WEBVTT
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We were able to solve our
sports scheduling problem
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with 4 teams, 24 decision
variables, and 22
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basic constraints,
pretty quickly.
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However, the problem
size increases rapidly.
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The same problem
with 10 teams, would
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have 585 decision variables
and 175 basic constraints.
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For scheduling major
league baseball,
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the problem has 100,000
decision variables
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and 200,000 constraints.
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For small problems, spreadsheet
softwares, like LibreOffice,
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are great.
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But for large
problems like this,
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solving them in LibreOffice
would be impossible.
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So how are integer
optimization models like this
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solved in practice?
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Many different tricks are
used to solve large integer
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optimization problems.
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One is to reformulate
the problem.
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The sports scheduling
problem with more teams
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is often solved by
changing the formulation.
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Instead of the
decision variables
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we discussed in this
lecture, the variables
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are sequences of games.
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Additionally, the problem can
be split into three smaller
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problems that can each be self
separately and much faster
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than just solving
the whole problem.
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Another trick that's
often used, is
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what are called
Heuristic methods.
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These methods find good, but not
necessarily optimal decisions.
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A good decision is
sometimes accepted
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since the problem
is so much easier
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to solve using a
heuristic method.
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In addition to changing
the formulation
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in using heuristics, there are
general purpose optimization
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solvers that can
solve large problems.
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These include CPLEX,
Gurobi, GLPK and Cbc,
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a COIN-OR project.
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Most practitioners who solve
large optimization problems
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use one of these
software packages.
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And in the past 20 years, the
speed of integer optimization
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solvers has increased
by a factor of 250,000,
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which doesn't even include the
increasing speed of computers.
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Assuming a modest
machine speedup of 1,000,
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this means that a
problem that can
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be solved in one second
today, took seven years
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to solve 20 years ago.
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Because of this
increase in speed
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were able to solve much
larger and more complicated
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optimization problems today,
than just a few years ago.
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So how about the sports
scheduling problem?
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When the Sports Scheduling
Group was started in 1996,
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integer optimization software
was too slow to be useful.
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Now, they can use
powerful solvers
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to generate sports schedules.
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Even with these
solvers, it can take
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months to make the major
league baseball schedule.
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This is due to several reasons,
including the enormous list
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of ever changing
constraints that they
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have to account for, the
need to define priorities
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on the constraints to find a
feasible solution, and the fact
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that it takes several iterations
to get a good schedule.
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But even with these
challenges, analytics
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offers a significant edge
in sports scheduling.
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The use of optimization
allows for the addition
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of new constraints
or schedule changes.
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A new schedule can
easily be generated
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based on an updated
requirement or request.
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Now, all professional sports
and most college sports,
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construct their schedules
using optimization.
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In this lecture, we've seen
one powerful use of integer
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optimization, but this
method has a huge number
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of applications,
which you'll see
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more of in the second
lecture, The Recitation,
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and in the homework assignment.