A minimum expected response model: Formulation, heuristic solution, and application

Responding to true emergencies in the shortest possible time saves lives, prevents permanent injuries and reduces suffering. Most covering models consider an emergency cover if an ambulance is available within a given time or distance threshold. From a modeling perspective, shorter or longer responses within this threshold are all tallied as covered; conversely, the emergencies immediately outside the threshold are considered uncovered. However, if the shorter responses are given more weight along with the volume of such incidents, while still meeting system-wide coverage requirements, both customers and providers can benefit from reduced response times. We formulate a model to determine the locations for a given set of ambulances to minimize the system-wide expected response distances while meeting coverage requirements. We solve the model with a heuristic search algorithm and present computational and comparative statistics using data from an existing Emergency Medical Services agency.