Ambulance dispatching and relocation problem considering overcrowding of emergency departments

An important issue in emergency medical services (EMS) is ambulance dispatching and relocation. EMS response time is usually measured by the response time of an ambulance (RTA), the time between receiving a call and the ambulance's arrival at the scene. EMS's success also depends on response time to the patient (RTP), the time between receiving a call and starting the service to the patient in a hospital. This study aims to use RTP to decide about ambulance dispatching and relocation. RTP is affected by the distance of the patient to the chosen hospital and the crowding in the hospital. Thus, this study integrates ambulance dispatching and relocation with hospital selection to better provide both RTA and RTP along with coverage while considering an overcrowded emergency department (ED). A mixed-integer linear programming model is developed to solve the proposed problem. The model's performance and the impact of the ED overcrowding factor have been examined in the context of a real case study from Utrecht, Netherlands. Findings reveal that considering RTP in joint ambulance dispatching and relocation has a 39% positive impact on the patient's average response time. Further, considering ED crowding with RTP results in 91% and 9% improvement in RTP and RTA with the same demand coverage, compared to typical ambulance dispatching and relocation problems, respectively.