Developing and solving an integrated model for production routing in sustainable closed-loop supply chain

Social and environmental sustainability has gained increasing importance in today's complex supply chains. Accordingly, an integrated model for production routing in the sustainable closed-loop supply chain is presented in the current study. A three-objective mathematical model is also proposed to minimize supply chain costs, maximize social responsibility or social benefits, and finally, minimize environmental emissions. Sample trial problems are solved in three groups of the small, medium, and large size using the BCO algorithm. To prove the efficiency of this algorithm, its results are compared with the results using the NSGA-II algorithm in terms of comparative metrics such as quality, diversity, and spacing, as well as the runtime to the solution. According to the results, in all cases, the BCO algorithm outperformed the NSGA-II algorithm as it achieved more qualitative and near-optimal solutions. Also, the diversity metric values showed that the BCO algorithm is stronger in the exploration and extraction of the solution feasible region. The results of the metric of spacing and runtime to solution also showed that the NSGA-II algorithm achieves the solution in lower runtime than the BCO algorithm and searches solutions space in a more uniform manner. (c) 2021 Elsevier Ltd. All rights reserved.