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4OR

, Volume 8, Issue 4, pp 365–374 | Cite as

Round robin tournaments and three index assignments

  • Dirk Briskorn
  • Andreas Drexl
  • Frits C. R. Spieksma
Research Paper

Abstract

Scheduling a sports league can be seen as a difficult combinatorial optimization problem. We study some variants of round robin tournaments and analyze the relationship with the planar three-index assignment problem. The complexity of scheduling a minimum cost round robin tournament is established by a reduction from the planar three-index assignment problem. Furthermore, we introduce integer programming models. We pick up a popular idea and decompose the overall problem in order to obtain two subproblems which can be solved sequentially. We show that the latter subproblem can be casted as a planar three-index assignment problem. This makes existing solution techniques for the planar three-index assignment problem amenable to sports league scheduling.

Keywords

Combinatorial optimization Computational complexity Sports league scheduling Round robin tournaments Planar three index assignments 

MSC classification (2000)

90C27 68Q25 

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Copyright information

© Springer-Verlag 2010

Authors and Affiliations

  • Dirk Briskorn
    • 1
  • Andreas Drexl
    • 2
  • Frits C. R. Spieksma
    • 3
  1. 1.Seminar für ABWL, Supply Chain Management und ProduktionUniversität zu KölnKölnGermany
  2. 2.Lehrstuhl für Produktion und LogistikChristian-Albrechts-Universität KielKielGermany
  3. 3.Department of Operations Research and Business StatisticsKatholieke Universiteit LeuvenLeuvenBelgium

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