A Binomial Decision Tree to Manage Yield-Uncertainty in Multi-Round Academic Admissions Processes

Admissions to academic programs often involve filling a number of seats by making offers to a ranked list of qualified candidates over a finite number of rounds. Two sources of uncertainty need consideration when making admission offers: first, a random fraction of offers is accepted by applicants; and second, a random fraction of applicants who initially indicate acceptance subsequently withdraw. We develop a binomial decision-tree model to determine the number of admission offers to be made while considering (a) the expected costs of exceeding or falling short of target enrollment, and (b) the fact that the more competitive students are also less likely to enroll. Insights from the model are validated using a multi-year empirical dataset of admission offers, acceptances and post-acceptance withdrawals for an MBA program. We find that having multiple rounds to make offers helps admissions offices achieve enrollment targets with greater precision. Additional rounds are particularly valuable when the uncertainty of yield rate is high. In a counterintuitive result, we identify conditions under which the recommended number of offers increases with the uncertainty in yield. We also show that it might be possible to improve the quality of an admitted class by sending out more offers sooner