Journal of the Operational Research Society

, Volume 62, Issue 12, pp 2133–2145 | Cite as

A branching scheme for minimum cost tournaments with regard to real-world constraints

General Paper

Abstract

Single round robin tournaments are a well-known class of sports leagues schedules. We consider leagues with a set T of n teams where n is even. Costs are associated with each possible match. Moreover, stadium availability, fixed matches, and regions’ capacities are taken into account. The goal is to find the minimum cost tournament among those having the minimum number of breaks and being feasible with regard to these additional constraints. A branching scheme is developed where branching is done by fixing a break for a team. Thus, the focus is on identifying breaks leading to an infeasible home away pattern set in order to avoid the resulting infeasible subtrees of a branch and bound tree.

Keywords

sports league scheduling round robin tournaments home-away-pattern set break stadium region branch-and-bound 

References

  1. Achterberg T, Koch T and Martin A (2005). Branching rules revisited. Eur J Opl Res 33: 42–54.Google Scholar
  2. Bartsch T, Drexl A and Kröger S (2006). Scheduling the professional soccer leagues of Austria and Germany. Comp Opns Res 33: 1907–1937.CrossRefGoogle Scholar
  3. Briskorn D (2008). Feasibility of home-away-pattern sets for round robin tournaments. Opns Res Lett 36: 283–284.CrossRefGoogle Scholar
  4. Briskorn D and Drexl A (2007). Branching based on home–away–pattern sets. In: Waldmann K-H and Stocker UM (eds). Operations Research Proceedings 2006–Selected Papers of the Annual International Conference of the German Operations Research Society (GOR), Karlsruhe, September 6th–8th 2006. Springer: Berlin, Germany, pp 523–528.Google Scholar
  5. Briskorn D and Drexl A (2009a). A branching scheme for finding cost-minimal round robin tournaments. Eur J Opl Res 197 (1): 68–76.CrossRefGoogle Scholar
  6. Briskorn D and Drexl A (2009b). IP models for round robin tournaments. Comp Opns Res 36 (3): 837–852.CrossRefGoogle Scholar
  7. Briskorn D, Drexl A and Spieksma FCR (2010). Round robin tournaments and three index assignment. 4OR 8 (4): 365–374.Google Scholar
  8. Brucker P and Knust S (2006). Complex Scheduling. Springer: Berlin.Google Scholar
  9. Della Croce F and Oliveri D (2006). Scheduling the Italian football league: An ILP-approach. Comp Opns Res 33: 1963–1974.CrossRefGoogle Scholar
  10. de Werra D (1980). Geography, games and graphs. Disc Appl Math 2: 327–337.CrossRefGoogle Scholar
  11. de Werra D (1981). Scheduling in sports. In: Hansen P (ed). Studies on Graphs and Discrete Programming. North-Holland: Amsterdam, the Netherlands, pp 381–395.CrossRefGoogle Scholar
  12. de Werra D (1982). Minimizing irregularities in sports schedules using graph theory. Disc Appl Math 4: 217–226.CrossRefGoogle Scholar
  13. de Werra D (1985). On the multiplication of divisions: The use of graphs for sports scheduling. Networks 15: 125–136.CrossRefGoogle Scholar
  14. de Werra D (1988). Some models of graphs for scheduling sports competitions. Disc Appl Math 21: 47–65.CrossRefGoogle Scholar
  15. de Werra D, Ekim T and Raess C (2006). Construction of sports schedules with multiple venues. Disc Appl Math 154: 47–58.CrossRefGoogle Scholar
  16. Drexl A and Knust S (2007). Sports league scheduling: Graph- and resource-based models. Omega 35: 465–471.CrossRefGoogle Scholar
  17. Durán G, Guajardo M, Miranda J, Sauré D and Weintraub A (2007). Scheduling the Chilean soccer league by integer programming. Interfaces 37: 539–552.CrossRefGoogle Scholar
  18. Edmonds J (1965). Paths, trees, and flowers. Canad J Math 17: 449–467.CrossRefGoogle Scholar
  19. Goossens D and Spieksma F (2009). Scheduling the Belgian soccer league. Interfaces 39 (2): 109–118.CrossRefGoogle Scholar
  20. Horbach A, Bartsch T and Briskorn D (2010). Optimally scheduling real world sports leagues by reduction to SAT. J Scheduling, DOI 10.1007/S10951-010-0194-9.Google Scholar
  21. Kendall G (2008). Scheduling English football fixtures over holiday periods. J Opl Res Soc 59: 743–755.CrossRefGoogle Scholar
  22. Kendall G, Knust S, Ribeiro CC and Urrutia S (2010). Invited review: Scheduling in sports: An annotated bibliography. Comp Opns Res 37 (1): 1–19.CrossRefGoogle Scholar
  23. Knust S (2010). Classification of literature on sports scheduling. http://www.inf.uos.de/knust/sportlit_class/. 10 September 2010.
  24. Knust S and Lücking D (2009). Minimizing costs in round robin tournaments with place constraints. Comp Opns Res 36: 2937–2943.CrossRefGoogle Scholar
  25. Miyashiro R, Iwasaki H and Matsui T (2003). Characterizing feasible pattern sets with a minimum number of breaks. In: Burke E and de Causmaecker P (eds). The 4th International Conference on the Practice and Theory of Automated Timetabling, Selected Revised Papers. Lecture Notes in Computer Science, Vol. 2740, Springer: Berlin, Germany, pp 78–99.Google Scholar
  26. Nurmi K (2010). Sports scheduling problem—Terminology, problem model, benchmark instances, best solutions. http://www.bit.spt.fi/cimmo.nurmi/ssp.htm, 10 September 2010.
  27. Nurmi K, Goossens D, Bartsch T, Bonomo F, Briskorn D, Duran G, Kyngs J, Marenco J, Ribeiro C, Spieksma F, Urrutia S and Wolf R (2010). A framework for a highly constrained sports scheduling problem. In: Ao S-I, Katagiri H, Xu L and Chan AH-S (eds.) Proceedings of the International MultiConference of Engineers and Computer Scientists 2010. Vol III. Newswood Limited: Hong-Kong, pp 1991–1997.Google Scholar
  28. Rasmussen RV (2008). Scheduling a triple round robin tournament for the best Danish soccer league. Eur J Opl Res 185: 795–810.CrossRefGoogle Scholar
  29. Rasmussen RV and Trick MA (2007). A Benders approach for the constrained minimum break problem. Eur J Opl Res 177: 198–213.CrossRefGoogle Scholar
  30. Rasmussen RV and Trick MA (2008). Round robin scheduling—A survey. Eur J Opl Res 188: 617–636.CrossRefGoogle Scholar
  31. Ribeiro CC and Urrutia S (2007). Scheduling the Brazilian soccer tournament with fairness and broadcast objectives. Lect Notes Comp Sci 3867: 149–159.Google Scholar
  32. Schreuder JAM (1992). Combinatorial aspects of construction of competition Dutch professional football leagues. Disc Appl Math 35: 301–312.CrossRefGoogle Scholar
  33. Siek JG, Lee L-Q and Lumsdaine A (2001). The Boost Graph Library: User Guide and Reference Manual. Addison-Wesley Professional: Amsterdam.Google Scholar
  34. Tarjan RE (1983). Data Structures and Network Algorithms. Society for Industrial and Applied Mathematics: Philadelphia.CrossRefGoogle Scholar

Copyright information

© Operational Research Society 2011

Authors and Affiliations

  1. 1.Universität zu KölnKölnGermany

Personalised recommendations