Threshold Control Policy Optimization for Real-Time Reverse Referral Decision of Chinese Comprehensive Hospitals

In recent years, imbalanced utilization of medical resources is widely concerned within the tiered Chinese hospital system. Reverse referral, as a measure of promoting patient flows from upper level hospitals (ULHs) to lower level hospitals (LLHs), has demonstrated its advantages on alleviating ULH workload and balancing resource utilization between ULHs and LLHs. Nevertheless, it remains unclear on how to control the reverse referral decision process at the operational level. In this paper, we consider an ULH-dominant setting at which the LLH must accept patient referrals from the ULH whenever it has available beds. We focus our attention on an easy-to-implement threshold policy for the ULH to make the reverse referral decision. To investigate, we first formulate an analytically tractable queueing model for a simplified reverse referral process. We then investigate a more general patient flow control model, for which we analyze the patient population dynamics with a Markov chain process, and apply the concept of state-dependent Markovian arrival process to generate an infinitesimal generator of the system. We use RG factorization to compute the system performance measures. We next formulate a threshold optimization problem with the objective of maximizing the ULH profit. Simulation experiments are performed, which conclude that the threshold control policy is insensitive to the service time distribution. Finally, we report real-world inspired numerical studies, from which we generate insights into effective adjustment of the control threshold in response to the system parameters and discuss potential hindrance from the LLH incorrectly informing its real-time resource availability to the ULH. Our work is the first that applies systems engineering to the real-time reverse referral decision problem in China. It provides the novel perspective of resource balancing to patient flow control studies in the care transition management literature. Note to Practitioners —It is recognized, in almost all countries with insufficient health care delivery infrastructure, that the care coordination is a key strategy to improve the effectiveness, safety, and efficiency of the health care system. Through communicating/sharing knowledge, multiple care organizations work together to create a proactive care plan for the patients to meet their needs and preferences, especially dealing with transitions of care. With the promotion of population care management, practitioners throughout the world have increasingly acknowledged the importance of patient flow streamlining, resource alignment within each population, and linking to community care resources from acute care facilities. However, applying care coordination in everyday routines of a medical practice can be overwhelming, even when it is obvious that the changes will improve patient care and provide efficiency. In this paper, we investigate an easy-to-implement patient flow control policy in making reverse referral decisions for patients receiving postdischarge care. We expect to improve provider’s profit with improved operational management. Through our analyses, we want to stress the importance of applying systems engineering and mathematical modeling to study care coordination and interorganization patient flow control. We also want to advocate knowledge sharing and accountability establishment, as a well-functioned partnership between hospitals at different tiers may very much rely on them.