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In this lecture, we'll
see how optimization

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can be used to construct
sports schedules.

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Specifically, we'll
introduce the method

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of integer optimization.

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Sports is a $300
billion industry.

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This is twice as big as
the automobile industry

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and seven times as big
as the movie industry.

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This includes tickets for
games, team merchandise,

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salaries for players, etc.

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Almost every single
country participates

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in the sports industry.

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For this industry to
remain so large sports

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teams are very important.

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They key revenue for sports
teams comes from TV networks.

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TV networks paid
$513 million per year

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for English Premier League
soccer, $766 million

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per year for the National
Basketball Association, or NBA,

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and $3 billion per year for
the National Football League,

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or NFL.

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These TV networks are
paying such large amounts

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to ensure that they will have
a good schedule of sports games

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to convince fans to
tune in and watch

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the games on their network.

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In addition to the TV
networks, good sports schedules

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are important for
other reasons too.

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One is that extensive traveling,
caused by a poor schedule,

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can cause player fatigue, which
can reflect badly on the team.

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Also, ticket sales tend to
be better on the weekends,

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so teams like to
have games scheduled

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for weekends to
increase revenue.

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Additionally, it's better
to play division teams,

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or direct competitors
for playoff spots,

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near the end of the season since
teams have more information.

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For these reasons and many more,
everyone in the sports industry

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is incentivized to have
a good schedule of games.

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All competitive sports
require schedules

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defining which pairs of teams
play each other and when.

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Until recently, sports
schedules were mostly

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constructed by hand.

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This is incredibly
time consuming.

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With just 10 teams, there
are over one trillion

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possible schedules, where every
team plays every other team.

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There are many
constraints defined

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by the TV networks,
teams, cities, and others.

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TV networks want games
to occur at prime times,

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like in the evening.

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Teams want games
on the weekends.

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Cities want games
that don't conflict

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with other major events, etc.

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This requires looking through
all trillion possible schedules

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to find one that satisfies
all of the constraints.

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For major league baseball,
a husband and wife team

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constructed the
schedules for 24 years.

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They mostly built
the schedule by hand

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and used a giant wall of
magnets to schedule 2,430 games

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each year.

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Not only is this
approach time consuming,

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but it's very difficult
to add new constraints.

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If one new constraint is added
that might make the schedule

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infeasible and the process would
have to start all over again.

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There have been many
interesting constraints

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that have been added
by interesting people.

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In 2008, the owners
and TV networks

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were not the only ones who
cared about the schedule.

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President Barack Obama
and Senator John McCain

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complained about the schedule.

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2008 was an election
year and President Obama

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and Senator McCain were the
leading presidential nominees.

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The Democratic and Republican
National Conventions

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conflicted with
the game scheduling

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so the schedule
had to be adjusted.

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After that was settled, the Pope
complained about the schedule.

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The Pope visited New
York on April 20, 2008.

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He traditionally always
holds mass in Yankee Stadium,

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but a game was
scheduled that same day.

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The schedule had
to be readjusted

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to move the Yankee game.

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These are just a couple
examples of the wide variety

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of constraints that
have to be accounted

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for when building
a sports schedule.

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Recognizing how difficult it was
to construct sports schedules

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by hand, in 1996
a company called

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the Sports Scheduling
Group was started.

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The founders were Doug
Bureman, a former baseball vice

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president, and three academics--
George Nemhauser, Michael

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Trick, and Kelly Easton.

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Instead of generating
sports schedules by hand,

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they use a computer.

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They've been scheduling
college sports since 1999

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and major league
baseball since 2005.

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They rely on optimization to
build the schedules, which

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can easily adapt when new
constraints are added.

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In this lecture, we'll introduce
one of the techniques they use,

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called integer optimization,
to construct a sports schedule.