## Abstract

The sport teams grouping problem (STGP) concerns the assignment of sport teams to round-robin tournaments. The objective is to minimize the total travel distance of the participating teams while simultaneously respecting fairness constraints. The STGP is an NP-Hard combinatorial optimization problem highly relevant in practice. This paper investigates the performance of some complimentary optimization approaches to the STGP. Three integer programming formulations are presented and thoroughly analyzed: two compact formulations and another with an exponential number of variables, for which a branch-and-price algorithm is proposed. Additionally, a meta-heuristic method is applied to quickly generate feasible high-quality solutions for a set of real-world instances. By combining the different approaches’ results, solutions within 1.7% of the optimum values were produced for all feasible instances. Additionally, to support further research, the considered STGP instances and corresponding solutions files were shared online.

## Keywords

Sport teams grouping problem Branch-and-price Column generation Decomposition strategies Integer programming Meta-heuristic## Notes

### Acknowledgements

Work supported by the Belgian Science Policy Office (BELSPO) in the Inter-university Attraction Pole COMEX (http://comex.ulb.ac.be) and by the Leuven Mobility Research Centre (L-Mob). Editorial support provided by Luke Connolly, KU Leuven. Additionally, we would like to thank Movetex, in particular Dieter De Naeyer and Ken De Norre–De Groof, for the insightful discussions concerning the problem and for making the real-world instances available.

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