Fairness in the Ambulance Location Problem: Maximizing the Bernoulli-Nash Social Welfare

In this paper we discuss how to position ambulances across an EMS region in a fair way. We argue that an appropriate measure of fairness is the so-called Bernoulli-Nash Social Welfare Function. We introduce a mathematical model that determines the ambulance configuration that maximizes this welfare measure. This fairness is contrasted with the more classical ambulance models that aim for efficiency by maximizing the overall average performance. We juxtapose the Bernoulli-Nash optimal solution with the most efficient solution and show that the most efficient ambulance configuration benefits people living in cities, at the cost of people living in remote areas. The Bernoulli-Nash solution on the other hand, provides a more balanced performance across the region. Furthermore, we demonstrate how our model can be applied using a variety of performance measures, such as a survival function and the probability of an ambulance arriving within a response time threshold. Our numerical work uses a case study based on one of the Netherlands’ largest EMS regions.