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A branch-and-price algorithm for scheduling sport leagues

Author

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  • D Briskorn

    (Institut für Betriebswirtschaftslehre, Christian-Albrechts-Universität zu Kiel)

  • A Drexl

    (Institut für Betriebswirtschaftslehre, Christian-Albrechts-Universität zu Kiel)

Abstract

A single round robin tournament can be described as a league of a set T of n teams (n even) to be scheduled such that each team plays exactly once against each other team and such that each team plays exactly once per period resulting in a set P of n−1 periods. Matches are carried out at one of the stadiums of both opponents. A team playing twice at home or twice away in two consecutive periods is said to have a break in the latter of both periods. There is a vast field of requests arising in real-world problems. For example, the number of breaks is to be minimized due to fairness reasons. It is well known that at least n−2 breaks must occur. We focus on schedules having the minimum number of breaks. Costs corresponding to each possible match are given and the objective is to minimize the sum of cost of arranged matches. Then, sports league scheduling can be seen as a hard combinatorial optimization problem. We develop a branch-and-price approach in order to find optimal solutions.

Suggested Citation

  • D Briskorn & A Drexl, 2009. "A branch-and-price algorithm for scheduling sport leagues," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 60(1), pages 84-93, January.
    • Handle: RePEc:pal:jorsoc:v:60:y:2009:i:1:d:10.1057_palgrave.jors.2602515
    DOI: 10.1057/palgrave.jors.2602515
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    References listed on IDEAS

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    1. Dirk Briskorn & Andreas Drexl, 2007. "Branching Based on Home-Away-Pattern Sets," Operations Research Proceedings, in: Karl-Heinz Waldmann & Ulrike M. Stocker (ed.), Operations Research Proceedings 2006, pages 523-528, Springer.
    2. P. C. Gilmore & R. E. Gomory, 1961. "A Linear Programming Approach to the Cutting-Stock Problem," Operations Research, INFORMS, vol. 9(6), pages 849-859, December.
    3. Anuj Mehrotra & Michael A. Trick, 1996. "A Column Generation Approach for Graph Coloring," INFORMS Journal on Computing, INFORMS, vol. 8(4), pages 344-354, November.
    4. Rasmussen, Rasmus V. & Trick, Michael A., 2007. "A Benders approach for the constrained minimum break problem," European Journal of Operational Research, Elsevier, vol. 177(1), pages 198-213, February.
    5. William Cook & André Rohe, 1999. "Computing Minimum-Weight Perfect Matchings," INFORMS Journal on Computing, INFORMS, vol. 11(2), pages 138-148, May.
    6. Briskorn, Dirk & Drexl, Andreas, 2006. "Scheduling sports leagues using branch- and price," Manuskripte aus den Instituten für Betriebswirtschaftslehre der Universität Kiel 609, Christian-Albrechts-Universität zu Kiel, Institut für Betriebswirtschaftslehre.
    7. 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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    Cited by:

    1. Karsu, Özlem & Morton, Alec, 2015. "Inequity averse optimization in operational research," European Journal of Operational Research, Elsevier, vol. 245(2), pages 343-359.
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    3. Young Dae Ko & Seung Hwan Jung & Sung Hee Kim & Sung Wook Lee, 2018. "Sustainable Sport Scheduling Approach Considering Team Equity for the Korean Professional Baseball League," Sustainability, MDPI, vol. 10(2), pages 1-11, February.

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