Integrated Scheduling and Capacity Planning with Considerations for Patients’ Length‐of‐Stays

Motivated by the shortcoming of current hospital scheduling and capacity planning methods which often model different units in isolation, we introduce the first dynamic multi-day scheduling model that integrates information about capacity usage at more than one location in a hospital. In particular, we analyze the first dynamic model that accounts for patients' length-of-stay and downstream census in scheduling decisions. Via a simple and innovative variable transformation, we show that the optimal number of patients to be allowed in the system is increasing in the state of the system and in the downstream capacity. Moreover, the total system cost exhibits decreasing marginal returns as the capacity increases at any location independently of another location. Through numerical experiments on realistic data, we show that there is substantial value in making integrated scheduling decisions. In contrast, localized decision rules that only focus on a single location of a hospital can result in up to 60% higher expenses.