Sports Scheduling and the Real World Michael Trick Carnegie
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 Issues Quality of schedule? Expansion Interleague
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 season Double round
robin: 13*4=52 Two series per week! (Almost)
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Series While teams play 162 games (over 182 days), think in
terms of series Home stand: consecutive home series Away 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 Requirements half weekends home half summer
weekends home Stadium unavailability Required open/finish No
repeaters Requests/preferences Holiday requests Semi-repeaters
Preferred summer matchups Preferred 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 dont match up well
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Matchings Solve series of matchings Costs depend on previous
solution Nice idea: cant make it work: requirements and patterns
lead quickly to infeasibility
Leaves: Integer Programming Normal formulation: x(i,j,t) doesnt
work Use 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 @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 @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
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 - Y NY 1-Y NY 2 0
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Lots and Lots of Other Things Costs based on Buremans knowledge
Additional constraints for other requirements Nasty IP that doesnt
solve Various simplifications to get reasonable answers
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Results Solutions are slow in coming Results good enough to be
MLBs 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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Thats the Ticket! Much easier! 9 teams, 16 games over 18 slots
(due to the bye game) Few travel issues Lots 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 (mens/womens) for four years.
Also Patriot league, MAC
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Result (in Academia) Good aspects Operations Research
publication appeared just as first games being played Lead to much
further refinements (and Eastons dissertation)
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Results (the Bad Side) Reality had different objective than
academia: Reality: one day fine Academia: 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 messy
Baseball messiness is not underlying issue: try to solve
http://mat.gsia.cmu.edu/TOURN (MLB instances without the
details)http://mat.gsia.cmu.edu/TOURN 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 useful column
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)!