Supply chain network design (SCND) is an important strategic decision determining the structure of each entity in the supply chain, which has an important impact on the long-term development of a company. An efficient and effective supply chain network is of vital importance for improving customer satisfaction, optimizing the allocation of resources, and increasing profitability. The environmental concerns and social responsibility awareness of the whole society have spurred researchers and managers to design sustainable supply chains (SSCs) integrating the economic, environmental, and social factors. In addition, the innate uncertainty of the SCND problem requires an integrated method to cope. In this regard, this study develops a multi-echelon multi-objective robust fuzzy closed-loop supply chain network (CLSCN) design model under uncertainty including all three dimensions of sustainability. This model considers the total cost minimization, carbon caps, and social impact maximization concurrently to realize supply chain sustainability, and is able to make a balance between the conflicting multiple objectives. Meanwhile, the uncertainty of the parameters is divided into two categories and addressed with two approaches: the first category is missed working days related to social impact, which is solved by the fuzzy membership theory; the second category is the demand and remanufacturing rate, which is settled by a robust optimization method. To validate the ability and applicability of the model and solution approach, a numerical example is conducted and solved using ILOG CPLEX. The result shows that the supply chain network structure and the value of the optimization objectives will change when considering sustainability and different degrees of uncertainty. This will enable supply chain managers to reduce the environmental impact and enhance the social benefits of their supply chain activities, and design a more stable supply chain to better cope with the influence of uncertainty.
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