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Emergency Medical Service (EMS) managers continuously strive to improve the coverage performance, i.e., the percentage of calls responded to within a specific target time, to save lives in case of life-threatening emergencies. This goal can be achieved by dynamically adjusting the location of rescue teams during a day in response to some temporal or geographical fluctuations such as demand patterns, traffic conditions, or the number of teams on duty. This relocation is known as the multi-period redeployment problem. In this study, we propose a discrete simulation-based optimization model to adress the multi-period redeployment problem in the French EMS of the Val-de-Marne department (France), named SAMU 94. The proposed model uses an iterative method that combines the use of a mathematical model to find the optimal locations of rescue teams with the use of the SAMU 94 simulation model implemented in Arena software, to evaluate the busy fraction parameters required to solve the mathematical model. The model performance was compared with that of the simulation-based optimization software, OptQuest. The experimental results demonstrated that the iterative method could produce solutions with better coverage performance, 20 times faster than OptQuest.

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The French Emergency Medical services, known as SAMU, are public safety systems responsible for the coordination of pre-hospital care under emergency conditions throughout a given geographic region. The goal of such systems is to respond timely and adequately to population calls by providing first aid services and transferring patients, when needed, to the appropriate care facility. In this paper, we propose a multiperiod version of the Maximum Expected Covering Location Problem applied to the case of the SAMU 94 responsible for the Val-de-Marne department (France). The assumption that the busy fractions are identical for all demand points is relaxed by adopting an iterative method to compute a priori estimates of these parameters in the model using an ARENA discrete-event simulation model of the SAMU 94. The solutions obtained from the mathematical model are then assessed by simulation regarding the time required to respond to an emergency call by getting to the patient location, known as response time, which is a critical aspect for the SAMU providers. Experimental results showed that the proposed method increased average percentage of most serious calls responded to within the target time of 15 minutes up to 15% compared to the current system performance.

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