Bi-objective facility location under uncertainty with an application in last-mile disaster relief

• Published in: Annals of operations research Vol. 319; no. 2; pp. 1689 - 1716
• Main Authors: Nazemi, Najmesadat, Parragh, Sophie N., Gutjahr, Walter J.
• Format: Journal Article
• Language: English
• Published: New York Springer US 01.12.2022; Springer; Springer Nature B.V
• Subjects: Analysis; Austria; Business and Management; Combinatorics; Decision making; Demand analysis; Disaster relief; Facility management; Facility management systems; Mathematical optimization; Operations research; Operations Research/Decision Theory; Optimization; Original Research; Stochastic programming; Theory of Computation; Uncertainty; Austria; Uncertainty; Humanitarian relief; Multi-objective optimization; Facility location problem
• ISSN: 0254-5330; 1572-9338
• DOI: 10.1007/s10479-021-04422-4

Multiple and usually conflicting objectives subject to data uncertainty are main features in many real-world problems. Consequently, in practice, decision-makers need to understand the trade-off between the objectives, considering different levels of uncertainty in order to choose a suitable solution. In this paper, we consider a two-stage bi-objective single source capacitated model as a base formulation for designing a last-mile network in disaster relief where one of the objectives is subject to demand uncertainty. We analyze scenario-based two-stage risk-neutral stochastic programming, adaptive (two-stage) robust optimization, and a two-stage risk-averse stochastic approach using conditional value-at-risk (CVaR). To cope with the bi-objective nature of the problem, we embed these concepts into two criterion space search frameworks, the ϵ -constraint method and the balanced box method, to determine the Pareto frontier. Additionally, a matheuristic technique is developed to obtain high-quality approximations of the Pareto frontier for large-size instances. In an extensive computational experiment, we evaluate and compare the performance of the applied approaches based on real-world data from a Thies drought case, Senegal.