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Sports Scheduling and the “Real World” Michael Trick Carnegie Mellon University May, 2000
Outline • Working with Major League Baseball • Working with College Basketball • Some Real Life conclusions
The Beginnings January 1996. Phone call from Doug Bureman (former Executive VP for the Pirates). Want to look at scheduling Major League Baseball?
Current Schedulers: Henry and Holy Stevenson Issues Quality of schedule? Expansion Interleague Play Major League Baseball
Natural Response Sure!! How hard can this be? “How about the end of February (1996)?” Little did I know……
Defining the Problem Approximately 150 pages of requests, requirements Countless amount of informal information (known to all of baseball, but never written)
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…)
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.
Keys to Schedule Quality Two primary drivers of schedule quality: DISTANCE FLOW
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
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 Other Aspects
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
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
Matchings Solve series of matchings Costs depend on previous solution Nice idea: can’t make it work: requirements and patterns lead quickly to infeasibility
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 @PHI NYM @Pit Mon
Leaves: Integer Programming Normal formulation: x(i,j,t) doesn’t 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)
Formulation • Sample Variables: X1 @NY @MON X2 @PHI @MON @NY X3 H H Y1 H H Y2
Constraints • One thing per time: X1+X2+Y1+Y2 1 X1 @NY @MON X2 @PHI @MON H H Y1 H H Y2
Constraints • No Away followed by Away X1+X3 1 X2 @PHI @MON @NY X3
Constraints • Stronger (needed!): X1+X2+X3+Y2 1 X1 @NY @MON X2 @PHI @MON @NY X3 H H Y2
Constraints • Single team constraints set packing/partitioning problem • Many constraints known: conflict graph has nice structure
Linking Constraints • Constraints from different teams linked by “If a at b then b at home” constraints: X1+X3 - YNY1-YNY2 0
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
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!
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?
That’s 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
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)
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 …
Result (in Academia) Good aspects Operations Research publication appeared just as first games being played Lead to much further refinements (and Easton’s dissertation)
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)).
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)
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.
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, ……
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)!