Referral coordination mechanisms in healthcare management

Referral systems are widely used to coordinate heterogeneous healthcare providers (e.g., general hospitals (GHs) and community healthcare centers (CHCs)) for improved efficiency. This paper investigates referral coordination within a typical two-tiered system centered around a general hospital (GH) and a community healthcare center (CHC). Specifically, we compare the coordination value of two prevalent mechanisms: one-way referral and two-way referral. We develop a queueing-theoretic model to derive optimal capacity and pricing decisions for the GH and the CHC under each mechanism and then evaluate their relative effectiveness, with key metrics including total system profit, healthcare service prices, and patient waiting times. Our base model yields two key findings. First, counterintuitively, under certain conditions, the one-way referral mechanism can outperform both the two-way mechanism and a non-coordinated baseline. Second, within the one-way framework, full cooperation between the GH and CHCs can lead to a Pareto improvement, benefiting all stakeholders (i.e., the GH, the CHCs, and the patients). This finding is based on an analysis extended to a system of one GH and multiple CHCs, where we show how a profit allocation scheme can be designed to foster such cooperation. Further analysis of a congested system with referral-dependent arrival rates reveals that the two-way mechanism becomes unequivocally superior. Finally, numerical studies confirm that optimal profits across all scenarios increase with the arrival rates of both severe patients in the GH and common patients in the CHCs.