Over the years, several ambulance location models have been discussed in the literature. Most of these models have been further developed to take more complicated situations into account. However, the existing standard models that are often used in case studies have never been compared computationally according to the criteria used in practice. In this paper, we compare several ambulance location models on coverage and response time criteria. In addition to four standard ambulance location models from the literature, we also present two models that focus on average and expected response times. The computational results show that the maximum expected covering location problem (MEXCLP) and the expected response time model (ERTM) perform the best over all considered criteria. However, as the computation times for ERTM are long, the average response time model (ARTM) could be a good alternative. Based on these results, we also propose four alternative models that combine the good coverage provided by MEXCLP and the quick response times provided by ARTM. All four considered models provide balanced solutions in terms of coverage and response times. However, the multiple response times target model (MRTTM) outperforms the other models based on computation time.

Many ambulance providers operate both advanced life support (ALS) and basic life support (BLS) ambulances. Typically, only an ALS ambulance can respond to an emergency call, whereas non-urgent patient transportation requests can be served by either an ALS or a BLS ambulance. The total capacity of BLS ambulances is usually not enough to fulfill all non-urgent transportation requests. The remaining transportation requests then have to be performed by ALS ambulances, which reduces the coverage for emergency calls. We present a model that determines the routes for BLS ambulances while maximizing the remaining coverage by ALS ambulances. Different from the classical dial-a-ride problem, only one patient can be transported at a time, and not all requests are known in advance. Throughout the day, new requests arrive, and we present an online model to deal with these requests.

Background Ambulance services play a crucial role in providing pre-hospital emergency care. In order to ensure quick responses, the location of the bases, and the distribution of available ambulances among these bases, should be optimized. In mixed urban-rural areas, this optimization typically involves a trade-off between backup coverage in high-demand urban areas and single coverage in rural low-demand areas. The aim of this study was to find the optimal distribution of bases and ambulances in the Vestfold region of Norway in order to optimize ambulance coverage. Method The optimal location of bases and distribution of ambulances was estimated using the Maximum Expected Covering Location Model. A wide range of parameter settings were fitted, with the number of ambulances ranging from 1 to 15, and an average ambulance utilization of 0, 15, 35 and 50%, corresponding to the empirical numbers for night, afternoon and day, respectively. We performed the analysis both conditioned on the current base structure, and in a fully greenfield scenario. Results Four of the five current bases are located close to the mathematical optimum, with the exception of the northernmost base, in the rural part of the region. Moving this base, along with minor changes to the location of the four other bases, coverage can be increased from 93.46% to 97.51%. While the location of the bases is insensitive to the workload of the system, the distribution of the ambulances is not. The northernmost base should only be used if enough ambulances are available, and this required minimum number increases significantly with increasing system workload. Conclusion As the load of the system increases, focus of the model shifts from providing single coverage in low-demand areas to backup coverage in high-demand areas. The classification rule for urban and rural areas significantly affects results and must be evaluated accordingly.

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 – unknown – optimal 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.

Since ambulance providers are responsible for life-saving medical care at the scene in emergency situations and since response times are important in these situations, it is crucial that ambulances are located in such a way that good coverage is provided throughout the region. Most models that are developed to determine good base locations assume strict 0-1 coverage given a fixed base location and demand point. However, multiple applications require fractional coverage. Examples include stochastic, instead of fixed, response times and survival probabilities. Straightforward adaption of the well-studied MEXCLP to allow for coverage probabilities results in a non-linear formulation in integer variables, limiting the size of instances that can be solved by the model. In this paper, we present a linear integer programming formulation for the problem. We show that the computation time of the linear formulation is significantly shorter than that for the non-linear formulation. As a consequence, we are able to solve larger instances. Finally, we will apply the model, in the setting of stochastic response times, to the region of Amsterdam, the Netherlands.