Mathematical modeling for the closed-loop supply chain with consideration of sustainability risks: a hybrid optimization approach

This study presents a novel approach for managing sustainability risks in closed-loop supply chains (CLSCs) through a hybrid optimization model. To achieve this, we utilized published information from previous research to create a questionnaire with four sustainability risks and 18 sub-criteria. In this case, a bi-level mathematical model was proposed that considered the government's concerns regarding sustainability risks at the upper level and at the lower level were the decisions related to the manufacturers' activities in the CLSC network. In addition, a case study was conducted to demonstrate the validity. The findings highlight opportunities for cost reduction and operational efficiency through optimal capacity utilization. Moreover, the model promotes real-world adaptability by considering various scenarios and uncertain demands. Finally, we obtained specific results along with some management implications through a sensitivity analysis. The results of sustainability risk assessment based on a questionnaire and expert opinion showed that economic risks have the most significant impact among other risks.