Keywords: Sport Event Scheduling; Sport Competitions Models; Mathematical Model Applications; Integer Programming.

Abstract: In recent years, sport organizations are not only entertaining events attracting millions of audience worldwide, but also have they become growing industry in which billions of dollars are circulating. Significant amount of investments in sport events are controlled by associations such as FIFA, UEFA, and National Basketball Association (NBA), and they organize world-famous sport events such as FIFA World Cup, UEFA Champions League, or NBA men's professional basketball league. These events attract great amount of worldwide audiences through conventional and social media and can generate billions of dollars as revenue. A key aspect of these sport events is successful planning and scheduling of their games, which ensures each participant of the competition is equally treated, and no participant gain advantage over its competitors through the course of the event. The preparation of well-organized sport event schedules may sometimes lead to complicated modeling problems. In this research, we first define such a sport event scheduling problem in which the days of the games has to be decided for a given fixture of a sport organization without violating some given restrictions that aim to preserve the equity among competitors. We then develop a mixed integer programming model for the defined problem that uses combinatorial optimization techniques. In the final step, we test our model with the data set of 2013-2014 season of the Turkish Super League (top-tier men's professional football league in Turkey) organized by Turkish Football Federation (TFF) in three different decision environments: (i) game-day scheduling of league games all at once by ignoring national cup and international (European cup) fixtures, (ii) game-day scheduling of league games all at once by considering predetermined national cup and international (European cup) fixtures, and (iii) deciding the days of league games in real time (i.e. week by week) when national cup and international fixtures become clear after their games have been completed. In all three decision environments, the performance of our model, i.e. how successful our model is in preserving the equity among competitors, has been compared to the performance of the game-day scheduling decisions of Turkish Football Federation. We show that in all decision environments our game-day schedule performs at least 7.8% better than TFF’s schedule. This result proves that organizers of the sport events can give much effective and equitable decisions by the help of mathematical modeling techniques as opposed to the current practice, in which the game-day schedule is decided manually.