Modeling congestion in a competitive Facility Location Problem

Assigning the right Emergency Room (ER) to persons in medical need is a pivotal mission of the Emergency Medical Dispatcher (EMD). In order to minimize the delay between the call and the medical care, EMD need to take into account the travel time and the waiting time at the an ER. The goal of opening an ER is to maximize the demand capture, either to make profit or to relieve other ERs. To achieve this, it is possible to locate the facilities and assign them capacity of service: number of beds or staff members. In this report, a non-linear integer programming formulation is established to model this type of allocation. The formulation is agent-based to encompass individual disparities through discrete choice modelling (DCM).