Intraday dynamic rescheduling under patient no-shows

Patient no-shows are a major source of uncertainty for outpatient clinics. A common approach to hedge against the effect of no-shows is to overbook. The trade-off between patient's waiting costs and provider idling/overtime costs determines the optimal level of overbooking. Existing work on appointment scheduling assumes that appointment times cannot be updated once they have been assigned. However, advances in communication technology and the adoption of online (as opposed to in-person) appointments make it possible for appointments to be flexible. In this paper, we describe an intraday dynamic rescheduling model that adjusts upcoming appointments based on observed no-shows. We formulate the problem as a Markov Decision Process in order to compute the optimal pre-day schedule and the optimal policy to update the schedule for every scenario of no-shows. We also propose an alternative formulation based on the idea of 'atomic' actions that allows us to apply a shortest path algorithm to solve for the optimal policy more efficiently. Based on a numerical study using parameter estimates from existing literature, we find that intraday dynamic rescheduling can reduce expected cost by 15% compared to static scheduling.