So let's go through an example. Where let's take the film industry as our context and say that if I managed to launch this independent film, I'm going to make $4 million in profit. But if it's a failure, I'm going to lose a million dollars. We've got a company that's offering, they're saying for $100,000, we going to conduct a study, and it's going to help you forecast whether or not this movie is going to be successful. Well, what we want to know is should I make that $100,000 investment? So what's the information that we're going to have available to us? Well, we know the likelihood In general of the movie being a success or failure. So that's our prior information down here. We also have information about the reliability of this company advanced market knowledge, AMK's reliability. So when they say that movies are going to be successful, so for those movies that are successful, they said that their client should launch those movies 90% of the time. Given that the movie was successful, how likely were they to actually recommend a launch? They did it 90% of the time. But when the movies are failure, so given that the movies were failures, they also recommended launching those movies 20% of the time. So they're not always right, right. So let's construct the decision tree to help us in terms of whether or not we should pay a $100,000 for this. All right, so here are the decisions that we have to make. So initially, I could decide not to launch the movie. Save myself the headache, doesn't cost me anything. I decide to introduce the movie on my own. There is a 60% chance of success. There is a 40% chance of failure. We have payouts associated that, so we can calculated the expected value of the 0.6 multiplied by the 4 million, 0.4, multiplied by the negative 1 million, add them together, come up with a $2 million expected payout, all right. Or we say let's go and collect this information. Let's pay this company to collect additional information for us. Well, the next step, the company goes out and collects this information, they come back with a recommendation. It's go or no-go decision that they are recommending. But even if they say go, we don't know what the outcome will be with a 100% chance. So if they say don't launch the movie, I make the decision not to introduce it, I make nothing, but keep in mind I've paid a 100,000 for that information. They might say you should go and introduce the movie. Well, based on their, or I could rather, I could make the decision to go and launch the movie, going against their advice. So given that they said don't launch the movie, what are the chances that that movie's going to be a success? That's one question mark. What are the chances that movie's going to be a failure? That's another question mark. I need to calculate those probabilities before I can evaluate whether or not I should trust that advice and same thing when they say, I should launch the movie. If I discard their advice, don't introduce it, I make no money, I'm out the 100,000 for the information. If they say launch, what's the likelihood of success given their recommendation? What's the likelihood of failure given those recommendations? So those are the probabilities that we need to fill in the blanks for. All right, so how do we go about doing that? So let's break this problem down looking at some joint probabilities. What we know so far is probability of success, this is our prior information, is 60%. Probability of failure is going to be 40%. That's some of the information that we already have. All right, well, based on the reliability information and using the multiplication role, we can construct what's the probability of saying that we should launch the movie, that it's a go decision, and the movie is going to be successful. Well, we're going to use the product rule. What's the probability that they said go, given that movies were successful? That reliability information was 90%. We had that previously. The prior information, 60% chance of probability. Multiply them together, that's going to give me the 54%. Similar approach for probability of them recommending we launch the movie and it being a failure. Well, of those movies that were failures, they said that the movie should be launched 20% of the time. Overall, probability of a failure is 40%, joint probability is 8%. All right, now we can take the same approach to fill in the last two cells on this grid. Now, if I were to add up the probability, going across the row, I've got 54%, I've got 8%. What's the probability of saying that I should go ahead and launch the movie? It's going to be 62%. Now we can actually go and fill out the remainder of this table using addition rules, right. So my probability of success is 60%. My probability of success and go was 54%. So what remains, well, this is only going to be a 6% probability remaining. This one's going to be a 32% probability, again 40%, I've already accounted for 8%, that's where that's coming from. So the probability of the no-go is going to be 38%, and that's coming from just adding from across this row, the 6% and the 32%. Or saying, well if I don't launch the movie 1 minus the 62%, I'm recommending don't launch with 38%. So let's first focus on that 62 and 38% and fill that in on the table, then we'll come back for the rest. All right, so the information that we've filed in so far, based on the company saying go verses no-go, how frequently does that happen? The go recommendation comes 60% of the time, the no-go recommendation comes 38% of the time. Now we're going to move down to calculating once we've moved down each of this paths, the success and failure given the go and no-go decision. Okay, so we filled this table in. Now what we want to do is calculate those conditional probabilities, and this is where that Bayes' rule or Bayes' theorem is going to come into play for us. So what we want to know is given that AMK said go, and we said that happens 62% of the time. What fraction of that time are we going to have successes? Well, that's going to be coming from here. So of the 62%, what fraction are going to be those successes? It's going to end up being that 0.54 divided by 0.62. So to show you where we're coming from with this, let's go back to our multiplication rule. We had conditional probabilities. Ultimately, we have this information already that we say go, and it is a success. We would like to calculate, what we're ultimately looking to calculate is what's the probability of a success given that they said go. Well, in order to get that, what we're going to use is the joint probability for go and success divided by the marginal probability of just saying go. All right, so I'm going to go back to that previous slides where we had these figures. So we're going to fill in what's the probability of a success given that they said, go? All right, so probability of success given that they said go, it's 0.54 is our joint probability, the 0.62 is our marginal probability. If I want the probability of success given that they said, go, Bayes' theorem tells me it's going to be 0.54 / 0.62. All right, so we're going to be able to fill that one in. What's the probability of failure, given that they said go? Well, then we'd be looking at 0.08 divided by the 0.62 to get the probability based on the company telling us to go ahead. So let's fill in those blanks on our decision tree, and we'll see how things look. All right, so 0.54 / 0.62, so probability of success when they say go is 87%. Probability of a failure when they say go is only 13%. We can calculate the same thing for when they say no-go, comes up to be 16% and 84%. All right, so now that we have these probabilities listed on our decision tree, we actually have all the information that we need to go through and make an informed decision of should we collect this additional information. So let's see what that looks like. If I were to calculate the expected value when they say go, all right, there's an 87% chance that I get $4 million, there's a 13% chance that I lose a million dollars. So if I multiply 0.87 by 4 plus 0.13 by -1, that sum gives me the expected outcome of 3.35 million when they said to go ahead and launch the movie. So, if they say go, looks like I expect to make money. So I'm going to decide to launch the film. What about when they say no-go? Well, 0.16 times the 4 million, that's my chance of success. 0.84 times a $1 million loss. If I add those two products together, that's going to give me -0.2 million as my expected outcome. I'm probably going to decide not to launch the movie if those are my options. I'm better off not launching the film. All right, so now we've gotta take a step back. We say, when they say go, I expect to make $3.35 million. When they say no-go, I'm not going to launch the movie, so I make nothing. All right, so our next step is to say, all right, what's the overall expected payout going to be? Because I don't know what they're going to come back and tell me. Right, so If I were to now look at 0.62 multiplied by 3.35 plus 0.38, and I'm going to multiply that by 0, because that's what we get. That's my overall expected payout. All right, 0.62 multiplied by 3.35 plus 0 is 2.08 million. That's my revenue piece, but rather, that's my expected profit, but I haven't paid for the information yet. AMK was saying we want $100,000 for the information. All right, well, let's see how would I do on my own, and let's return to this lower part of the chart here where, what if I decided to launch the movie without any additional research. Well, 60% chance that I get $4 million, 40% chance I lose $1 million. Expected payout there is 2 million. So what is AMK's market research doing for me? My expected increase in profit is only $80,000. I'm not going to be willing to pay $100,000 if I'm only expecting to get 80,000 back from that. So yes, there's value in the information they're providing, but not enough to warrant $100,000 investment, all right. So what we've had to do here is, we've calculated expected profit without the information, expected profit with the additional information, and we're looking at the difference to say how much is this information actually doing for me? So some of the considerations might be what's the cost? If it were a lower price point, if it was a $50,000 investment it might make sense for us. Could also be that it delays our decision making. And we say well, we're waiting for the research, so we can't launch it. So that's going to have to be something that's factored in. If their recommendations were more reliable, if they weren't recommending as many failures, or they were recommending more of the movies that were ultimately successful, that might make the information more valuable. Ultimately, for a company making that decision on how much to spend on marketing research, what's at stake if we get it wrong? Are we facing a small loss, or are we facing potentially catastrophic failure? And so that's what we've gotta look at. We looked at, in this case, on the scale it was failure or success. If we want to be a little bit more granule, we've got catastrophic failure. We've also got blockbusters successes. And we're looking at the full spectrum in the middle. And it will be nice to know how well likely are these different possible outcomes? If we can in some way characterize that in terms of how likely is catastrophic failure, how likely is that blockbuster success, what does that look like for us? Anything that we can do to kind of tilt the odds in our favor by collecting more information might be worth it. But we gotta work through kind of this value of information analysis to make that decision. All right, so when we're looking at making those decisions, we've got to identify what outcomes are possible, and that's something that's random. It's not something that we can control. We're going to look at using a technique called Monte Carlo simulation to try to simulate out all of these different possible outcomes to get a sense for what's the average outcome going to be. How likely is it that we get those different outcomes, what's the payoff associated with those different outcomes, what kind of decision roles are we using? But ultimately, what we want to be able to map out is what are the pieces that are random that we have to account for uncertainty with? What are pieces that we can actually control and how do the actions we take impact the measures that we're interested in? That's what these decisions support tools that we're going to be building in Excel going to look like. In one of the exercises that we'll do shortly, we're going to look at an inventory management tool where we make the decision of how much inventory to order, but we don't know with certainty what demand is going to look like. So depending on my cost structure, that might have an impact on how much inventory I'm willing to order. Well, there may be different cost structures, I might have storage costs that are really high. Maybe I have low storage costs. Maybe I get a discount if I'm ordering in different quantities. So that order quantity decision is the action that we get to control. Demand is the piece that we don't get to control. So we want to make the decision that optimizes our profit based on what we control taking into account those pieces that we can't. So that's what we're going to work on in our next lab exercise.
