A new partial coverage locating model for cooperative fire services

The location and allocation of fire service facilities, especially for those facilities expecting high demand and severe conditions, require consideration of the cooperative behavior of multi-type fire vehicles in different fire station locations, the gradual decline of coverage with increasing distance, and the sufficient number of fire vehicles given specific requirements of the Urban Fire Rescue Specification (UFRS) of China. This paper presents a mixed integer nonlinear program (MINLP) model that integrates a cooperative mechanism of multi-type vehicles, partial distance coverage of single-type vehicle (PDC-S), and partial quantity coverage of single-type vehicle (PQC-S) into an integrated maximal covering location model for cooperative fire services, therein offering partial distance and quantity coverage of multi-type vehicles (PDQC-M). Numerical experiments with a testing example validate our model and demonstrate that the BARON algorithms can be used to effectively solve the problem. An empirical case study of Harbin (China) and a series of sensitivity analyses are conducted to illustrate the effects of station size and total budget on PDQC-M provided by cooperative fire services.