Optimal placement of ambulance stations using data-driven direct and surrogate search methods.

Objective: In this paper, we implement and validate a set of optimization approaches that were applied on ambulance data from the Västerbotten county in Sweden collected 2018, with the objective to find the optimal placement of the ambulance stations (or stand-by positions) in Umeå, a municipality in the county with regards to median of response times for priority 1 alarms, the most urgent type of alarms (MRT1).

Methods: Here, we use data-driven approaches for optimizing the placement of ambulance stations. For a given allocation, i.e. placement of the stations, a large-scale simulation is conducted to estimate the allocation's MRT1. Since the inherent mechanism of the simulation function is very complex, the optimization problem has a black-box nature. We use two methods belonging to important classes for solving the problem of black-box optimization: GPS (smooth-free) and surrogate (smooth-based) methods. Both methods can be used on either local or global data and implemented using a one-by-one approach or an all-together approach. To study the mentioned methods and approaches, we consider several real-world scenarios pertaining to the placement of ambulance stations in Umeå municipality.

Results: Relocating the ambulance stations in Umeå can reduce MRT1 around 80-100 seconds in comparison with the current allocation. Using global data leads to better solutions with lower MRT1-values, although they demand more computational time. The results of GPS and surrogate methods are similar, but the surrogate method is less sensitive to the starting position. One-by-one approach is more effective and less time-consuming than the all-together approach.

Conclusion: The results confirm that relocating ambulance stations can lead to a significant decrease in MRT1 and it also can compensate for the loss of an ambulance resource partially. To reduce the dimensionality and the cost of optimization methods, it can be better to use one-by-one approach than all-together.