Revenue Management for a Primary-Care Clinic in the Presence of Patient Choice

TLDR: A Markov decision process model is developed for the appointment-booking problem in which the patients' choice behavior is modeled explicitly and it is proved that the optimal policy is a threshold-type policy as long as the choice probabilities satisfy a weak condition.

Abstract: In addition to having uncertain patient arrivals, primary-care clinics also face uncertainty arising from patient choices. Patients have different perceptions of the acuity of their need, different time-of-day preferences, as well as different degrees of loyalty toward their designated primary-care provider (PCP). Advanced access systems are designed to reduce wait and increase satisfaction by allowing patients to choose either a same-day or a scheduled future appointment. However, the clinic must carefully manage patients' access to physicians' slots to balance the needs of those who book in advance and those who require a same-day appointment. On the one hand, scheduling too many appointments in advance can lead to capacity shortages when same-day requests arrive. On the other hand, scheduling too few appointments increases patients' wait time, patient-PCP mismatch, and the possibility of clinic slots going unused. The capacity management problem facing the clinic is to decide which appointment requests to accept to maximize revenue. We develop a Markov decision process model for the appointment-booking problem in which the patients' choice behavior is modeled explicitly. When the clinic is served by a single physician, we prove that the optimal policy is a threshold-type policy as long as the choice probabilities satisfy a weak condition. For a multiple-doctor clinic, we partially characterize the structure of the optimal policy. We propose several heuristics and an upper bound. Numerical tests show that the two heuristics based on the partial characterization of the optimal policy are quite accurate. We also study the effect on the clinic's optimal profit of patients' loyalty to their PCPs, total clinic load, and load imbalance among physicians.