A Bi-Objective Model to Design Closed-Loop Supply Chain Network under Uncertainty

By increasing attention to environmental issues, the problem of design closed-loop supply chain has been more important. The integrated design of closed-loop supply chains as one of the most important issues in the management of supply chains involve determining the location and number of required facilities (production, collection, recycling and disposal) in the forward and reverse supply chain, inventories in every facility and flows between them. In this paper, a closed-loop supply chain with diverse products (multi-product) has been studied and a linear bi-objective mathematical model is proposed to reduce the total costs and the emissions in the network with determining the strategic and operational variables. Because of the uncertainty in parameters of proposed model such as customer demands or returns, the proposed model under uncertainty (robust optimization) is developed. The closed-loop supply chain of glass bottles is studied and modeled to minimize the total costs and production of carbon dioxide by proposed model. Finally, a sensitivity analysis of robust optimization model was conducted.