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.