Referral coordination mechanisms in healthcare management

Referral is a common approach in healthcare systems to coordinate hospitals with different service quality and capabilities to improve system efficiency. We focus on a typical system comprising two types of hospitals: general hospitals (GHs) and community healthcare centers (CHCs). We investigate and compare the coordination value of two common referral mechanisms: the single-way and two-way referral mechanisms. By constructing a queueing model, we explicitly characterize the optimal service capacity and pricing decisions for each type of hospital (GHs and CHCs) under each mechanism, and compare the performance of the two referral mechanisms. Our findings from the base model are as follows. First, counterintuitively, under certain conditions, the single-way referral mechanism can outperform both the two-way referral mechanism and the no-coordination scenario. Second, focusing on the single-way referral mechanism, we find that cooperation among all hospitals can lead to a win-win outcome for the GH, CHCs, and patients. We also examine a congested system with referral-scheme-dependent arrival rates and find that the two-way referral mechanism always outperforms both the single-way mechanism and no coordination. Numerical studies show that the optimal profit under any of the three scenarios increases with the arrival rate of severe patients and the arrival rate of common patients at the CHC.