Distributionally robust truck-drone collaborative delivery network design for urban-rural warehouses: A normal-emergency perspective

As an emerging form of logistics infrastructure, urban-rural warehouses operate as hubs for daily distribution in normal situation, yet can be rapidly reconfigured into dispatch stations for relief supplies during emergency. From a normal-emergency perspective, this study addresses the uncertain truck-drone collaborative delivery network design problem for the urban-rural warehouses. With this regard, we present a two-stage distributionally robust optimization (DRO) model based on the worst-case mean-quantile-deviation criterion. This model jointly optimizes decisions related to front-warehouse location, capacity planning, drone deployment, and material pre-positioning in the first (normal) stage, as well as resource allocation and transportation mode selection in the second (emergency) stage. Meanwhile, we construct box and polyhedral ambiguity sets based on statistical distance to capture uncertainties in demand and disaster-affected areas. Moreover, we reformulate the original models into the corresponding computationally tractable forms by applying duality theory, which can be solved using Gurobi. Particularly, we further develop a multi-cut Benders decomposition algorithm for larger-scale instances. The case study of Beijing shows that our DRO solutions exhibit superior robustness and stability in both out-of-sample tests and worst-case scenarios. By developing an evaluation index system based on the Economic Efficiency Index (EEI), the Warehouse Resource Return Rate (WRRR), and the Warehouse Flexibility Index (WFI), we also demonstrate that our DRO model yields high efficiency in normal operation and strong adaptability and resilience in emergency response.