A closed loop supply chain network design problem with multi-mode demand satisfaction in fuzzy environment

A new closed loop supply chain network design problem is considered in this study. In comparison to the literature, the problem considers a more complete set of stages in the network e.g. simultaneous consideration of supplier, plant, distribution center, customer, and collection, recovering, recycling, and disposal centers. The problem makes location, capacity, allocation, demand mode and material/product flow decisions for optimizing net benefit including sales revenue, fixed establishing cost of facilities, transportation cost, material purchasing cost, production cost, and inventory holding cost. As a novelty, for the first time multi-mode demand satisfaction is considered in a closed loop supply chain problem. As another contribution, in order to be close to real-world situations, the problem is tackled in a fuzzy environment by using trapezoidal fuzzy parameters which yield a trapezoidal fuzzy objective function value. As solution methodology, considering the fuzzy objective function, the problem is reformulated as a multi-objective fuzzy mixed integer linear problem and is crisped using credibility measure of the fuzzy constraints. Finally, the crisp multi-objective version of the problem is solved by several hybrid fuzzy programming approaches to obtain a good efficient solution. Applying several numerical test problems, the SO method performs better than other approaches.