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

TL;DR

This paper introduces a novel subset-based CVaR reformulation for bi-objective stochastic facility location, employing an approximate cutting-plane method integrated with multiple solution strategies to improve computational efficiency.

Contribution

It presents a new subset-based polyhedral CVaR formulation and an approximate cutting-plane algorithm, enhancing solution approaches for complex bi-objective risk-averse facility location problems.

Findings

The proposed method effectively solves the reformulated problem.

Embedding the cutting-plane into existing methods improves computational performance.

Approximate solutions are comparable to exact methods in quality.

Abstract

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.