Hierarchical supplement location-allocation optimization for disaster supply warehouses in the Beijing–Tianjin–Hebei region of China

Research on the emergency facility location-allocation problem has important theoretical and practical significance for responses to large-scale emergencies. During the actual planning of disaster supply warehouses (DSWs), reconstruction and expansion projects usually need to fully exploit different levels of designated facilities to achieve resource integration. This article presents a hierarchical supplement location-allocation (HSLA) optimization model for DSWs in both the preparedness and response phases to address the above concerns. The model minimizes the total number and cost of DSWs for the facility location problem and the total distance for delivering supplies at all levels for the supply allocation problem. A modified particle swarm optimization algorithm is applied to derive solutions to the HSLA model. The model is demonstrated for the Beijing-Tianjin-Hebei (BTH) region in China. The results show that twelve of the 180 counties, which account for 6.03% of the total area of the BTH region are not covered by county-, prefectural- and provincial-level DSWs. In addition, three sets of optimization schemes for the location-allocation problem for DSWs at the three levels and one final mixed optimal scheme (one county-level DSW, two prefectural-level DSWs, and one provincial-level DSW should be newly built or upgraded in four counties) are suggested based on the supplemental optimization site selection. This model is believed to remain more consistent with the knowledge of DSW planners and policy makers by incorporating the multi-level coverage and supplemental site selection concept into the location-allocation problem. The method can be easily duplicated to expand or build new emergency facilities at different levels in addition to DSWs. The results provide a scientific reference for DSW location-allocation planning in the BTH region.