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An Integrated Constraint Programming Approach to Scheduling Sports Leagues with Divisional and Round-Robin Tournaments

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8451))

Abstract

Previous approaches for scheduling a league with round-robin and divisional tournaments involved decomposing the problem into easier subproblems. This approach, used to schedule the top Swedish handball league Elitserien, reduces the problem complexity but can result in suboptimal schedules. This paper presents an integrated constraint programming model that allows to perform the scheduling in a single step. Particular attention is given to identifying implied and symmetry-breaking constraints that reduce the computational complexity significantly. The experimental evaluation of the integrated approach takes considerably less computational effort than the previous approach.

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References

  1. Benoist, T., Laburthe, F., Rottembourg, B.: Lagrange relaxation and constraint programming collaborative schemes for travelling tournament problems. In: Proceedings CPAIOR, vol. 1, pp. 15–26 (2001)

    Google Scholar 

  2. Briskorn, D.: Sports Leagues Scheduling. Lecture Notes in Economics and Mathematical Systems, vol. 603. Springer (2008)

    Google Scholar 

  3. Easton, K., Nemhauser, G.L., Trick, M.A.: The traveling tournament problem description and benchmarks. In: Walsh, T. (ed.) CP 2001. LNCS, vol. 2239, pp. 580–584. Springer, Heidelberg (2001)

    Chapter  Google Scholar 

  4. Fronček, D., Meszka, A.: Round robin tournaments with one bye and no breaks in home-away patterns are unique. In: Multidisciplary Scheduling: Theory and Applications, pp. 331–340. MISTA, New York (July 2005) ISSN 2305-249X

    Google Scholar 

  5. Henz, M.: Scheduling a major college basketball conference—revisited. Operations Research 49(1), 163–168 (2001)

    Article  MathSciNet  Google Scholar 

  6. Henz, M., Müller, T., Thiel, S.: Global constraints for round robin tournament scheduling. European Journal of Operational Research 153(1), 92–101 (2004)

    Article  MathSciNet  Google Scholar 

  7. Larson, J., Johansson, M.: Constructing schedules for sports leagues with divisional and round-robin tournaments. Journal of Quantitative Analysis in Sports (to appear, 2014) doi:10.1515/jqas-2013-0090

    Google Scholar 

  8. Perron, L.: Alternate modeling in sport scheduling. In: van Beek, P. (ed.) CP 2005. LNCS, vol. 3709, pp. 797–801. Springer, Heidelberg (2005)

    Google Scholar 

  9. Pesant, G.: A regular language membership constraint for finite sequences of variables. In: Wallace, M. (ed.) CP 2004. LNCS, vol. 3258, pp. 482–495. Springer, Heidelberg (2004)

    Chapter  Google Scholar 

  10. Rasmussen, R.V., Trick, M.A.: The timetable constrained distance minimization problem. In: Beck, J.C., Smith, B.M. (eds.) CPAIOR 2006. LNCS, vol. 3990, pp. 167–181. Springer, Heidelberg (2006)

    Chapter  Google Scholar 

  11. Rasmussen, R.V., Trick, M.A.: Round robin scheduling - a survey. European Journal of Operational Research 188(3), 617–636 (2008)

    Article  MathSciNet  Google Scholar 

  12. Rasmussen, R.: Scheduling a triple round robin tournament for the best Danish soccer league. European Journal of Operational Research 185, 795–810 (2008)

    Article  MathSciNet  Google Scholar 

  13. Régin, J.C.: A filtering algorithm for constraints of difference in CSPs. In: 12th National Conference on Artificial Intelligence (AAAI-1994), pp. 362–367 (1994)

    Google Scholar 

  14. Régin, J.-C.: Generalized arc consistency for global cardinality constraint. In: Clancey, W.J., Weld, D.S. (eds.) AAAI/IAAI, vol. 1, pp. 209–215. AAAI Press / The MIT Press (1996)

    Google Scholar 

  15. Régin, J.-C.: The symmetric alldiff constraint. In: Dean, T. (ed.) IJCAI, pp. 420–425. Morgan Kaufmann (1999)

    Google Scholar 

  16. Régin, J.-C.: Minimization of the number of breaks in sports scheduling problems using constraint programming. DIMACS Series in Discrete Mathematics and Theoretical Computer Science 57, 115–130 (2001)

    Article  MathSciNet  Google Scholar 

  17. Ribeiro, C., Urrutia, S.: Scheduling the Brazilian soccer tournament with fairness and broadcast objectives. In: Burke, E.K., Rudová, H. (eds.) PATAT 2007. LNCS, vol. 3867, pp. 147–157. Springer, Heidelberg (2007)

    Chapter  Google Scholar 

  18. Russell, R.A., Urban, T.L.: A constraint programming approach to the multiple-venue, sport-scheduling problem. Computers & Operations Research 33(7), 1895–1906 (2006)

    Article  Google Scholar 

  19. Schaerf, A.: Scheduling sport tournaments using constraint logic programming. Constraints 4(1), 43–65 (1999)

    Article  MathSciNet  Google Scholar 

  20. Trick, M.A.: A schedule-then-break approach to sports timetabling. In: Burke, E., Erben, W. (eds.) PATAT 2000. LNCS, vol. 2079, pp. 242–253. Springer, Heidelberg (2001)

    Chapter  Google Scholar 

  21. Trick, M.A.: Integer and constraint programming approaches for round-robin tournament scheduling. In: Burke, E.K., De Causmaecker, P. (eds.) PATAT 2002. LNCS, vol. 2740, pp. 63–77. Springer, Heidelberg (2003)

    Chapter  Google Scholar 

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Larson, J., Johansson, M., Carlsson, M. (2014). An Integrated Constraint Programming Approach to Scheduling Sports Leagues with Divisional and Round-Robin Tournaments. In: Simonis, H. (eds) Integration of AI and OR Techniques in Constraint Programming. CPAIOR 2014. Lecture Notes in Computer Science, vol 8451. Springer, Cham. https://doi.org/10.1007/978-3-319-07046-9_11

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  • DOI: https://doi.org/10.1007/978-3-319-07046-9_11

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-07045-2

  • Online ISBN: 978-3-319-07046-9

  • eBook Packages: Computer ScienceComputer Science (R0)

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