A decomposition scheme for Wasserstein distributionally robust emergency relief network design under demand uncertainty and social donations

Abstract

Social donations have played a crucial role in providing effective emergency relief and need to be particularly valued and used wisely. In this study, we address a Wasserstein distributionally robust emergency relief network design problem with demand uncertainty by taking into account the social donations. Specifically, we first formulate the problem into a two-stage stochastic programming model that requires the probability distribution information of the uncertain demand is completely known in advance, where the first stage decides on the location and pre-positioning of resources, and the second stage optimizes the delivery volume of the reserved and donated supplies offered by social organizations and individual. As the probability distribution of the demand cannot be known precisely (i.e., ambiguous) in reality, we further extend the stochastic model to a Wasserstein distributionally robust optimization model, in which the ambiguous demand is captured by the Wasserstein ambiguity set. Theoretically, we derive the tractable deterministic reformulations of the proposed distributionally robust optimization model under Type-$\infty$ and Type-1 Wasserstein metrics. To solve the extensive reformulations, we design a decomposition scheme on the basis of the Benders decomposition framework by adopting aggregated multiple cuts, cut-loop stabilization at root node and stabilized k-opt local branching acceleration strategies. Finally, we carry out numerical experiments to illustrate the computational advantage of the proposed solution method over the single acceleration implementation on hypothetical instances, and demonstrate the superiority of the proposed modeling approach compared with the traditional stochastic programming and robust optimization models on a real case study. The results show that the distributionally robust optimization approach used better trade-offs between cost and risk.