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Problem Title: Airline Overbooking

  Year: 2002      
  Student Level: Undergraduate      
  Source: MCM      
  Commentary: Yes (1)      
  Student Papers: Yes (6)      

You're all packed and ready to go on a trip to visit your best friend in New York City. After you check in at the ticket counter, the airline clerk announces that your flight has been overbooked. Passengers need to check in immediately to determine if they still have a seat.

Historically, airlines know that only a certain percentage of passengers who have made reservations on a particular flight will actually take that flight. Consequently, most airlines overbook-that is, they take more reservations than the capacity of the aircraft. Occasionally, more passengers will want to take a flight than the capacity of the plane leading to one or more passengers being bumped and thus unable to take the flight for which they had reservations.

Airlines deal with bumped passengers in various ways. Some are given nothing, some are booked on later flights on other airlines, and some are given some kind of cash or airline ticket incentive.

Consider the overbooking issue in light of the current situation:
Less flights by airlines from point A to point B
Heightened security at and around airports
Passengers' fear
Loss of billions of dollars in revenue by airlines to date

Build a mathematical model that examines the effects that different overbooking schemes have on the revenue received by an airline company in order to find an optimal overbooking strategy, i.e., the number of people by which an airline should overbook a particular flight so that the company's revenue is maximized. Insure that your model reflects the issues above, and consider alternatives for handling "bumped" passengers. Additionally, write a short memorandum to the airline's CEO summarizing your findings and analysis.


Author-Judge's Commentary: The Outstanding Airline Overbooking Papers

William P. Fox
Dept. of Mathematics
Francis Marion University

  Student Papers      

Things That Go Bump in the Flight

Bethel College, St. Paul, MN


Optimal Overbooking

Duke University, Durham, NC


Models for Evaluating Airline Overbooking

Harvey Mudd College, Claremont, CA


Probabilistically Optimized Airline Overbooking Strategies, or "Anyone Willing to Take a Later Flight?!"

University of Colorado, Boulder, CO


ACE is High

Wake Forest University, Winston-Salem, NC


Bumping for Dollars: The Airline Overbooking Problem

Wake Forest University, Winston-Salem, NC