New Heuristics for the Operation of an Ambulance Fleet under Uncertainty

Abstract

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.

Figures (15)

• Figure 1: Sequences of trips for the classes of service $C_{1}$, $C_{2}$, $C_{3}$, $C_{4}$. The letters above the time axis represent locations for the corresponding time instants. Specifically, CA: call arrival, D: departure of the ambulance to the emergency scene, C: emergency scene, H: hospital, CB: cleaning station, B: staging station. Also, the trip type numbers 2, 3, 4, 5, 6, 7, and 8 are shown above the time axis for all classes of service. These trip type numbers correspond to those used in websiteambrouting24. indexAmb is the index of the allocated ambulance.
• Figure 2: Discretization of the service region of Rio de Janeiro SAMU into $10 \times 10$ rectangles, and a heatmap of the intensity of emergency call rates aggregated by emergency type and time period for the period January 2016--February 2018.
• Figure 3: Aggregated estimates of the intensities over the week for 3 estimators: (i) Empirical: the empirical intensities, (ii) Rectangular $10 \times 10$: regularized model with the $10 \times 10$ rectangular space discretization, and (iii) Covariates, rectangular $10 \times 10$: model with covariates with the $10 \times 10$ rectangular space discretization.
• Figure 4: Mean allocation costs for each heuristic.
• Figure 5: Mean allocation costs for each rollout heuristic.

Theorems & Definitions (6)

• Example 2.1
• Example 2.2
• Example 4.1
• Example 7.1
• Example 7.2
• Example 7.3