Abstract
The Referee Assignment Problem (RAP) is a novel arising problem in sports management, in which a limited number of referees with different qualifications and availabilities should be assigned to a set of games already scheduled, in order to respect a list of constraints. Number and nature of these constraints may significantly vary for sports, nation and type of league. Almost each tournament has its own particular set of constraints to be satisfied, therefore it is very difficult to generalize this problem. The goal of the problem is to find a feasible assignment, i.e., a configuration which allows to respect all the constraints given. An extension of the RAP is the Fair Referee Assignment Problem (FRAP), in which the objective is to minimize the violation of a set of soft (optional) constraints, while satisfying all the hard (mandatory) ones. In this work, the Italian Major Soccer League, the so-called SERIE A, is addressed, and an integer programming model for the related FRAP is proposed. Soft and hard constraints have been formulated according to the rules suggested by the AIA (Italian Referee Association) which is in charge of referee assignment for the SerieA. The model has been tested on a real instance taken from the season 2011/2012. Results obtained show the efficacy and the effectiveness of the model.
References
Alarcon, F., G. Duran, and M. Guajardo. 2014. “Referee Assignment in the Chilean Football League using Integer Programming and Patterns.” International Transactions in Operational Research, 21(3):415–438.10.1111/itor.12049Search in Google Scholar
Armstrong, J. and J. Willis. 1993. “Scheduling the Cricket World Cup: A Case Study.” Journal of the Operational Research Society 44(11):1067–1072.Search in Google Scholar
Bartsch, T., A. Drexl, and S. Kroger. 2006. “Scheduling the Professional Soccer Leagues of Austria and Germany.” Computer and Operations Research 33(7):1907–1937.10.1016/j.cor.2004.09.037Search in Google Scholar
Biajoli, F., A. Chaves, O. Mine, M. Souza, R. Pontes, and A. Lucena. 2004. “Scheduling the Brazilian Soccer Championship: A Simulated Annealing Approach.” in Fifth international conference on the practice and theory of automated timetabling, PATAT2004.Search in Google Scholar
Clarke, S. 1998. “Dynamic Programming in One-Day Cricket—Optimal Scoring Rates.” Journal of the Operational Research Society 39(4):331–337.10.1057/jors.1988.60Search in Google Scholar
Della Croce, F. and D. Oliveri. 2006. “Scheduling the Italian Football league: An ILP-Based Approach.” Computers and Operations Research 33(7):1963–1974.10.1016/j.cor.2004.09.025Search in Google Scholar
Dinitz, J. and D. Stinson. 2005. “On Assigning Referees to Tournament Schedules.” Bulletin of the Institute of Combinatorics and its Applications 44:22–28.Search in Google Scholar
Duarte, A., C. Ribeiro, E. H. Urrutia, and S. Hauesler. 2007a. “Referee Assignment in Sports Leagues.” Lecture Notes in Computer Science 3867:158–173.10.1007/978-3-540-77345-0_11Search in Google Scholar
Duarte, A., C. Ribeiro, and S. Urrutia. 2007b. “A Hybrid ILS Heuristic to the Referee Assignment Problem with an Embedded MIP Strategy.” Lecture Notes in Computer Science 4771:82–95.10.1007/978-3-540-75514-2_7Search in Google Scholar
Duran, G., T. Noronha, C. Ribeiro, S. Souyris, and A. Weintraub. 2006. “Branch-and-Cut for a Real-Life Highly Constrained Soccer Tournament Scheduling Problem.” in Sixth international conference on the practice and theory of automated timetabling, PATAT2006.Search in Google Scholar
Duran, G., M. Guajardo, J. Miranda, D. Saure, S. Souyris, A. Weintraub, and R. Wolf. 2007. “Scheduling the Chilean Soccer League by Integer Programming.” Interfaces 37:539–552.10.1287/inte.1070.0318Search in Google Scholar
Evans, J. 1988. “A Microcomputer-Based Decision Support System for Scheduling Umpires in the American Baseball League.” Interfaces 18:42–51.10.1287/inte.18.6.42Search in Google Scholar
Evans, J., J. Hebert, and R. Deckro. 1984. “Play Ball: The Scheduling of Sports Officials.” Perspectives in Computing 4:18–29.Search in Google Scholar
Farmer, A., J. Smith, and L. Miller. 2007. “Scheduling Umpire Crews for Professional Tennis Tournaments.” Interfaces 37:187–196.10.1287/inte.1060.0259Search in Google Scholar
Freeze, R. 1974. “An Analysis of Baseball Batting Order by Monte Carlo Simulation.” Operations Research 22(4):728–735.10.1287/opre.22.4.728Search in Google Scholar
Goossens, D. and R. Spieksma. 2012. “Soccer Schedules in Europe: An Overview.” Journal of scheduling 15(5):641–651.10.1007/s10951-011-0238-9Search in Google Scholar
Hersh, M. and S. Ladany. 1989. “Optimal Pole-Vaulting Strategy.” Operations Research 37(1):172–175.10.1287/opre.37.1.172Search in Google Scholar
Kendall, G., S. Knust, C. Ribeiro, and S. Urrutia. 2010. “Scheduling in Sports: An Annotated Bibliography.” Computers and Operations Research 37(1):1–19.10.1016/j.cor.2009.05.013Search in Google Scholar
Lamghari, A. and J. Ferland. 2011. “Assigning Judges to Competitions of Several Rounds using Tabu Search.” European Journal of Operational Research 210:694–705.10.1016/j.ejor.2010.10.034Search in Google Scholar
Normann, J. 1985. “Dynamic Programming in Tennis: When to use a Fast Serve.” Journal of the Operational Research Society 36(1):75–77.Search in Google Scholar
Normann, J. and S. Clarke. 2007. “Dynamic Programming in Cricket: Optimizing Batting Order for a Sticky Wicket.” Journal of the Operational Research Society 58(12):1678–1682.10.1057/palgrave.jors.2602309Search in Google Scholar
Rasmussen, R. 2008. “Scheduling a Triple Round Robin Tournament for the Best Danish Soccer League.” European Journal of Operational Research 185:795–810.10.1016/j.ejor.2006.12.050Search in Google Scholar
Ribeiro, C. and S. Urrutia. 2006. “Scheudling the Brazilian Soccer Championship.” in Sixth international conference on the practice and theory of automated timetabling, PATAT2006.Search in Google Scholar
Russell, R. and J. Leung. 1994. “Devising a Cost Effective Schedule for a Baseball League.” Operations Research 42(4):614–625.10.1287/opre.42.4.614Search in Google Scholar
Saltzman, R. and R. Bradford. 1996. “Optimal Realignments of the Teams in the National Football League.” European Journal of Operational Research 93(3):469–475.10.1016/0377-2217(96)00135-XSearch in Google Scholar
Schonberger, J., D. Mattfeld, and H. Kopfer. 2004. “Memetic Algorithm Timetabling for Non-Commercial Sport Leagues.” European Journal of Operational Research 153(1):102–116.10.1016/S0377-2217(03)00102-4Search in Google Scholar
Schreuder, J. 1992. “Combinatorial Aspects of Construction and Competition Dutch Professional Football League.” Discrete Applied Mathematics 35:301–312.10.1016/0166-218X(92)90252-6Search in Google Scholar
Sphicas, G. and S. Ladany. 1977. Optimal Strategies in Sport., New York: North-Holland, chapter Dynamic policies in the long jump., 101–112.Search in Google Scholar
Trick, M. and H. Yildiz. 2011. “Benders’ Cuts Guided Large Neighborhood Search for the Traveling Umpire Problem.” Naval Research Logistics 58:771–781.10.1002/nav.20482Search in Google Scholar
Trick, M. and H. Yildiz. 2012. “Locally Optimized Crossover for the Traveling Umpire Problem.” European Journal of Operational Research 216:286–292.10.1016/j.ejor.2011.07.049Search in Google Scholar
Trick, M., H. Yildiz, and T. Yunes. 2012. “Scheduling Major League Baseball Umpires and the Traveling Umpire Problem.” Interfaces 42:232–244.10.1287/inte.1100.0514Search in Google Scholar
Urban, T. and R. Russell. 2003. “Scheduling Sports Competitions on Multiple Venues.” European Journal of Operational Research 148(2):302–311.10.1016/S0377-2217(02)00686-0Search in Google Scholar
Van Voorhis, T. 2002. “Highly Constrained College Basketball Scheduling.” Journal of the Operational Research Society 53(6):603–609.10.1057/palgrave.jors.2601356Search in Google Scholar
Washburn, A. 1991. “Still More on Pulling the Goalie.” Interfaces 21:59–64.10.1287/inte.21.2.59Search in Google Scholar
Wright, M. 2009. “50 years of or in Sport.” Journal of the Operational Research Society 60:161–168.10.1057/jors.2008.170Search in Google Scholar
Yavuz, M., U. Inan, and A. Figlali. 2008. “Fair Referee Assignments for Professional Football Leagues.” Computers and Operations Research 35(9):2937–2951.10.1016/j.cor.2007.01.004Search in Google Scholar
©2014 by Walter de Gruyter Berlin/Boston
Articles in the same Issue
- Frontmatter
- Editorial
- Introduction to the MathSport papers
- Research Articles from the MathSport International Conference
- On the winning probabilities and mean durations of volleyball
- The older they rise the younger they fall: age and performance trends in men’s professional tennis from 1991 to 2012
- Developing an improved tennis ranking system
- Constructing schedules for sports leagues with divisional and round-robin tournaments
- Standings in sports competitions using integer programming
- Between-seasons competitive balance in European football: review of existing and development of specially designed indices
- Fair referee assignment for the Italian soccer serieA
- To lead or not to lead: analysis of the sprint in track cycling
- Importance of descending skill for performance in fell races: a statistical analysis of race results
- General Research Articles
- An Oracle method to predict NFL games
- Using random forests to estimate win probability before each play of an NFL game
- Reversal of fortune: a statistical analysis of penalty calls in the National Hockey League
- Realignment in the NHL, MLB, NFL, and NBA
- Estimating the effects of age on NHL player performance
- Uncovering Formula One driver performances from 1950 to 2013 by adjusting for team and competition effects
- Evaluating the ability of goalkeepers in English Premier League football
- Skill importance in women’s soccer
Articles in the same Issue
- Frontmatter
- Editorial
- Introduction to the MathSport papers
- Research Articles from the MathSport International Conference
- On the winning probabilities and mean durations of volleyball
- The older they rise the younger they fall: age and performance trends in men’s professional tennis from 1991 to 2012
- Developing an improved tennis ranking system
- Constructing schedules for sports leagues with divisional and round-robin tournaments
- Standings in sports competitions using integer programming
- Between-seasons competitive balance in European football: review of existing and development of specially designed indices
- Fair referee assignment for the Italian soccer serieA
- To lead or not to lead: analysis of the sprint in track cycling
- Importance of descending skill for performance in fell races: a statistical analysis of race results
- General Research Articles
- An Oracle method to predict NFL games
- Using random forests to estimate win probability before each play of an NFL game
- Reversal of fortune: a statistical analysis of penalty calls in the National Hockey League
- Realignment in the NHL, MLB, NFL, and NBA
- Estimating the effects of age on NHL player performance
- Uncovering Formula One driver performances from 1950 to 2013 by adjusting for team and competition effects
- Evaluating the ability of goalkeepers in English Premier League football
- Skill importance in women’s soccer