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Sports Scheduling and the “Real World”
Michael TrickCarnegie Mellon University
May, 2000
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Outline
• Working with Major League Baseball
• Working with College Basketball• Some Real Life conclusions
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The Beginnings
January 1996. Phone call from Doug Bureman (former Executive VP for the Pirates). Want to look at scheduling Major League Baseball?
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Major League Baseball
Current Schedulers: Henry and Holy Stevenson
IssuesQuality of schedule?ExpansionInterleague Play
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Natural Response
Sure!! How hard can this be?
“How about the end of February (1996)?”
Little did I know……
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Defining the Problem
Approximately 150 pages of requests, requirements
Countless amount of informal information (known to all of baseball, but never written)
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Underlying Problem (circa 1996)
Two leagues: National League and American League
Fourteen teams per league (now 16/14)No interleague play (now ~6
series/team)26 week seasonDouble round robin: 13*4=52Two series per week! (Almost…)
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Series
While teams play 162 games (over 182 days), think in terms of seriesHome stand: consecutive home seriesAway trip: consecutive away series
Quality of schedule is based almost solely on the quality of these.
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Keys to Schedule Quality
Two primary drivers of schedule quality:
DISTANCE
FLOW
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Key aspects
Distance not cost (primarily) wear and team: primarily cross time
zone
Flow ideal is 2 H, 2 A, 2 H, 2 A … three is OK, one is possible, 4 avoided
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Other Aspects
Requirementshalf weekends homehalf summer
weekends homeStadium
unavailabilityRequired open/finishNo repeaters
Requests/preferences
Holiday requestsSemi-repeatersPreferred summer
matchupsPreferred
open/finish
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Why Was I Confident?Lots of ideas:
Combinatorial design: looks at tournaments
Matching: Every slot is a matching: solve series of matchings
Greedy with local search: always works well
Integer Programming: if necessary
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Combinatorial Design
• Looks at tournaments, but not our tournaments– Example: Find tournament with
minimum number of AA or HH– Our requirements don’t match up well
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Matchings
Solve series of matchingsCosts depend on previoussolution
Nice idea: can’t makeit work: requirementsand patterns leadquickly to infeasibility
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Local Search: No! Slot ATL NYM PHI MON FLA PIT
0 FLA @PIT @MON PHI @ATL NYM
1 NYM @ATL FLA @PIT @PHI MON
2 PIT @FLA MON @PHI NYM @ATL
3 @PHI MON ATL @NYM PIT @FLA
4 @MON FLA @PIT ATL @NYM PHI
5 @PIT @PHI NYM FLA @MON ATL
6 PHI @MON @ATL NYM @PIT FLA
7 MON PIT @FLA @ATL PHI @NYM
8 @NYM ATL PIT @FLA MON @PHI
9 @FLA PHI @NYM PIT ATL @MON
NYM@PHI Mon@Pit
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Leaves: Integer ProgrammingNormal formulation: x(i,j,t) doesn’t
workUse “column generation ideas” a la
airline crew scheduling• Change variables: decision is on
trips/home stands– one variable for each road trip (start slot,
duration, opposing teams)– one variable for each home trip (start
slot, duration)
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Formulation
• Sample Variables:
@NY @MON
@MON @PHI
@NY
H H
H
X1
X2
X3
Y1
Y2H
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Constraints
• One thing per time: X1+X2+Y1+Y2 1
@NY @MON
@MON @PHI
H H
H
X1
X2
Y1
Y2H
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Constraints
• No Away followed by Away X1+X3 1
@MON @PHI
@NY
X2
X3
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Constraints
• Stronger (needed!): X1+X2+X3+Y2 1
@NY @MON
@MON @PHI
@NY
H
X1
X2
X3
Y2H
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Constraints
• Single team constraints set packing/partitioning problem
• Many constraints known: conflict graph has nice structure
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Linking Constraints
• Constraints from different teams linked by “If a at b then b at home” constraints:
X1+X3 - YNY1-YNY2 0
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Lots and Lots of Other Things
• Costs based on Bureman’s knowledge
• Additional constraints for other requirements
• Nasty IP that doesn’t solve• Various simplifications to get
reasonable answers
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Results
• Solutions are slow in coming• Results good enough to be MLB’s
“backup schedulers” for the last four years
• Henry and Holly are pretty good!
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Experiences in Basketball• Apply knowledge to
other leagues• Met up with George
Nemhauser (and later, Kelly Easton) at Georgia Tech
• Schedule the Atlantic Coast Conference?
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That’s the Ticket!
Much easier! 9 teams, 16 games over 18 slots (due to the bye game)
Few travel issuesLots and lots of discussion with the
person responsible
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Technique Developed
Three phases:Find H/A patterns (IP)Assign games to H/A patterns (IP)Assign teams to H/A patterns (enumerate)
(details in Operations Research paper)
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Result (in Practice)Worked great!
Complete search of possibilities within a day (after 10 minute setup: automatic)
Iterated a dozen times (or more) over two month period to create chosen schedule
Result: scheduled ACC (men’s/women’s) for four years. Also Patriot league, MAC …
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Result (in Academia)
Good aspectsOperations Research publication appeared just as first games being played
Lead to much further refinements (and Easton’s dissertation)
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Results (the Bad Side) Reality had different objective than
academia:Reality: one day fineAcademia: “I can do better” (particularly in CP community)
Misguided (IMHO) view: CP beat IP on this problem (CP better for the complete enumeration phase: no good IP (but better enumerations possible)).
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Important?Absolutely!
MLB: $1.5 billion+/year, much from people/groups who care very much about the schedule
ACC: ESPN TV contract predicated on being able to provide adequate schedule ($10 million+/year)
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Lessons from the “Real World”Real problems are incredibly messyBaseball
messiness is not underlying issue: try to solve http://mat.gsia.cmu.edu/TOURN (MLB instances without the details)
messiness makes it impossible to attack without an insider (Doug in my case)
Technique must take advantage of this information: algorithmist as partner.
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Lessons from “Real World”
State of the Art is usefulcolumn generation (or branch and price) provided insight to reasonable formulation: seen over and over again in IRS budgeting, telemarketer employee scheduling, electronics inventory setting, ……
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Lessons From the “Real World”
Never say something can be done in a month (unless you want to be reminded of that for five years)!