Closed-Loop Sustainable Supply Chain Design Under Uncertainties

Abstract

This paper studies an integrated forward and reverse (closed-loop) supply chain network design problem with sustainable concerns under the uncertain environment. We are interested in the logistics flow, capacity expansion, and technology investments of existing and potential facilities in the multi-stage closed-loop supply chain. First, a deterministic multi-objective mixed integer programming model capturing the tradeoffs between the total cost and the carbon dioxide (CO2) emission is developed to tackle the multi-stage closed-loop supply chain design problem from both economic and environmental perspectives. Then, due to the uncertainty in supply side, customer demand and return quantities, the robust counterpart of the proposed multi-objective supply chain design model is presented using the robust optimization theory. Both deterministic and robust multi-objective supply chain design models are transformed into single-objective models to obtain non-dominated compromise solutions using LP-metrics-based compromise programming method. In the numerical evaluation and results, we analyzed the relationship between the total cost and carbon emission in integrated supply chain network and verified robustness of the proposed robust multi-objective supply chain design model by the generated non-dominated compromise supply chain design solutions.