Using the “Floating Patients” method to balance crowding between the hospital emergency department and other departments

This paper proposes a model and a corresponding scheduling algorithmic approach to reduce crowding in an emergency department (ED), and to provide patients with faster and better service. This approach relies on the “Floating Patients” (FP) method, in which the ED triage can send some patients directly to hospitalization departments instead of providing them with full examinations in the ED. In contrast to previous work in this vein, our technique takes a holistic approach, considering crowding not only in the ED but also in other departments in the hospital. It also considers the extent to which information has been made available about the patient's condition (e.g., through referring physicians), in addition to other factors such as the severity of the patient's condition and the effect of crowding on treatment time. A key benefit of this method is that it enables triage staff (the decision maker) to control and balance the crowding in the ED with crowding in other hospitalization departments. We define the model and propose an efficient Fully Polynomial Time Approximation Scheme (FPTAS) to solve it. In addition, we present a numerical example to validate our approach.