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A Lagrangian approach for minimum cost tournaments

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  • Briskorn, Dirk
  • Horbach, Andrei

Abstract

Single round robin tournaments are a well known class of sports leagues schedules. We consider leagues with a set T of n teams where n is even. Costs are associated to each possible match. Since matches are carried out at one of both opponents venues matches may be forbidden in certain periods due to unavailability of stadiums. The goal is to find the minimum cost tournament among those having no forbidden match. We employ a Lagrangian relaxation approach in order to obtain tight lower bounds. Moreover, we develop a cost-oriented repair mechanism yielding a feasible tournament schedule to each Solution of the relaxed problem.

Suggested Citation

  • Briskorn, Dirk & Horbach, Andrei, 2009. "A Lagrangian approach for minimum cost tournaments," Manuskripte aus den Instituten für Betriebswirtschaftslehre der Universität Kiel 647, Christian-Albrechts-Universität zu Kiel, Institut für Betriebswirtschaftslehre.
    • Handle: RePEc:zbw:cauman:647
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    References listed on IDEAS

    as
    1. Baker, Barrie M. & Sheasby, Janice, 1999. "Accelerating the convergence of subgradient optimisation," European Journal of Operational Research, Elsevier, vol. 117(1), pages 136-144, August.
    2. Dirk Briskorn, 2008. "Alternative IP Models for Sport Leagues Scheduling," Operations Research Proceedings, in: Jörg Kalcsics & Stefan Nickel (ed.), Operations Research Proceedings 2007, pages 403-408, Springer.
    3. Rasmussen, Rasmus V. & Trick, Michael A., 2008. "Round robin scheduling - a survey," European Journal of Operational Research, Elsevier, vol. 188(3), pages 617-636, August.
    4. Drexl, Andreas & Knust, Sigrid, 2007. "Sports league scheduling: Graph- and resource-based models," Omega, Elsevier, vol. 35(5), pages 465-471, October.
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