A machine learning–enhanced two-stage stochastic vehicle routing framework for post-disaster humanitarian logistics

We study post–disaster routing and delivery of water from Points of Distribution (PODs) to affected populations under travel time uncertainty. Road blockage and debris complicate routing decisions, increase logistics costs for relief agencies, and impose unnecessary suffering on survivors. To address this relief–routing problem, we introduce a two-stage stochastic vehicle routing model that minimizes expected social cost, the sum of logistics and deprivation costs. In the first stage, the model determines vehicle loads and routes using preliminary estimates of travel times. In the second stage, the model updates arrival times. We examine alternative scenario–selection methods and adapt Deep Embedded Clustering (DEC) to identify representative travel time scenarios that preserve variability while improving tractability. Using Puerto Rico after Hurricane Maria (2017) as a case study, we conduct numerical analyses to compare different water distribution strategies under travel time uncertainty. We find that the hybrid strategy (i.e., bottled and bulk) performs best when accurate travel time estimates are unavailable; bulk distribution is a pragmatic option when relief agencies are forced to assume travel times; and bottled distribution can be preferable under near–perfect information. We also investigate how water scarcity and per-distance transportation costs affect delivery strategies. Our results indicate that intensified scarcity and rationing necessitate point-to-point distribution, increasing agency logistics costs while reducing survivors’ waiting times. In contrast, higher per-distance transportation costs raise logistics expenses but leave deprivation costs largely unchanged, suggesting that costs increase is absorbed by agency budgets rather than resulting in additional delays for survivors.