Pareto optimization for control agreement in patient referral coordination

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Imbalanced utilization of medical resources between hospitals at different levels is prevalent in China. Through coordination of an upper-level hospital (ULH) and a lower-level hospital (LLH), ULH-referrals are encouraged so that the ULH can transfer less urgent patients to the LLH to alleviate the utilization imbalance. To the entire system, the patient referral coordination is dependent not only on the agreed transfer quantity but perhaps more on the patient flow characteristics and simultaneously mutual decisions from both the ULH and the LLH. In this paper, we thus investigate a control agreement framework between the ULH and the LLH that helps both hospitals to maximize their respective benefits. More specifically, a control agreement framework allows each hospital applies a threshold-based policy to make decisions on either referral (by ULH) or acceptance (by LLH). And a Pareto-based negotiation process is proposed to carry out the control agreement. To optimize the threshold pair from both hospitals, we formulate a Pareto optimization problem with objectives being revenue-and-monetarized-patient-blockage related benefits of the two hospitals. Given the complexity in analyzing patient flows of the system, we develop a multi-fidelity model-based optimization approach, which integrates the advantages of queueing model and discrete event simulation. Specifically, we adopt the idea of ordinal transformation and optimal sampling. In a real-world case study, we investigate the control policy in light of the referral coordination practice between Shanghai No. 6 People's Hospital and No. 8 People's Hospital. Our Pareto-optimization approach is applicable to many service systems with waiting time sensitive customers. Our work provides a novel perspective of operational level coordination design for the service outsourcing/sharing management literature.