Asymptotic Analysis of Multi-Class Advance Patient Scheduling

Reduced capacity for elective medical procedures during the COVID-19 pandemic has created significant backlogs. A key question that health policy-makers are facing nowadays is what strategy should be adopted for scheduling patients to avoid undue significant additional costs. To address this question, we consider an advance scheduling problem with different classes of patients whose requests for service arrive at the system in a stochastic manner. We assume that the system incurs daily resource cost as well as patient waiting costs, while the cost of waiting to receive an appointment is different than the cost of waiting to be served after receiving an appointment. Thus, at any given time, the service provider should decide whether to schedule the patients waiting inline, and if so, which available appointment times should be assigned to them. We formulate the problem in an asymptotic regime and analyze it based on both fluid and diffusion approximations. The analysis includes the derivation of useful properties and characterization of the optimal scheduling policy, establishing that it can be determined by a simple function of the system state at the time. This function fully determines which waiting patients should be scheduled and which available time slots in the booking window should be allocated to them. We examine the performance of the proposed multi-class advance patient scheduling policy numerically, illustrating that it accurately prioritizes the patients waiting to receive an appointment and efficiently balances the workload across the days in the booking window.