An exact approach for the balanced k-way partitioning problem with weight constraints and its application to sports team realignment
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In this work a balanced k-way partitioning problem with weight constraints is defined to model the sports team realignment. Sports teams must be partitioned into a fixed number of groups according to some regulations, where the total distance of the road trips that all teams must travel to play a double round robin tournament in each group is minimized. Two integer programming formulations for this problem are introduced, and the validity of three families of inequalities associated to the polytope of these formulations is proved. The performance of a tabu search procedure and a branch and cut algorithm, which uses the valid inequalities as cuts, is evaluated over simulated and real-world instances. In particular, an optimal solution for the realignment of the Ecuadorian football league is reported and the methodology can be suitable adapted for the realignment of other sports leagues.
KeywordsInteger programming models Graph partitioning Tabu search Sports team realignment
This research was partially supported by the 15-MathAmSud-06 “PACK-COVER: Packing and covering, structural aspects” trilateral cooperation project. We are grateful to the anonymous referees for their useful comments which led to a significantly improved presentation of this work.
- Anjos M, Ghaddar B, Hupp L, Liers F, Wiegele A (2013) Solving k-way graph partitioning problems to optimality: the impact of semidefinite relaxations and the bundle method. In: Jünger M, Reinelt G (eds) Facets of combinatorial optimization: Festschrift for Martin Grötschel. Springer, Berlin, pp 355–386CrossRefGoogle Scholar
- Fairbrother J, Letchford A, Briggs K (2017) A two-level graph partitioning problem arising in mobile wireless communications. arXiv:1705.08773
- McDonald B, Pulleyblank W (2014) Realignment in the NHL, MLB, NFL, and NBA. J Quant Anal Sports 10(2):225–240Google Scholar
- Mitchell JE (2001) Branch-and-cut for the k-way equipartition problem. Technical report, Department of Mathematical Sciences, Rensselaer Polytechnic InstituteGoogle Scholar