This paper presents a brief description of some existing models of facility location problems (FLPs) in solid waste management. The study provides salient information on commonly used distance functions in location models along with their corresponding mathematical formulation. Some of the optimization techniques that have been applied to location problems are also presented along with an appropriate pseudocode algorithm for their implementation. Concerning the models and solution techniques, the survey concludes by summarizing some recent studies on the applications of FLPs to waste collection and disposal. It is expected that this paper will contribute in no small measure to an integrated solid waste management system with specific emphasis on issues associated with waste collection, thereby boosting the drive for effective and efficient waste collection systems. The content will also provide early career researchers with some necessary starting information required to formulate and solve problems relating to FLP.

A new model for the efficient collection of solid waste in urban residential areas is proposed as a set covering facility location problem. The model finds the optimal location of waste collection sites such that all the customers are covered. An important feature of the model is that, rather than aggregate the quantity of waste from a group of demand points, it is assumed that the volume of waste of different types is known for each customer. This assumption encourages point-of-collection sorting which helps provide an improved solution to the problem of waste collection. A Lagrangian relaxation (LR) of the problem was developed, and the resulting dual problem was solved using an LR procedure in which the vectors of Lagrangian multipliers were updated through the subgradient optimisation. A simple linear relaxation heuristic was developed to obtain a feasible solution to the primal problem. Five newly constructed datasets mimicking the scenario of a local municipality were used to test the efficiency of the model and the solution technique. Preliminary results and comparison with existing results showed that the proposed model is efficient as considerable reductions were obtained for the total number of activated collection sites and allocated containers.