Public Hospital Inpatient Room Allocation and Patient Scheduling Considering Equity

Abstract

This article studies the optimal allocation of inpatient rooms for multiple types of patients in public hospitals and the patient scheduling problem with planned acceptance ratios (ARs). For public hospitals, it is important to allocate limited resources to multiple types of patients and manage patient access for maximizing hospital revenue and upholding service equity. The problem is formulated as two-stage models. Considering uncertainties in patients’ arrival and length of stay, we first propose a nonlinear stochastic programming (NSP) model for inpatient room allocation with the objective of maximizing revenue under the constraints of maintaining equity. To solve this problem, we transform the complex NSP model into a deterministic mixed-integer linear programming model, which is solved by CPLEX, by reformulating the chance constraints as knapsack constraints based on a linearization technique and a simulation model. Given the allocated capacity and planned AR, we further propose a two-stage stochastic mixed-integer program combined with a goal program model to optimize patient scheduling. To solve the model, a Benders decomposition based on the sample average approximation approach is proposed. The real data-based experimental results demonstrate the applicability and effectiveness of our models and approaches. The impacts of some parameters on the objective and decisions are also explored. A simulation procedure is developed to compare the performances of different patient scheduling methods, from which the results show that our proposed approach outperforms a benchmark policy. Note to Practitioners —Inpatient rooms are critical resources for hospitals. Against the background of aging populations and environmental problems, the twofold predicament—involving escalating healthcare demands and insufficient room-based resources—has led to the necessity for hospitals to operate more effectively and efficiently. Capacity management and patient scheduling are thus the two most important operations for hospital management. Because of the self-financing feature of hospitals and the quasi-public nature of medical services, it is important for public hospitals to judiciously allocate limited room capacities to multiple types of patients for balancing revenue and equity and schedule the arrival demands dynamically according to the planned capacity and acceptance ratio. In this article, we propose mathematical models and solution approaches for these two-stage problems, and their applicability and effectiveness are demonstrated by experiments based on real data. The managerial insights suggest that hospitals should improve the service equity gradually according to their financial situation because of the increasing marginal cost and should apply the scientific approaches and techniques, rather than by their experiences, to aid their management for better performance. By using approaches proposed in this article, hospital managers can be equipped with a decision support tool for effective capacity allocation and patient scheduling decisions. The parameters of our models could be tuned based on the preferences of different hospitals. Furthermore, these approaches can be applied to other settings with similar problems, such as government budget allocation considering both utility and equity, and service system management with waiting time requirement.