Bi-objective facility location in the presence of uncertainty
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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 location-allocation model to design 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. We propose a decomposition-based algorithm to deal with the computationally challenging representation of the two-stage CVaR model. Additionally, a matheuristic technique is developed to obtain high-quality approximations of the Pareto frontier for large-size instances. Finally, we evaluate and compare the performance of the applied approaches based on real-world data from a Thies drought case, Senegal.
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