Integrated Scheduling and Capacity Planning with Considerations for Patients' Length-of-Stays

Despite the fact that hospital care is often delivered in successive stages, current healthcare scheduling and capacity planning methods usually treat different hospital units in isolation. To address such a shortcoming, we introduce the first Markov decision process model for scheduling surgical patients on a daily basis, explicitly taking into account patient length-of-stay in hospital after surgeries and inpatient census. By way of a simple and yet innovative variable transformation, we reveal the hidden submodularity structure in our model. This transformation, in particular, allows us to show that the optimal number of patients to admit increases when the waitlist of surgical patients is longer, given the number of patients recovering downstream is fixed. We conduct extensive simulation experiments to study the applicability of our theoretical model in various settings. Our simulations based on real data demonstrate substantial values in making integrated scheduling decisions that simultaneously consider capacity usage at all locations in a hospital, especially when demand and system capacities are balanced or more elective patients present in the patient mix. The traditional scheduling policy, which is solely driven by operating room usage, however, can lead to significantly suboptimal use of downstream capacity and, as our numerical experiments show, may result in up to a three-fold increase in total expenses. In contrast, a scheduling policy based on downstream capacity usage often performs relatively close to the integrated scheduling policy, and therefore may serve as a simple, effective scheduling heuristic for hospital managers-especially when the downstream capacity is costly and less flexible.