Location-Allocation-Routing Approach To Solid Waste Collection And Disposal

ABSTRACT

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 di_erent 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 encient.