A probabilistic multi-period optimization approach for the ambulance location problem

An Emergency Medical Service (EMS) is a service providing first care to patients. A key performance issue for an EMS system is the early response, which substantially increases the probability of full recovery. Since the location of emergency vehicles plays a fundamental role in EMS management, the problem of locating ambulances has been extensively investigated in the optimization literature. A variety of models have been proposed, ranging from deterministic and static models to dynamic and probabilistic ones, with the aim of capturing the dynamic and probabilistic aspects of the problem while being able to solve real-life instances. In this work we propose a probabilistic multi-period ambulance location model, which takes into account the main aspects of the problem and allows to relocate ambulances during the considered time horizon. We show that medium-size instances can be solved to optimality with state-of-the-art mixed integer programming solvers and we propose a Lagrangian-based approach to tackle larger instances, which provides lower and upper bounds. Tests are carried out on real-life data from the city of Milano.