please complete Problems 3-19, 3-27, 3-37, 3-41, and 3-45 Only these 5 problems need to be done.
Discussion Questions and Problems
Discussion Questions
3-1 Give an example of a good decision that you made
that resulted in a bad outcome. Also give an example
of a bad decision that you made that had a good outcome. Why was each decision good or bad?
3-2 Describe what is involved in the decision process.
3-3 What is an alternative? What is a state of nature?
3-4 Discuss the differences among decision making under certainty, decision making under risk, and decision making under uncertainty.
3-5 What techniques are used to solve decision-making
problems under uncertainty? Which technique results in an optimistic decision? Which technique results in a pessimistic decision?
3-6 Define opportunity loss. What decision-making criteria are used with an opportunity loss table?
3-7 What information should be placed on a decision
tree?
3-8 Describe how you would determine the best decision
using the EMV criterion with a decision tree.
3-9 What is the difference between prior and posterio
probabilities?
3-10 What is the purpose of Bayesian analysis? Describe
how you would use Bayesian analysis in the
decision-making process.
3-11 What is the EVSI? How is this computed?
3-12 How isthe efficiency ofsample information computed?
3-13 What is the overall purpose of utility theory?
3-14 Briefly discuss how a utility function can be assessed. What is a standard gamble, and how is it
used in determining utility values?
3-15 How is a utility curve used in selecting the best decision for a particular problem?
3-16 What is a risk seeker? What is a risk avoider? How
does the utility curve for these types of decision
makers differ?
Problems
3-17 Kenneth Brown is the principal owner of Brown Oil,
Inc. After quitting his university teaching job, Ken
has been able to increase his annual salary by a factor of over 100. At the present time, Ken is forced
to consider purchasing some more equipment fo
Brown Oil because of competition. His alternatives
are shown in the following table:
Equipment
Favorable
Market
($)
Unfavorable
Market
($)
Sub XXXXXXXXXX, XXXXXXXXXX,000
Oiler J 250, XXXXXXXXXX,000
Texan 75,000 -18,000
For example, if Ken purchases a Sub 100 and if
there is a favorable market, he will realize a profit
of $300,000. On the other hand, if the market is
Note: means the problem may be solved with QM for Windows; means the problem may be solved with Excel QM; and means the problem may be
solved with QM for Windows and/or Excel QM.
102 Chapter 3 • Decision Analysis
unfavorable, Ken will suffer a loss of $200,000.
But Ken has always been a very optimistic decision
maker.
(a) What type of decision is Ken facing?
(b) What decision criterion should he use?
(c) What alternative is best?
3-18 Although Ken Brown (discussed in Problem 3-17) is
the principal owner of Brown Oil, his
other Bob is
credited with making the company a financial success. Bob is vice president of finance. Bob attributes
his success to his pessimistic attitude about business
and the oil industry. Given the information from
Problem 3-17, it is likely that Bob will a
ive at a
different decision. What decision criterion should
Bob use, and what alternative will he select?
3-19 The Lu
icant is an expensive oil newsletter to which
many oil giants subscribe, including Ken Brown (see
Problem 3-17 for details). In the last issue, the lette
described how the demand for oil products would be
extremely high. Apparently, the American consume
will continue to use oil products even if the price of
these products doubles. Indeed, one of the articles in
the Lu
icant states that the chances of a favorable
market for oil products was 70%, while the chance
of an unfavorable market was only 30%. Ken would
like to use these probabilities in determining the best
decision.
(a) What decision model should be used?
(b) What is the optimal decision?
(c) Ken believes that the $300,000 figure for the Su
100 with a favorable market is too high. How
much lower would this figure have to be for Ken
to change his decision made in part b?
3-20 Mickey Lawson is considering investing some
money that he inherited. The following payoff table
gives the profits that would be realized during the
next year for each of three investment alternatives
Mickey is considering:
State of Nature
Decision
Alternative
Good
Economy
Poo
Economy
Stock market 80,000 -20,000
Bonds 30,000 20,000
CDs 23,000 23,000
Probability XXXXXXXXXX
(a) What decision would maximize expected profits?
(b) What is the maximum amount that should be
paid for a perfect forecast of the economy?
3-21 Develop an opportunity loss table for the investment
problem that Mickey Lawson faces in Problem 3-20.
What decision would minimize the expected opportunity loss? What is the minimum EOL?
3-22 Allen Young has always been proud of his personal
investment strategies and has done very well ove
the past several years. He invests primarily in the
stock market. Over the past several months, however, Allen has become very concerned about the
stock market as a good investment. In some cases, it
would have been better for Allen to have his money
in a bank than in the market. During the next year,
Allen must decide whether to invest $10,000 in the
stock market or in a certificate of deposit (CD) at an
interest rate of 9%. If the market is good, Allen believes that he could get a 14% return on his money.
With a fair market, he expects to get an 8% return. If
the market is bad, he will most likely get no return
at all—in other words, the return would be 0%.
Allen estimates that the probability of a good market
is 0.4, the probability of a fair market is 0.4, and the
probability of a bad market is 0.2, and he wishes to
maximize his long-run average return.
(a) Develop a decision table for this problem.
(b) What is the best decision?
3-23 In Problem 3-22, you helped Allen Young determine
the best investment strategy. Now, Young is thinking
about paying for a stock market newsletter. A friend
ofYoung said that these types of letters could predict
very accurately whether the market would be good,
fair, or poor. Then, based on these predictions, Allen
could make better investment decisions.
(a) What is the most that Allen would be willing to
pay for a newsletter?
(b) Young now believes that a good market will give
a return of only 11% instead of 14%. Will this
information change the amount that Allen would
e willing to pay for the newsletter? If your answer is yes, determine the most that Allen would
e willing to pay, given this new information.
3-24 Today’s Electronics specializes in manufacturing
modern electronic components. It also builds the
equipment that produces the components. Phyllis
Weinberger, who is responsible for advising the
president of Today’s Electronics on electronic manufacturing equipment, has developed the following
table concerning a proposed facility:
Profit ($)
Strong
Market
Fai
Market
Poo
Market
Large facility 550,000 110, XXXXXXXXXX,000
Medium-sized
facility
300,000 129, XXXXXXXXXX,000
Small facility 200,000 100,000 -32,000
No facility 0 0 0
(a) Develop an opportunity loss table.
(b) What is the minimax regret decision?
Discussion Questions and Problems 103
3-25 Brilliant Color is a small supplier of chemicals
and equipment that are used by some photographic
stores to process 35mm film. One product that Brilliant Color supplies is BC-6. John Kubick, president
of Brilliant Color, normally stocks 11, 12, or 13
cases of BC-6 each week. For each case that John
sells, he receives a profit of $35. Like many photographic chemicals, BC-6 has a very short shelf life,
so if a case is not sold by the end of the week, John
must discard it. Since each case costs John $56, he
loses $56 for every case that is not sold by the end of
the week. There is a probability of 0.45 of selling 11
cases, a probability of 0.35 of selling 12 cases, and a
probability of 0.2 of selling 13 cases.
(a) Construct a decision table for this problem. Include all conditional values and probabilities in
the table.
(b) What is your recommended course of action?
(c) If John is able to develop BC-6 with an ingredient that stabilizes it so that it no longer has to be
discarded, how would this change your recommended course of action?
3-26 Megley Cheese Company is a small manufacturer of
several different cheese products. One of the products is a cheese spread that is sold to retail outlets.
Jason Megley must decide how many cases of cheese
spread to manufacture each month. The probability
that the demand will be six cases is 0.1, seven cases
is 0.3, eight cases is 0.5, and nine cases is 0.1. The
cost of every case is $45, and the price that Jason
gets for each case is $95. Unfortunately, any cases
not sold by the end of the month are of no value, due
to spoilage. How many cases of cheese should Jason
manufacture each month?
3-27 Farm Grown, Inc., produces cases of perishable food
products. Each case contains an assortment of vegetables and other farm products. Each case costs $5
and sells for $15. If there are any cases not sold by
the end of the day, they are sold to a large food processing company for $3 a case. The probability that
daily demand will be 100 cases is 0.3, the probability that daily demand will be 200 cases is 0.4, and
the probability that daily demand will be 300 cases
is 0.3. Farm Grown has a policy of always satisfying
customer demands. If its own supply of cases is less
than the demand, it buys the necessary vegetables
from a competitor. The estimated cost of doing this
is $16 per case.
(a) Draw a decision table for this problem.
(b) What do you recommend?
3-28 In Problem 3-27, Farm Grown, Inc. has reason to
elieve the probabilities may not be reliable due
to changing conditions. If these probabilities are
ignored, what decision would be made using the
optimistic criterion? What decision would be made
using the pessimistic criterion?
3-29 Mick Ka
a is the manager of MCZ Drilling Products, which produces a variety of specialty valves fo
oil field equipment. Recent activity in the oil fields
has caused demand to increase drastically, and a
decision has been made to open a new manufacturing facility. Three locations are being considered,
and the size of the facility would not be the same
in each location. Thus, overtime might be necessary
at times. The following table gives the total monthly
cost (in $1,000s) for each possible location unde
each demand possibility. The probabilities for the
demand levels have been determined to be 20% fo