Integration of Facility Location and Hypercube Queuing Models in Emergency Medical Systems

The purpose of emergency medical systems (EMS) is to save lives and reduce injuries with a quick response in emergencies. The performance of these systems is highly dependent on the locations of ambulances and the policy for dispatching them to the customers (i.e., patients). In this study, two new mathematical models are presented to combine the decisions about the location and dispatching policy by integrating the location and hypercube queuing models. In the presented models, the flow-balance equations of the hypercube queuing model are considered as the constraints of the location model. In the first model, the status of each server is idle or busy at any moment, as in the classic hypercube queuing model. In the second model, the travel time is considered independent of the on-scene time, and the status of each server is idle, busy, and traveling, or busy and serving a customer on the incident site. To verify the models, some small-sized examples are first solved exactly. Then, an optimization framework based on the genetic algorithm is presented due to the complexity of the models for solving larger-sized examples. Two approaches (i.e., the exact and simulation-optimization) are used to extend the framework. The results demonstrate that the proposed optimization framework can obtain proper solutions compared to those of the exact method. Finally, several performance measures are considered that can only be calculated using the second model.