Cross-Cluster Referrals and Subsidy Schemes in Multi-Cluster Healthcare Systems

Problem definition: Excessive and highly variable waiting times for specialty services are a long-standing problem for public healthcare systems. Healthcare authorities in some jurisdictions have begun to experiment with schemes to improve system performance, including cross-cluster referrals which allow patients to switch from their home cluster to other clusters with shorter waiting times, and opt-out subsidies which help patients seeking services from private providers outside the public system. However, few studies in the literature have examined the structure of the problem or offered analytical insights to the design of such schemes. Methodology/results: We construct a multi-cluster service network model to study optimal routing policies under both individual and system optimization. We define externalities in a network setting and establish their properties, and further identify conditions under which referrals are effective or counterproductive in reducing system costs. We also show that lowering the switching cost could inadvertently degrade overall system performance. In contrast to the classic result for single-cluster systems (e.g. Naor 1969), our analysis of opt-out and switching incentives reveals that fixed subsidies generally cannot fully coordinate a multi-cluster system due to the cross-cluster effect of externalities. However, they can effectively reduce system costs in wide ranges of system parameter values. We further show that dynamic (state-dependent) subsidies can achieve perfect alignment between individual and system optimization. Managerial implications: Our study suggests that cross-cluster referrals are effective when there is a substantial workload imbalance but without excessive system congestion. They should be implemented with proper operational control: referrals should be promoted when the workload imbalance is high, but discouraged when the overall system workload is very high while the imbalance is insubstantial. Furthermore, fixed opt-out and switching subsidies can effectively improve system performance under different demand conditions and should be applied strategically: focusing on switching subsidies when the system workload is moderate and the imbalance is substantial, but shifting the focus to opt-out subsidies when the overall system workload is high.