Real-Time Ambulance Dispatching and Relocation

In this study, we develop a flexible optimization framework for real-time ambulance dispatching and relocation. In addition to ambulance redeployment, we consider a general dispatching and relocation strategy by which the decision maker has the option to (i) select any available ambulance to dispatch to a call or to queue the call and (ii) send an idle ambulance to cover the location of an ambulance just dispatched to a call. We formulate the problem as a stochastic dynamic program, and, because the state space is unbounded, an approximate dynamic programming (ADP) framework is developed to generate high-quality solutions. We assess the quality of our solutions by developing a lower bound on the expected response time and computing a lower bound on the expected fraction of late calls of any relocation policy. We test the performance of our policies and available benchmarks on an emergency medical services system in Mecklenburg County, North Carolina. The results show that our policies are near optimal and significantly outperform available benchmarks. In particular, our ADP policy reduces the expected response time and fraction of high-priority late calls by 12% and 30.6%, respectively, over the best available static benchmarks in the case study. Moreover, the results provide insights on the contribution of each dispatching, redeployment, and reallocation strategy.