Contracting for Referral Coordination in a Tiered Service Network via Pareto Optimization

Balanced resource utilization across tiered service networks is critical in service-oriented industries. Formulating robust referral (outsourcing) coordination contracts between primary and secondary service providers is essential to mitigate operational bottlenecks, declines in service quality, and increased risks of client dissatisfaction. However, designing effective referral agreements is complex, relying not only on achieving the desired profitability and service level from referrals at both providers but also on managing the impact of additional customers who are not covered by the referral agreement. In healthcare, this is evident in patient referral coordination between hospitals and skilled nursing facilities (SNFs), where patient preference for outpatient rehab at reputable hospitals leads to overcrowding and resource misalignment, while SNFs remain underutilized even when their inpatient rehab service is available. To address this, we propose an operational-level control protocol for arranging referral decisions between the two care facilities to maximize their respective benefits. This framework allows an easy-to-implement threshold policy based on their bed occupancy levels. To maximize revenue and relieve patient blockage at either facility, we explore Pareto optimality on the threshold pair. This involves executing a modified ordinal transformation and optimal sampling (OTOS) algorithm along with multi-fidelity modeling of patient flows, wherein the low-fidelity model is a tandem queuing network with multiple customer classes, and the high-fidelity model is a discrete-event simulation. We investigate the efficacy of the proposed contract through case studies based on healthcare claims data. We also demonstrate the effectiveness of the modified OTOS algorithm over standard simulation optimization algorithms.