Scheduling a round robin tennis tournamentunder courts and players availability constraints

Abstract

A practical problem encountered by the management of a tennis club is theorganization of a tennis tournament for the club members. The tournament participants aresplit into different series: in each series, every player plays once a week with adifferent opponent in a round robin tournament. All matches are subject to a time limitcorresponding to one hour. All the series share the same pool of courts, whose weeklyavailability is predefined. In addition, the players have their own availabilityconstraints. Given the courts and players availability, the objective is to schedule thetournament with no violation of the constraints or, more realistically, in order tomaximize the number of feasible matches. This problem can be formulated as a maximummatching problem, with the additional constraint that each player must play just once aweek. It can also be modeled as a maximum clique problem. A two‐step heuristicprocedure is proposed to solve the problem: first, the round robin tournaments ofeach series are generated, then the matches of each tournament are assignedto the available courts for every week by means of a local search procedure. The procedurehas been succesfully implemented and is currently used by the tennis club.