Improving relief operations via optimizing shelter location with uncertain covariates

Designing an efficient shelter location planning is crucial to the rapid implementation of relief operations under the uncertain number of casualties. In practice, the uncertain number of casualties is closely related to disaster severity, whereas previous studies ignore such correlations when modeling uncertainties. In this paper, the scenario-wise ambiguity set is adopted to capture the correlation between the uncertain number of casualties and uncertain covariates, i.e., disaster severity. We develop a two-stage scenario-wise distributionally robust (SDR) model, where the shelter location and capacity allocation decisions are made here-and-now, and recourse decisions to transport casualties are made after the uncertainties on the number of casualties and covariate information have been realized. We approximate the non-convex model into a tractable form, i.e., second-order cone programming (SOCP), which can be solved efficiently by an outer approximation (OA) algorithm for a large-scale computation case. The numerical results with real-world data show that covariate integration (CVI) can contribute to saving costs and improving relief efficiency, and illustrate the computational superiority of the proposed OA algorithm. The results further demonstrate that establishing shelters with large capacities and near the affected areas has indeed had a positive impact on improving relief efficiency.