Data-Driven Models for Capacity Allocation of Inpatient Beds in a Chinese Public Hospital

Hospital beds are a critical but limited resource shared between distinct classes of elective patients. Urgent elective patients are more sensitive to delays and should be treated immediately, whereas regular patients can wait for an extended time. Public hospitals in countries like China need to maximize their revenue and at the same time equitably allocate their limited bed capacity between distinct patient classes. Consequently, hospital bed managers are under great pressure to optimally allocate the available bed capacity to all classes of patients, particularly considering random patient arrivals and the length of patient stay. To address the difficulties, we propose data-driven stochastic optimization models that can directly utilize historical observations and feature data of capacity and demand. First, we propose a single-period model assuming known capacity; since it recovers and improves the current decision-making process, it may be deployed immediately. We develop a nonparametric kernel optimization method and demonstrate that an optimal allocation can be effectively obtained with one year's data. Next, we consider the dynamic transition of system state and extend the study to a multiperiod model that allows random capacity; this further brings in substantial improvement. Sensitivity analysis also offers interesting managerial insights. For example, it is optimal to allocate more beds to urgent patients on Mondays and Thursdays than on other weekdays; this is in sharp contrast to the current myopic practice.