Protect the Decision, Not the Disaster: Regret-Robust Capacity Sizing and Positioning with Transportation Recourse

Abstract

An operator who positions mobile resources before a disruption faces two uncertainties that are usually treated as one: how the joint state of demand and travel conditions will vary, and which part of the resulting cost the positioning decision can actually change. Standard distributionally robust optimization (DRO) protects total cost, and therefore spends much of its protection on disruption costs that every feasible design would pay. This paper evaluates the worst-case regret of a design and compares it with the worst-case premium of total-cost DRO, and shows that the regret-to-premium ratio can be bounded before any robust model is solved: from marginals for the dependence question, and from single-scenario optima and one transport linear program for the regret question. The worst-case law is a relabelling of the operating record, reassigning every recorded period wholesale to another recorded period, except at most one, which is split. The comparator that exposes the largest worst-case regret is found by a single mixed-integer program. We derive an explicit radius where the sample-average design is exactly regret-robust. For finite scenario and design sets we compute a design's worst-case regret exactly, bound it from quantities a planner already has, and show on fleet and EMS data how law-relative regret changes capacity and positioning choices relative to sample-average and worst-cost planning. We apply the decision tree to several years of New York fleet data, including the year before Hurricane Sandy, and to two emergency-service events. The test flags the pre-Sandy year as exposed. The training-support regret bounds cover realized test regret in three of four fleet folds. On Ida, where the regret-robust allocation differed from the sample-average one, it moved units toward the boroughs the storm loaded and cost less than the sample-average design.