Alternative IP Models for Sport Leagues Scheduling

  • Dirk Briskorn
Conference paper
Part of the Operations Research Proceedings book series (ORP, volume 2007)


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, ij, 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.


Valid Inequality Linear Programming Relaxation Consecutive Period Break Variable Single Break 
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  1. 1.
    D. Briskorn and A. Drexl. Integer Programming Models for Round Robin Tournaments. Computers & Operations Research. Forthcoming.Google Scholar
  2. 2.
    D. Briskorn and A. Drexl. Branching Based on Home-Away-Pattern Sets. In K.-H. Waldmann and U. M. Stocker, editors, Operations Research Proceedings 2006-Selected Papers of the Annual International Conference of the German Operations Research Society (GOR), Karlsruhe, September 6th–8th 2006, pages 523–528. Springer, Berlin, Germany, 2007.Google Scholar
  3. 3.
    S. Knust. Classification of literature on sports scheduling. (August 02, 2007).Google Scholar
  4. 4.
    R. Miyashiro, H. Iwasaki, and T. Matsui. Characterizing Feasible Pattern Sets with a Minimum Number of Breaks. In E. Burke and P. de Causmaecker, editors, Proceedings of the 4th International Conference on the Practice and Theory of Automated Timetabling, Lecture Notes in Computer Science 2740, pages 78–99. Springer, Berlin, Germany, 2003.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Dirk Briskorn
    • 1
  1. 1.Lehrstuhl für Produktion & LogistikChristian-Albrechts-Universität zu KielGermany

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