1. Lake Highlands Soccer Association Game Scheduling Sherif Khalifa Senior Design Project May 9, 2008

2. INTRODUCTION Background, Objective, & Development

3. Problem Background Lake Highlands Soccer Association –Inefficient Game Scheduling –No Model in place –Schedules manually done by hand

4. Development Approach Unlike most professional sports scheduling problems, the objective of the problem is not to identify a low-cost, low- travel schedule. Rather, it is simply to identify all feasible schedules, that is, a series of competitions that satisfies the specified conditions.

5. Development Approach Mathematical Programming Vs. Constraint Programming - CP Problems have variables and constraints. The objective is to identify all feasible solutions. typically uses variables with discrete value sets. designed for combinatorial problems. - MP Problems have variables, constraints, and an objective function. The objective is to identify optimal feasible solution. It can have continuous and integer variables. It is not well-suited to many combinatorial problems

6. Development Approach The goal is to construct all possible feasible schedules for the league’s games. Developed a Constraint Programming model Solved it using ILOG OPL to achieve the desired solution.

7. Methodology – CP Model Steps: 1.Assign variables to all parameters. 2.Create constraints for all the teams, times, and competitions. 3.Solve the model.

8. MODEL DEVELOPMENT Variables & Constraints

9. Variables Team = 1..7 & 1..6 Teams that are to be paired for a series of competitions Time is a function of Week and Slot Week = 1..8 & 1..12 Slot = 1..3 X is a function of Week, Slot, and Teams. X = 1 – if competition is assigned to teams during a period of time. 0 – Otherwise

10. Constraints (League 1) 7 Teams, 10 Games, 1 Field 3 Games/Day, 1 Day/Week. First 2 Games are Friendlies (Do Not Count) Each Team Plays the other teams once. Each Team has 2 conflict dates (Bye Weeks) The Top 6 will play in a Mini-Tournament 2 of the Teams cannot play in the mornings. 12 weeks to complete the entire season.

11. Constraints (League 2) 6 Teams, 10 Games, 1 Field 3 Games a Day, 1 Day a Week Each team plays the other teams twice. Each team has 2 conflict dates (Bye Weeks) 2 of the teams cannot play in the mornings. 12 weeks to complete the entire season.

12. Variables/Constraints (League 1)

13. Variables/Constraints (League 2)

14. CONCLUSION Solution & Value to Client

15. A Feasible Solution (League 1)

16. A Feasible Solution (League 2)

17. Value to Client Time efficiency - Saves hours and hours of manually planning a league schedule. Obtain feasible solutions within seconds from compiling. With a few changes to the variables and constraints, you can make a schedule for any specifically desired league.

18. Q & A Any Questions ?