Near-Optimal Dispatch Policies for Emergency Medical Services

Problem definition: Emergency medical services (EMS) are vital for ensuring timely and effective healthcare delivery. Ambulance dispatching in EMS directly influences patient outcomes. These systems face the challenge of managing limited resources to respond promptly to emergency calls while maintaining the capacity to address potential future incidents. Methodology/results: We model the problem as a continuous-time stochastic system and determine the dispatch decision for each sequentially arriving call to minimize the system-wide average cost. To address this problem, we develop an easy-to-implement and near-optimal policy based on Lagrangian relaxation of the original problem. Using a novel proof technique, we show that our policy achieves performance within $O(\sqrt{1/\theta })$ of the optimal, where $\theta$ represents the scaling factor for the number of ambulances and arrival rates. Additionally, in the low-traffic regime, where arrival and service rates are scaled such that traffic intensity approaches zero, our policy remains asymptotically optimal. Managerial implications: Numerical experiments show that the proposed policy performs well compared with optimal solutions. The results also demonstrate the benefits of proactively deploying flexible units, while requiring only infrequent use of this resource. This also supports a key insight: a small amount of flexibility, when used strategically, can enhance system efficiency. Our case study, based on real data from New York City, further shows that the proposed policy effectively reduces system costs associated with patient response times. Empirically, it consistently outperforms widely used benchmark policies in both small and large system settings.

Funding: C. Hua was partly supported by the National Natural Science Foundation of China [Grants 72301172, 72394370:72394375, and 72495130:72495132] and Shanghai Jiao Tong University Office of Liberal Arts [Grant ZHWK2502]. T. Wang was partly supported by the National Natural Science Foundation of China [Grants 72221001, 72192833/72192830, and 72131010] and the Research Grants Council of Hong Kong [Grant GRF 11502225]. J. Zhang was partly supported by the National Natural Science Foundation of China [Grant 72394361] and the Guangdong Provincial Key Laboratory of Mathematical Foundations for Artificial Intelligence [Grant 2023B1212010001]. Z. Zhou was partly supported by the National Natural Science Foundation of China [Grants 72588101 and 72571231].

Supplemental Material: The online appendix is available at https://doi.org/10.1287/msom.2025.0529.