Simultaneous scheduling of football games and referees using Turkish league data

Abstract

Assignment decisions of referees to football (soccer) games are highly debated in sports media. Referee assignments are typically done on a weekly basis as the league progresses. However, this practice ignores important workload constraints on referees. Moreover, referees' skill levels should also be considered in determining their assignments. In this article, we first give a mixed integer linear program formulation for the problem of simultaneously generating a game schedule and assigning main referees to games by incorporating specific rules in the Turkish league. We also approach this problem using a genetic algorithm (GA) because of the computational difficulties in solving the problem. In the GA solution pool, we suggest using templates for referee assignments that follow several referee-related workload constraints. We explain how these templates can be obtained by solving a mixed integer linear model prior to running the GA. The usage of these templates for referee assignments is conceptually similar to using a basic match schedule for game scheduling such as the one used in the Turkish Football League. We use the Turkish Football League fixtures for 2010–2013 as a case study. Experiments with the GA using real-world data show a rather modest performance in terms of computation time and objective function value. Our numerical results indicate that the problem is extremely hard to solve.