Distributional Robustness and Inequity Mitigation in Disaster Preparedness of Humanitarian Operations.

This article focuses on designing a predisaster relief network under uncertain demands, emphasizing three key humanitarian operation aspects: shortages, equity, and uncertainty. It introduces the shortage severity measure (SSM), a distributionally robust risk metric based on worst-case conditional value-at-risk (CVaR), to evaluate shortage risks under demand uncertainty, and formulates a mixed-integer lexicographic optimization problem to achieve equitable resource allocation across disaster-prone regions. A novel branch-and-bound algorithm is developed to solve this nonconvex, mixed-integer lexicographic problem exactly, complemented by two approaches—an exact method and an affinely adjustable robust counterpart (AARC)—for optimal postdisaster adaptable resource reallocation. Using a case study of the 2010 Yushu earthquake in China, the study demonstrates that incorporating equity in both predisaster deployment and postdisaster reallocation significantly improves fairness in shortage distribution with only a modest increase in total shortage, and that event-wise ambiguity sets leveraging disaster magnitude information enhance decision-making under uncertainty compared to classical stochastic and robust models.