Background: Helicopter emergency medical services (HEMS) are important in many health care systems. In order to best utilize this expensive healthcare service, the location of HEMS bases is key. Concurrency conflicts is a prominent deviation for not completing missions, yet is often overlooked in mathematical modelling. The aim of the present study was to calculate optimal air ambulance base locations when accounting for the potential unavailability of helicopters due to concurrency conflicts. Methods: We used incident data for Norway from 2015. Optimal helicopter base locations were estimated using the Maximum Expected Covering Location Problem (MEXCLP) optimization model, allowing for estimation of the impact of concurrency conflicts by introducing a busy fraction parameter in the model. We explored busy fractions of 0, 0.10, 0.20 and 0.30, representing helicopters on the HEMS bases being busy 0, 10, 20 and 30% of the time, respectively. Both greenfield scenarios and simulations conditioned on the existing base structure were explored. Results: The 428 municipalities had a median (5–95 percentile) of 10 (2–38) incidents. Assuming a helicopter is always available, the existing bases cover an estimated 73.6% of the incidents within 30 min. Increasing the busy fraction in the calculations resulted in a significant decrease in estimated coverage. Re-arranging the currently available 14 helicopters in a greenfield analysis increases coverage to 91.9%. Increasing the busy fraction in the models, the mathematically optimal solutions put increasingly more emphasis on the more densely populated greater Oslo area, removing helicopters from northern Norway and the coastal areas, where population is more spread. Conclusion: The busy fraction significantly impacts the optimal location of air ambulance bases, with higher busy fractions resulting in more helicopters being placed in the more densely populated areas where demand is higher. However, the actual busy fractions reported in the Norwegian HEMS system seem to be of a magnitude small enough to have little impact on the optimal location of HEMS bases and helicopters. To determine the impact of adjusting for non-homogeneous busy fractions across the country more refined busy fraction models are needed.

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.

Background: Helicopter emergency medical services are important in many health care systems. Norway has a nationwide physician manned air ambulance service servicing a country with large geographical variations in population density and incident frequencies. The aim of the study was to compare optimal air ambulance base locations using both population and incident data. Methods: We used municipality population and incident data for Norway from 2015. The 428 municipalities had a median (5-95 percentile) of 4675 (940-36,264) inhabitants and 10 (2-38) incidents. Optimal helicopter base locations were estimated using the Maximal Covering Location Problem (MCLP) optimization model, exploring the number and location of bases needed to cover various fractions of the population for time thresholds 30 and 45 min, in green field scenarios and conditioned on the existing base structure. Results: The existing bases covered 96.90% of the population and 91.86% of the incidents for time threshold 45 min. Correlation between municipality population and incident frequencies was -0.0027, and optimal base locations varied markedly between the two data types, particularly when lowering the target time. The optimal solution using population density data put focus on the greater Oslo area, where one third of Norwegians live, while using incident data put focus on low population high incident areas, such as northern Norway and winter sport resorts. Conclusion: Using population density data as a proxy for incident frequency is not recommended, as the two data types lead to different optimal base locations. Lowering the target time increases the sensitivity to choice of data.

Background Helicopter emergency medical services are an important part of many healthcare systems. Norway has a nationwide physician staffed air ambulance service with 12 bases servicing a country with large geographical variations in population density. The aim of the study was to estimate optimal air ambulance base locations. Methods We used high resolution population data for Norway from 2015, dividing Norway into >300 000 1 km×1 km cells. Inhabited cells had a median (5–95 percentile) of 13 (1–391) inhabitants. Optimal helicopter base locations were estimated using the maximal covering location problem facility location optimisation model, exploring the number of bases needed to cover various fractions of the population for time thresholds 30 and 45 min, both in green field scenarios and conditioning on the current base structure. We reanalysed on municipality level data to explore the potential information loss using coarser population data. Results For a 45 min threshold, 90% of the population could be covered using four bases, and 100% using nine bases. Given the existing bases, the calculations imply the need for two more bases to achieve full coverage. Decreasing the threshold to 30 min approximately doubles the number of bases needed. Results using municipality level data were remarkably similar to those using fine grid information. Conclusions The whole population could be reached in 45 min or less using nine optimally placed bases. The current base structure could be improved by moving or adding one or two select bases. Municipality level data appears sufficient for proper analysis.