Designing a Bi-Objective Closed-Loop Supply Chain Problem with Shortage and All Unit Discount: “Nondominated Sorting Genetic Algorithm II” and “Multi-Objective Particle Swarm Optimization”

Abstract

Nowadays, due to environmental issues, government rules and economic interests have increased attention to the collection and recovery of products, which has led to the formation of new concepts such as reverse and closed-loop supply chains. The implementation of the closed-loop supply chain as a solution to sustainable development is expanding from one hand and increasing the profitability of companies on the other. For this purpose, a mathematical model was developed to design an integrated closed-loop supply chain network, which is a combination of two-problem localization problems and flow optimization. The proposed model was designed to minimize network costs and to maximize the level of responsiveness to customers. The cost parameters of establishing centers in this model are uncertain; to overcome the model’s uncertainties, stochastic programming is used. In the mathematical model, supplier, manufacturer, distributor and customer in the direct supply chain and collection/rehabilitation, destruction, recycling centers and, second-type distribution center for sale of second-hand products as well as second-hand products customers in the reverse flow are considered, to be closer to the real today world. This model is multi-periodic mix integer nonlinear programming where the shortage has allowed. To motivate and encourage customers to buy more, in addition to getting closer to the real world and it happens more in practice, is considered all units of discount for transportation cost in the forward flow. To solve this model Non-Dominated Sorting Genetic Algorithm II (NSGA-II) and Multi-Objective Particle Swarm Optimization (MOPSO) is using. The parameter tuning was done using the Taguchi method. Then, the important criteria for measurement and comparison of performance algorithms have used, including the Mean Ideal Distance, Diversification Metric, Number of Pareto-optimal Solutions, and the Quality Metric. Results of the Comparative metrics show that NSGA-II outperforms MOPSO in almost all cases in achieving the best trade-off solutions.