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Scheduling sports leagues using branch- and price

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  • Briskorn, Dirk
  • Drexl, Andreas

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 both opponents' stadiums. 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 arranged matches' cost. Then, sports league scheduling can be seen as a hard combinatorial optimization problem. We develop a branch & price approach in order to find optimal solutions.

Suggested Citation

  • 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.
    • Handle: RePEc:zbw:cauman:609
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    References listed on IDEAS

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    1. 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.
    2. 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.
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    1. 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.
    2. Christian-Albrechts-Universität zu Kiel, Institut für Betriebswirtschaftslehre (Ed.), 2007. "Jahresbericht 2006," Manuskripte aus den Instituten für Betriebswirtschaftslehre der Universität Kiel 614, Christian-Albrechts-Universität zu Kiel, Institut für Betriebswirtschaftslehre.
    3. Briskorn, Dirk & Drexl, Andreas, 2007. "A branching scheme based on First-Break-Then-Schedule decomposition," Manuskripte aus den Instituten für Betriebswirtschaftslehre der Universität Kiel 623, Christian-Albrechts-Universität zu Kiel, Institut für Betriebswirtschaftslehre.

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