To Carve Out or Not: Managing the Routine and Same-day Appts for Outpatient Clinics

Faced with challenges of patient no-show behavior in the advanced scheduling system and the demand variability effect in the open-access system, outpatient clinics may use a combination of both policies. When this happens, the typical decision rule is the "carve-out scheduling" (COS) policy. The COS system, which stipulates that the decision-maker cannot assign two patients of different classes to a slot, may often experience increasing underutilization and long waiting times. Alternatively, the policy "mixed appointment scheduling" (MAS), which allows for possible assignment of the two patient classes to a slot, may be desirable. Whether the MAS policy would perform better than the COS, and under what business settings are the performance gaps worthwhile, are questions we seek to address. We answer these questions by proposing a new model to determine the optimal appointment scheduling decision for routine and same-day patients under the MAS condition. We show that the priority service discipline, together with uncertainty in demand, destroys the multimodularity of the objective function in the component of the same-day schedule. Thus, the joint problem of determining the optimal routine and same-day schedules becomes hard to solve. We provide various characterizations that allow for the efficient identification of the optimal decision policy. Our numerical results reveal that the MAS policy helps to lower system cost, increase utilization, and reduce service delay when the same-day demand to clinic capacity ratio is within a moderate limit.