A Reliability Model Applied to Emergency Service Vehicle Location

This article proposes a reliability model for emergency service vehicle location. Emergency services planners must solve the strategic problem of where to locate emergency services stations and the tactical problem of the number of vehicles to place in each station. We view the problem from a system reliability perspective, where system failure is interpreted as the inability of a vehicle to respond to a demand call within an acceptable amount of time. Our model handles the stochastic problem aspects in a more explicit way than previous models in the literature. Based on a reliability bound on the probability of system failure, we derive a 0-1 integer programming (IP) optimization model. We propose the augmentation of the IP using certain valid inequalities as a preprocessing technique, and solve the IP using a branch-and-bound procedure. Our computational results show that the preprocessing technique is highly effective. Also, sensitivity studies show that the planner can produce a variety of different desired solution characteristics by appropriate manipulation of parameters. We feel that the reliability perspective should have applications beyond this context and hope that it will lead to ideas for similar optimization models in the context of designing reliable systems.