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

Abstract

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.

Fair Assignment of Matchdays in the Turkish Super League under a Rest Mismatch Minimization Objective

“…For example, Atan and Çavdaroğlu (2018) and Çavdaroğlu and Atan (2020) minimize rest mismatches, Rasmussen and Trick (2007), Durán, Guajardo and Sauré (2017), Recalde, Torres and Vaca (2013) and Bulck and Goossens (2020) minimize breaks, Kendall and Westphal (2013) minimizes travel distances, Guedes and Ribeiro (2011), Januario and Urrutia (2016), and Günneç and Demir (2019) minimize carry over effects. Some other studies weigh these performance related objectives against more economic ambitions such as gate revenue and attendance maximization subject to constraints that arise from league organization in different countries (see Durán, Guajardo and Wolf-Yadlin 2012, Rasmussen 2008, Goossens and Spieksma 2009, Ribeiro and Urrutia 2012, Durán et al 2007, Bartsch, Drexl and Kröger 2006.…”

“…As indicated earlier, our mathematical model is an extension of the model described in Göçgün and Bakır (2022). The authors propose an integer programming formulation for a class of matchday scheduling problems faced by TFF, adapting the Monden heuristic.…”