A priority-based firefly algorithm for network design of a closed-loop supply chain with price-sensitive demand

摘要

During the last decades, the importance of saving natural resources and protecting environment through recycling and safe disposal has increased the attention to reverse logistics. Separate optimization of the reverse and forward logistics may cause sub-optimality; hence, the integrated optimization is taken into account. In this paper, respecting both forward and reverse flows simultaneously, a multi-stage closed-loop supply chain is developed with some dedicated and hybrid facilities. Since in many industries the demand depends on selling price, a price-sensitive demand is taken into consideration. Accordingly, a mixed integer linear programming model is developed to make location, allocation, and price decisions, with the aim of maximizing total profit regarding capacity and number of opened facilities constraints. Given that the proposed model is not easily solved through exact methods, a relatively new population-based metaheuristic, namely firefly algorithm (FA) is proposed to find the solutions of large-scale problems. The proposed FA uses an efficient solution representation based on the priority-based encoding. Moreover, the algorithm utilizes a heuristic backward procedure for decoding. The proposed approach efficiency is checked by GAMS/CPLEX solver for small-sized problems. For largesized problems, the performance is compared with a differential evolution algorithm, a genetic algorithm, and an FA relying on the conventional priority-based encoding through statistical tests and a chess rating system. The results indicate the superiority of the proposed approach in both FA structure and encoding-decoding procedure.