Sports Scheduling and the Real World

1
Sports Scheduling and the Real World

• Michael Trick
• Carnegie Mellon University
• May, 2000

2
Outline

• Working with Major League Baseball
• Working with College Basketball
• Some Real Life conclusions

3
The Beginnings

• January 1996. Phone call from Doug Bureman
  (former Executive VP for the Pirates). Want to
  look at scheduling Major League Baseball?

4
Major League Baseball

• Current Schedulers Henry and Holy Stevenson

• Issues
• Quality of schedule?
• Expansion
• Interleague Play

5
Natural Response

• Sure!! How hard can this be?
• How about the end of February (1996)?
• Little did I know

6
Defining the Problem

• Approximately 150 pages of requests, requirements
• Countless amount of informal information (known
  to all of baseball, but never written)

7
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 13452
• Two series per week! (Almost)

8
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.

9
Keys to Schedule Quality

• Two primary drivers of schedule quality

DISTANCE
FLOW
10
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

11
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

12
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

13
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

14
Matchings

• Solve series of matchings
• Costs depend on previous
• solution
• Nice idea cant make
• it work requirements
• and patterns lead
• quickly to infeasibility

15
Local Search No!

• Slot ATL NYM PHI MON FLA
  PIT
• 0 FLA _at_PIT _at_MON PHI _at_ATL
  NYM
• 1 NYM _at_ATL FLA _at_PIT _at_PHI
  MON
• 2 PIT _at_FLA MON _at_PHI NYM
  _at_ATL
• 3 _at_PHI MON ATL _at_NYM PIT
  _at_FLA
• 4 _at_MON FLA _at_PIT ATL _at_NYM
  PHI
• 5 _at_PIT _at_PHI NYM FLA _at_MON
  ATL
• 6 PHI _at_MON _at_ATL NYM _at_PIT
  FLA
• 7 MON PIT _at_FLA _at_ATL PHI
  _at_NYM
• 8 _at_NYM ATL PIT _at_FLA MON
  _at_PHI
• 9 _at_FLA PHI _at_NYM PIT ATL
  _at_MON

NYM
_at_PHI
Mon
_at_Pit
16
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)

17
Formulation

• Sample Variables

X1
_at_NY
_at_MON
X2
_at_PHI
_at_MON
_at_NY
X3
H
H
Y1
H
Y2
H
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Constraints

• One thing per time X1X2Y1Y2 ? 1

X1
_at_NY
_at_MON
X2
_at_PHI
_at_MON
H
H
Y1
H
Y2
H
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Constraints

• No Away followed by Away X1X3 ? 1

X2
_at_PHI
_at_MON
_at_NY
X3

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Constraints

• Stronger (needed!) X1X2X3Y2 ? 1

X1
_at_NY
_at_MON
X2
_at_PHI
_at_MON
_at_NY
X3

H
Y2
H
21
Constraints

• Single team constraints set packing/partitioning
  problem
• Many constraints known conflict graph has nice
  structure

22
Linking Constraints

• Constraints from different teams linked by If a
  at b then b at home constraints
• X1X3 - YNY1-YNY2 ? 0

23
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

24
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!

25
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?

26
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

27
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)

28
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

29
Result (in Academia)

• Good aspects
• Operations Research publication appeared just as
  first games being played
• Lead to much further refinements (and Eastons
  dissertation)

30
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)).

31
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)

32
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)
• messiness makes it impossible to attack without
  an insider (Doug in my case)
• Technique must take advantage of this
  information algorithmist as partner.

33
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,

34
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)!