The first case in this work concerns the problem of inpatient bed allocation for two classes of patients (scheduled and non-scheduled) that should be hospitalized each day. The research is motivated by an issue that has developed in the design of bed allocation and patient admission scheduling practices in a Chinese hospital: the West China Hospital (WCH). The scheduled class, also called backlogged elective admissions, are selected from a waiting list before their admission 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 hospitalization services is uncertain when backlogged elective patients are scheduled. Admitting too many of these 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. In this way, the problem faced by the hospital 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 which perform well under empirical distributions. Numerical analyses to confirm our theoretical results and practical insights are presented.

The second portion of this work is motivated by the appointment booking of specialist services at the ambulatory care center (ACC) in a major public hospital in Hong Kong. We study scheduling policies in a healthcare system in which patients’ waiting times for medical consultations are governed by the Hong Kong Hospital Authority. Specifically, the ACC accepts only advanced booking, and patients should receive consultation within a stipulated target waiting time. We study two forms of scheduling: allocation scheduling and advance scheduling. The decisions involved in the former are consultation quotas for each day, and the choices of the latter regard the specific consultation date for each patient. We formulate these two scheduling problems as discrete-time, finite horizon MDPs, and we develop a structure for optimal policies. To overcome the cure of dimensionality, we resort to the approximate dynamic programming approach. For the advance scheduling problem, we propose a heuristic policy that is based on the solution of allocation scheduling. We show that when the waiting time target is two periods, the heuristic policy is optimal. We conduct several numerical experiments to test the performance of the ADP-based heuristic policies for allocation scheduling and advance scheduling. The results show that for most of the settings, our proposed heuristic for advance scheduling outperforms several other policies implemented in practice.