Locating and Dispatching Two Types of Ambulances under Uncertainty and Partial Coverage

Abstract: This paper addresses an emergency vehicle covering and planning problem that arises from a real-world application. A limited number of two heterogeneous types of ambulances must be located at different city points and dispatched to emergency scenes, considering the uncertainty of the emergency. One of the main challenges is to determine whether an emergency can be fully covered on time, partially covered but with longer response times than ideal, partially covered with delays, or not covered at all. To this end, we use a gradual decay function to represent the partial coverage, within a two-stage integer stochastic program. To find solutions of good quality, we propose a location-allocation methodology that relies on the solution of an auxiliary surrogate model, which is faster to solve. Several aspects were evaluated in our empirical work. First, the benefit of introducing a partial coverage function is assessed, finding 84% fewer uncovered emergencies, which directly translates into saved lives. We also found that the proposed solution methodology produces solutions of very good quality significantly faster than the ones obtained when solving the original model.