What is the known information in this problem?
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There are 8 teams. These teams are known as Team 0, Team 1, Team 2, Team 3, Team 4, Team 5, Team 6, Team 7. (Solver arrays start at
[0].) Teams can play at home (in the stadium in their home town) or away (at a stadium in another team's town).
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There are 4 time periods in each week and 7 weeks.
Here is another way of looking at the information about periods and weeks. The intersection of each period and week forms a slot. This slot can be identified by the coordinates: the period, the week. There are 28 slots available for matches between teams. The matches can be identified by a single integer.
Table 9.1 Slots for Scheduling
|
Week 0 |
Week 1 |
Week 2 |
Week 3 |
Week 4 |
Week 5 |
Week 6 |
|---|
Period 0 |
Match 0
Slot (0,0) |
Match 1
Slot (0,1) |
Match 2
Slot (0,2) |
Match 3
Slot (0,3) |
Match 4
Slot (0,4) |
Match 5
Slot (0,5) |
Match 6
Slot (0,6) |
Period 1 |
Match 7
Slot (1,0) |
Match 8
Slot (1,1) |
Match 9
Slot (1,2) |
Match 10
Slot (1,3) |
Match 11
Slot (1,4) |
Match 12
Slot (1,5) |
Match 13
Slot (1,6) |
Period 2 |
Match 14
Slot (2,0) |
Match 15
Slot (2,1) |
Match 16
Slot (2,2) |
Match 17
Slot (2,3) |
Match 18
Slot (2,4) |
Match 19
Slot (2,5) |
Match 20
Slot (2,6) |
Period 3 |
Match 21
Slot (3,0) |
Match 22
Slot (3,1) |
Match 23
Slot (3,2) |
Match 24
Slot (3,3) |
Match 25
Slot (3,4) |
Match 26
Slot (3,5) |
Match 27
Slot (3,6) |
What are the variables or unknowns in this problem?
Basically, the unknown information is which teams play in which slots. However, this information can be broken down into the following variables:
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Which team is playing at home in each slot?
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Which team is playing away in each slot?
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Which slot? This is a variable represented by the coordinates: the period, the week.
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Which match is played in each slot? This variable represents roughly the same information as which slot, but is represented by a single integer.
What are the constraints on these variables?
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All matches are different. (Each team must play each other team exactly once.)
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Each team must play every week, but only once.
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No team plays in the same time period more than twice.
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The variables (home team, away team, slot, and match) must be linked to each other.
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