PS7a
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MISC
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Industrial Engineering
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Dec 6, 2023
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Uploaded by wilsonkhieu
IEOR 166 Problem Set 7A
References:
Clemen 2
nd
Ed: pp. 70-77, 101-109, 435-449; (or 3
rd
Ed: pp. 76-83, 118-127, 531-547)
M&O: Sections 2.1-2.3 and Chapter 4.
Note that Problem Set 7B (write an exam question) is to be turned in separately.
Do Clemen 12.7 (both editions), and the following.
1.
An aircraft company is considering using a new lightweight 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 has a net present value of $10 million (M) to the aircraft manufacturer. In this
dollar range, assume that the company is a risk-neutral decision maker. 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 are uncertain about the number of Superlight
fasteners that would need replacement during routine maintenance in the warranty period. They translate
this to (net present value) costs of $30M with probability 0.3, $12.5M with probability 0.5, and $7.5M
with probability 0.2. Label these possible cases High, Moderate, and Low repair cost. These costs include
parts and labor. The alternative to the Superlight is the Basic fastener, which, although heavier than
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 NPV of repair costs associated with
Basic fastener failure is $9M.
a. Construct and evaluate the decision tree for the fastener decision. Should the company use Superlights
or Basic fasteners? What is the EMV of each alternative?
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
found regarding the Superlight, the Test group manager claims that the test program would be of value.
The details on the test are as follows: if Superlights will have High repair cost, the test batch will pass the
test with probability of only 30%; if the Superlights will have Moderate repair cost, they will pass the test
with probability 80%, and if they will be Low in repair cost they will pass with probability 90%. The Test
group manager cautions that a lot of time and hardware would be needed to conduct the test.
b. Construct a probability tree with the test result and the repair cost uncertainties. If the test is conducted
what is the probability that the test batch will pass?
c. Construct and evaluate the decision tree for the test decision. How much should the company be willing
to spend on the test program?
2.
Consider the decision sapling in which you can choose either a sure thing worth $5M or a gamble that
has probability of 0.4 of giving a return of $2M; otherwise the return on the gamble will be $7M.
Suppose we can purchase a forecast for the gamble, where the forecast has probability p of being
accurate. (So the false positive and false negative rates are both 1-p).
a.
What is the EMV of the gamble given the forecast is that the return will be $7M? If it is $2M?
b.
If the forecast is $7M, for what range of p will it be optimal to choose the gamble?
c.
Give an expression for the EVII as a function of p, and graph it.
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