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.