Robust optimization of sustainable closed-loop supply chain network considering product family

The closed-loop supply chain (CLSC) has gained considerable attention as it refers to all forward and reverse logistics in the chain and retrieves the value of returning products. This configuration also allows considering socio-economic and ecologic matters at the same time. This paper reveals a CLSC regarding sustainable objectives, while some uncertainties exist. A robust optimization approach is presented to overcome this uncertainty. As a contribution that targets growing the chain’s market, products are supplied with specific modules to meet customer demands and create product families. The proposed model is developed under mixed-integer linear programming (MILP). The multi-objective model is converted to a single-objective model through the ε-constraint method and is solved using the Gams software package. A new equation is presented to select the best practice among Pareto fronts to score the non-dominated solutions scientifically. Several numerical instances with random parametric settings corroborate the model's effectiveness. According to a trade-off analysis, the environmental and social considerations led to a significant cost increase and are complied with economic objectives. Moreover, although the uncertain state leads to a larger decision space, robust optimization results are still reliable and practical for real-world situations. Consequently, both researchers and practitioners can benefit from the derived results.