Referee assignment in the Chilean football league using integer programming and patterns

Abstract

This article uses integer linear programming to address the referee assignment problem in the First Division of the Chilean professional football league. The proposed approach considers balance in the number of matches each referee must officiate, the frequency of each referee being assigned to a given team, the distance each referee must travel over the course of a season, and the appropriate pairings of referee experience or skill category with the importance of the matches. Two methodologies are studied, one traditional and the other a pattern-based formulation inspired by the home-away patterns for scheduling season match calendars. Both methodologies are tested in real-world and experimental instances, reporting results that improve significantly on the manual assignments. The pattern-based formulation attains major reductions in execution times, solving real instances to optimality in just a few seconds, while the traditional one takes anywhere from several minutes to more than an hour.