A hub-and-spoke network design for relocating emergency service vehicles

Abstract

Relocation involves the repositioning of idle Emergency Service (ES) vehicles among stations in order to reduce the response time. It is well-known in the literature that relocating idle vehicles provides better coverage in the network, which in turn reduces the response time to the next call. In classical emergency service networks, idle vehicles can be relocated between any two stations. This can cause long delays and increase the response times. In this study, we proposed for the first time a hub-and-spoke network to efficiently realize the relocation of idle vehicles. The proposed hub-and-spoke structure consolidates relocations among hubs, while hub-spoke relocations are implemented as needed. Such a structure helps to better organize the simultaneous movements of ES vehicles for relocation. We have developed a mathematical model to maximize the expected safely covered population. The model provides both the hub-spoke topology and the relocation plan (a compliance table), which shows the desired stations of idle vehicles depending on the system state. In the literature, the relocation plan does not show the relocation paths (movements) of the vehicles. We have presented an exact algorithm that computes the relocation paths for all possible call cases and system levels in advance. This helps the dispatcher to manage the system effectively. We performed a detailed simulation study for ES vehicles of a natural gas distributor to demonstrate the real-life suitability of the proposed system. Compared to the classical relocation network structure, the proposed system has improved the response time, relocation time, and travel time especially when the system is busy.