Hub Space Perspective-Based Collaborative Optimization of Emergency Material Allocation and Routing

With the rapid development of urbanization and the increasing frequency of large-scale disasters, large-scale integrated transportation hubs have gradually become vulnerable points in urban lifelines. In particular, the three-dimensional structure of hubs, including underground and above-ground levels, creates highly complex conditions for emergency management. Most existing studies on emergency logistics focus on external resource scheduling or single-layer evacuation. In contrast, the internal multi-level structure of hubs and the coordination of internal and external resources remain insufficiently addressed. This study investigates the multi-to-multi emergency supply allocation and path coordination problem in three-dimensional hubs. A mixed-integer programming model is developed, which integrates inventory pre-positioning, path scheduling, and the matching between multiple supply points and multiple demand points, aiming to achieve the rapid delivery of emergency materials. The model prioritizes supply time as the primary consideration, while avoiding system congestion by weighing the number of vertical channel usages. Given the high computational complexity of this problem, a Lagrangian relaxation algorithm is designed to decompose the problem, accelerate convergence, and improve scalability. A case study of the Beijing Sub-center transportation hub is conducted. Results show that the proposed model effectively captures the internal structural characteristics of the hub, and the algorithm demonstrates good convergence performance and scalability. The allocation scheme avoids excessive reliance on external resources, balances the burden among supply nodes, and ensures efficient response to demand points. This work provides practical insights for enhancing the resilience of large-scale transportation hubs under emergency scenarios.