Closed-loop supply chain network design under a fuzzy environment

Designing a logistic network is a strategic and critical problem that provides an optimal platform for the effective and efficient supply chain management. In this research, we address the application of fuzzy sets to design a multi-product, multi-period, closed-loop supply chain network. The presented supply chain includes three objective functions: maximization of profit, minimization of delivery time, and maximization of quality. In the context of fuzzy mathematical programming, the paper jointly considers fuzzy/flexible constraints for fuzziness, fuzzy coefficients for lack of knowledge, and fuzzy goal of decision maker(s). According to fuzzy components considered, a fuzzy optimization approach is adopted to convert the proposed fuzzy multi-objective mixed-integer linear program into an equivalent auxiliary crisp model to obtain the relevant solutions. Finally, the numerical experiments are given to demonstrate the significance of the proposed model as well as the solution approach.