Optimal ambulance location with random delays and travel times

We describe an ambulance location optimization model that minimizes the number of ambulances needed to provide a specified service level. The model measures service level as the fraction of calls reached within a given time standard and considers response time to be composed of a random delay (prior to travel to the scene) plus a random travel time. In addition to modeling the uncertainty in the delay and in the travel time, we incorporate uncertainty in the ambulance availability in determining the response time. Models that do not account for the uncertainty in all three of these components may overestimate the possible service level for a given number of ambulances and underestimate the number of ambulances needed to provide a specified service level. By explicitly modeling the randomness in the ambulance availability and in the delays and the travel times, we arrive at a more realistic ambulance location model. Our model is tractable enough to be solved with general-purpose optimization solvers for cities with populations around one Million. We illustrate the use of the model using actual data from Edmonton.