Applying Distributionally Robust Optimization frameworks to tackle travel-time uncertainty in the ambulance location and dispatching problem

The efficient management of Emergency Medical Services (EMS) relies on the strategic location of ambulances and their optimal dispatching, two decisions that are inherently challenged by considerable uncertainty. This paper addresses the ambulance location and dispatching problem under uncertain travel times, a factor often overlooked in the literature that nonetheless plays a critical role in response times. Travel-time uncertainty is represented by a finite, data-driven set of candidate probability distributions fitted to historical data. On this set we build three distribution-aware frameworks: a min–max model over the candidate set (Distributionally Robust Optimization), a model that averages performance over the set (Distributionally Stochastic Optimization), and a scenario-robust extension (Distributionally scenario Robust Optimization). The performance of the solutions they produced to a manageable subset of scenarios (in-sample experiments) is evaluated on different realizations of travel-time uncertainty (out-of-sample experiments) constructed on historical data from the EMS in the Basque Country (Spain). The results highlight the importance of explicitly modeling travel-time uncertainty in EMS system design. Finally, a Discrete Event Simulation model allows assessing the behavior of those solutions when the spatial and temporal variability of emergency call patterns are incorporated. The distribution-aware solutions align with Stochastic Optimization in similar average response time while improving the response time attained under the most adverse candidate distribution, and they avoid the conservatism of Robust Optimization.