Hybrid appointment for a single-physician clinic with no-shows and overbooking

Motivated by observations of actual clinic operations, we design a hybrid appointment system (HAS) for a single-physician clinic, in which the system serves a mix of acute and chronic-care patient by allowing both advance and same-day bookings to increase patient satisfaction. Because of the existence of no-shows of regular patients who book in advance, to maintain their revenue, clinics must carefully manage patients' access to balance the needs of regular patients with no-shows and same-day patients who always show up for their same-day appointments. In order to offset the negative effect of regular patients' no-shows on clinic revenue, overbooking is introduced into this system. The clinic decides which appointment requests are accepted to maximize revenue. For this purpose, A Markov Decision Process (MDP) model with regular patients' no-shows and overbooking is formulated. We characterize the structure of the optimal policies of the model. We prove that there exists an appointments' threshold on the optimal policy for the model, and the threshold increases with the increase of no-show probability.