A circular closed-loop supply chain network with an epsilon-constraint and NSGA-II approach

Abstract

Due to the lack of efficient waste management growing environmental pollutions leads to threatens the live of mankind and our planet. Good waste management need appropriate planning and monitoring at all different levels including designing, manufacturing, distribution, collection, recycling and disposal that require a circular approach. Circular supply chain, offers a new and compelling perspective to the supply chain sustainability domain. Therefor having proper solution approach for circular supply chains is of great value. To this end, in this paper suitable solution approaches has been presented for a multi-echelon, multi-product, multi-period and multi-objective mixed integer linear programing. This model is designed for a circular closed-loop supply chain that considered digital devices. The conflicting objectives of the model are to minimize total costs on the entire chain and environmental pollution and to maximize total rate of unemployment reduction. The Epsilon-constraint method is proposed to solve small size of the problem. A Pareto set of optimal solutions helped to assess the trade-offs involving the three objective. Because this problem is of NP-hard category, the non-dominated sorting genetic algorithm (NSGA-II) is used to find near optimal Pareto front for large size of the problem. To demonstrate the efficiency of the metaheuristic algorithm the answers obtained in small dimensions are compared with the answers obtained from the Epsilon-constraint method. The results show that the error percentage of the objective function compared to the epsilon method in all solved problems is less than 1%, which shows the effectiveness of the proposed algorithm. Reducing the solving time especially in the large dimensions of the problem is one of the advantages of this solution method. Using these methods allows decision makers to provide a set of efficient optimal solutions so that they can select the best point, according to the available budget and their organization policies.