Joint Location and Dispatching Decisions for Emergency Medical Service Systems

Emergency Medical Service (EMS) systems are a service that provides acute care and transportation to a place for definitive care, to people experiencing a medical emergency. The ultimate goal of EMS systems is to save lives. The ability of EMS systems to do this effectively is impacted by several resource allocation decisions including location of servers (ambulances), districting of demand zones and dispatching rules for the servers. The location decision is strategic while the dispatching decision is operational. Those two decisions are usually made separately although both affect typical EMS performance measures. The service from an ambulance is usually time sensitive (patients generally want the ambulances to be available as soon as possible), and the demand for service is stochastic. Regulators also impose availability constraints, the most generally accepted being that 90% of high priority calls (such as those related to cardiac arrest events) should be attended to within 8 minutes and 59 seconds. In the case of minimizing the mean response time as the only objective, previous works have shown that there are cases in which it might not be optimal to send the closest available server to achieve the minimum overall response time. Some researchers have proposed integrated models in which the two decisions are made sequentially. The main contribution of this work is precisely in developing the integration of location and dispatching decisions made simultaneously. Combining those decisions leads to complex optimization models in which even the formulation is not straightforward. In addition, given the stochastic nature of the EMS systems the models need to have a way to represent their probabilistic nature. Several researchers agree that the use of queuing theory elements in combination with location, districting and dispatching models is the best way to represent EMS systems. Often heuristic/approximate solution procedures have been