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For many real-world decision-making problems subject to uncertainty, it maybe essential to deal with multiple and often conflicting objectives whiletaking the decision-makers' risk preferences into account. Conditionalvalue-at-risk (CVaR) is a widely applied risk measure to addressrisk-averseness of the decision-makers. In this paper, we use the subset-basedpolyhedral representation of the CVaR to reformulate the bi-objective two-stagestochastic facility location problem presented in Nazemi et al. (2021). Wepropose an approximate cutting-plane method to deal with this morecomputationally challenging subset-based formulation. Then, the cutting planemethod is embedded into the epsilon-constraint method, the balanced-box method,and a recently developed matheuristic method to address the bi-objective natureof the problem. Our computational results show the effectiveness of theproposed method. Finally, we discuss how incorporating an approximation of thesubset-based polyhedral formulation affects the obtained solutions.

Bi-objective risk-averse facility location using a subset-based representation of the conditional value-at-risk