Optimal Overbooking

We construct several models to examine the effect of overbooking policies on airline revenue and costs in light of the current state of the industry, including fewer flights, increased security, passengers’ fear, and billions in losses. Using a plausible average ticket price, we model the waiting-time distribution for flights and estimate the average cost per involuntarily bumped passenger. For ticketholders bumped voluntarily, the interaction between the airline and ticketholders takes the form of a least-bid auction in which winners receive compensation for foregoing their flights. We discuss the precedent for this type of auction and introduce a highly similar continuous auction model that allows us to calculate a novel formula for the expected compensation required. Our One-Plane Model models expected revenue as a function of overbooking policy for a single plane. Using this framework, we examined the relationship between the optimal (revenue-maximizing) overbooking strategy and the arrival probability for ticketholders. We extend the model to consider multiple fare classes; doing so does not significantly alter optimal overbooking policy. Our Interactive Simulation Model takes into account estimates for average compensation costs. It simulates the interaction between 10 major U.S. airlines with a market base of 10,000 people, factoring in passenger arrival probability, flight frequency, compensation for bumping, and the behavior of rival airlines. Thus, we estimate optimal booking policy in a competitive environment. Simulations of this model with likely parameter values before and after September 11 gives robust results that corroborate the conclusions of the One-Plane Model and the compensation-cost formula.