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

• Published in: arXiv.org
• Main Authors: Nazemi, Najmesadat, Parragh, Sophie N, Gutjahr, Walter J
• Format: Paper Journal Article
• Language: English
• Published: Ithaca Cornell University Library, arXiv.org 13.02.2023
• Subjects: Computer Science - Discrete Mathematics; Cutting; Decision making; Mathematics - Optimization and Control; Operations research; Representations; Risk
• ISSN: 2331-8422
• DOI: 10.48550/arxiv.2302.06511

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.