Distributionally robust optimization of an emergency medical service station location and sizing problem with joint chance constraints

An effective Emergency Medical Service (EMS) system can provide medical relief supplies for common emergencies (fire, accident, etc.) or large-scale disasters (earthquake, tsunami, bioterrorism attack, explosion, etc.) and decrease morbidity and mortality dramatically. This paper proposes a distributionally robust model for optimizing the location, number of ambulances and demand assignment in an EMS system by minimizing the expected total cost. The model guarantees that the probability of satisfying the maximum concurrent demand in the whole system is larger than a predetermined reliability level by introducing joint chance constraints and characterizes the expected total cost by moment uncertainty based on a data-driven approach. The model is approximated as a parametric second-order conic representable program. Furthermore, a special case of the model is considered and converted into a standard second-order cone program, which can be efficiently solved with a proposed outer approximation algorithm. Extensive numerical experiments are conducted to illustrate the benefit of the proposed approach. Moreover, a dataset from a real application is also used to demonstrate the application of the data-driven approach.