An alternative scheduling approach for improving patient-flow in emergency departments

Overcrowding in hospitals, along with long lengths of stay, high arrival rates, budget constraints, and increasing demand for high service quality, create challenges for the work-flow and patient flow of hospital emergency departments (EDs). This paper proposes an algorithmic approach that seeks to enable ED decision makers (specifically, in the triage) to optimally schedule evaluations for patients who are waiting for treatment in the ED. The algorithm is an expansion of Karp’s job sequencing with deadlines problem Karp (1972) and is embedded in a simulation model. From a managerial perspective, overcrowding can cause substantial profit–loss to the ED and the other departments. We assume that, in order to prevent this profit–loss, the hospital management determines a maximal (fixed or dynamic) value for patients’ length of stay and for crowding levels in various departments, and that patients who cannot be evaluated in the ED in a timely fashion are redirected for treatment in other hospital departments. The latter approach (referred to as the ”floating patient” method) is practiced, for example, in Israel. To build the algorithm, we solve this problem gradually; first we solve a scenario in which the triage decision maker has full information on patients’ conditions and on how long their ED-treatments are expected to take. We then extend this problem in order to incorporate uncertainty as in real life scenarios: The triage decision maker (physician) needs to carry out initial examinations to obtain information on patient attributes and, at each point in time, decides whether to continue to examine patients or to stop the process (halting rule) and ”float” the remaining patients to other departments. Next, the physician determines the optimal schedule for the full ED evaluations of the examined patients. We embed the algorithm into a simulation procedure and run simulations using empirical data from a hospital in Israel. Implementation of the ”floating patient” method is shown to reduce patients’ length of stay, queues for beds in departments and the ED, and cumulative treatment time in the ED. These improvements reflect a better balance of work-rate and crowding between the ED and the other departments.