Enhanced coverage by integrating site interdependencies in capacitated EMS location models

In order to allocate limited resources in emergency medical services (EMS) networks, mathematical models are used to select sites and their capacities. Many existing standard models are based on simplifying assumptions, including site independency and a similar system-wide busyness of ambulances. In practice, when a site is busy, a call is forwarded to another site. Thus, the busyness of each site depends not only on the rate of calls in the surrounding area, but also on interactions with other facilities. If the demand varies across the urban area, assuming an average system-wide server busy fraction may lead to an overestimation of the actual coverage. We show that site interdependencies can be integrated into the well-known Maximum Expected Covering Location Problem (MEXCLP) by introducing an upper bound for the busyness of each site. We apply our new mathematical formulation to the case of a local EMS provider. To evaluate the solution quality, we use a discrete event simulation based on anonymized real-world call data. Results of our simulation-optimization approach indicate that the coverage can be improved in most cases by taking site interdependencies into account, leading to an improved ambulance allocation and a faster emergency care.