This article proposes a reliability model for the emergency service vehicle location problem. Emergency services planners must solve the strategic problem of where to locate emergency services stations and the tatical problem of the number of vehicles to place in each station. We view the problem as one of optimizing the reliability of a system, 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. To solve it, we propose valid inequalities as a preprocessing technique to augment the IP and solve the IP using a branch-and-bound-procedure. Our computational results show that the preprocessing techniques and highly effective. We feel that the reliability model should have applications beyond this context and hope that it till lead to ideas for similar optimization models for designing other systems.
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