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Recent increases in incidents make it unlikely for emergency systems to be able to meet incident requirements. In this paper, we formulate a new territorial measurement approach for the reliability of fire departments, the collapse index, to help decision makers determine their response capability. This new index expresses the maximum simultaneous workload in a pixel over one year, measured over time. Based on this index, we propose a new fire station (FS) optimum location model by applying the simulated annealing method in conjunction with a geographic information system. The formulation of the cost function as the minimum standard deviation of the FS workload, combined with the constraint that the maximum collapse index in any pixel must be less than a certain threshold, are two contributions of this work. Five optimisation processes are developed to locate between up to five FS and create collapse index maps in the Madrid Region. The maximum collapse index in a pixel with a new FS decreases from its initial value of 10,485 min to 2500 min when five new FS are built. The conclusion is that the proposed optimisation model meets the need for reliability in the emergency services and that the collapse index is a good measure to prevent overlapping in the system.

GIS-Based Simulated Annealing Algorithm for the Optimum Location of Fire Stations in the Madrid Region, Spain: Monitoring the Collapse Index