Scheduling the Belgian Football League During Special Periods
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SCHEDULING THE BELGIAN FOOTBALL LEAGUE DURING SPECIAL PERIODS Word count: 27.411 Sam Wauters Student number: 01306574 Promotor / Supervisor: Prof. Dr. Dries Goossens Commissioner: Xiajie Yi Master’s Dissertation submitted to obtain the degree of: Master in Business Engineering: Operations Management Academic year: 2018-2019 Deze pagina is niet beschikbaar omdat ze persoonsgegevens bevat. Universiteitsbibliotheek Gent, 2021. This page is not available because it contains personal information. Ghent Universit , Librar , 2021. IV Acknowledgements I would like to thank my supervisor, professor Goossens for giving me the opportunity to do this research under his guidance. Next, I would like to thank Xiajie Yi for the continuous and helpful feedback during this research process. A special thanks goes to my parents and sister for supporting me in my studies throughout the years by giving encouragements during the exams and the writing of this thesis. I also want to thank my girlfriend Sarah for the countless hours we worked together to write our dissertations. This accomplishment would not have been possible without the support of each of the above. V VI Table of Content List of Tables & Figures______________________________________________________ X 1. Introduction ____________________________________________________________ 1 Part 1: Literature ______________________________________________________ 3 2. Round-Robin Scheduling _________________________________________________ 5 2.1. Introduction ________________________________________________________________ 5 2.2. Terminology ________________________________________________________________ 6 2.3. Objectives ________________________________________________________________ 10 2.3.1. Break Minimization _____________________________________________________ 10 2.3.2. Travelling Distance Minimization ___________________________________________ 10 2.4. Constraints _______________________________________________________________ 14 2.4.1. Basic Constraints _______________________________________________________ 14 2.4.2. Externally given constraints _______________________________________________ 14 2.4.3. Fairness Constraints ____________________________________________________ 16 2.5. Solution Methods ___________________________________________________________ 18 2.5.1. Decomposition _________________________________________________________ 18 2.5.2. Integer Programming ____________________________________________________ 19 2.5.3. Constraint programming _________________________________________________ 26 2.5.4. Metaheuristic __________________________________________________________ 26 3. Belgian Pro League Football _____________________________________________ 28 3.1. Introduction & league format __________________________________________________ 28 3.2. Stakeholders ______________________________________________________________ 29 3.2.1. The Belgian Pro League _________________________________________________ 29 3.2.2. The TV broadcasters ____________________________________________________ 30 3.2.3. The police and the taxpayer ______________________________________________ 31 3.2.4. The clubs and their fans _________________________________________________ 31 3.3. Scheduling Methods ________________________________________________________ 32 Part 2: Case Study: Distance Minimization in the Jupiler Pro League __________ 35 4. Problem Description ____________________________________________________ 37 4.1. Introduction _______________________________________________________________ 37 4.2. Solution Method ____________________________________________________________ 38 VII 4.3. Constraints _______________________________________________________________ 39 4.4. Data _____________________________________________________________________ 41 4.4.1. Travelling Distance Matrix ________________________________________________ 41 4.4.2. Actual Schedules & Distances ____________________________________________ 42 4.5. Special Period Fairness Approaches ___________________________________________ 44 4.5.1. Fairness Approach 1: Total Distance Minimization _____________________________ 44 4.5.2. Fairness Approach 2: Limited Travelling Distance per Team per Round ____________ 44 4.5.3. Fairness Approach 3: Limited Difference Between Teams _______________________ 44 4.5.4. Fairness Approach 4: Limited Travelling Distance per Team over Special Rounds ____ 45 5. Model ________________________________________________________________ 46 5.1. Basic Model _______________________________________________________________ 46 5.1.1. Indices _______________________________________________________________ 46 5.1.2. Decision Variables ______________________________________________________ 48 5.1.3. Parameters ___________________________________________________________ 48 5.1.4. Objective Function ______________________________________________________ 49 5.1.5. Constraints ___________________________________________________________ 50 5.2. Fairness Approaches Constraints ______________________________________________ 52 5.2.1. Fairness Approach 1: Total Minimization ____________________________________ 52 5.2.2. Fairness Approach 2: Limited Travelling Distance per Team per Round ____________ 52 5.2.3. Fairness Approach 3: Limited Difference Between Teams _______________________ 53 5.2.4. Fairness Approach 4: Limited Travelling Distance per Team over Special Rounds ____ 53 6. Simulation & Results ___________________________________________________ 54 6.1. Fairness Approach 1: Total Distance Minimization _________________________________ 54 6.1.1. 2-Round Special Period __________________________________________________ 55 6.1.2. 4-Round Special Period __________________________________________________ 56 6.2. Fairness Approach 2: Limited Travelling Distance per Team per Round ________________ 58 6.2.1. 2-Round Special Period __________________________________________________ 59 6.2.2. 4-Round Special Period __________________________________________________ 61 6.3. Fairness Approach 3: Limited Difference Between Teams ___________________________ 63 6.3.1. 2-Round Special Period __________________________________________________ 64 6.3.2. 4-Round Special Period __________________________________________________ 65 6.4. Fairness Approach 4: Limited Travelling Distance per Team over Special Rounds ________ 67 6.5. Additional Approaches: ______________________________________________________ 70 6.5.1. Additional Approach 1: Using the actual home-away patterns ____________________ 70 6.5.2. Additional Approach 2: Combining Approach 2 and 4 __________________________ 74 VIII 7. Discussion ____________________________________________________________ 77 7.1. Season 2018-2019 _________________________________________________________ 77 7.2. Season 2017-2018 _________________________________________________________ 80 7.3. Season 2016-2017 _________________________________________________________ 81 8. Conclusion____________________________________________________________ 83 References _______________________________________________________________ 85 Appendices _________________________________________________________ 91 A. Distances _____________________________________________________________ 93 B. Actual Special Period Schedules _________________________________________ 96 C. Attractive Matches _____________________________________________________ 97 D. CPLEX Model & Data ___________________________________________________ 98 E. Resulting Tournament Schedules: Fairness Approach 1 _____________________ 106 F. Resulting Tournament Schedules: Fairness Approach 2 _____________________ 109 G. Resulting Tournament Schedules: Fairness Approach 3 _____________________ 112 H. Resulting Tournament Schedules: Fairness Approach 4 _____________________ 115 I. Resulting Tournament Schedules: Additional Approach 1 ___________________ 117 J. Resulting Tournament Schedules: Additional Approach 2 ___________________ 120 K. Home-Away Patterns __________________________________________________ 122 IX List of Tables & Figures Table 2-1: Timetable ..................................................................................................................... 7 Table 2-2: Complementary pattern sets for a 6-team tournament ................................................. 7 Table 2-3: Mirrored double round-robin tournament ...................................................................... 9 Table 3-1: Basic Match Schedule................................................................................................ 32 Table 4-1: Travelling Distances per Team: Season 2018-2019 ................................................... 42 Table 4-2: Travelling Distances per Team: Season 2017-2018 ................................................... 43 Table 4-3: Travelling Distances per Team: Season 2016-2017 ................................................... 43 Table 6-1: Total Overall Distances & Comparison Approach 1 .................................................... 54 Table 6-2: 2-Round Special Period Schedule 2018-2019 (Fairness 1) ........................................ 55 Table 6-3: 2-Round Individual Distance Comparison 2018-2019 (Fairness 1) ............................. 55 Table 6-4: 2-Round Special Period Schedule 2017-2018 (Fairness 1) ........................................ 55 Table 6-5: 2-Round Individual Distance Comparison 2017-2018 (Fairness 1) ............................. 55 Table 6-6: 2-Round Special Period Schedule