Abstract
Abstract The number of fire stations, and the area allocated to each station, that will minimize the sum of the relevant costs of the fire service and the cost of property damage due to fires is determined for a density of fires that is varying slowly with respect to location. A solution procedure is proposed when the cost of a fire is modelled as a nonlinear function of time. A closed-form solution for the area allocated to a fire station is given when the cost of a fire is a linear function of time. A numerical example is given to illustrate the method. The probability of a second fire alarm occurring while a fire is being fought is investigated.
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