A Bi-objective Mathematical Model for Closed-loop Supply Chain Network Design Problem

In this paper, a bi-objective mixed-integer linear optimization model for Closed-loop Supply Chain Network Design Problem (CLSCND) is developed. The proposed model includes both the forward and reverse directions and includes different types of facilities, namely, manufacturing/remanufacturing centers, warehouses, and disassembly centers. The first objective function tried to minimize the total cost of the supply chain, while the second one was aimed at maximizing the responsiveness of the network in both forward and reverse directions, simultaneously. To solve the proposed bi-objective model, an augmented ε-constraint method was implemented by which a set of Pareto-optimal solutions for the problem were generated. An illustrative numerical example is given in the study to show the applicability and efficiency of the presented optimization model.