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 due to road/bridge damages. 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 as a route-based mixed-integer program that captures uncertainty in demand and travel times via a unified chance constraint framework. This framework accommodates multiple uncertainty modeling approaches—standard chance-constraints, CVaR-based constraints, and distributionally robust chance-constraints 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 Chance-Constraints, 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.