An optimization model for a sustainable closed-loop supply chain considering efficient supplier selection and total quantity discount policies

Abstract

This paper addresses the sustainable closed-loop supply chain (SCLSC) design problem regarding selecting a supplier under total quantity discount with demand uncertainty and logistic flow uncertainty. The proposed model considers the three pillars of sustainability: the economic, environmental, and social realms. The model deals with the costs incurred by products-related manufacturing and minimizes the carbon dioxide emissions resulting from different manufacturing processes, as well as the attendant rate of injuries among the workers. Python edition 2019-07 software with the SCIPY solver was used to solve the model, using a sequential least squares programming algorithm (SLSQP) to obtain optimal solutions. A numerical study was conducted to validate the model. A sensitivity analysis was conducted to address the effects of both types of uncertainty on the optimal solution. It was found that the effect of a high rate of demand uncertainty is more severe than the effect of the uncertainty of the flow logistics in the reverse direction since the former generated a lower value of the optimal solution than the worst-case scenario generated by the uncertainty budget. Moreover, the higher the weight of environmental and social objectives, the higher the proportion of recycled products from the total production. This study proposes a robust optimization model for an SCLSC that considers two types of uncertainty: the uncertainty budget that is used for the logistics flow in the reverse direction for refurbished and redesigned products and the box of uncertainty that is used to address the demand uncertainty.