Coordinated referral and scheduling decisions for specialized healthcare services

This paper studies the coordination of referral and scheduling policies where access to specialized medical services, such as surgical procedures, imaging or other consultations, is managed through a centralized intake system. In this increasingly common mode of operation, a central body makes decisions regarding the allocation of patients between a set of providers, followed by the provider taking control of the scheduling and delivery of the required service. To study the coordination of the allocation and scheduling policies we present a sequential optimization model where both referrer and provider attempt to maximize the proportion of a heterogeneous set of patients receiving treatment within a targeted wait time. Motivated by observations of performance thresholds in queueing systems, we introduce an achievable region model which permits study of providers who vary in ability to coordinate scheduling different patient streams. We characterize optimal referral and scheduling policies for a range of demand patterns and operational abilities. We find that the optimal referral policy can result in large discrepancies in outcomes for different patient types but that the discrepancy in outcomes is muted when operational abilities are higher. In situations where operational abilities are low, it is optimal for the providers to prioritize patients by stream. Low capacity for both providers results in an optimal referral and scheduling policy where certain patients streams are deprioritized and with certainty will not be seen within their wait time targets. We also study the cost of enforcing parity between patient classes and find that the cost is reduced when providers have higher operational abilities. This paper illustrates how operational constraints lead to incentives to prioritize different patient streams. In particular, we show that when operations are challenging, a more hands-on design is required to ensure clinical intake systems maintain equitable access to the service.