A fuzzy-random programming for integrated closed-loop logistics network design by using priority-based genetic algorithm

Recovery of used products has steadily become interesting issue for research due to economic reasons and growing environmental or legislative concern. This paper presents a closed-loop logistics network design based on reverse logistics models. A mixed integer linear programming model is implemented to integrate logistics network design in order to prevent the sub-optimality caused by the separate design of the forward and reverse networks. The study presents a single product and multi-stage logistics network problem for the new and return products not only to determine subsets of logistics centers to be opened, but also to determine transportation strategy, which satisfies demand imposed by facilities and minimizes fixed opening and total shipping costs. Since the deterministic estimation of some parameters such as demand and rate of return of used products in closed loop logistics models is impractical, an uncertain programming is proposed. In this case, we assume there are several economic conditions with predefined probabilities calculated from historical data. Then by means of expert's opinion, a fuzzy variable is offered as customer's demand under each economic condition. In addition, demand and rate of return of products for each customer zone is presented by fuzzy-random variables, similarly. Therefore, a fuzzy-random programming is used and a priority-based genetic algorithm is proposed to solve large-scale problems.