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

TL;DR

This paper develops and compares multi-objective stochastic and robust optimization models for last-mile disaster relief network design under demand uncertainty, using real-world data from Senegal.

Contribution

It introduces a bi-objective two-stage model incorporating risk measures and develops solution frameworks including matheuristics for large instances.

Findings

Risk-averse CVaR approach effectively manages demand uncertainty.

The proposed methods generate diverse Pareto optimal solutions.

Computational results demonstrate the models' applicability to real-world disaster relief scenarios.

Abstract

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 $\epsilon$-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.