Abstract
Optimization in sports is a field of increasing interest. Combinatorial optimization techniques have been applied, for example, to game scheduling and playoff elimination. A common problem usually found in sports management is the assignment of referees to games already scheduled. There are a number of rules and objectives that should be taken into account when referees are assigned to games. We address a simplified version of a referee assignment problem common to many amateur leagues of sports such as soccer, baseball, and basketball. The problem is formulated by integer programming and its decision version is proved to be NP-complete. To tackle real-life large instances of the referee assignment problem, we propose a three-phase heuristic approach based on a constructive procedure, a repair heuristic to make solutions feasible, and a local search heuristic to improve feasible solutions. Numerical results on realistic instances are presented and discussed.
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References
Anagnostopoulos, A., Michel, L., Van Hentenryck, P., Vergados, Y.: A simulated annealing approach to the traveling tournament problem. Journal of Scheduling 9, 177–193 (2006)
Bodlaender, H.L., Jansen, K.: Restrictions of graph partition problems – Part I. Theoretical Computer Science 148, 93–109 (1995)
Corneil, D.G., Olariu, S., Stewart, L.: The ultimate interval graph recognition algorithm? In: Proceedings of the 9th Annual ACM-SIAM Symposium on Discrete Algorithms, pp. 175–180. SIAM, Philadelphia (1998)
Dinitz, J.H., Stinson, D.R.: On assigning referees to tournament schedules. Bulletin of the Institute of Combinatorics and its Applications 44, 22–28 (2005)
Duarte, A.R.: Challenge referee assignment problem instances (last visited on March 23, 2007), Online document at http://www.esportemax.org/rapopt
Easton, K., Nemhauser, G.L., Trick, M.: The traveling tournament problem: Description and benchmarks. In: Walsh, T. (ed.) CP 2001. LNCS, vol. 2239, pp. 580–584. Springer, Heidelberg (2001)
Easton, K., Nemhauser, G.L., Trick, M.: Sports scheduling. In: Leung, J.T. (ed.) Handbook of Scheduling: Algorithms, Models and Performance Analysis, pp. 52.1–52.19. CRC Press, Boca Raton, FL (2004)
Evans, J.R.: A microcomputer-based decision support system for scheduling umpires in the American baseball league. Interfaces 18, 42–51 (1988)
Evans, J.R., Hebert, J.E., Deckro, R.F.: Play ball – The scheduling of sports officials. Perspectives in Computing 4, 18–29 (1984)
Fisher, M.L., Jaikumar, R., Van Wassenhove, L.N.: A multiplier adjustment method for the generalized assignment problem. Management Science 32, 1095–1103 (1986)
Lourenço, H.P., Martin, O., Stützle, T.: Iterated Local Search. In: Glover, F., Kochenberger, G. (eds.) Handbook of Metaheuristics, pp. 321–353. Kluwer, Dordrecht (2003)
Martin, O., Otto, S.W.: Combining simulated annealing with local search heuristics. Annals of Operations Research 63, 57–75 (1996)
Martin, O., Otto, S.W., Felten, E.W.: Large-step Markov chains for the traveling salesman problem. Complex Systems 5, 299–326 (1991)
Nemhauser, G.L., Trick, M.A.: Scheduling a major college basketball conference. Operations Research 46, 1–8 (1997)
Rasmussen, R.V., Trick, M.A.: Round robin scheduling – A survey. Technical Report, Department of Operations Research, University of Aarhus (2006)
Ribeiro, C.C., Urrutia, S.: OR on the ball: Applications in sports scheduling and management. OR/MS Today 31, 50–54 (2004)
Ribeiro, C.C., Urrutia, S.: An application of integer programming to playoff elimination in football championships. International Transactions in Operational Research 12, 375–386 (2005)
Ribeiro, C.C., Urrutia, S.: Heuristics for the mirrored traveling tournament problem. European Journal of Operational Research 179, 775–787 (2007)
Wright, M.B.: Scheduling English cricket umpires. Journal of the Operational Research Society 42, 447–452 (1991)
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Duarte, A.R., Ribeiro, C.C., Urrutia, S., Haeusler, E.H. (2007). Referee Assignment in Sports Leagues. In: Burke, E.K., Rudová, H. (eds) Practice and Theory of Automated Timetabling VI. PATAT 2006. Lecture Notes in Computer Science, vol 3867. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-77345-0_11
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DOI: https://doi.org/10.1007/978-3-540-77345-0_11
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-77344-3
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