Optimal matchday schedule for Turkish professional soccer league using nonlinear binary integer programming

Sports scheduling problems are interesting optimization problems that require the decision of who play with whom, where and when to play. In this work, we study the sports scheduling problem faced by the Turkish Football Federation. Given the schedule of games for each round of the season, the problem is to determine the match days with the goal of having a fair schedule for each team. The criteria we employ to establish this fairness are achieving an equal distribution of match days between the teams throughout the season and the ideal assignment of games to different days in each round of the tournament. The problem is formulated as a nonlinear binary integer program and is solved optimally for each week. Our results indicate that significant improvements over the existing schedule can be achieved if the optimal solution is implemented.