Designing Ambulance Service Districts Under Uncertainty

For ambulances, quick response to a medical emergency is critical. Limiting response area for each ambulance may lead to shorter response times to emergency scenes and more evenly distributed workload for ambulances. We propose a two-stage stochastic mixed-integer programming model to address the service district design problem under uncertainty. The proposed model recommends how to locate ambulances to the waiting sites in the service area, and how to assign a set of demand zones to each ambulance at different backup levels. Our proposed Stochastic Service District Design (SSDD) model enables quick response times by jointly addressing the location and dispatching policies in a stochastic and dynamic environment. Each backup level is associated with a given response time threshold. The objective function is to maximize the expected number of covered calls while restricting the workload of each ambulance. The proposed model can be optimized offline as is commonly done for “patrol-beats” used in policing models. We evaluate the implementation of the proposed model via a discrete-event simulation, and compare the model with two baseline policies. Our computational results show a significant improvement in mean response time, reduction of 2 min, and statistically lower average workload of ambulances, of 4% on average, when the proposed model is fully implemented.