Cross-Cluster Referrals and Opt-out Subsidies in Healthcare Systems

Problem definition: Extremely long and varied waiting times for specialty services are a longstanding and pressing problem for many public healthcare systems, whereas private hospitals can provide the same services with minimal waiting times but at significant cost. We explore two approaches to tackle this problem: cross-cluster referrals, which enable patients to switch from their home cluster to other clusters for shorter waiting times, and opt-out subsidies, which involve subsidizing patients who choose to receive private services outside the public system. While these practices are observed in some healthcare systems, there are few related studies in the literature. Methodology/results: We establish a multi-cluster service network model to analyze the decision-making of individual patients and to determine the optimal patient-routing policy for overall system optimization. Additionally, we conduct both analytical and numerical investigations to explore the effective implementation of the two approaches. Our findings reveal that while cross-cluster referrals can generally improve system performance, they may paradoxically worsen system performance under certain conditions. Moreover, we demonstrate that the opt-out subsidy scheme is a justified measure of societal well-being, as it helps mitigate the negative externalities that arise from individual optimization. However, unlike the case of a single-server queue, a static subsidy scheme cannot, in general, fully coordinate the multi-cluster network due to the cross-cluster effect generated by patient referrals. Managerial implications: Cross-cluster referrals are effective when there is a significant disparity in waiting times between clusters. Furthermore, it is crucial to exercise proper operational control to prevent the potential pitfall of excessive referrals, which could ultimately worsen overall system performance. Although a fixed opt-out subsidy does not completely eliminate negative externalities, it is deemed publicly acceptable and has the capacity to encourage selfoptimizing patients to align their behavior more closely with the desired outcomes of a socially optimal system. This mechanism is particularly effective when all clusters are overloaded.