A robust optimization approach for multi-objective, multi-product, multi-period, closed-loop green supply chain network designs under uncertainty and discount

One of the basic requirements of the companies to survive in real-world competitive environments is to make their supply chains as efficient as possible. Due to recent governmental regulations, environmental issues, and the development of the concept of social responsibility, the closed-loop supply chain management has been focused by many researchers. A closed-loop supply chain includes both forward and reverse supply chain networks with the purpose of combining environmental considerations with the traditional supply chain network designs through the collection of used products and activities related to their reuse. In this paper, a bi-objective, multi-period, multi-product, closed-loop supply chain network is designed under environmental considerations, discounts, and uncertainties. The deterministic model of the chain is first solved by three multi-objective decision-making methods. Then, based on real-world uncertainties involved in some of the parameters, a robust optimization model is proposed and solved using decision-making methods. At the end, the best deterministic and robust models are selected based on the displaced ideal solution.