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To illustrate how linear
optimization works in revenue

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management, let us consider
a simple example --

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a flight from New
York to Los Angeles.

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In this flight, there are
two types of economy fares,

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Early Bird fares that cost
$238, and Last Minute fares

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that cost $617.

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In this flight, a
Boeing 757 is used

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that has 166 economy seats.

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Demand for these prices
has been forecasted

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using analytics tools,
looking at historical data

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and incorporating
models like time

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series or linear regression.

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Clearly, forecasts have
errors, and therefore, we

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need to assess the
sensitivity of our decisions

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to these errors.

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To illustrate the use
of linear optimization,

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we assume that demand has
already been forecasted.

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We'll illustrate how our
decisions on how many discount

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seats to sell vary as the
demand forecasts vary.

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If the demand for
regular seats is

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50, and for discounted
fares is 150,

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and the capacity is 166 seats,
then the optimal allocation

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is going to be to sell
the 50 seats to satisfy

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the regular demand, and then
we allocate the remaining 116

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seats to the
discounted fare class.

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If the regular demand
increases to 100 seats,

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then we allocate these 100 seats
to these customers, and only

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66 seats to discounted
fare customers.

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Finally, if the regular
demand increases to 200,

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then we allocate all of
our capacity, 166 seats,

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to these customers.

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While this seems
simple, what happens

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if we have 100 flights with
connections in tens of fares?

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We'll next see how to formulate
the problem mathematically

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and solve it in a systematic
way, using linear optimization.