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.