Appointment Requests from Multiple Channels: Characterizing Optimal Set of Appointment Days to Offer with Patient Preferences

We consider the appointment scheduling for a physician in a healthcare facility. Patients, of two types differentiated by their revenues and day preferences, contact the facility through either a call center to be scheduled immediately or a website to be scheduled the following morning. The facility aims to maximize the long-run average revenue, while ensuring that a certain service level is satisfied for patients generating lower revenue. The facility has two decisions: offering a set of appointment days and choosing the patient type to prioritize while contacting the website patients. Model 1 is a periodic Markov Decision Process (MDP) model without the service-level constraint. We establish certain structural properties of Model 1, while providing sufficient conditions for the existence of a preferred patient type and for the nonoptimality of the commonly used offer-all policy. We also demonstrate the importance of patient preference in determining the preferred type. Model 2 is the constrained MDP model that accommodates the service-level constraint and has an optimal randomized policy with a special structure. This allows developing an efficient method to identify a well-performing policy. We illustrate the performance of this policy through numerical experiments, for systems with and without no-shows.Supplemental Material: The online appendix is available at https://doi.org/10.1287/stsy.2022.0029 .