EXAMPLE 240 Chapter 6 6.2 NEW PRODUCT DECISIONS AT ACME WITH TECHNOLOGICAL UNCERTAINTY In this version of the example, we assume as before that the new product is still in the development stage. However, we now assume that there is a chance that the product will be a failure for technological reasons, such as a new drug that fails to meet FDA approval. At this point in the development process, Acme assesses the probability of technologi- cal failure to be 0.2. The $6 million fixed cost from before is now broken down into two components: $4 million for addition development costs and $2 million for fixed costs of marketing, the latter to be incurred only if the product is a technological success and the company decides to market it. The unit margin and the probability distribution of the prod- uct's sales volume if it is marketed are the same as before. How should Acme proceed? Objective To use a decision tree to find Acme's EMV-maximizing strategy for this two- stage decision problem. Decision Making under Uncertainty Figure 6.12 Decision Tree with Pble Techn logical Failure Where Do the Numbers Come From? The probability of technological failure might be based partly on historical data-the tech nological failure rate of similar products in the past but it is probably partly subjective. based on how the product's development has proceeded so far. The probability distibution of sales volume is a more difficult issue. When Acme makes its first decision, right now, it must look ahead to see how the market might look in the future, after the development stage, which could be quite a while from now. (The same issue is relevant in Example 6.1. although we didn't discuss it there.) This a difficult assessment, and it is an obvious candi date for an eventual sensitivity analys Solution The reason this is a two-stage decision problem is that Acne can decide right away to stop development and abandon the product, thus saving further fixed costs of development. However, if Acme decides to continue development and the product turns out to be a tech- nological success, a second decision on whether to market the product must still be made A spreadsheet model such as in Figure 6.1 for the single-stage problem could be devel oped to calculate the relevant EMV but this 't as easy as it sounds. A much better way is to use a decision tree, using the Precision Tree add-in. The finished tree appears in Figure 6.12. (See the file New Product Decisions Technological Uncertainty.) The fint decision is whether to continue development. If "Yes," the fixed development cost is incurred, so it is entered on this beach Then there is a probability node for the technological success or fail we. If it's a failure, there are no further costs, but the fixed development cost is lost it's a success, Acme must decide whether to market the product. From this point, the tree is exactly like the single-stage tree, except that the fixed development cost is gone. have purposely aided theme of Bay for now. It will be mod in the next vendos of the Ame Not For Sater Decision Problems 241 Figure 6.13 Risk Profile from Best Strategy N following the TRUE branches, you can see Acme's best strategy. The company should continue development, and if the product is a technological access, it should be marketed. The EMV, again the weighted average of all possible monetary outcomes with this strategy, is $99,200. However, this is only the expected value, or mean, of the prob ability distribution of monetary outcomes. You can see the full probability distribution by requesting a risk profile from Precision Tree (through the Decision Analysis dropdown). This appears, both in graphical and tabular form, in Figure 6.13. Note that Acme has a 64 chance of incurring a net loss with this strategy, including a possible loss of $4.38 million. This doesn't sound good. However, the company has a 36% of a net gain of $4.8 million and, in an expected value sense, this more than offsets the possible losses. Probabilities for Decision Tree New Product Decision cell B4, the tree automatically recalculates, with the results in Figure 6.14. With just this small change, the best decision changes completely. Now the company should discontinue development and abandon the product. There is evidently not a large enough chance of recovering the fixed development cost. Figure 6.14 Decision Tree with Larger Probability of Failure 14 15 m S SUNS 150% Precision Tree Tip: Placement of Results When you request a risk profile or other PrecisionTree reports, they are placed in a new workbook by default. If you would rather have then placed in the some workbook as your decision tree, select Application Settings from the Unilaties dropdown list on the Precision Tree ribbon, and change the "Place Reports In" setting to Active Workbook You only have to do this once. (The RISE add-in discussed in the next two chapters has this same setting.) We won't perform any systematic sensitivity analyses on this model (we ask you to do some in the problems), but it is easy to show that the best strategy is quite sensitive to the probability of technological failure. If you change this probability from 0.2 to 0.25 in 242 Chapter & Decision Making under Uncertainty Modeling Issues We return to the probability distribution of eventual sales volume. The interpretation here is that at the time of the first decision, Acme has assessed what the market might look like after the development stage, which could be quite a while from now. Again, this is a dif- ficult assessment. Acme could instead break this assessment into parts. It could first assess a probability distribution for how the general market for such products might change-up, down, or no change, for example-by the time development is completed. Then for each of these general markets, it could assess a probability distribution for the sales volume of its new product. By breaking it up in this way, Acme might be able to make a more accu- rate assessment, but the decision tree would be somewhat more complex. We ask you to explore this in one of the problems.■ The next example illustrates another possible multistage extension of the Acme deci- sion problem. This example provides an opportunity to introduce two important topics discussed earlier: Bayes' rule for updating probabilities and the value of information.

EXAMPLE 240 Chapter 6 6.2 NEW PRODUCT DECISIONS AT ACME WITH TECHNOLOGICAL UNCERTAINTY In this version of the example, we assume as before that the new product is still in the development stage. However, we now assume that there is a chance that the product will be a failure for technological reasons, such as a new drug that fails to meet FDA approval. At this point in the development process, Acme assesses the probability of technologi- cal failure to be 0.2. The $6 million fixed cost from before is now broken down into two components: $4 million for addition development costs and $2 million for fixed costs of marketing, the latter to be incurred only if the product is a technological success and the company decides to market it. The unit margin and the probability distribution of the prod- uct's sales volume if it is marketed are the same as before. How should Acme proceed? Objective To use a decision tree to find Acme's EMV-maximizing strategy for this two- stage decision problem. Decision Making under Uncertainty Figure 6.12 Decision Tree with Pble Techn logical Failure Where Do the Numbers Come From? The probability of technological failure might be based partly on historical data-the tech nological failure rate of similar products in the past but it is probably partly subjective. based on how the product's development has proceeded so far. The probability distibution of sales volume is a more difficult issue. When Acme makes its first decision, right now, it must look ahead to see how the market might look in the future, after the development stage, which could be quite a while from now. (The same issue is relevant in Example 6.1. although we didn't discuss it there.) This a difficult assessment, and it is an obvious candi date for an eventual sensitivity analys Solution The reason this is a two-stage decision problem is that Acne can decide right away to stop development and abandon the product, thus saving further fixed costs of development. However, if Acme decides to continue development and the product turns out to be a tech- nological success, a second decision on whether to market the product must still be made A spreadsheet model such as in Figure 6.1 for the single-stage problem could be devel oped to calculate the relevant EMV but this 't as easy as it sounds. A much better way is to use a decision tree, using the Precision Tree add-in. The finished tree appears in Figure 6.12. (See the file New Product Decisions Technological Uncertainty.) The fint decision is whether to continue development. If "Yes," the fixed development cost is incurred, so it is entered on this beach Then there is a probability node for the technological success or fail we. If it's a failure, there are no further costs, but the fixed development cost is lost it's a success, Acme must decide whether to market the product. From this point, the tree is exactly like the single-stage tree, except that the fixed development cost is gone. have purposely aided theme of Bay for now. It will be mod in the next vendos of the Ame Not For Sater Decision Problems 241 Figure 6.13 Risk Profile from Best Strategy N following the TRUE branches, you can see Acme's best strategy. The company should continue development, and if the product is a technological access, it should be marketed. The EMV, again the weighted average of all possible monetary outcomes with this strategy, is $99,200. However, this is only the expected value, or mean, of the prob ability distribution of monetary outcomes. You can see the full probability distribution by requesting a risk profile from Precision Tree (through the Decision Analysis dropdown). This appears, both in graphical and tabular form, in Figure 6.13. Note that Acme has a 64 chance of incurring a net loss with this strategy, including a possible loss of $4.38 million. This doesn't sound good. However, the company has a 36% of a net gain of $4.8 million and, in an expected value sense, this more than offsets the possible losses. Probabilities for Decision Tree New Product Decision cell B4, the tree automatically recalculates, with the results in Figure 6.14. With just this small change, the best decision changes completely. Now the company should discontinue development and abandon the product. There is evidently not a large enough chance of recovering the fixed development cost. Figure 6.14 Decision Tree with Larger Probability of Failure 14 15 m S SUNS 150% Precision Tree Tip: Placement of Results When you request a risk profile or other PrecisionTree reports, they are placed in a new workbook by default. If you would rather have then placed in the some workbook as your decision tree, select Application Settings from the Unilaties dropdown list on the Precision Tree ribbon, and change the "Place Reports In" setting to Active Workbook You only have to do this once. (The RISE add-in discussed in the next two chapters has this same setting.) We won't perform any systematic sensitivity analyses on this model (we ask you to do some in the problems), but it is easy to show that the best strategy is quite sensitive to the probability of technological failure. If you change this probability from 0.2 to 0.25 in 242 Chapter & Decision Making under Uncertainty Modeling Issues We return to the probability distribution of eventual sales volume. The interpretation here is that at the time of the first decision, Acme has assessed what the market might look like after the development stage, which could be quite a while from now. Again, this is a dif- ficult assessment. Acme could instead break this assessment into parts. It could first assess a probability distribution for how the general market for such products might change-up, down, or no change, for example-by the time development is completed. Then for each of these general markets, it could assess a probability distribution for the sales volume of its new product. By breaking it up in this way, Acme might be able to make a more accu- rate assessment, but the decision tree would be somewhat more complex. We ask you to explore this in one of the problems.■ The next example illustrates another possible multistage extension of the Acme deci- sion problem. This example provides an opportunity to introduce two important topics discussed earlier: Bayes' rule for updating probabilities and the value of information.

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Question

Starting with the finished version of Example 6.2, attached, change the decision criterion to "maximize expected utility," using an exponential utility function with risk tolerance $5,000,000. Display certainty equivalents on the tree.

a. Keep doubling the risk tolerance until the company's best strategy is the same as with the EMV criterion—continue with development and then market if successful.

The risk tolerance must reach $ ____________ before the risk averse company acts the same as the EMV-maximizing company.

b. With a risk tolerance of $320,000,000, the company views the optimal strategy as equivalent to receiving a sure $____________ , even though the EMV from the original strategy (with no risk tolerance) is $ ___________ .

Transcribed Image Text:EXAMPLE 240 Chapter 6 6.2 NEW PRODUCT DECISIONS AT ACME WITH TECHNOLOGICAL UNCERTAINTY In this version of the example, we assume as before that the new product is still in the development stage. However, we now assume that there is a chance that the product will be a failure for technological reasons, such as a new drug that fails to meet FDA approval. At this point in the development process, Acme assesses the probability of technologi- cal failure to be 0.2. The $6 million fixed cost from before is now broken down into two components: $4 million for addition development costs and $2 million for fixed costs of marketing, the latter to be incurred only if the product is a technological success and the company decides to market it. The unit margin and the probability distribution of the prod- uct's sales volume if it is marketed are the same as before. How should Acme proceed? Objective To use a decision tree to find Acme's EMV-maximizing strategy for this two- stage decision problem. Decision Making under Uncertainty Figure 6.12 Decision Tree with Pble Techn logical Failure Where Do the Numbers Come From? The probability of technological failure might be based partly on historical data-the tech nological failure rate of similar products in the past but it is probably partly subjective. based on how the product's development has proceeded so far. The probability distibution of sales volume is a more difficult issue. When Acme makes its first decision, right now, it must look ahead to see how the market might look in the future, after the development stage, which could be quite a while from now. (The same issue is relevant in Example 6.1. although we didn't discuss it there.) This a difficult assessment, and it is an obvious candi date for an eventual sensitivity analys Solution The reason this is a two-stage decision problem is that Acne can decide right away to stop development and abandon the product, thus saving further fixed costs of development. However, if Acme decides to continue development and the product turns out to be a tech- nological success, a second decision on whether to market the product must still be made A spreadsheet model such as in Figure 6.1 for the single-stage problem could be devel oped to calculate the relevant EMV but this 't as easy as it sounds. A much better way is to use a decision tree, using the Precision Tree add-in. The finished tree appears in Figure 6.12. (See the file New Product Decisions Technological Uncertainty.) The fint decision is whether to continue development. If "Yes," the fixed development cost is incurred, so it is entered on this beach Then there is a probability node for the technological success or fail we. If it's a failure, there are no further costs, but the fixed development cost is lost it's a success, Acme must decide whether to market the product. From this point, the tree is exactly like the single-stage tree, except that the fixed development cost is gone. have purposely aided theme of Bay for now. It will be mod in the next vendos of the Ame Not For Sater Decision Problems 241 Figure 6.13 Risk Profile from Best Strategy N following the TRUE branches, you can see Acme's best strategy. The company should continue development, and if the product is a technological access, it should be marketed. The EMV, again the weighted average of all possible monetary outcomes with this strategy, is $99,200. However, this is only the expected value, or mean, of the prob ability distribution of monetary outcomes. You can see the full probability distribution by requesting a risk profile from Precision Tree (through the Decision Analysis dropdown). This appears, both in graphical and tabular form, in Figure 6.13. Note that Acme has a 64 chance of incurring a net loss with this strategy, including a possible loss of $4.38 million. This doesn't sound good. However, the company has a 36% of a net gain of $4.8 million and, in an expected value sense, this more than offsets the possible losses. Probabilities for Decision Tree New Product Decision cell B4, the tree automatically recalculates, with the results in Figure 6.14. With just this small change, the best decision changes completely. Now the company should discontinue development and abandon the product. There is evidently not a large enough chance of recovering the fixed development cost. Figure 6.14 Decision Tree with Larger Probability of Failure 14 15 m S SUNS 150% Precision Tree Tip: Placement of Results When you request a risk profile or other PrecisionTree reports, they are placed in a new workbook by default. If you would rather have then placed in the some workbook as your decision tree, select Application Settings from the Unilaties dropdown list on the Precision Tree ribbon, and change the "Place Reports In" setting to Active Workbook You only have to do this once. (The RISE add-in discussed in the next two chapters has this same setting.) We won't perform any systematic sensitivity analyses on this model (we ask you to do some in the problems), but it is easy to show that the best strategy is quite sensitive to the probability of technological failure. If you change this probability from 0.2 to 0.25 in 242 Chapter & Decision Making under Uncertainty Modeling Issues We return to the probability distribution of eventual sales volume. The interpretation here is that at the time of the first decision, Acme has assessed what the market might look like after the development stage, which could be quite a while from now. Again, this is a dif- ficult assessment. Acme could instead break this assessment into parts. It could first assess a probability distribution for how the general market for such products might change-up, down, or no change, for example-by the time development is completed. Then for each of these general markets, it could assess a probability distribution for the sales volume of its new product. By breaking it up in this way, Acme might be able to make a more accu- rate assessment, but the decision tree would be somewhat more complex. We ask you to explore this in one of the problems.■ The next example illustrates another possible multistage extension of the Acme deci- sion problem. This example provides an opportunity to introduce two important topics discussed earlier: Bayes' rule for updating probabilities and the value of information.

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