Operational decision making for a referral coordination alliance- When should patients be referred and where should they be referred to?

In China, due to lack of clear regulation on care pathway of patients, it is commonly observed that the system experiences substantial utilization imbalance. One way to address this challenge is through creating healthcare alliances. Among the alliance, patients can be referred from high utilized hospitals to low utilized ones for services that can be provided in both types of hospitals with similar service qualities. Such an alliance system, usually includes one upper level high utilized hospital (ULH) (e.g. a Comprehensive Hospital) and several lower level hospital (LLH) that are low utilized (e.g. Community Hospitals). The alliance hopes to reduce waiting time of the system, especially the waiting time in the high utilized hospital. As a result, the utilization of the low utilized hospitals will be improved. Nevertheless, it remains unclear how to control the referral decision process. In this paper, we investigate when patients at the ULH will need to be referred to the LLH and to which LLH they should be referred to. Firstly, we focus our attention on an easy-to-implement threshold policy for the ULH for making the decision whether to referral patients. Then, we analyze five different selection strategies (Random Transfer, Maximum Number of Beds Available, Minimum Number of Beds Available, Maximum Available Beds Rate Status, and Minimum Available Beds Rate Status) to determine the LLH to which the patient is referred to. Simulation experiments are performed to make these analyses. Opposite to the intuition that it is best to send patients to the LLH with the most available beds, the results show that sending patients to the LLH with the lowest available bed rate (Minimum Available Beds Rate Status) is the best strategy. This is because that the ULH's waiting time is more important in the objective, sending patients to an LLH that its current available resources are more likely to be occupied by its own normal patients later, will help improve the overall probability that the ULH successfully refer patients out in the long run. Secondly, we also developed a PSO-OCBA method which integrates the idea from Optimal Computing Budget Allocation (OCBA) into the searching Particle Swarm Optimization (PSO) algorithm for generating best control threshold. We find that if we can adaptively achieve the optimal K with the different selection strategies, the difference of the performance between the five strategies will be highly reduced. Our research is the first work that applies system engineering to the real-time referral decision problem between one ULH and several LLHs. It provides a novel perspective of patient referral control studies in the coordination alliance operation literature.