Abstract
Motivated by high rates of opt-out in a public school district, we consider the problem of yield management in matching settings where agents have priorities at each item. The goal is to determine how much to overbook or 'inflate' capacities for each item to minimize reassignment costs due to stochastic opt-out. Such yield management problems arise in several applications, such as assigning students to schools or colleges, allocating airplane seats, or scheduling medical appointments. We show that the presence of priorities generates a bullwhip effect, where less popular items face higher yield uncertainty due to externalities created by more popular items. We provide a Greedy heuristic for inflating capacities that minimizes total cost, and show that under the resulting capacities the bullwhip effect results in higher rates of overbooking and higher costs for less popular items. Simulations using data from a school district validate our theoretical results, and informed overbooking in the district for the 2023-24 school year.