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An exact approach for the balanced k-way partitioning problem with weight constraints and its application to sports team realignment

Abstract

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.

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Acknowledgements

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.

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Correspondence to Diego Recalde.

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A preliminary version of this paper appeared at ISCO 2016.

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Recalde, D., Severín, D., Torres, R. et al. An exact approach for the balanced k-way partitioning problem with weight constraints and its application to sports team realignment. J Comb Optim 36, 916–936 (2018). https://doi.org/10.1007/s10878-018-0254-1

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Keywords

  • Integer programming models
  • Graph partitioning
  • Tabu search
  • Sports team realignment