A Dispatching Model for Server-to-Customer Systems That Balances Efficiency and Equity

The decision about which servers to dispatch to which customers is an important aspect of service systems. This decision is complicated when servers must be equitably—as well as efficiently—dispatched to customers. In this paper, we formulate a model for determining how to optimally dispatch distinguishable servers to prioritized customers given a set of equity constraints. 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 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. Four types of equity constraints are considered—two of which reflect customer equity and two of which reflect server equity—all of which draw upon the decision analytic and social science literature to compare the effects of different notions of equity on the resulting dispatching policies. The Markov decision processes are formulated as equity-constrained linear programming models. A computational example is applied to an EMS system to compare the different equity models.