A Facility Location and Equipment Emplacement Technique Model with Expected Coverage for the Location of Fire Stations in the Concepción Province, Chile

In this paper, the Facility Location and Equipment Emplacement Technique model with Expected Covering (FLEET-EXC) model is introduced, an emergency facility location problem that maximizes the coverage of expected demand. This model also considers multiple regions, demand types, vehicle types, and region-dependent dispatching rules. This work presents a mixed-integer linear programming model that considers vehicles average utilization to compute expected demand coverage. Because the optimal solution depends on these parameters, we propose an iterative procedure as a solving method, where a Hypercube Queueing Model is used to compute the utilization of the vehicles. The goal of this procedure is to update parameters until the resulting vehicle utilizations from the optimal solution are the same as the ones used to compute the expected demand of the MIP mentioned above model. Finally, a case study on Concepcion province, Chile is presented. A full factorial experiment design is proposed to analyze the effect of locating and relocating fire stations, finding optimal solutions for each experiment. The synergy produced by relocation and location of new facilities notoriously improves the emergency coverage, providing insights for strategic decision making.