In the cases that the historical data of an uncertain event is not available, belief degree‐based uncertainty theory is a useful tool to reflect such uncertainty. This study focuses on uncertain bi‐objective supply chain network design problem with cost and environmental impacts under uncertainty. As such network may be designed for the first time in a geographical region, this problem is modelled by the concepts of belief degree‐based uncertainty theory. This article is almost the first study on belief degree‐based uncertain supply chain network design problem with environmental impacts. Two approaches such as expected value model and chance‐constrained model are applied to convert the proposed uncertain problem to its crisp form. The obtained crisp forms are solved by some multi‐objective optimization approaches of the literature such as TH, Niroomand, MMNV. A deep computational study with several test problems are performed to study the performance of the crisp models and the solution approaches. According to the results, the obtained crisp formulations are highly sensitive to the changes in the value of the cost parameters. On the other hand, Niroomand and MMNV solution approaches perform better than other solution approaches from the solution quality point of view.

中文翻译：

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具有环境影响的双目标两阶段供应链网络设计问题的不确定位置分配决策

在不确定事件的历史数据不可用的情况下，基于置信度的不确定性理论是反映此类不确定性的有用工具。本研究着重于不确定性下具有成本和环境影响的不确定性双目标供应链网络设计问题。由于此类网络可能是在某个地理区域内首次设计的，因此该问题是通过基于信任度的不确定性理论的概念来建模的。本文几乎是对基于信念度的具有环境影响的不确定供应链网络设计问题的首次研究。应用了两种方法，例如期望值模型和机会约束模型，将提出的不确定性问题转换为清晰的形式。所得的脆性形式通过文献中的一些多目标优化方法（例如TH，Mroom的Niroomand。进行了包含几个测试问题的深入计算研究，以研究清晰模型的性能和求解方法。根据结果​​，获得的脆性配方对成本参数值的变化高度敏感。另一方面，从解决方案质量的角度来看，Niroomand和MMNV解决方案方法的性能优于其他解决方案方法。