epsilon method

The present study aims to optimize a green closed-loop supply chain (GCLSC) network while minimizing carbon emissions and maximizing product shipments. The proposed model incorporates unbalanced factors such as capacity level, input current limit to each distribution center, and facility environmental level. We considered emission control levels for locating distribution centers as well as the reduction in CO2 emissions at all levels of the supply chain. Moreover, all types of expenditures in a closed-loop supply chain including manufacturing, distribution, recovery, assembly, and disassembly in the model are considered. Consideration of these assumptions closes this study to reality and makes this study an innovative one. Moreover, to account for demand uncertainty, a robust optimization method, the Bertsimas and Sim optimization approach, is used. The Epsilon Constraint Method and non-dominated sorting genetic algorithm II (NSGA-II) were employed to solve multi-objective functions with unknown demand, and the genetic algorithm is used to solve large-scale problems. The results indicate that the proposed approach achieves the objectives of reducing costs, minimizing environmental impact. Moreover, the NSGA-II algorithm outperforms other solution methods in terms of the number and diversity of solutions on the Pareto front. Specifically, the Pareto boundary obtained by NSGA-II contains a larger number of solutions compared to the different types of epsilon constraint methods. Additionally, the diversity of solutions on the Pareto front is higher in the NSGA-II algorithm, indicating a more well-spread and diverse set of solutions. These findings highlight the superiority of NSGA-II as a powerful and effective algorithm for multi-objective optimization problems in green closed-loop supply chain networks.