© J. Christopher Beck 20081 Lecture 21: Sports Scheduling 1.
Transcript of © J. Christopher Beck 20081 Lecture 21: Sports Scheduling 1.
© J. Christopher Beck 2008 1
Lecture 21:Sports Scheduling 1
© J. Christopher Beck 2008 2
Outline ACC Basketball Scheduling
HAPs Algorithm Flow Chart
Single Round Robin Scheduling HAPs again Alg 10.2.2 Example 10.2.3
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Readings
P Ch 10.6,10.2 Questions
10.1, 10.2, 10.4, 10.5, 10.6, 10.8
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ACC Scheduling
Atlantic Coast ConferenceBasketball 9 teams: Clem, Duke, FSU, GT, UMD, NC,
NCSt, UVA, Wake Double Round Robin
Home and Away Total # of games to be played? What is the maximum # of games per
slot? And, therefore the # of slots?
2 slots/week:weekday &
weekend
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Constraints & Preferences
No team should play more than two Home or two Away games consecutively A Bye is considered an Away game
No team should play more than two consecutive weekends Away or at Home
Each team must have at least 2 Home or 1 Home, 1 Bye in the first 5 weeks
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More Constraints & Preferences
No team can be Away for both slots in the final week
Final weekend is usually reserved for “rival” pairings Duke-UNC, Clem-GT, NCSt-Wake,
UMD-UVA Duke-UNC must appear in slots 9 and
18Even with only 9 teams this is a hard problem.
Try to decompose the solving into sub-problems.
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Mirroring
Since it is a double RR, we can halve the problem size by finding a single RR and “mirroring” the second half Perfect mirroring not always possible
Team 1
3 -4 2
Team 2
-4 3 -1
Team 3
-1 -2 4
Team 4
2 1 -3
-3 4 -2
4 -3 1
1 2 -4
-2 -1 3
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Home Away Patterns (HAPs)
Each team has a pattern of Home & Away games: HAHAAHHAAH …, AAHHAHHA …, etc.
First (Step 1) find of a set of HAPs Independent of the teams – just find
strings of Hs, As, (and maybe Bs) Then (Step 2) match patterns to
games and finally (Step 3) assign the teams
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Of Course it is More Complicated in the Real World
Findfeasiblepatterns
Findpattern
sets
Assigngames
Assignteams topatterns
Choosefinal
schedule
38 patternsof length 18
17 patternsets
826 timetables 17 schedules
Step 1 Step 2 Step 3
Figure 10.3
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Something a Bit Easier
Complete the single RR timetable Don’t worry about Home/Away games
slot 1 2 3 4 5
Team a b f c
Team b a f
Team c d e a
Team d c e
Team e f d c
Team f e a b
Does thisremind youof anything?
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Home & Away
Now take the full time table and add Home/Away games
slot 1 2 3 4 5
Team a b f c
Team b a f
Team c d e a
Team d c e
Team e f d c
Team f e a b
Minimize breaks Break: two
consecutive Home or two consecutive Away games
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Single Round Robin Tournament
Assume n teams and that n is even Every team plays every other team It is possible to construct a
schedule with n-1 slots each with n/2 games
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IP for Simple Single RR
1,,1;,...,11)(1
ntnjxxn
ijitijt
jixxn
tjitijt
1
1
1)(
Each team plays exactly once in each slot
Each team plays each other team exactly once
Pure IP model xijt = 1 iff team i plays at home
against team j in slot t
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CP for Simple Single RR
xit = team that team i plays in slot t
xit є {1,…,n} xit ≠ i xit = j xjt = i all-different(xi)
slot 1 2 3 4 5
Team a
Team b
Team c
Team d
Team e
Team f
all-different
e
b
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Simple RR Model IsToo Simple
No optimization function No balancing of Away/Home games This motivates the introduction of
HAPs and the definition of breaks Recall: a break is two consecutive
games that are both Home or both Away
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What if n is Odd?
One team gets a Bye in every slot HAPs get more complex
String of Hs, As, & Bs Breaks need to be redefined
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Alg 10.2.2
Step 1: Find a collection of n HAPs Step 2: Assign a game to each
entry in the pattern set Step 3: Assign teams to patterns
Why do we need (at least) n HAPs?
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Alg 10.2.2
Step 1: Find a collection of n HAPs Step 2: Assign a game to each entry
in the pattern set Step 3: Assign teams to patterns
Create a 5 team single round robin Minimize breaks (at which step?)
Now create a double RR schedule
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Next Week
We start to read some papers These are real papers, published in the
research literature. You should not expect to completely
understand them in the first reading. You should read them (at least once)
before lecture and (at least once) after. 1 next week, 2 week after, 1 more
later