An optimal dispatching model for server-to-customer systems with classification errors

The decision of which servers to dispatch to which customers is an important aspect of serverto-customer systems. Such decisions are complicated when servers have different operating characteristics, customers are prioritized, and there are errors in assessing customer priorities. In this paper, we formulate a model for determining how to optimally dispatch distinguishable 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 model is developed that captures how to optimally dispatch ambulances (servers) to prioritized patients (customers). It is assumed that customers arrive sequentially, with the priority and location of each customer becoming known upon arrival, with classification errors in these customer priorities. The proposed model determines how to optimally dispatch heterogeneous servers to customers to maximize the long run average utility in a Markov decision process. The utilities and transition probabilities are location-dependent, with respect to both the server and customer locations. The analysis considers two cases for approaching the classification errors that correspond to overand underresponding to perceived customer priority. A computational example is applied to an EMS system in order to determine the optimal policy for dispatching ambulances to patients in order to maximize patient survival.