Emergency Medical Service System Design under Service Level Constraints for Heterogeneous Patients

We study the problem of locating Emergency Medical Service (EMS) facilities in the presence of service level constraints for patients with acuity levels ranging from resuscitation to non-urgent. Each patient arriving at any EMS facility is triaged as either resuscitation/high priority or less urgent/low priority, where high priority patients are always served on a priority basis. The problem is to optimally locate EMS facilities and allocate their service zones to satisfy the following coverage and service level constraints: (i) each user zone is served by an EMS facility that is within a given coverage radius; (ii) at least h proportion of the resuscitation cases at any EMS facility should be admitted immediately without having to wait; (iii) at least l proportion of the cases belonging to low priority class at any EMS facility should not have to wait for more than l minutes. For this, we model the network of EMS facilities as spatially distributed M/M/1 priority queues, whose locations and user allocations need to be determined. The resulting integer programming problem is challenging to solve, especially in absence of any known analytical expression for the waiting time distribution of low priority customers in an M/M/1 priority queue. We develop a cutting plane based solution algorithm, exploiting the concavity of the waiting time distribution of low priority customers to approximate its non-linearity using tangent planes, determined numerically using matrix geometric method. Using a case study of locating EMS facilities in Austin, Texas, we present computational results and managerial insights.