LOCATION-ALLOCATION-ROUTING APPROACHudTO SOLID WASTE COLLECTION AND DISPOSAL

摘要

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