Referee Assignment in Sports Leagues

Abstract

Optimization in sports is a field of increasing interest. Combinatorial optimization techniques have been applied, for example, to game scheduling and playoff elimination. A common problem usually found in sports management is the assignment of referees to games already scheduled. There are a number of rules and objectives that should be taken into account when referees are assigned to games. We address a simplified version of a referee assignment problem common to many amateur leagues of sports such as soccer, baseball, and basketball. The problem is formulated by integer programming and its decision version is proved to be NP-complete. To tackle real-life large instances of the referee assignment problem, we propose a three-phase heuristic approach based on a constructive procedure, a repair heuristic to make solutions feasible, and a local search heuristic to improve feasible solutions. Numerical results on realistic instances are presented and discussed.

50 years of OR in sport

“…I have been able to find just two papers for baseball -Evans et al (1984) and Evans (1988); three for football- Zakarya et al (1989), Gil Lafuente (2004), andYavuz et al (2008); two for cricket- Wright (1991) and Wright (2007); plus one (Duarte et al, 2007) which may be applicable to several sports. Heuristic or metaheuristic methods have been used, except in the case of Gil Lafuente who uses an exact method.…”

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

“…The OF is the one suggested by Duarte et al. (), which minimizes the sum over all referees of the absolute value of the difference between the target and the actual number of games assigned to each referee. Basic constraints .…”

“…Duarte et al. () define a referee assignment problem that seeks an efficient assignment of referees to a sports season calendar by minimizing the sum over all referees of the differences between the desired match assignments for each referee and the ones they are actually assigned by the definitive solution. Gil Lafuente and Rojas Mora () suggest an assignment method that uses confidence intervals to incorporate the degree of uncertainty inherent in the assessments of each referee's experience and skill category given the subjective nature of such information.…”

Metaheuristic methods based on Tabu search for assigning judges to competitions

“…These applications induce combinatorial optimization problems usually solved with heuristic or metaheuristic methods. Among others, we mention the following references: Duarte et al (2006Duarte et al ( ) and (2007aDuarte et al ( ), (2007b, and Yavuz et al (2008). Evans et al (1984) use a minimum cost flow formulation.…”