Background: This paper deals with the location of emergency medical stations where ambulances waiting to be dispatched are parked. The literature reports a lot of mathematical programming models used to optimize station locations. Most studies evaluate the models only analytically applying the same simplifying assumptions that were used in the modelling phase. In addition, they concentrate on systems operating one type of emergency units in homogeneous urban areas. The goal of our study is to identify which optimization criterion the emergency medical service (EMS) outcomes benefit from the most and which model should be used to design tiered systems in large urban–rural areas. Methods: A bi-criteria mathematical programming model is proposed. The criteria include the accessibility of high-priority patients within a short time limit and average response time to all patients. This model is being compared to the p-median model with a single response time objective and to a hierarchical pq-median model that considers two different vehicle types. A detailed computer simulation model is used to evaluate the solutions. The methodology is verified in the conditions of the Slovak Republic using real historical data on 149,474 ambulance trips performed in 2015. Results: All mathematical models improve EMS performance by relocating some stations compared to the current distribution. The best results are achieved by the hierarchical median-type model. The average response time is reduced by 58 s, the number of calls responded to within 15 min is increased by 5% and the number of high-priority calls responded to within 8 min by 6%. Conclusions: The EMS systems operating in heterogeneous areas should be designed to minimize response times, and not to maximize the number of calls served within a given time limit.

For design fair public service system using the weighted p-median problem exist some approaches which use reduction coefficients. These coefficients allow to take probability of failure/occupation of service center into account and to make the location-allocation model more realistic. If the nearest service center is occupied by some other user, the demand is served from the second nearest service center. In cases we have no data for calculating reduction coefficients from real data, can be a simulation model used. This paper describes creating the microscopic simulation model of emergency medical service system and publishes simulation results for reduction coefficients. The model was implemented under the conditions of the Slovak Republic in the simulation tool Anylogic. Travel times were calculated by using the transportation network data from the OpenStreetMap.

The reorganization of an emergency medical system means that we look for new locations of ambulance stations with the aim of improving the accessibility of the service. We applied two tools that are well known in the operations research community, namely mathematical programming, and computer simulation. Using the hierarchical pq-median model, we proposed optimal locations of the stations throughout the country and within large towns. Several solutions have been calculated that differ in the number of stations that are supposed to be relocated to new positions. The locations proposed by the mathematical programming model were evaluated via computer simulation. The approach was demonstrated under the conditions of the Slovak Republic using real historical data on ambulance dispatches. We have concluded that (i) the distribution of the stations proposed by the hierarchical pq-median model overcomes the current distribution; the performance of the system has significantly improved even if only 10% of the stations are relocated to new municipalities; (ii) the variant that relocates 40% of the stations is a reasonable compromise between the benefits and induced costs; (iii) optimizing station locations in big towns can significantly improve the local as well as the nationwide performance indicators; the response times in two regional capitals has reduced by more than 4 min.

This paper deals with optimizing the location of ambulance stations in a two-tiered emergency medical system in an urban environment. Several variants of station distribution are calculated by different mathematical programming models and are evaluated by a detailed computer simulation model. A new modification of the modular capacitated location model is proposed. Two ways of demand modelling are applied; namely, the aggregation of the ambient population and the aggregation of permanent residents at the street level. A case study of the city of Prešov, Slovakia is used to assess the models. The performance of the current and proposed sets of locations is evaluated using real historical data on ambulance trips. Computer simulation demonstrates that the modular capacitated location model, with the ambient population demand, significantly reduces the average response time to high-priority patients (by 79 s in the city and 62 s in the district) and increases the percentage of high-priority calls responded to within 8 min (by almost 4% in the city and 5% in the district). Our findings show that a significant improvement in the availability of the service can be achieved when ambulances are not accumulated at a few stations but rather spread over the city territory.