Optimal matchday schedule for Turkish professional soccer league using nonlinear binary integer programming
Sports scheduling problems are interesting optimization problems that require the decision of who play with whom, where and when to play. In this work, we study the sports scheduling problem faced by the Turkish Football Federation. Given the schedule of games for each round of the season, the problem is to determine the match days with the goal of having a fair schedule for each team. The criteria we employ to establish this fairness are achieving an equal distribution of match days between the teams throughout the season and the ideal assignment of games to different days in each round of the tournament. The problem is formulated as a nonlinear binary integer program and is solved optimally for each week. Our results indicate that significant improvements over the existing schedule can be achieved if the optimal solution is implemented
1] S¨ozc¨u (2016). Fenerbah¸ce TFF’ye ba¸svurdu (Fenerbah¸ce consulted TFF) [online]. Available from: https://skor.sozcu.com.tr/ 2016/12/30/fenerbahce-tffye-basvurdu -maclara-cikmayiz-tepkisi-572320/amp [Accessed 1 September 2021].
[2] Ajansspor (2017). Hafta i¸ci trib¨unler dolmuyor (Tribunes are not full on weekdays) [online]. Available from: https://ajansspo r.com/haber/hafta-ici-tribunler-dolm uyor-118912 [Accessed 1 September 2021].
[3] Habert¨urk (2011). Trib¨unler dolmuyor (Tribunes are not full) [online]. Available from: https://www.haberturk.com/spor/futbo l/haber/686439-tribunler-dolmuyor [Accessed 1 September 2021].
[4] Yeni¸ca˘g (2009). TFF’ye b¨uy¨uk tepki (A huge reaction against TFF) [online]. Available from: https://www.yenicaggazetesi.co m.tr/tffye-buyuk-tepki-21521h.htm [Accessed 1 September 2021].
[5] S¨ozc¨u (2017). Be¸sikta¸s’a cumalar yaramıyor (Be¸sikta¸s does not benefit from Fridays) [online]. Available from:https://www.goal.com/tr/amp/haber/besiktasacumalar-yaramiyor/1wtdm3xat35i41tzisu6ezqjv9 [Accessed 1 September 2021].
[6] Sondakika (2017). Trabzonspor’a cuma g¨un¨u oynadı˘gı ma¸clar yaramıyor (Trabzonspor does not benefit from Friday matches) [online]. Available from: https://www.sond akika.com/haber/haber-trabzonspor-acuma-gunu-oynadigi-maclar-yaramiyor [Accessed 1 September 2021]
[7] Yeni¸ca˘g (2010). Kartala cuma yaramıyor (Kartal does not benefit from Fridays) [online]. Available from: https://www.fanati k.com.tr/amp/kartala-cuma-yaramiyor- 175352 [Accessed 1 September 2021].
[8] Fotoma¸c (2018). Ba¸sak¸sehire pazartesi ma¸cları yaramıyor (Ba¸sak¸sehir does not benefit from Monday matches) [online]. Available from: https://m.fotomac.com.tr/medip ol-basaksehir/2018/02/27/basaksehi re-pazartesi-maclari-yaramiyor/amp [Accessed 1 September 2021].
[9] Kim, T. (2019). Optimal approach to game scheduling of multiple round-robin tournament: Korea professional baseball league in focus. Computers and Industrial Engineering, 136, 95–105.
[10] Rasmussen, R.V. & Trick, M.A. (2008). Round robin scheduling—a survey. European Journal of Operational Research, 188(3), 617–636.
[11] Ribeiro, C.C. (2012). Sports scheduling: Problems and applications. International Transactions in Operational Research, 19(1- 2), 201–226.
[12] Kendall, G., Knust, S., Ribeiro, C.C., & Urrutia, S. (2010). Scheduling in sports: An annotated bibliography. Computers and Operations Research, 37(1), 1–19.
[13] Atan, T., & C¸ avdaro˘glu, B. (2018). Minimization of rest mismatches in round robin tournaments. Computers and Operations Research, 99, 78–89.
[14] C¸ avdaro˘glu, B., & Atan, T. (2020). Determining matchdays in sports league schedule to minimize rest differences. Operations Research Letters, 48(3), 209–216.
[15] Rasmussen, R.V., & Trick, M.A. (2007). A Benders approach for the constrained minimum break problem. European Journal of Operational Research, 177(1), 198–213.
[16] Duran, G., Guajardo, M., & Saure, D. (2017). Scheduling the South American Qualifiers to the 2018 FIFA World Cup by integer programming. European Journal of Operational Research, 262(3), 1109–1115.
[17] Recalde, D., Torres, R., & Vaca, P. (2013). Scheduling the professional Ecuadorian football league by integer programming. Computers and Operations Research, 40(10), 2478–2484.
[18] Bulck, D.V., & Goossens, D. (2020). Handling fairness issues in time-relaxed tournaments with availability constraints. Computers and Operations Research, 115, 1048–1056.
[19] Kendall, G., & Westphal, S. (2013). Sports Scheduling: Minimizing Travel for English Football Supporters. In: A. Uyar, E. Ozcan, N. Urquhart eds. Automated Scheduling and Planning. Studies in Computational Intelligence. Springer, Berlin, Heidelberg, 61–90.
[20] Guedes, A.C.B., & Ribeiro, C.C. (2011). A heuristic for minimizing weighted carry-over effects in round robin tournaments. Journal of Scheduling, 14(6), 655–667.
[21] Januario, T., & Urrutia, S. (2016). A new neighborhood structure for round robinscheduling problems. Computers and Operations Research, 70, 127–139.
[22] G¨unne¸c, D., & Demir, E. (2019). Fairfixture: Minimizing carry-over effects in football leagues. Journal of Industrial and Management Optimization, 15(4), 1565–1577.
[23] Dur´an, G., Guajardo, M. & Wolf-Yadlin, R. (2012). Operations research techniques for scheduling Chile’s second division soccer league. Interfaces, 42(3), 273–285.
[24] Rasmussen, R.V. (2008). Scheduling a triple round robin tournament for the best Danish soccer league. European Journal of Operational Research, 185(2), 795–810.
[25] Goossens, D., & Spieksma, F. (2009). Scheduling the Belgian soccer league. Interfaces, 39(2), 109–118.
[26] Ribeiro, C.C., & Urrutia, S. (2012). Scheduling the Brazilian soccer tournament: Solution approach and practice. Interfaces, 42(3), 260–272.
[27] Dur´an, G., Guajardo, M., Miranda, J., Saur´e, D., Souyris, S., Weintraub, A., & Wolf, R. (2007). Scheduling the Chilean soccer league by integer programming. Interfaces, 37(6), 539–552.
[28] Bartsch, T., Drexl, A., & Kr˙oger, S. (2006). Scheduling the professional soccer leagues of Austria and Germany. Computers and Operations Research, 33(7), 1907–1937.
[29] Briskorn, D., & Drexl, A. (2009). IP models for round robin tournaments. Computers and Operations Research, 36(3), 837–852.
[30] Dur´an, G., Dur´an, S., Marenco, J., Mascialino, F., & Rey, P.A. (2019). Scheduling Argentina’s professional basketball leagues: A variation on the Travelling Tournament Problem. European Journal of Operational Research, 275(3), 1126–1138.
[31] Haselgrove, J., & Leech, J. (1977). A tournament design problem. The Amer. Math. Monthly, 84(3), 198–201.
[32] de Werra, D. (1981). Scheduling in Sports. In: P. Hansen, ed. Studies on Graphs and Discrete Programming. North Holland, 381–395.
[33] Elf, M., & Junger, M. (2003). Minimizing breaks by maximizing cuts. Operations Research Letters, 31(5), 343–349.
[34] van’t Hof, P., Post, G., & Briskorn, D. (2010). Constructing fair round robin tournaments with a minimum number of breaks. Operations Research Letters, 38(6), 592–596.
[35] Yi, X., Goossens, D., & Nobibon, F.T. (2020). Proactive and reactive strategies for football league timetabling. European Journal of Operational Research, 282(2), 772–785.
[36] Jane, W.J. (2014). The relationship between outcome uncertainties and match attendance: New evidence in the National Basketball Association. Review of Industrial Organization, 45(2), 177–200.
[37] Tainsky, S., & Winfree, J.A. (2010). ShortRun Demand and Uncertainty of Outcome in Major League Baseball. Review of Industrial Organization, 37(3), 197–214.
[38] Buraimo, B., & Simmons, R. (2009). A tale of two audiences: Spectators, television viewers and outcome uncertainty in Spanish football. Journal of Economics and Business, 61(4), 326–338.
[39] Szymanski, S. (2003). The economic design of sporting contests. Journal of Economic Literature, 41(4), 1137–1187.
[40] Benz, M.A., Brandes, L., & Franck, E. (2009). Do soccer associations really spend on a good thing? Empirical evidence on heterogeneity in the consumer response to match uncertainty of outcome. Contemporary Economic Policy, 27(2), 216–235.
[41] Goller, D., & Krumer, A. (2020). Let’s meet as usual: Do games played on non-frequent days differ? Evidence from top European soccer leagues. European Journal of Operational Research, 286(2), 740–754.
[42] Garcia, J., & Rodriguez, P. (2002). The determinants of football match attendance revisited: Empirical evidence from the Spanish football league. Journal of Sports Economics, 3(1), 18–38.
[43] Forrest, D., & Simmons, R. (2006). New issues in attendance demand: The case of the English football league. Journal of Sports Economics, 7(3), 247–266.
[44] Baimbridge, M., Cameron, S., & Dawson, P. (1996). Satellite Television and the Demand for Football: A Whole New Ball Game? Scottish Journal of Political Economy, 43(3), 317–333.
[45] Turkish Football Federation (TFF) Website (2021). Available from: https://www.tff. org [Accessed 1 September 2021].
[46] Vollman, T., Berry, W., Whybark, D., & Jakobs, F. (2011). Manufacturing Planning and Control for Supply Chain Management. 5th ed. McGraw-Hill, New York.
[47] Yavuz, M., Inan, U.H., & Fı˘glalı, A. (2008). ˙ Fair referee assignments for professional football leagues. Computers and Operations Research, 35(9), 2937–2951.
[48] Knust, S., & von Thaden, M. (2006). Balanced home-away assignments. Disrete Optimization, 3(4), 354–365.
[49] Goossens, D.R., & Spieksma, F.C.R. (2012). Soccer schedules in Europe: an overview. Journal of Scheduling, 15, 641–651.
[50] G¨o¸cg¨un, Y. (2018). Dynamic Scheduling with Cancellations: An Application to Chemotherapy Appointment Booking. An International Journal of Optimization and Control: Theories and Applications, 8(2), 161-169.
[51] G¨o¸cg¨un, Y. (2021). Performance Comparison of Approximate Dynamic Programming Techniques for Dynamic Stochastic Scheduling. An International Journal of Optimization and Control: Theories and Applications, 11(2), 178-185.