection and disposal. For instance, more than 60% reductions were obtained for the number of collection points to be activated and the container allocations for the different wastes considered. Numerical results from the disposal model showed that there is a general reduction in the total distance covered by a vehicle and a slight improvement in the number of customers visited. Result comparison with those found in literature suggested that our models are very efficient

Proceedings of the 26th International Symposium on Theoretical Aspects of Computer Science (STACS'09)

The Symposium on Theoretical Aspects of Computer Science (STACS) is held alternately in France and in Germany. The conference of February 26-28, 2009, held in Freiburg, is the 26th in this series. Previous meetings took place in Paris (1984), Saarbr¨ucken (1985), Orsay (1986), Passau (1987), Bordeaux (1988), Paderborn (1989), Rouen (1990), Hamburg (1991), Cachan (1992), W¨urzburg (1993), Caen (1994), M¨unchen (1995), Grenoble (1996), L¨ubeck (1997), Paris (1998), Trier (1999), Lille (2000), Dresden (2001), Antibes (2002), Berlin (2003), Montpellier (2004), Stuttgart (2005), Marseille (2006), Aachen (2007), and Bordeaux (2008). ..