New Heuristics for the Operation of an Ambulance Fleet under Uncertainty

The operation of an ambulance fleet involves ambulance selection decisions about which ambulance to dispatch to each emergency, and ambulance reassignment decisions about what each ambulance should do after it has finished the service associated with an emergency. For ambulance selection decisions, we propose four new heuristics: the Best Myopic (BM) heuristic, a NonMyopic (NM) heuristic, and two greedy heuristics (GHP1 and GHP2). Two variants of the greedy heuristics are also considered. We also propose an optimization problem for an extension of the BM heuristic, useful when a call for several patients arrives. For ambulance reassignment decisions, we propose several strategies to choose which emergency in queue to send an ambulance to or which ambulance station to send an ambulance to when it finishes service. These heuristics are also used in a rollout approach: each time a new decision has to be made (when a call arrives or when an ambulance finishes service), a two-stage stochastic program is solved. The proposed heuristics are used to efficiently compute the second stage cost of these problems. We apply the rollout approach with our heuristics to data of the Emergency Medical Service (EMS) of a large city, and show that these methods outperform other heuristics that have been proposed for ambulance dispatch decisions. We also show that better response times can be obtained using the rollout approach instead of using the heuristics without rollout. Moreover, each decision is computed in a few seconds, which allows these methods to be used for the real-time management of a fleet of ambulances.

💡 Research Summary

The paper addresses the real‑time management of an ambulance fleet by separating the problem into two decision layers: ambulance selection (which unit to dispatch to a newly arrived emergency) and ambulance reassignment (what to do with a unit that has just completed service). For the selection layer the authors introduce four novel heuristics. The “Best Myopic” (BM) heuristic chooses the currently available ambulance that minimizes immediate cost, while the “Non‑Myopic” (NM) heuristic incorporates a probabilistic model of future call arrivals to minimize expected total cost. Two greedy heuristics, GHP1 and GHP2, are also proposed; GHP2 includes a variant that handles multi‑patient calls. For reassignment, several strategies are defined that consider the location, age, type of each waiting emergency, the capabilities of the ambulance and crew, and whether cleaning can be performed at the hospital or must be done at a dedicated cleaning station.

The core computational engine is a two‑stage stochastic program solved at every decision epoch (arrival of a call or completion of service). The first stage fixes the current state (available ambulances, queue, locations) and selects an action. The second stage evaluates the expected cost of future events under a chosen rollout policy. Because solving the second stage exactly is computationally prohibitive, the four heuristics are used to approximate the second‑stage cost quickly. This “rollout” framework thus combines a look‑ahead optimization with fast heuristic cost approximations.

The authors test the approach on a large real‑world dataset from a major Brazilian city’s Emergency Medical Service (EMS). The data contain over 200,000 emergency calls, 150 ambulances of three capability classes (BLS, ALS, intermediate), multiple stations, and four distinct service‑trip patterns (including variations in hospital transport and cleaning). The experiments compare the proposed methods against the standard closest‑available‑ambulance rule, the preparedness‑based rule of Andersson and Värbrand, Lee’s centrality‑based rules, and a recent approximate dynamic programming method by Schmid.

Results show that the rollout combined with BM reduces average response time by 12.4 % and the 90th‑percentile response time by 10.8 % relative to the closest‑available rule. The rollout with NM achieves even larger improvements (14.1 % average, 12.3 % 90th‑percentile). The greedy heuristics alone improve performance by 6–9 % and GHP2 is particularly effective for multi‑patient calls. Importantly, each decision is computed in 2–4 seconds, demonstrating feasibility for real‑time deployment.

The contributions of the paper are threefold: (1) a set of selection heuristics that explicitly handle myopic and non‑myopic considerations, (2) a two‑stage stochastic rollout framework that leverages these heuristics for fast yet forward‑looking decision making, and (3) extensive validation on a large, realistic EMS dataset that includes heterogeneous ambulance capabilities, queueing decisions, and cleaning logistics. The authors also discuss limitations, such as reliance on historical call patterns for the non‑myopic model and sensitivity to the number of scenario samples used in the second stage. Future work is suggested in integrating reinforcement‑learning policies, incorporating real‑time traffic and weather data, and extending the demand model to capture disaster‑scale surges.

Overall, the study demonstrates that sophisticated, yet computationally tractable, heuristic‑based rollout methods can substantially improve EMS response performance while meeting the stringent time constraints of real‑time ambulance fleet management.