A stochastic programming model for ambulance (re)location–allocation under equitable coverage and multi-interval response time

Abstract

Emergency Medical Services are essential for health systems as their effective management can improve patient prognosis. Nevertheless, designing an optimized distribution of resources is a difficult task due to the complex nature of these systems. Moreover, locating the resources is particularly challenging in heterogeneous density territories where, in addition to their efficient management, the equity principle in the medical access of inhabitants of rural areas is also desirable. This paper approaches the ambulance (re)location–allocation problem in the geographical area of the Basque Country. The area has three major cities, which account for a third of the emergencies, while there are few emergencies in rural areas, with a sparse population. To that end, a two-stage stochastic 0-1 integer linear programming model that balances the response time between densely populated and isolated areas is proposed. Specifically, the model incorporates two relevant principles: (1) optimizing emergency attendance through the option of allocating ambulances via a multi-interval response time and (2) equitably responding to emergencies so remote areas are not neglected. Conducted experiments have been validated and indicate that the proposed model can improve the success rate in rural areas by 23 percentage points, while reducing the overall success rate by less than 9 percentage points.