Advertisement

A Branch-and-Price Algorithm for Scheduling Sport Leagues

  • D. Briskorn
  • A. Drexl
Part of the OR Essentials book series (ORESS)

Abstract

Round robin tournaments (RRTs) cover a huge variety of different types of sports league schedules arising in practice. The focus in this paper is on single RRTs where scheduling is temporally constrained, which means that matches have to be scheduled in a given minimum number of periods. We consider a set T of n teams. If n is odd, we easily can add a dummy team and, hence, we can assume, that n is even without loss of generality. In a single RRT, each team plays exactly once against each other team, either at home or away. Furthermore, a team i⋲T has to play exactly once in each period and, hence, we have a set P of n−1 periods altogether.

Keywords

Feasible Solution Column Generation Master Problem Current Node Depth First Search 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Anagnostopoulos A, Michel L, van Hentenryck P and Vergados Y (2006). A simulated annealing approach to the travelling tournament problem. J Scheduling 9: 177–193.CrossRefGoogle Scholar
  2. Barnhart C, Johnson EL, Nemhauser GL, Savelsbergh MWP and Vance PH (1996). Branch-and-price: Column generation for solving huge integer programs. Opns Res 46: 316–329.CrossRefGoogle Scholar
  3. Bartsch T (2001). Sportligaplanung — Ein Decision Support System zur Spielplanerstellung. Deutscher Universita¨tsverlag: Wiesbaden (in German).Google Scholar
  4. Bartsch T, Drexl A and Kröger S (2006). Scheduling the professional soccer leagues of Austria and Germany. Comput Opns Res 33: 1907–1937.CrossRefGoogle Scholar
  5. Briskorn D and Drexl A (2006). Scheduling sports leagues using branch-and-price. In: Burke E and Rudova H (eds). Proceedings of the Sixth International Conference on the Practice and Theory of Automated Timetabling. Springer: Berlin: Germany, pp 367–369.Google Scholar
  6. Briskorn D and Drexl A (2007). Branching based on home-away-pattern sets. In: GOR Proceedings 2006. Springer: Berlin, Germany.Google Scholar
  7. Briskorn D, Drexl A and Spieksma FCR (2006). Round robin tournaments and three index assignment. Working Paper.Google Scholar
  8. Brucker P and Knust S (2006). Complex Scheduling. Springer: Berlin.Google Scholar
  9. Cook W and Rohe A (1999). Computing minimum-weight perfect matchings. INFORMS J Comput 11: 138–148.CrossRefGoogle Scholar
  10. de Werra D (1980). Geography, games and graphs. Discrete 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. Discrete Appl Math 4: 217–226.CrossRefGoogle Scholar
  13. de Werra D (1985a). On the multiplication of divisions: The use of graphs for sports scheduling. Networks 15: 125–136.CrossRefGoogle Scholar
  14. de Werra D (1985b). Some models of graphs for scheduling sports competitions. Discrete Appl Math 21: 47–65.CrossRefGoogle Scholar
  15. de Werra D, Ekim T and Raess C (2006). Construction of sports schedules with multiple venues. Discrete 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. Easton K, Nemhauser G and Trick M (2001). The travelling tournament problem: Description and benchmarks. In: Walsh T (ed). Proceedings of Principles and Practice of Constraint Programming — CP 2001. Lecture Notes in Computer Science, Vol. 2239. Springer: Berlin, pp 580–585.CrossRefGoogle Scholar
  18. Edmonds J (1965). Maximum matching and a polyhedron with (0,1) vertices. J Res Natl Bureau Standards Sect B 69(B): 125–130.CrossRefGoogle Scholar
  19. Gilmore PC and Gomory RE (1961). A linear programming approach to the cutting-stock problem. Opns Res 9: 849–859.CrossRefGoogle Scholar
  20. Kendall G (2007). Scheduling English football fixtures over holiday periods. J Opl Res Soc. Advance online publication, (doi: 10.1057/palgrave.jors.2602382).Google Scholar
  21. Kirkman TP (1847). On a problem in combinations. Cambridge Dublin Math J 2: 191–204.Google Scholar
  22. Kuhn HW (1955). The Hungarian method for the assignment problem. Naval Res Logistics Quart 2: 83–97.CrossRefGoogle Scholar
  23. Lasdon LS (1970). Optimization theory for large systems. North-Holland: Amsterdam, The Netherlands.Google Scholar
  24. Lowerre BT (1976). The HARPY speech recognition system. Ph.D thesis, Carnegie-Mellon University, USA.Google Scholar
  25. Mehrotra A and Trick MA (1996). A column generation approach for graph coloring. INFORMS J Comput 8: 344–354.CrossRefGoogle Scholar
  26. Miyashiro R, Iwasaki H and Matsui T (2003). Characterizing feasible pattern sets with a minimum number of breaks. In: Burke E., de Causmaecker P, (eds). Proceedings of the Fourth International Conference on the Practice and Theory of Automated Timetabling, Lecture Notes in Computer Science, Vol. 2740. Springer: Berlin, Germany, pp 78–99.CrossRefGoogle Scholar
  27. Rasmussen RV (2008). Scheduling a triple round robin tournament for the best Danish soccer league. Eur J Opl Res 185: 795–810.CrossRefGoogle Scholar
  28. Rasmussen RV and Trick MA (2007). A benders approach for the constrained minimum break problem. Eur J Opl Res 177: 198–213.CrossRefGoogle Scholar
  29. Rubin S (1978). The ARGOS image understanding system. Ph.D thesis, Carnegie-Mellon University, USA.Google Scholar
  30. Ryan DM and Foster BA (1981). An integer programming approach to scheduling. In: Wren A (ed). Computer scheduling of public transport. urban passenger vehicle and crew scheduling. North-Holland: Amsterdam, The Netherlands, pp 269–280.Google Scholar
  31. Schreuder JAM (1980). Constructing timetables for sport competitions. Math Programming Study 13: 58–67.CrossRefGoogle Scholar
  32. Schreuder JAM (1992). Combinatorial aspects of construction of competition dutch professional football leagues. Discrete Appl Math 35: 301–312.CrossRefGoogle Scholar
  33. Urrutia S and Ribeiro CC (2004). Minimizing travels by maximizing breaks in round robin tournament schedules. Electronic Notes Discrete Math 18(C): 227–231.CrossRefGoogle Scholar
  34. Vance PH, Barnhart C, Johnson EL and Nemhauser GL (1994). Solving binary cutting stock problems by column generation and branch-and-bound. Comput Optim Appl 3: 111–130.CrossRefGoogle Scholar

Copyright information

© Operational Research Society 2015

Authors and Affiliations

  • D. Briskorn
  • A. Drexl

There are no affiliations available

Personalised recommendations