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.
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Briskorn, D., Drexl, A. & Spieksma, F.C.R. Round robin tournaments and three index assignments. 4OR-Q J Oper Res 8, 365–374 (2010). https://doi.org/10.1007/s10288-010-0123-y
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DOI: https://doi.org/10.1007/s10288-010-0123-y
Keywords
- Combinatorial optimization
- Computational complexity
- Sports league scheduling
- Round robin tournaments
- Planar three index assignments