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

The referee assignment problem in sports scheduling is addressed for the First Division of the Chilean professional football league using integer linear programming. Various criteria that enhance the transparency and objectivity of the assignment process are considered. As well as better balances in the number of matches each referee must officiate, the frequency each is assigned to a given team, and the distances each must travel over the course of a season, these improvements include the generation of appropriate pairings of referee experience or skill category with the importance of certain matches. The model is solved using two approaches, one traditional and the other a pattern‐based approach inspired by the well‐known home‐away patterns for scheduling season matches. The two approaches are implemented for real instances of the problem, reporting results that significantly improve the manual assignment. Also, the pattern‐based approach achieves major reductions in solution times over the traditional formulation.