Inpatient bed allocation policy under uncertain capacity

This paper concerns the problem of inpatient bed allocation for two classes of patients (scheduled and non-scheduled) when there is uncertainty about daily available capacity. In the afternoon of each day, patients from the scheduled class, also called backlogged elective admissions, are selected from a waiting list, for the admission on the next day. The non-scheduled class, also called emergent admissions, are new requests that arise randomly each day with emergent needs. The capacity of available beds for a medical specialty to provide hospitalization services is uncertain when backlogged elective patients are chosen. Admitting too many of elective patients may result in exceeding a day’s capacity, which can potentially necessitate “overflowing” or “postponing” some emergent requests that should be performed as soon as possible. Therefore, the problem faced by the medical specialty facility at the decision-making point of each day is how many of the backlogged elective patients can be admitted. We formulate this problem as a Markov decision process (MDP) and study the structural properties of the model to characterize the nature of the optimal policy. We propose easy-to-implement policies (the fixed quota policy and the best fixed quota policy), which perform well under fitted distributions. By reporting numerical analyses using real data from a Chinese public hospital, we finally compare the improvements that our proposed solutions could bring to the hospital with the existing practices under several different cost structures.