Seattle Mariners Season Tickets. Seven friends formed a consortium to purchase a pair of Seattle Mariners season tickets for 1996. To assign the game tickets, each participant rank-ordered each of the 81 games. A computer program was then developed that assigned to each participant, in turn, the game he had ranked highest of those not yet assigned. The problem with this scheme was that participants tended to rank games in clusters that reflected their highest priorities, because the games were rank-ordered only once. For example, one of the participants was originally from New York City, so he gave all of the games when the N. Y. Yankees visited Seattle the highest ranking. As might be expected, he received the tickets for all four of those games. As a result of this and similar rankings, the assignment of tickets to individual participants was often not well distributed across the entire season. Post-assignment trades of tickets among some of the participants subsequently alleviated this problem.
For the 1997 season, the consortium added one participant and decided to purchase four season tickets. These two factors greatly complicated the problem of allocating the tickets.
To solve this more complicated problem, a large number of 0-1 integer decision variables were defined based on whether or not a particular individual was assigned one or both pairs of tickets to a particular game. Rules were then formulated in an attempt to ensure that each participant received the mix of tickets he desired. Finally, each participant rank-ordered each game, so that a score to measure his level of satisfaction with a particular assignment of tickets could be computed. Putting this all together, the available tickets were allocated so as to minimize the dissatisfaction of the participant who was most dissatisfied.
Overall, the participants were very satisfied with the way this scheme worked in 1997, and the consortium planned to use the same system, with one minor adjustment, in 1998. All of the participants planned to again be part of the consortium in 1998, and there was even a waiting list for others who had asked to join the consortium.