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Multiple and usually conflicting objectives subject to data uncertainty aremain 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 suitablesolution. In this paper, we consider a two-stage bi-objective single sourcecapacitated model as a base formulation for designing a last-mile network indisaster 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-aversestochastic approach using conditional value-at-risk (CVaR). To cope with thebi-objective nature of the problem, we embed these concepts into two criterionspace search frameworks, the $\epsilon$-constraint method and the balanced boxmethod, to determine the Pareto frontier. Additionally, a matheuristictechnique is developed to obtain high-quality approximations of the Paretofrontier for large-size instances. In an extensive computational experiment, weevaluate and compare the performance of the applied approaches based onreal-world data from a Thies drought case, Senegal.

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