Alternative IP Models for Sport Leagues Scheduling

Abstract

Round robin tournaments (RRT) cover a huge variety of real world sports tournaments. Given a set of teams T we restrict all what follows to single RRTs, i.e. each pair of teams i ∈ T and j ∈ T, j < i, meets exactly once and each team i ∈ T plays exactly once in each period of the tournament. We denote the set of periods by P where |P| = |T|−1. Team i ∈ T is said to have a break in period p ∈ P if and only if i plays at home or away, respectively, in p−1 and p. In most professional sports leagues in Europe the number of breaks has to be minimized. It is well known that the number of breaks cannot be less than n−2. Moreover, this number can be reached for each even |T|. We consider cost c i,j,p, i, j ∈ T, i ≠ j, p ∈ P, for each match of team i at home against team j in period p. The objective is to minimize the overall cost. Models for sports league scheduling have been the topic of extensive research. For the sake of shortness we refuse to give a survey and refer to Briskorn and Drexl [1] for integer programming (IP) models for sports scheduling and to Knust [3] for an extended overview of literature. In section 2 we formulate IP models whose linear programming (LP) relaxation are strengthend in the following by means of valid inequalities. Section 3 provides computational results obtained by employing state of the art solver Cplex and a short conlcusion.