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Case Study

1) XanderXander prefers more money to less and follows the five rules of actional thought. He has

given you the following preference probabilities for deals with $20 as the worst outcome and$200 as the best outcome:

value ($) preference probability

20 0.00

50 0.28

100 0.61

130 0.76

150 0.84200 1.00

Xander should choose alternative D1 or D2 ?

>>> Alternative D1

$130

>>> Alternative B1

$50

0.2 Outcome C1

0 0.6 Outcome A1

0 $100

>>> Alternative B2

>>> Alternative D2 0 0.4 Outcome A2

$200

0.8 Outcome C2

$200

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2) Consider the following decision

Using the u-function u(x)=0.2x+5, what is the u-value of the preferred alternative for the above

decision?

$20

A

B

$60

$30.5

.3 $75.2

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3) Bighorn oil companyBighorn oil company has leased the drilling rights on a large parcel of land in Wyoming

that may or may not contain an oil reserve. A competitor has offered to lease the land for

$200,000 cash in return for drilling rights and all rights to any oil that might be found.

The offer will expire in three days. If Bighorn does not take the deal, it will be faced with

he deci-sion of whether to drill for oil on its own. Drilling costs are projected to be 400,000. The

company feels that there are four possible outcomes from drilling:

1.dry hole (no oil or natural gas)

2.natural gas

3.natural gas and some oil

4.oil only

If drilling yields a dry hole, the land will be basically worthless, because it is located inhe bad-lands of Wyoming. If natural gas is discovered, Bighorn will recover only its rilling costs.

If nat-ural gas and some oil is discovered, revenue is projected to be 800,000. Finally, if only

oil is dis-covered, revenues will be $1,600,000.

How to make a decision ?

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4) Aircraft companyAn aircraft company is considering using a new light-weight fastener, called the

Superlight, to rivet certain sheet metal parts together. These particular items are not safety-of-

flight critical, and so the decision of whether to use them is a financial one.

The weight savings realized by using Superlights instead of the Basic fastener is has a

value of $100K to the aircraft manufacturer.

The Superlight fastener has never been used before on a production aircraft, however,

and engineers are wary of its durability. From what little they know of the design and initial lab

tests, they have high uncertainty about the number of Superlight fasteners that would need

replacement during routine maintenance. They translate this to costs of $300K with probability

of 0.3, $120K with probability 0.5, and $75K with probability 0.2. (Label these possible cases

High, Moderate, and Low repair cost, for future reference.) These costs include both parts and

labor.

The alternative to the Superlight is the Basic fastener, which, although heavier than the

Superlight, has been used extensively on past aircraft. Stress engineers feel that the Basic has

a tried and true performance record: they conclude from past statistics that the repair cost

associated with Basic fastener failure is $125K.

The Test Engineering group could run a batch of Superlights through a test program to

determine their strength and durability characteristics under simulated flight conditions. Given

what the stress group has told him regarding the Superlight, the Test group manager claims

that his test program would be of value. He says that for Superlights with High repair cost, the

test batch will pass his test with a likelihood of only 30%. If the Superlights have Moderate

repair cost, they will pass the test with a probability of 80%, and if they would be Low in repair

cost a 90% probability of passing is estimated. The Test group manager cautions that a lot of

time and hardware would be needed to conduct the test.

In these dollar ranges, assume that the aircraft company is a risk-neutral decision

maker.

4.1) What is the certain equivalent for the best alternative?

4.2) What is the value of clairvoyance on the repair costs for the Superlights?

4.3) What is the value of the Test Engineering groups test program?

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5) Harris Publishing CompanyConsider the decision facing the Harris Publishing Company, which recently received a manuscript written by

a former government official about the private life of a very influential member of the United States government. The

author will grant Harris full rights to the book for a guaranteed up-front payment of $400,000 plus a per copy royalty

ifthe book is published. The basic question facing Harriss management is whether to sign the contract with this

author or risk losing the book to another publisher. Even if it signs, Harris will publish the book only if the manuscriptreceives a favorable review from the editorial board. However, several uncertainties make this decision difficult. The

executive editor, who is the person ultimately responsible for making the decision, has outlined the following items

for consideration:

1. There is an 80% (0.80) chance that the content of the book is accurate. If the content is accurate, the

author will be paid $2.00 per copy for each hardcover book sold and $0.80 per copy for each paperback. No royalties

will be paid if the manuscript is not accurate.

2. If the content is not accurate, there is a 0.90 chance that a libel suit will be filed; and if so, experience

indicates the publisher will settle out of court for $1,800,000.

3. For hardcover publication, the following demand distribution has been assessed:

4. The fixed production costs for the hardcover book will be $700,000 before any copies are printed, and

the cost of printing and binding is $16.00 per copy. The number of copies to be printed can match any projected

demand. The wholesale selling price of the hardcover book will be $24.00.

5. For paperback publication, the following demand distribution has been assessed:

6. The fixed costs for paperback publication are $400,000, the printing and binding costs are $2.00 per

copy, and the wholesale selling price is $8.00 each.

7. The accuracy of the books content will be known only after the book has been published and sold.

8. The editor has assessed the probability that the manuscript will get a favorable review from the editorial

board as 0.80.

The decision in this case is complicated by the many uncertainties involved. In situations such as these, a

decision tree can be used to provide a framework to help make the decision. The following steps are used to develop

and apply a decision tree to a decision problem such as the one the Harris Publishing Company is facing.