  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.
