A Stochastic Mathematical Appointment Overbooking Model for Healthcare Providers to Improve Profits

This paper develops a stochastic mathematical overbooking model (SMOM) for determining the optimal number of patient appointments to accept to maximize expected total profits for diverse healthcare environments. Overbooking is necessary to alleviate the detrimental effects of no-shows that are experienced by healthcare providers. Compared with traditional simple deterministic overbooking approaches, SMOM is unique since it considers the probability distributions of no-shows and walk-ins to obtain the optimal solution. Usually, healthcare providers would only have no-show data based on their current practices, so the authors provide a method to extrapolate the conditional probability to estimate what happens when overbooking occurs. SMOM is then compared with two alternative strategies: the base case of no overbooking and the naive statistical overbooking approach (NSOA) that simply adds the mean number of no-shows minus the mean number of walk-ins to the number of appointments to accept. It is shown using data collected for 59 physicians in a medical clinic that SMOM compared with the base case can increase profits by 43.72% on average whereas NSOA improves profits by 29.66% on average. Sensitivity analyses demonstrate SMOM is robust under a diversity of healthcare environments and cost structures.