A bi-objective multi-period facility location problem for household e-waste collection

This paper addresses the multi-period facility location problem during the market expansion stage, where the decision maker plans to add a certain number of new facilities in each period to gradually increase the accessibility of the infrastructural collection network. In order to consider the trade-off between cost efficiency and service coverage, we propose a multi-period bi-objective 0-1 integer programming formulation for the problem. We develop three metaheuristics to solve the problem. The first metaheuristic is based on the NSGA II framework with the traditional operators for the single-period location problem. The second metaheuristic is based on the local search strategy, where five new neighbourhood structures are designed. The last metaheuristic integrates the former two algorithms. The proposed modelling framework is justified by a case study of the system infrastructure design in Vancouver for E-waste collection. To demonstrate the computational performance of the proposed modelling framework, sixty random instances of different sizes (200 or 500 demand points), with different demand distributions (Uniform, Normal and Gamma distributions) are generated. We compare the proposed modelling framework with two popular multi-objective metaheuristics, MOEA/D and NNIA. Computational results show that the proposed metaheuristic based on local search is the most efficient for searching Pareto solutions of the problem.