A simulation-optimization algorithm for return strategies in emergency medical systems

In an emergency medical system, the locations of ambulance stations has a direct impact on response time. In this paper, two location models are presented in combination with the hypercube queuing model to maximize coverage probability. In the first model, the locations of free and busy ambulances are considered in the system states, and the hypercube model can be analyzed accurately. The model contains a large number of states, and cannot be used for large-sized problems. For this reason, the second model is presented with the same assumptions as in the first model, except that the locations of busy ambulances are not included in the system state, but approximated based on the arrival rates. Both models are offline and dynamic, in which an ambulance does not necessarily return to the station from which it has been dispatched. Two strategies are defined for returning ambulances to the stations from the customer’s location. In the first strategy, the ambulance is returned to the nearest station after completion of its mission, and in the second strategy, it returns to the empty station that covers the highest demand rate. For evaluation of the performance of the proposed models, small-sized examples are solved for both return strategies using the GAMS software. A simulation-optimization approach combined with a simulated annealing algorithm and a discrete-event simulation are used for solving large-sized problems. Moreover, real data from a case study are used to demonstrate the performance of the models in the real world.