Abstract
The carry-over effects value is one of the various measures one can consider to assess the quality of a round robin tournament schedule. We introduce and discuss a new, weighted variant of the minimum carry-over effects value problem. The problem is formulated by integer programming and an algorithm based on the hybridization of the Iterated Local Search metaheuristic with a multistart strategy is proposed. Numerical results are presented.
Similar content being viewed by others
References
Anderson, I. (1999). Balancing carry-over effects in tournaments. In F. Holroyd, K. Quinn, C. Rowley, & B. Webb (Eds.), CRC research notes in mathematics. Combinatorial designs and their applications (pp. 1–16). London: Chapman & Hall.
Costa, F. N., Urrutia, S., & Ribeiro, C. C. (2008). An ILS heuristic for the traveling tournament problem with fixed venues. In E. K. Burke & M. Gendreau (Eds.), Proceedings of the 7th international conference on the practice and theory of automated timetabling, Montréal
de Werra, D. (1980). Geography, games and graphs. Discrete Applied Mathematics, 2, 327–337.
de Werra, D. (1981). Scheduling in sports. In P. Hansen (Ed.), Annals of discrete mathematics: Vol. 11. Studies on graphs and discrete programming (pp. 381–395). Amsterdam: North-Holland.
Dinitz, J. H. (1996). Starters. In C. J. Colbourn & J. H. Dinitz (Eds.), The CRC press series on discrete mathematics and its applications. The CRC handbook of combinatorial designs (pp. 467–473). Boca Raton: CRC Press.
Duarte, A. R., Ribeiro, C. C., Urrutia, S., & Haeusler, E. (2007). Referee assignment in sports leagues. In Lecture notes in computer science: Vol. 3867. Practice and theory of automated timetabling VI (pp. 158–173). Berlin: Springer.
Easton, K., Nemhauser, G., & Trick, M. A. (2001). The travelling tournament problem: description and benchmarks. In T. Walsh (Ed.), Lecture notes in computer science: Vol. 2239. Principles and practice of constraint programming (pp. 580–585). Berlin: Springer.
Flatberg, T., Nilssen, E., & Stølevik, M. (2009). Scheduling the topmost football leagues of Norway. In Book of abstracts of the 23rd European conference on operational research, Bonn (p. 240).
Glover, F. (1996). Ejection chains, reference structures and alternating path methods for traveling salesman problems. Discrete Applied Mathematics, 65, 223–253.
Glover, F., & Laguna, M. (1997). Tabu search. Dordrecht: Kluwer Academic.
Glover, F., Laguna, M., & Martí, R. (2000). Fundamentals of scatter search and path relinking. Control and Cybernetics, 29(3), 653–684.
Goodbread, C. (2010). SEC aims to fix schedule problem by month’s end. Online reference at http://www.tidesports.com/article/20100409/NEWS/100409591, last visited on August 14, 2010.
Goossens, D., & Spieksma, F. (2009). Does the carry-over effect exist? In Book of abstracts of the 23rd European conference on operational research, Bonn (p. 288).
Gutin, G., & Punnen, P. (Eds.) (2002). The traveling salesman problem and its variations. Dordrecht: Kluwer Academic.
Hansen, P., & Mladenovic, N. (2002). Variable neighborhood search. In F. Glover & G. Kochenberger (Eds.), Handbook of metaheuristics (pp. 145–184). Dordrecht: Kluwer Academic.
Henz, M., Müller, T., & Thiel, S. (2004). Global constraints for round robin tournament scheduling. European Journal of Operational Research, 153, 92–101.
Kendall, G., Knust, S., Ribeiro, C. C., & Urrutia, S. (2010). Scheduling in sports: An annotated bibliography. Computers & Operations Research, 37, 1–19.
Kirkman, T. (1847). On a problem in combinations. Cambridge Dublin Mathematical Journal, 2, 191–204.
Lawler, E. L., Lenstra, J. K., Rinnooy Kan, A. H. G., & Shmoys, D. B. (Eds.) (1985). The traveling salesman problem: a guided tour of combinatorial optimization. New York: Wiley.
Lourenço, H. R., Martin, O. C., & Stutzle, T. (2003). Iterated local search. In F. Glover & G. A. Kochenberger (Eds.), Handbook of metaheuristics (pp. 321–353). Dordrecht: Kluwer Academic.
Lucena, A. P., Ribeiro, C. C., & Santos, A. C. (2010) A hybrid heuristic for the diameter constrained minimum spanning tree problem. Journal of Global Optimization, 46, 363–381.
Martin, O. C., Otto, S. W., & Felten, E. W. (1991). Large-step Markov chains for the traveling salesman problem. Complex Systems, 5, 299–326.
Miyashiro, R., & Matsui, T. (2006). Minimizing the carry-over effects value in a round robin tournament. In Proceedings of the 6th international conference on the practice and theory of automated timetabling, Brno (pp. 460–463).
Mladenovic, N., & Hansen, P. (1997). Variable neighborhood search. Computers & Operations Research, 34, 1097–1100.
Noronha, T. F., Ribeiro, C. C., Duran, G., Souyris, S., & Weintraub, A. (2007). A branch-and-cut algorithm for scheduling the highly-constrained Chilean soccer tournament. In Lecture notes in computer science: Vol. 3867. Practice and theory of automated timetabling VI (pp. 174–186). Berlin: Springer.
Rasmussen, R. V., & Trick, M. A. (2008). Round robin scheduling—a survey. European Journal of Operational Research, 188, 617–636.
Ribeiro, C. C., & Urrutia, S. (2007a). Scheduling the Brazilian soccer tournament with fairness and broadcast objectives. In Lecture notes in computer science: Vol. 3867. Practice and theory of automated timetabling VI (pp. 147–157). Berlin: Springer.
Ribeiro, C. C., & Urrutia, S. (2007b). Heuristics for the mirrored traveling tournament problem. European Journal of Operational Research, 179, 775–787.
Ribeiro, C., & Urrutia, S. (2009c). Bicriteria integer programming approach for scheduling the Brazilian national soccer tournament. In Proceedings of the third international conference on management science and engineering management, Bangkok (pp. 46–49).
Russell, K. G. (1980). Balancing carry-over effects in round robin tournaments. Biometrika, 67, 127–131.
Trick, M. A. (2000). A schedule-then-break approach to sports timetabling. In E. Burke & W. Erben (Eds.), Lecture notes in computer sciences: Vol. 2079. Selected papers from the third international conference on practice and theory of automated timetabling III (pp. 242–253). Berlin: Springer.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Guedes, A.C.B., Ribeiro, C.C. A heuristic for minimizing weighted carry-over effects in round robin tournaments. J Sched 14, 655–667 (2011). https://doi.org/10.1007/s10951-011-0244-y
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10951-011-0244-y