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RICHARD DE NEUFVILLE:
We don't have

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a way of calculating
when's the optimal time.

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There are some methods
for dealing with that,

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such as dynamic programming.

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But dynamic programming
implies there's

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nothing you can do about it
to affect future aspects.

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This is the so-called path
independence function.

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And the whole point
of having flexibility

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is precisely that
you can do things

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so that that powerful
method does not work for us.

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And there are so many paths.

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If we think about 2,000
samples of what may happen,

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that's only 2,000
samples of what

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may be a million
possibility of paths

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as a combination of the
different probabilities

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at different times of prices
and quantities and so forth.

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It's much too large
to be searched.

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So the procedure
is to define what

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we know as decision rules,
the a priori condition

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for when to exercise
flexibility.

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These a priori conditions may
be set by higher-level mandate.

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This is standard
operating procedure.

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And here's what you do.

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Or it could be this is the way
the management wants to behave.

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And this is what we are looking
at as how they will behave.

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So an example of
it is the one we

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use for the parking garage,
which was in the base case--

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we tried various samples
at other points--

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that expand if the
observed demand is greater

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than the capacity
over two years,

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whereas this implies
you don't do an advance.

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You wait until the
demand is there.

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And you just don't
take into account

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there's a special event,
a one-time event that

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may not be repeated.

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So you might want
to wait until you're

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more sure that the demand
is going to be there.

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So you might wait two years.

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So it's not a stupid one.

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It's not obviously the best one.

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You can try different ones.

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But it's to say,
this is the way we're

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going to think about
the management behaving.

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Now, this doesn't
have to be a rule that

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applies over the entire period.

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For example, you might
want to change it.

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If you have a 20-year
lease on the land, which

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is the example appropriate
to the Garage case,

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you might say, well,
we're not going to expand

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in the last five years.

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It will be enough time
to pay off any investment

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so that the decision rule
is OK for the first 15 years

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but not for the end of life,
the last five years of it.

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So trying to mimic
what would seem

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to make sense from a
management point of view.

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Once you have those,
the automation

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of the implementation of
flexibility is to say,

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as we go through-- as the
computer goes through time

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from period 1 to
period 2 to period 3,

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each period checks to
see whether the decision

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rule is invoked.

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That is, have the
conditions been met?

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If the conditions have been
met, for example, the capacity

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has been less than
the actual demand,

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then you would say,
all right, we're

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going to make the investment
to build an extra floor.

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It's going to cost money.

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Going increase the capacity.

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You include that expense
in the cash flow.

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You increase the capacity for
the analysis or the next period

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when the situation or
the capacity is expanded.

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And so you can go
through a simulation

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and maybe never the
decision will be invoked.

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Maybe they'll invoke second
year, third year, fifth year,

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eighth year.

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Could be invoked many times.

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And this process is very
powerful in comparison

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with alternative features.

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So it can analyze many
flexibilities simultaneously,

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whereas simultaneously
because you

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might have a decision
about plant capacity.

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You may also have
decisions about pricing.

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You may say, well, I'm going
to increase my plant capacity.

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And I'm going to
cut my price by 20%

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so I increase my market share
or stimulate my market share.

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Or market's so good, I'm
going to increase capacity.

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But I'm also going
to raise prices.

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So you can have not
just one flexibility

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but a range of flexibilities
that you can have

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and some that you may
never have, never use.

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For example, if
things are going well,

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you're not going to
have the capacity

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to close the plant down.

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But if things are
going badly, maybe that

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would be a
flexibility you'd like

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to invoke under
those circumstances

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so that the simulation
enables you to look at lots

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of different kinds of
flexibilities in lots

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of different situations.

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Now, ultimately the
question is, what's

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the value of this flexibility?

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Why should I go to the effort
of creating this ability

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to change my system
or to invoke it?

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Or how much do I get out of it?

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Maybe it's easy to--

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it doesn't require
any extra effort

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to be able to have a
flexibility, for example,

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to close the plant.

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Maybe I don't have to do
anything special in advance.

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But what's the value
of having that thought?

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So you get the outcomes
or plan flexibility.

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For example, if we're doing it
in monetary terms, it's NPV.

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It's expected NPV,
the target curve.

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You get that with
the flexibility.

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And then you compare them.

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And the value of the
flexibility of the first order

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is the difference in the
ENPV, the expectations

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of the different with and
without the flexibility.

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And when you compare
the target curves,

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you show where that
value comes from.

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Does it come from making
it small at the beginning

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so we don't have losses?

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Is it coming from having
greater capacity if needed?

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But you can see that we
can develop that idea

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by comparing the target curves.

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So the takeaway from this
first portion is simulation

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defines the outcome
distributions,

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the target curves,
and consequently

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the value of flexibility.

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It is computationally efficient.

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Secondly, we can deal with
all kinds of uncertainties.

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It's not limited
by some assumption

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that the distribution has
to be this way or that way

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or like the dynamic
program has to be

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path independent, et cetera.

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A nice aspect of it also is that
it's relatively easy to explain

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to the decision makers.

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Why?

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Because you say, well, look.

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We're looking at
all the combinations

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to see what happens.

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You don't have any
complicated math to explain.

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You don't have decision trees,
which can be very complicated.

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We don't have any
high-powered theory,

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which is what's appropriate
for a financial options

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analysis, which will be in
the second half of the course.

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So the bottom line
is that simulation

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can be a very good approach.

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It's powerful.

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It goes through lots of cases,
and it's relatively easy.

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