We address the problem of dynamic ambulance repositioning, in which the goal is to minimize the expected fraction of late arrivals. The decisions on how to redeploy the vehicles have to be made in real time, and may take into account the status of all other vehicles and accidents. This is generally considered a difficult problem, especially in urban areas, and exact solution methods quickly become intractable when the number of vehicles grows. Therefore, there is a need for a scalable algorithm that performs well in practice.We propose a polynomial-time heuristic that distinguishes itself by requiring neither assumptions on the region nor extensive state information. We evaluate its performance in a simulation model of emergency medical services (EMS) operations. We compare the performance of our repositioning method to so-called static solutions: a classical scenario in which an idle vehicle is always sent to its predefined base location. We show that the heuristic performs better than the optimal static solution for a tractable problem instance. Moreover, we perform a realistic urban case study in which we show that the performance of our heuristic is a 16.8% relative improvement on a benchmark static solution. The studied problem instances show that our algorithm fulfils the need for real-time, simple redeployment policies that significantly outperform static policies.
We address the problem of ambulance dispatching, in which we must decide which ambulance to send to an incident in real time. In practice, it is commonly believed that the 'closest idle ambulance' rule is near-optimal and it is used throughout most literature. In this paper, we present alternatives to the classical closest idle ambulance rule. Most ambulance providers as well as researchers focus on minimizing the fraction of arrivals later than a certain threshold time, and we show that significant improvements can be obtained by our alternative policies. The first alternative is based on a Markov decision problem (MDP), that models more than just the number of idle vehicles, while remaining computationally tractable for reasonably-sized ambulance fleets. Second, we propose a heuristic for ambulance dispatching that can handle regions with large numbers of ambulances. Our main focus is on minimizing the fraction of arrivals later than a certain threshold time, but we show that with a small adaptation our MDP can also be used to minimize the average response time. We evaluate our policies by simulating a large emergency medical services region in the Netherlands. For this region, we show that our heuristic reduces the fraction of late arrivals by 18 % compared to the 'closest idle' benchmark policy. A drawback is that this heuristic increases the average response time (for this problem instance with 37 %). Therefore, we do not claim that our heuristic is practically preferable over the closest-idle method. However, our result sheds new light on the popular belief that the closest idle dispatch policy is near-optimal when minimizing the fraction of late arrivals.
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