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

Author

Listed:
  • Diego Recalde

    (Escuela Politécnica Nacional
    Escuela Politécnica Nacional)

  • Daniel Severín

    (Universidad Nacional de Rosario and CONICET)

  • Ramiro Torres

    (Escuela Politécnica Nacional)

  • Polo Vaca

    (Escuela Politécnica Nacional)

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.

Suggested Citation

  • Diego Recalde & Daniel Severín & Ramiro Torres & Polo Vaca, 2018. "An exact approach for the balanced k-way partitioning problem with weight constraints and its application to sports team realignment," Journal of Combinatorial Optimization, Springer, vol. 36(3), pages 916-936, October.
    • Handle: RePEc:spr:jcomop:v:36:y:2018:i:3:d:10.1007_s10878-018-0254-1
    DOI: 10.1007/s10878-018-0254-1
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    References listed on IDEAS

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    1. Saltzman, Robert M. & Bradford, Richard M., 1996. "Optimal realignments of the teams in the National Football League," European Journal of Operational Research, Elsevier, vol. 93(3), pages 469-475, September.
    2. FERREIRA, Carlos E. & MARTIN, Alexander & de SOUZA, Cid C. & WEISMANTEL, Robert, 1998. "The node capacitated graph partitioning problem: A computational study," LIDAM Reprints CORE 1335, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    3. John E. Mitchell, 2003. "Realignment in the National Football League: Did they do it right?," Naval Research Logistics (NRL), John Wiley & Sons, vol. 50(7), pages 683-701, October.
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    Cited by:

    1. Diego Recalde & Ramiro Torres & Polo Vaca, 2020. "An exact approach for the multi-constraint graph partitioning problem," EURO Journal on Computational Optimization, Springer;EURO - The Association of European Operational Research Societies, vol. 8(3), pages 289-308, October.
    2. Li, Miao & Davari, Morteza & Goossens, Dries, 2023. "Multi-league sports scheduling with different leagues sizes," European Journal of Operational Research, Elsevier, vol. 307(1), pages 313-327.
    3. Antonis Antonopoulos & Aris Pagourtzis & Stavros Petsalakis & Manolis Vasilakis, 2023. "Faster algorithms for k-subset sum and variations," Journal of Combinatorial Optimization, Springer, vol. 45(1), pages 1-21, January.

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