Improving Humanitarian Relief via Optimizing Shelter Location With Uncertain Covariates

Abstract

We study the shelter location problems in preparation for natural disasters under uncertain demands. The operators attempt to design an efficient shelter location and casualty allocation plan to carry out relief operations in anticipation of uncertain demands quickly. In practice, the uncertain demands are closely related to disaster intensity, whereas previous studies ignore such correlations when modeling the uncertainties. To this end, we develop a novel scenario-based distributionally robust (SDR) model and optimize the decisions of shelter location, allowing uncertain evacuation demands to be correlated with other uncertain covariates such as disaster severity. Our model also unifies both scenario-based stochastic optimization and distribution-ally robust optimization and utilizes historical demands and covariate information to deliver adequate and robust relief planning. We approximate the non-convex model into a tractable form, the second-order cone programming (SOCP), which can be efficiently solved by an outer approximation (OA) algorithm under the large-scale computation case. The numerical results with real-world data show the advantages of “covariate integration (CVI)” on cost-saving, rescue rate improving compared with traditional distributionally robust optimization, and computational efficiency using the OA algorithm. We find that the advantage still holds with the CVI approach under different spatial distribution and capacity of the candidate shelters, and the establishment of shelters with larger capacity before the disaster has greater rescue efficiency than without covariates (WCV).