Fair referee assignment for the Italian soccer serieA

The Referee Assignment Problem (RAP) is a novel arising problem in sports management, in which a limited number of referees with different qualifications and availabilities should be assigned to a set of games already scheduled, in order to respect a list of constraints. Number and nature of these constraints may significantly vary for sports, nation and type of league. Almost each tournament has its own particular set of constraints to be satisfied, therefore it is very difficult to generalize this problem. The goal of the problem is to find a feasible assignment, i.e., a configuration which allows to respect all the constraints given. An extension of the RAP is the Fair Referee Assignment Problem (FRAP), in which the objective is to minimize the violation of a set of soft (optional) constraints, while satisfying all the hard (mandatory) ones. In this work, the Italian Major Soccer League, the so-called SERIE A, is addressed, and an integer programming model for the related FRAP is proposed. Soft and hard constraints have been formulated according to the rules suggested by the AIA (Italian Referee Association) which is in charge of referee assignment for the SerieA. The model has been tested on a real instance taken from the season 2011/2012. Results obtained show the efficacy and the effectiveness of the model.