Lake Highlands Soccer
Association
Game Scheduling
Sherif Khalifa
Senior Design Project
May 9, 2008
Background, Objective, & Development
INTRODUCTION
Problem Background
• Lake Highlands Soccer
Association
–Inefficient Game Scheduling
–No Model in place
–Schedules manually done by
hand
Development
Approach
Unlike most professional sports
scheduling problems, the
objective of the problem is not
to identify a low-cost, lowtravel schedule.
Rather, it is simply to identify all
feasible schedules, that is, a
series of competitions that
satisfies the specified
conditions.
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
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.
Methodology – CP
Model
Steps:
1. Assign variables to all
parameters.
2. Create constraints for
all the teams, times, and
competitions.
3. Solve the model.
Variables & Constraints
MODEL DEVELOPMENT
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
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.
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.
Variables/Constraints
(League 1)
Variables/Constraints
(League 2)
Solution & Value to Client
CONCLUSION
A Feasible Solution
(League 1)
A Feasible Solution
(League 2)
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.
Q&A
Any Questions ?