For many real-world decision-making problems subject to uncertainty, it may be essential to deal with multiple and often conflicting objectives while taking the decision-makers' risk preferences into account. Conditional value-at-risk (CVaR) is a widely applied risk measure to address risk-averseness of the decision-makers. In this paper, we use the subset-based polyhedral representation of the CVaR to reformulate the bi-objective two-stage stochastic facility location problem presented in Nazemi et al. (2021). We propose an approximate cutting-plane method to deal with this more computationally challenging subset-based formulation. Then, the cutting plane method is embedded into the epsilon-constraint method, the balanced-box method, and a recently developed matheuristic method to address the bi-objective nature of the problem. Our computational results show the effectiveness of the proposed method. Finally, we discuss how incorporating an approximation of the subset-based polyhedral formulation affects the obtained solutions.

翻译：在诸多面临不确定性的现实决策问题中，往往需要在考虑决策者风险偏好的同时，处理多个且通常相互冲突的目标。条件风险价值（CVaR）是一种广泛用于刻画决策者风险规避特性的风险度量。本文利用基于子集的多面体表示重构了Nazemi等人（2021）提出的双目标两阶段随机设施选址问题。针对计算更具挑战性的子集表示形式，我们提出了一种近似割平面方法。随后，将该割平面方法嵌入到epsilon-约束法、平衡盒法以及一种最新开发的元启发式方法中，以处理问题的双目标特性。计算结果表明了所提方法的有效性。最后，我们讨论了融入子集多面体表示的近似对求解结果的影响。