LINTHICUM, MD, October 21 - When friends buy Mariners' seasons tickets together, who goes to the Yankees game?
That was the problem faced by Thomas A. Grandine of Issaquah, Washington, who came up with a unique solution: write a math model complete with a series of algorithms to assign games fairly. His technique is published in the current edition of Interfaces: An International Journal of the Institute for Operations Research and the Management Sciences.
INFORMS is holding its semi-annual convention at Washington State Convention & Trade Center and The Sheraton Seattle Hotel & Towers from Sunday, October 25 to Wednesday, October 28.
The Challenge
Grandine, a numerical analyst with Boeing, first bought a single pair of Mariners seasons' tickets for a group of friends two years ago. "After assigning Mariner season tickets in a rather unsatisfying way in 1996 to the individuals who had agreed to buy and divide them," he writes, "we devised a more sophisticated approach in 1997 that poses and solves a mixed-integer-programming problem, and we obtained much more satisfactory results."
The friends - Al, Roger, Sid, Fritz, Mike, Jim, and Grandine - had tickets for 81 home games to distribute in 1996. Each had different requests. That year, they ranked the games in order of request and let a computer assign seats. They found that a simple computer program was limited in its ability to satisfy members of the group. Roger, for example, received tickets to all the Yankee games. 10 out of 12 of the author's seats were for games before the All-Star break. By the end of the year, the group was unhappy.
In 1997, the group grew and the number of seasons tickets they purchased increased to four. The complexity of the problem grew, too.
Mike from Portland wanted to attend an entire series on a trip to Seattle. Others had requests such as two seats rather than four to a given game, attending only one game per series, or tickets for back-to-back Friday and Saturday games. The list of special needs, or constraints, rose to 268, thus multiplying the complexity of distribution.
Operations Research Applied to Sports
To distribute the seats fairly and bring order to chaos, the author used his training in operations research to write the problem as a mathematical model that could be used to distribute the tickets.
Constructing the model required the participants to sit down with pen and paper and list their preferences. They listed their ideal season-ticket package, the number of tickets needed per game, special requests, and, ultimately, their ranking of preferred games.
After the model was written and tested, the author discovered some remaining issues of dissatisfaction and modified the program again.
The favorable results are evident in the statistics: The author writes, "Of the 141 assignments of tickets that were made, 66 of the 141 (46.7%) were made to someone who had ranked that game in his top 10. Another 39 (27.7%) were made to someone who had ranked that game from 11 to 20, while 23 (16.3%) were made to someone who had ranked that game from 21 to 30. Only 9 assignments were made to picks ranked 31 to 40, and only 4 assignments were made to someone who had picked a game in his bottom half."
Indeed, says the author, "the arrangement has worked so well that additional friends have asked to join our group, and we currently have a waiting list!"
For additional information on the INFORMS semi-annual conference in Seattle, including a full list of workshops, visit the web site at http://www.informs.org/Conf/Seattle98/
The Institute for Operations Research and the Management Sciences (INFORMS) is an international scientific society with 12,000 members, including Nobel Prize laureates, dedicated to applying scientific methods to help improve decision-making, management, and operations. Members of INFORMS work in business, government, and academia. They are represented in fields as diverse as airlines, health care, law enforcement, the military, the stock market, and telecommunications.
Journal
Interfaces