Distributionally robust scheduling optimization for pharmaceutical delivery using coordinated mother-end drones under post-earthquake road disruptions

Severe road disruptions, demand uncertainty, and weather-induced delays pose critical challenges to humanitarian logistics following large-scale earthquakes. A coordinated mother-end drone system as the exclusive mode of delivery is introduced to address these challenges in scenarios where ground transportation is fully disabled. We develop a location-routing optimization model that incorporates a K−means clustering algorithm for temporary depots location, assignment of mother drones, allocation of medical supplies and end-drones, and last-mile scheduling-routing for end-drones within a two-stage robust optimization framework for mother-end drone coordination. To address the data scarcity associated with uncertain variables such as demand and flight time, we adopt a moment-based distributionally robust optimization, which ensures service feasibility under high-risk scenarios while effectively controlling worst-case delay costs. Nonlinear chance constraints are further linearized and reformulated as a tractable mixed-integer linear programming problem, enhancing computational efficiency. A case study based on the 2025 M7.9 Myanmar earthquake demonstrates the model’s ability to generate cost-effective and reliable drone dispatch schemes under varying degrees of uncertainty. Comparative results confirm the proposed model’s superiority over the deterministic, classical stochastic programming, and robust optimization benchmarks. Managerial insights are drawn regarding dynamic risk preferences, drone performance, and rational partitioning of disaster-affected regions, offering practical guidance for emergency drone dispatching under post-earthquake road disruptions.