A model for optimally dispatching ambulances to emergency calls with classification errors in patient priorities

The decision of which servers to dispatch to which customers is an important aspect of service systems. Such decisions are complicated when servers have different operating characteristics, customers are prioritized, and there are errors in assessing customer priorities. This article formulates a model for determining how to optimally dispatch servers to prioritized customers given that dispatchers make classification errors in assessing the true customer priorities. These issues are examined through the lens of Emergency Medical Service (EMS) dispatch, for which a Markov Decision Process (MDP) model is developed that captures how to optimally dispatch ambulances (servers) to prioritized patients (customers). It is assumed that patients arrive sequentially, with the location and perceived priority of each patient becoming known upon arrival. The proposed model determines how to optimally dispatch ambulances to patients to maximize the long-run average utility of the system, defined as the expected coverage of true high-risk patients. The utilities and transition probabilities are location dependent, with respect to both the ambulance and patient locations. The analysis considers two cases for approaching the classification errors that correspond to over- and under-responding to perceived patient risk. A computational example is applied to an EMS system. The optimal policies under different classification strategies are compared to a myopic policy and the effect that classification errors have on the performance of these policies is examined. Simulations suggest that the policies remain effective when they are applied to more realistic situations.