Robust optimization of sustainable closed-loop supply chain considering carbon emission schemes

Abstract

In the context of the circular economy, this paper focuses on developing an optimal sustainable Closed-Loop Supply Chain (CLSC) by considering such Carbon Emission Schemes (CESs) as carbon cap, carbon cap-and-trade, and carbon tax. A risk-based robust mixed-integer linear programming is formulated using a scenario-based Conditional Value-at-Risk (CVaR) to deal with demand uncertainty. The results reveal that the model performance is affected by both the Decision-Maker's (DM's) risk-aversion and the CESs. However, in all the CESs, the more conservative the DM, the lower the cost performance, and the greater the cost/solution robustness. The carbon cap-and-trade policy not only has the best cost-performance but, ignoring the very small amount of cost robustness deficit compared to the carbon cap model, can also be considered acceptable in the case of robustness. The cost-saving that the carbon cap-and-trade policy brings to the optimistic DM is greater than that brings to the pessimistic one. However, different levels of the DM's risk aversion have a negligible effect on the cost increase of the carbon tax model compared to the carbon cap one.