In this study, researchers initiate an approach combining spatial information and integer optimization for emergency medical service location planning. Emergency medical services have been established in many countries all over the world. Good first care improves the outcome of patients in terms of hospital stay duration, chances of full recovery and of treatment costs.

The research is motivated by a recent call for bids to restructure the location of emergency medical services in the Austrian federal state of Lower Austria by the local state government. Our framework allows for constraints on the places where an emergency care physician is stationed. 

Accounting for the fact that for economic reasons, it might not be feasible to arbitrarily place emergency care physicians. We use maximum coverage linear programs to get accurate solutions for the problem instances (depending on the maximum allowed number of emergency care physicians and the constraints of their placement).

We optimize for the maximum number of covered residents given certain parameters. The travelling distances are calculated by means of a digital road graph. Moreover, we analyze the coverage of the day population as there are significant shifts in the number of persons present at daytime.

For every problem instance we have calculated the ten best solutions and examined the variance among them. For the demand point aggregation we have used a cell grid. Using our method we can show that with less emergency care physicians more residents can be covered.

This is highly applicable to low populated areas where the coverage becomes better. There is little variance from the best to the second best solution: There are only small changes (usually only one cell is shifted) between the best and the second best solution. The coverage of the day population except for a few problem instances is always better than the coverage of the residents (reflecting the fact that many residents commute to more densely populated areas).

In our study, researchers show that their solutions provide better coverage of residents with fewer emergency care physicians than the status.