عنوان مقاله [English]
During recent years, the reduction of the natural resources, besides the importance of the environment issues, has led governments to pay attention to closed-loop supply chain concepts, which encompass recycling as well as preparation of products and avoid the sub-optimality caused by a separate design of forward and reverse logistics. Governments may define some policies,
such as financial intensity, for those companies that perform recycling activities. Companies may move toward redesigning theirs supply chain structure by considering recycling and collection centers to get financial advantages.In this paper, considering a reward/penalty mechanism, a nonlinear programming model with the aim of minimizing the total cost is proposed for making
decisions about recycling rate, locations of recycling sites, and redesigning of the transportation network in a closed-loop supply chain. Fuzzy concept is applied to cope with uncertainty of parameters in real situation. Costs, demand, and capacity are presumed as the sources of uncertainty. Robust possibilistic programming is applied to improve robustness of the decisions in
contrast with the uncertainty. Due to the complexity of the model and loss of the efficiency of the exact solvers, especially in large-sized problems, a differential evolution (DE) algorithm as a population-based meta-heuristic is developed to solve the model. Since the performance of evolutionary algorithms can be strongly affected by the problem representation, a heuristic procedure
based on priority-based encoding is designed to show a solution whose efficiency is higher than the standard form of priority-based encoding. Parameters of the proposed algorithm are adjusted using response surface methodology. The performance of the proposed DE is checked by GAMS software in small-sized problems. In large-scale problems, besides the common criteria such
as the best solution, average solution, and relative percent deviation, the performance is compared with a parameter-tuned genetic algorithm using a chess rating system. The results of numerical examples demonstrate the acceptable performance of the proposed solution approach.