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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

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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 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

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Constraints Stronger (needed!): X1+X2+X3+Y2 1 @NY@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 - 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)!