a multi-objective fuzzy approach to closed-loop supply chain network design with regard to dynamic pricing

During the last decade, reverse logistics networks received a considerable attention due to economic importance and environmental regulations and customer awareness. integration of leading and reverse logistics networks during logistical network design is one of the most important factors in supply chain. in this research, an integer linear programming model is presented to design a multi-layer reverseleading, multi-product, and multi-period integrated logistics network by considering multi-capacity level for facilities under uncertainty condition. this model included three objectives: maximizing profit, minimizing delay of goods delivering to customer, and minimizing returned raw material from suppliers. this research gives financial incentives to encourage customers in order to return their used product. considering that the remaining value of used products is the main incentive of a company to buy second-handed goods, a dynamic pricing approach is determined to define purchase price for these types of products, and based on that, the percentage of returned products were collected by customers. in addition, in this study, parameters have uncertainty features and are vague; therefore, at first, they are converted into exact parameters and, then, because model is multi-objective, the fuzzy mathematical programming approach is used to convert multiobjective model into a single objective; finally, the model by version 8 of lingo is run. in order to solve a large-sized model, a nondominated sorting genetic algorithm ii (nsga-ii) was applied. computational results indicate the effect of the proposed purchase price on encourage customers to return the used products