Solving the dynamic ambulance relocation and dispatching problem using approximate dynamic programming

Emergency service providers are supposed to locate ambulances such that in case of emergency patients can be reached in a time‐efficient manner. Two fundamental decisions and choices need to be made real‐time. First of all immediately after a request emerges an appropriate vehicle needs to be dispatched and send to the requests’ site. After having served a request the vehicle needs to be relocated to its next waiting location. We are going to propose a model and solve the underlying optimization problem using approximate dynamic programming (ADP), an emerging and powerful tool for solving stochastic and dynamic problems typically arising in the field of operations research. Empirical tests based on real data from the city of Vienna indicate that by deviating from the classical dispatching rules the average response time can be decreased from 4.60 to 4.01 minutes, which corresponds to an improvement of 12.89%. Furthermore we are going to show that it is essential to consider time‐dependent information such as travel times and changes with respect to the request volume explicitly. Ignoring the current time and its consequences thereafter during the stage of modeling and optimization leads to suboptimal decisions.