A genetic algorithm approach for optimising a closed-loop supply chain network with crisp and fuzzy objectives

This paper proposes a mixed integer programming model for a closed-loop supply chain (CLSC) network with multi-periods and multi-parts under two main policies as secondary market pricing and incremental incentive policies. In the first policy, customers order and receive products from distribution centres, but at next period, they can trade among themselves with used products that are returned in a secondary market. Financial incentives are offered to the customers to influence the returns, and the correct amount of collections at different prices is determined by the second policy. In addition to the base case (crisp) formulation, a fuzzy multi-objective extension is applied to solve CLSC network problem with fuzzy objectives to represent vagueness in real-world problems. Then, developed genetic algorithm approach is applied to solve real size crisp and fuzzy CLSC problems. The effectiveness of the proposed meta-heuristic approach is investigated and illustrated by comparing its results with GAMS-CPLEX on a set of crisp/fuzzy problems with different sizes