0:05

So let's go through an example.

Â Where let's take the film industry as our context and say that if I managed to

Â launch this independent film, I'm going to make $4 million in profit.

Â But if it's a failure, I'm going to lose a million dollars.

Â We've got a company that's offering, they're saying for $100,000,

Â we going to conduct a study, and it's going to help you forecast whether or

Â not this movie is going to be successful.

Â Well, what we want to know is should I make that $100,000 investment?

Â 0:52

this company advanced market knowledge, AMK's reliability.

Â So when they say that movies are going to be successful,

Â so for those movies that are successful,

Â they said that their client should launch those movies 90% of the time.

Â Given that the movie was successful,

Â how likely were they to actually recommend a launch?

Â They did it 90% of the time.

Â But when the movies are failure, so given that the movies were failures,

Â they also recommended launching those movies 20% of the time.

Â So they're not always right, right.

Â So let's construct the decision tree to help us in terms of whether or

Â not we should pay a $100,000 for this.

Â All right, so here are the decisions that we have to make.

Â So initially, I could decide not to launch the movie.

Â Save myself the headache, doesn't cost me anything.

Â I decide to introduce the movie on my own.

Â There is a 60% chance of success.

Â There is a 40% chance of failure.

Â 1:55

We have payouts associated that, so we can calculated the expected

Â value of the 0.6 multiplied by the 4 million, 0.4,

Â multiplied by the negative 1 million, add them together,

Â come up with a $2 million expected payout, all right.

Â Or we say let's go and collect this information.

Â Let's pay this company to collect additional information for us.

Â Well, the next step, the company goes out and collects this information,

Â they come back with a recommendation.

Â It's go or no-go decision that they are recommending.

Â But even if they say go,

Â we don't know what the outcome will be with a 100% chance.

Â So if they say don't launch the movie, I make the decision not to introduce it,

Â I make nothing, but keep in mind I've paid a 100,000 for that information.

Â They might say you should go and introduce the movie.

Â Well, based on their, or I could rather, I could make the decision to go and

Â launch the movie, going against their advice.

Â So given that they said don't launch the movie,

Â what are the chances that that movie's going to be a success?

Â That's one question mark.

Â What are the chances that movie's going to be a failure?

Â That's another question mark.

Â I need to calculate those probabilities before I can evaluate whether or not I

Â should trust that advice and same thing when they say, I should launch the movie.

Â If I discard their advice,

Â don't introduce it, I make no money, I'm out the 100,000 for the information.

Â If they say launch, what's the likelihood of success given their recommendation?

Â What's the likelihood of failure given those recommendations?

Â So those are the probabilities that we need to fill in the blanks for.

Â All right, so how do we go about doing that?

Â 3:34

So let's break this problem down looking at some joint probabilities.

Â What we know so

Â far is probability of success, this is our prior information, is 60%.

Â Probability of failure is going to be 40%.

Â That's some of the information that we already have.

Â All right, well, based on the reliability information and using the multiplication

Â role, we can construct what's the probability of saying that we should

Â launch the movie, that it's a go decision, and the movie is going to be successful.

Â Well, we're going to use the product rule.

Â What's the probability that they said go, given that movies were successful?

Â That reliability information was 90%.

Â We had that previously.

Â The prior information, 60% chance of probability.

Â Multiply them together, that's going to give me the 54%.

Â Similar approach for probability of them recommending we

Â launch the movie and it being a failure.

Â Well, of those movies that were failures,

Â they said that the movie should be launched 20% of the time.

Â Overall, probability of a failure is 40%, joint probability is 8%.

Â All right, now we can take the same approach to fill in

Â the last two cells on this grid.

Â Now, if I were to add up the probability, going across the row,

Â I've got 54%, I've got 8%.

Â What's the probability of saying that I should go ahead and launch the movie?

Â It's going to be 62%.

Â Now we can actually go and

Â fill out the remainder of this table using addition rules, right.

Â So my probability of success is 60%.

Â My probability of success and go was 54%.

Â So what remains, well, this is only going to be a 6% probability remaining.

Â This one's going to be a 32% probability, again 40%,

Â I've already accounted for 8%, that's where that's coming from.

Â So the probability of the no-go is going to be 38%, and

Â that's coming from just adding from across this row, the 6% and the 32%.

Â Or saying, well if I don't launch the movie 1 minus the 62%,

Â I'm recommending don't launch with 38%.

Â So let's first focus on that 62 and 38% and

Â fill that in on the table, then we'll come back for the rest.

Â All right, so the information that we've filed in so far,

Â based on the company saying go verses no-go, how frequently does that happen?

Â The go recommendation comes 60% of the time,

Â the no-go recommendation comes 38% of the time.

Â Now we're going to move down to calculating once we've moved down each of

Â this paths, the success and failure given the go and no-go decision.

Â 6:21

Okay, so we filled this table in.

Â Now what we want to do is calculate those conditional probabilities, and

Â this is where that Bayes' rule or Bayes' theorem is going to come into play for us.

Â So what we want to know is given that AMK said go, and

Â we said that happens 62% of the time.

Â What fraction of that time are we going to have successes?

Â Well, that's going to be coming from here.

Â So of the 62%, what fraction are going to be those successes?

Â It's going to end up being that 0.54 divided by 0.62.

Â So to show you where we're coming from with this,

Â let's go back to our multiplication rule.

Â We had conditional probabilities.

Â 7:05

Ultimately, we have this information already that we say go,

Â and it is a success.

Â We would like to calculate, what we're ultimately looking to calculate

Â is what's the probability of a success given that they said go.

Â Well, in order to get that, what we're going to use is the joint probability for

Â go and success divided by the marginal probability of just saying go.

Â All right, so

Â I'm going to go back to that previous slides where we had these figures.

Â So we're going to fill in what's the probability of a success given that they

Â said, go?

Â All right, so probability of success given that they said go,

Â it's 0.54 is our joint probability, the 0.62 is our marginal probability.

Â If I want the probability of success given that they said, go,

Â Bayes' theorem tells me it's going to be 0.54 / 0.62.

Â All right, so we're going to be able to fill that one in.

Â What's the probability of failure, given that they said go?

Â Well, then we'd be looking at 0.08 divided by the 0.62 to

Â get the probability based on the company telling us to go ahead.

Â So let's fill in those blanks on our decision tree, and

Â we'll see how things look.

Â 8:21

All right, so 0.54 / 0.62, so probability of success when they say go is 87%.

Â Probability of a failure when they say go is only 13%.

Â We can calculate the same thing for when they say no-go,

Â comes up to be 16% and 84%.

Â All right, so now that we have these probabilities listed on our decision tree,

Â we actually have all the information that we need to go through and

Â make an informed decision of should we collect this additional information.

Â So let's see what that looks like.

Â If I were to calculate the expected value when they say go, all right,

Â there's an 87% chance that I get $4 million,

Â there's a 13% chance that I lose a million dollars.

Â So if I multiply 0.87 by 4 plus 0.13 by -1,

Â that sum gives me the expected outcome of 3.35

Â million when they said to go ahead and launch the movie.

Â So, if they say go, looks like I expect to make money.

Â So I'm going to decide to launch the film.

Â What about when they say no-go?

Â Well, 0.16 times the 4 million, that's my chance of success.

Â 0.84 times a $1 million loss.

Â If I add those two products together,

Â that's going to give me -0.2 million as my expected outcome.

Â I'm probably going to decide not to launch the movie if those are my options.

Â I'm better off not launching the film.

Â All right, so now we've gotta take a step back.

Â We say, when they say go, I expect to make $3.35 million.

Â When they say no-go, I'm not going to launch the movie, so I make nothing.

Â All right, so our next step is to say, all right,

Â what's the overall expected payout going to be?

Â Because I don't know what they're going to come back and tell me.

Â 10:31

That's my revenue piece, but rather, that's my expected profit, but

Â I haven't paid for the information yet.

Â AMK was saying we want $100,000 for the information.

Â All right, well, let's see how would I do on my own, and

Â let's return to this lower part of the chart here where,

Â what if I decided to launch the movie without any additional research.

Â Well, 60% chance that I get $4 million, 40% chance I lose $1 million.

Â Expected payout there is 2 million.

Â So what is AMK's market research doing for me?

Â My expected increase in profit is only $80,000.

Â I'm not going to be willing to pay $100,000 if I'm only expecting to get

Â 80,000 back from that.

Â So yes, there's value in the information they're providing, but

Â not enough to warrant $100,000 investment, all right.

Â 11:33

So some of the considerations might be what's the cost?

Â If it were a lower price point,

Â if it was a $50,000 investment it might make sense for us.

Â Could also be that it delays our decision making.

Â And we say well, we're waiting for the research, so we can't launch it.

Â So that's going to have to be something that's factored in.

Â If their recommendations were more reliable, if they

Â weren't recommending as many failures, or they were recommending more of the movies

Â that were ultimately successful, that might make the information more valuable.

Â Ultimately, for a company making that decision on

Â how much to spend on marketing research, what's at stake if we get it wrong?

Â Are we facing a small loss, or are we facing potentially catastrophic failure?

Â And so that's what we've gotta look at.

Â We looked at, in this case, on the scale it was failure or success.

Â If we want to be a little bit more granule, we've got catastrophic failure.

Â We've also got blockbusters successes.

Â And we're looking at the full spectrum in the middle.

Â And it will be nice to know how well likely are these different

Â possible outcomes?

Â If we can in some way characterize that in terms of how likely is catastrophic

Â failure, how likely is that blockbuster success, what does that look like for us?

Â Anything that we can do to kind of tilt the odds in our favor by collecting

Â more information might be worth it.

Â But we gotta work through kind of this value of information analysis to

Â make that decision.

Â 12:52

All right, so when we're looking at making those decisions, we've got to identify

Â what outcomes are possible, and that's something that's random.

Â It's not something that we can control.

Â We're going to look at using a technique called Monte Carlo simulation to

Â try to simulate out all of these different possible outcomes to get a sense for

Â what's the average outcome going to be.

Â How likely is it that we get those different outcomes, what's the payoff

Â associated with those different outcomes, what kind of decision roles are we using?

Â But ultimately, what we want to be able to map out is what are the pieces that

Â are random that we have to account for uncertainty with?

Â What are pieces that we can actually control and

Â how do the actions we take impact the measures that we're interested in?

Â That's what these decisions support tools that we're going to be building

Â in Excel going to look like.

Â In one of the exercises that we'll do shortly, we're going to look at

Â an inventory management tool where we make the decision of how much inventory to

Â order, but we don't know with certainty what demand is going to look like.

Â So depending on my cost structure,

Â that might have an impact on how much inventory I'm willing to order.

Â Well, there may be different cost structures,

Â I might have storage costs that are really high.

Â Maybe I have low storage costs.

Â Maybe I get a discount if I'm ordering in different quantities.

Â So that order quantity decision is the action that we get to control.

Â Demand is the piece that we don't get to control.

Â So we want to make the decision that optimizes our profit based on

Â what we control taking into account those pieces that we can't.

Â So that's what we're going to work on in our next lab exercise.

Â