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.

Providers of Emergency Medical Services (EMS) are typically concerned with keeping response times short. A powerful means to ensure this, is to dynamically redistribute the ambulances over the region, depending on the current state of the system. In this paper, we provide new insight in how to optimally (re)distribute ambulances. We study the impact of (1) the frequency of redeployment decision moments, (2) the inclusion of busy ambulances in the state description of the system, and (3) the performance criterion on the quality of the distribution strategy. In addition, we consider the influence of the EMS crew workload, such as (4) chain relocations and (5) time bounds, on the execution of an ambulance relocation. To this end, we use trace-driven simulations based on a real-life dataset of ambulance providers in the Netherlands. In doing so, we differentiate between rural and urban regions, which typically face different challenges when it comes to EMS. Our results show that: (1) taking the classical 0-1 performance criterion for assessing the fraction late arrivals only differs slightly from taking expert-opinion based S-curve for evaluating *

Providers of Emergency Medical Services (EMS) face the online ambulance dispatch problem, in which they decide which ambulance to send to an incoming incident. Their objective is to minimize the fraction of arrivals later than a target time. Today, the gap between existing solutions and the optimum is unknown, and we provide a bound for this gap.Motivated by this, we propose a benchmark model (referred to as the offline model) to calculate the optimal dispatch decisions assuming that all incidents are known in advance. For this model, we introduce and implement three different methods to compute the optimal offline dispatch policy for problems with a finite number of incidents. The performance of the offline optimal solution serves as a bound for the performance of an -unknownoptimal online dispatching policy.We show that the competitive ratio (i.e., the worst case performance ratio between the optimal online and the optimal offline solution) of the dispatch problem is infinitely large; that is, even an optimal online dispatch algorithm can perform arbitrarily bad compared to the offline solution. Then, we performed benchmark experiments for a large ambulance provider in the Netherlands. The results show that for this realistic EMS system, when dispatching the closest idle vehicle to every incident, one obtains a fraction of late arrivals that is approximately 2.7 times that of the optimal offline policy. We also analyze another online dispatch heuristic, that manages to reduce this gap to approximately 1.9. This constitutes the first quantification of the gap between online and offline dispatch policies.

Background A primary task of the Norwegian helicopter emergency medical services (HEMS) is to provide advanced medical care to the critical ill and injured outside of hospitals. Where HEMS bases are located, directly influences who in the population can be reached within a given response time threshold and who cannot. When studying the locations of bases, the focus is often on efficiency, that is, maximizing the total number of people that can be reached within a given set time. This approach is known to benefit people living in densely populated areas, such as cities, over people living in remote areas. The most efficient solution is thus typically not necessarily a fair one. This study aims to incorporate fairness in finding optimal air ambulance base locations. Methods We solve multiple advanced mathematical optimization models to determine optimal helicopter base locations, with different optimization criteria related to the level of aversion to inequality, including the utilitarian, Bernoulli-Nash and iso-elastic social welfare functions. This is the first study to use the latter social welfare function for HEMS. Results Focusing on efficiency, a utilitarian objective function focuses on covering the larger cities in Norway, leaving parts of Norway largely uncovered. Including fairness by rather using an iso-elastic social welfare function in the optimization avoids leaving whole areas uncovered and in particular increases service levels in the north of Norway. Conclusions Including fairness in determining optimal HEMS base locations has great impact on population coverage, in particular when the number of base locations is not enough to give full coverage of the country. As results differ depending on the mathematical objective, the work shows the importance of not only looking for optimal solutions, but also raising the essential question of ‘optimal with respect to what’.

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This paper reports on the results of the VeRoLog Solver Challenge 2016-2017: the third solver challenge facilitated by VeRoLog, the EURO Working Group on Vehicle Routing and Logistics Optimization. The authors are the winners of second and third places, combined with members of the challenge organizing committee. The problem central to the challenge was a rich VRP: expensive and therefore scarce equipment was to be redistributed over customer locations within time windows. The difficulty was in creating combinations of pickups and deliveries that reduce the amount of equipment needed to execute the schedule, as well as the lengths of the routes and the number of vehicles used. This paper gives a description of the solution methods of the above-mentioned participants. The second place method involves sequences of 22 low level heuristics: each of these heuristics is associated with a transition probability to move to another low level heuristic. A randomly drawn sequence of these heuristics is applied to an initial solution, after which the probabilities are updated depending on whether