Asymptotic Analysis of Multi-Class Advance Patient Scheduling

Advance patient scheduling plays a pivotal role in improving service quality and ensuring efficiency in healthcare systems. It is a daily task that health providers need to deal with in order to minimize patients' waiting times while trying to utilize the available resources efficiently. Despite its impact in practice, the structure of the optimal policy for scheduling multiple classes of patients is unknown. The main challenge is to dynamically assign patients to future appointment time slots in the booking horizon, considering their waiting costs. This paper develops the \emph{first} theoretical framework to characterize the optimal policy for advance scheduling of multiple classes of patients with heterogeneous service requirements and waiting costs. We analyze the problem in an asymptotic regime and derive the diffusion-optimal policy, establishing that it follows a state-dependent threshold structure. Leveraging the theoretical analysis and the properties of the optimal policy, we propose a practical scheduling policy that fully determines which patients to schedule and which time slots in the booking horizon to assign to them. Finally, empirical analysis of the proposed policy using data from two hospitals illustrates that it appropriately reserves capacity for future emergency patients, efficiently prioritizes the patient classes, and addresses the trade-off between resource utilization and waiting costs