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 pa-tients 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.