This paper proposes a two-stage multi-objective possibilistic integer linear programming sustainable supply chain network design model, minimizing the economic, environmental goals and maximizing the social sustainability goals. The proposed model determines the openings of facilities and the amount of flow of goods across the supply chain. It introduces supplier green image factors in the design of the supply chain network. The model has considered epistemic uncertainty to model the unknown capacity, cost, and demand. The proposed study has been carried out in two stages. In the first stage, BWM (Best-Worst method) and TOPSIS are applied to evaluate the green image weights of suppliers. Further, these green weights are being used in the second phase for the supply chain network design. The study has adopted combined possibilistic programming and Epsilon (ε) constraint method, which was reported infrequently in the literature. Epsilon (ε) constraint method generates distinct Pareto-optimal solutions, which provided a large combination of the trade-off between the cost, emission, and social sustainability. The results facilitate decision-makers to take the decision in an uncertain environment.

本文提出了一个两阶段的多目标可能整数线性规划可持续供应链网络设计模型，该模型最小化了经济，环境目标并最大化了社会可持续性目标。提议的模型确定了设施的开放程度以及整个供应链中的货物流量。它在供应链网络的设计中引入了供应商绿色形象因素。该模型考虑了认知不确定性，以对未知的容量，成本和需求进行建模。拟议的研究分两个阶段进行。在第一阶段，将BWM（最佳-最差方法）和TOPSIS应用于评估供应商的绿色形象权重。此外，这些绿色权重已在第二阶段用于供应链网络设计。该研究采用了可能性规划和Epsilon（ε）约束方法相结合的方法，该方法在文献中很少报道。Epsilon（ε）约束方法生成独特的帕累托最优解，该解提供了成本，排放量和社会可持续性之间的折衷方案。结果有助于决策者在不确定的环境中做出决策。