Last-Mile Humanitarian Logistics Planning with Isolated Communities

Problem definition: This paper addresses the critical challenge of delivering humanitarian aid to points of distribution (PoDs) after a disaster under uncertainty, particularly when some PoDs become isolated because of road/bridge damage. Motivated by the Eta and Iota hurricanes in Honduras, we introduce a new last-mile humanitarian logistics planning problem that jointly determines the location and capacity of staging areas (SAs), the fleet sizes of heterogeneous mobile units (ground and aerial), the allocation of mobile units to SAs, and routing decisions ensuring all PoDs are served within a target delivery time. Mobile units can perform multiple trips within this window, enabling efficient fleet-size optimization. Methodology/results: We formulate this problem as a parallel drone–vehicle routing problem with location and fleet-size decisions modeled through a route-based mixed-integer program that captures uncertainty in demand and travel times by a unified chance-constraint (CC) framework. This framework accommodates multiple uncertainty modeling approaches: standard chance constraints, conditional-value-at-risk-based constraints, and distributionally robust CCs, along with a deterministic benchmark, allowing decision makers to control robustness levels under varying data availability. To solve this complex problem exactly, we develop a tailored branch-and-price algorithm, where the nonlinear pricing subproblem is reformulated as a shortest path problem with CCs, efficiently solved by a customized dynamic programming approach with new dominance conditions. Notably, the complexity of the uncertainty model remains comparable to the deterministic counterpart, making our approach practical and scalable. Managerial implications: A case study and synthetic instances demonstrate our framework’s versatility and practical relevance. Our results uncover critical trade-offs between robustness and investment, the effects of delivery time targets and isolation on network structure and fleet size, and differences across uncertainty modeling approaches. They also highlight the role of aerial fleet composition on operational efficiency and economic performance. These analyses provide actionable guidance on network configuration, fleet sizing, and preferred modeling approaches under limited data and resources typically seen in humanitarian response.

Supplemental Material: The online appendix is available at https://doi.org/10.1287/msom.2024.1197.