Using a SAT-solver to schedule sports leagues
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Tournament schedules of sports leagues have to satisfy several types of constraints such as stadium unavailability, fixed matches, forbidden matches, minimum number of breaks. Usually, there is no schedule satisfying all given constraints and, hence, some of the constraints are considered as ‘soft’ ones. There are various models appropriately describing the environment of sport leagues. Only heuristic methods are known from the literature for solving instances of real life dimensions. We consider here a model which satisfies the demands of many sports leagues. We solve our model by reduction to series of instances of the propositional satisfiability problem and adaption of a satisfiability solver for these specific instances. We test our method on two real life examples and solve the problem optimally within our model in each case. Our solver shows good computational results also on generated test instances, which are motivated by real life requirements. It can be easily extended to meet the demands of other sports leagues.
KeywordsTimetabling Sports Sports league scheduling Round robin tournaments Soft constraints Propositional satisfiability
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- Briskorn, D. (2009). A branching scheme for minimum cost tournaments with regard to real world constraints (Working Paper). Google Scholar
- Briskorn, D., & Drexl, A. (2007). Branching based on home–away–pattern sets. In K.-H. Waldmann & U. M. Stocker (Eds.), Operations research proceedings 2006—selected papers of the annual international conference of the german operations research society (GOR) (pp. 523–528). Karlsruhe, September 6th–8th 2006. Berlin: Springer. Google Scholar
- Briskorn, D., Drexl, A., & Spieksma, F. C. R. (2010, to appear). Round robin tournaments and three index assignment. 4OR. Google Scholar
- Brucker, P., & Knust, S. (2006). Complex scheduling. Berlin: Springer. Google Scholar
- de Werra, D. (1981). Scheduling in sports. In P. Hansen (Ed.), Studies on graphs and discrete programming (pp. 381–395). Amsterdam: North-Holland. Google Scholar
- Eén, N., & Sörensson, N. (2004). Theory and applications of satisfiability testing. In Lecture notes in computer science. An extensible SAT-solver (pp. 502–518). Berlin: Springer. Google Scholar
- Knust, S. (2009). Classification of literature on sports scheduling. http://www.inf.uos.de/knust/sportlit_class/. Accessed January 29th, 2009.
- Moskewicz, M. W., Madigan, C. F., Zhao, Y., Zhang, L., & Malik, S. (2001). Chaff: Engineering an efficient SAT solver. In DAC (pp. 530–535). Google Scholar
- Ribeiro, C. C., & Urrutia, S. (2007). Scheduling the Brazilian soccer tournament with fairness and broadcast objectives. In Lecture notes in computer science (Vol. 3867, pp. 149–159). Berlin: Springer. Google Scholar
- Sebastiani, R. (2007). Lazy satisfiability modulo theories. Journal on Satisfiability, Boolean Modeling and Computation, 3, 141–224. Google Scholar
- Zhang, H., Li, D., & Shen, H. (2004). A SAT based scheduler for tournament schedules. In Theory and applications of satisfiability testing, 7th international conference, SAT04 (pp. 191–196). Google Scholar