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Fundamentals of Decision Theory Models l CHAPTER 3

TRUE/FALSE 3.1

Decision Theory is described as a consequence or outcome, normally expressed in a monetary value, which occurs as a result of a particular alternative and state of nature.

*3.2

Decision Theory is a process for organizing information and making decisions.

3.3

Expected Monetary Value (EMV) is the average or expected monetary outcome of a decision if it can be repeated a large number of times.

*3.4

Expected Monetary Value (EMV) is the payoff you should expect to occur when you choose a particular alternative.

*3.5

When we speak about the “goodness” or “badness” of a decision, we are talking about the degree to which the decision process is logical.

3.6

Decision-making under uncertainty exists when a decision is made where several outcomes or states of nature may occur as a result of the decision or choice of alternative, and the probabilities of these outcomes or states of nature are known.

3.7

A good decision may result in an unfavorable outcome whereas a bad decision may result in a favorable outcome.

3.8

The decision-maker has little or no control over a state of nature.

3.9

NASA uses a decision-making process to decide when to replace heat protection tiles on the space shuttle.

3.10

Decision-making under risk is a probabilistic decision situation.

3.11

Bad decisions always result in bad or unfavorable outcomes.

*3.12

The difference in decision-making under risk and decision-making under uncertainty is that under risk, we think we know the probabilities of the states of nature, while under uncertainty we do not know the probabilities of the states of nature.

3.13

As a consequence of computer limitations, one should limit the number of decision alternatives and possible states of nature.

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Fundamentals of Decision Theory Models l CHAPTER 3

3.14

EMV is the exact monetary value used in decision theory.

*3.15

The only good decision model is a computerized decision model.

3.16

KLM has developed a DSS to help determine the size and organization of the maintenance work force.

3.17

EVPI is equivalent to the expected value with perfect or certain information.

*3.18

EVPI (Expected Value of Perfect Information) is a measure of the maximum value of additional information.

*3.19

There are six steps in Decision Theory, and these steps and the decision maker should expect to execute one step only a single time, and in the proper sequence.

3.20

EOL will always result in the same decision as EMV.

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Fundamentals of Decision Theory Models l CHAPTER 3

3.21

When using the EOL as a decision criteria, the best decision is the alternative with the least EOL value.

3.22

Sensitivity analysis techniques investigate how a decision might change based on input changes to the problem data.

*3.23

Whenever we use a decision model, we should always perform a sensitivity analysis on the results.

*3.24

A major purpose of sensitivity analysis is to help us understand within what limits our preferred solution holds.

3.25

The maximax decision criteria maximizes the maximum outcome for every alternative.

3.26

The maximin decision criteria minimizes the maximum outcome for every alternative.

3.27

Marginal analysis is an aid to decision-making when there are a large number of alternatives and/or states of nature.

3.28

A decision table is a useful tool when one is attempting to make a set of decisions in sequence.

3.29

A common mistake of decision-makers is to concentrate only on the more positive outcomes.

3.30

Decision-making under risk implies a greater amount of information or knowledge than decisionmaking under uncertainty.

3.31

When we make a decision under risk, we will receive as an outcome the calculated expected monetary value.

3.32

When we are attempting to make a decision under risk, it is possible for two alternatives to have the same expected outcome.

3.33

When we are attempting to make a business decision, the decision criteria should always be to minimize cost.

3.34

If we are considering additional information before making a decision, we should never spend more for this information than the expected value of perfect information.

65

Fundamentals of Decision Theory Models l CHAPTER 3

3.35

If we decide to purchase additional information before making a decision, the value of this additional information will always be equal to the expected value of perfect information.

*3.36

The decision theory processes of maximizing Expected Monetary Value and minimizing Expected Opportunity Loss should lead us to choose the same alternatives.

3.37

Decision-making under uncertainty implies that we have no objective estimates of probabilities. We should therefore not bother to conduct sensitivity analysis.

3.38

The several criteria (maximax, maximin, equally likely, criterion of realism, minimax) used for decision-making under uncertainty may lead to the choice of different alternatives.

3.39

The criterion of realism can be used when there are more than two states of nature.

3.40

Marginal analysis can only be performed with discrete distributions.

*3.41

In practice, it is sometimes difficult to identify all consequences of choosing a particular alternative.

66

Fundamentals of Decision Theory Models l CHAPTER 3

*3.42

In practice, it is always easy to quantify values for all outcomes.

MULTIPLE CHOICE 3.43

In decision theory, conditional values refer to (a) (b) (c) (d) (e)

3.44

Which of the following is not considered to be a decision-making environment? (a) (b) (c) (d) (e)

3.45

alternatives. states of nature. expected monetary value. expected value of perfect information. payoffs.

risk certainty uncertainty unknown none of the above

Expected monetary value (EMV) is (a) the average or expected monetary outcome of a decision if it can be repeated a large number of times. (b) the average or expected value of the decision if you know what would happen ahead of time. (c) the average or expected value of information if it were completely accurate. (d) the amount you would lose by not picking the best alternative. (e) a decision criterion that places an equal weight on all states of nature.

3.46

A pessimistic decision-making criterion is (a) (b) (c) (d) (e)

maximax. equally likely. maximin. decision-making under certainty. minimax.

67

Fundamentals of Decision Theory Models l CHAPTER 3

3.47

A popular decision criteria for making decisions under risk is (a) (b) (c) (d) (e)

3.48

Which of the following is true about the expected value of perfect information? (a) (b) (c) (d) (e)

3.49

minimax maximax criterion of realism equally likely EMV

The Laplace decision criteria is also known as the (a) (b) (c) (d) (e)

3.52

the expected loss function. marginal analysis. the standard deviation. the average sales. the unit normal loss integral.

Which of the following models is not used for decision-making under uncertainty? (a) (b) (c) (d) (e)

3.51

It is the amount you would pay for any sample study. It is calculated as EMV minus EOL. It is calculated as expected value with perfect information minus maximum EMV. It is the amount charged for marketing research. none of the above

When the number of alternatives is large, a particularly effective approach to decision-making is to use (a) (b) (c) (d) (e)

3.50

maximax. maximin. minimax. select the best payoff. select the alternative with the highest expected monetary value.

maximax criteria. maximin criteria. equally likely criteria. criteria of realism. minimax criteria.

The Hurwicz decision criteria is also known as the (a) (b) (c) (d) (e)

maximax criteria. maximin criteria. equally likely criteria. criteria of realism. minimax criteria.

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Fundamentals of Decision Theory Models l CHAPTER 3

*3.53

Assume you have a decision to make, and that this decision involves a choice of one of three alternatives. The expected payoffs are: Alternative #1: $3,712,345, Alternative #2: $3,712,323, and Alternative #3: $3,712,356. Based on your model of the decision, which alternative should you choose? (a) (b) (c) (d)

Alternative #1 Alternative #2 Alternative #3 When the outcomes are so close in value, no decision should be made, but rather one should try a new model. (e) none of the above 3.54

If product demand follows a normal distribution and we want to apply marginal analysis, we need to know (a) (b) (c) (d) (e)

3.55

the mean sales estimate. the standard deviation of the sales estimate. the marginal profit. the marginal loss. all of the above

EVPI is (a) (b) (c) (d) (e)

the expected value of a decision if you knew what would happen ahead of time. the expected value of perfect information. EMV  EOL. the amount you would lose by not picking the best alternative. the expected monetary value of that decision which produces the longest expected monetary value.

69

Fundamentals of Decision Theory Models l CHAPTER 3

3.56

A good decision is not (a) (b) (c) (d) (e)

3.57

Daily sales for a perishable food product are known to be 8, 9, 10, or 11 cases with probabilities 0.2, 0.3, 0.4, and 0.1, respectively. Cases not sold during the day are worthless, but cases can only be produced in the morning before the store opens. The cost of producing one of these is $4 while the selling price is $7. If you wish to maximize expected profit, how many cases should be produced each day? (a) (b) (c) (d) (e)

*3.58

necessarily the one that gives the best final results. based upon appropriate quantitative results. one that considers all alternatives. based upon all available appropriate information. all of the above

8 9 10 11 none of the above

Daily sales for a perishable food product are known to be 8, 9, 10, or 11 cases with probabilities 0.2, 0.3, 0.4, and 0.1, respectively. Cases not sold during the day are worthless, but cases can only be produced in the morning before the store opens. The cost of producing one of these is $4 while the selling price is $7. If you choose to produce 10 cases in the morning to sell, what is the probability that all 10 cases will be sold that day? (a) (b) (c) (d) (e)

0.20 0.30 0.40 0.10 0.50

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Fundamentals of Decision Theory Models l CHAPTER 3

*3.59

Daily sales for a perishable food product are known to be 8, 9, 10, or 11 cases with probabilities 0.2, 0.3, 0.4, and 0.1, respectively. Cases not sold during the day are worthless, but cases can only be produced in the morning before the store opens. The cost of producing one of these is $4 while the selling price is $7. If you choose to produce 10 cases in the morning to sell, what is the probability that you will be able to meet today’s demand? (a) (b) (c) (d) (e)

*3.60

Daily sales for a perishable food product are known to be 8, 9, 10, or 11 cases with probabilities 0.2, 0.3, 0.4, and 0.1, respectively. Cases not sold during the day are worthless, but cases can only be produced in the morning before the store opens. The cost of producing one of these is $4 while the selling price is $7. How many cases should you produce to maximize profit? (a) (b) (c) (d) (e)

*3.61

8 9 10 11 none of the above

The maximax decision criterion (a) (b) (c) (d) (e)

3.63

8 9 10 11 none of the above

Daily sales for a perishable food product are known to be 8, 9, 10, or 11 cases with probabilities 0.2, 0.3, 0.4, and 0.1, respectively. Cases not sold during the day are worthless, but cases can only be produced in the morning before the store opens. The cost of producing one of these is $4 while the selling price is $8. How many cases should you produce to maximize profit? (a) (b) (c) (d) (e)

3.62

0.20 0.30 0.40 0.10 0.90

minimizes the maximum opportunity loss. maximizes the minimum outcome. yields the best of the worst possible outcomes when the probability is favorable. produces the alternative with the highest possible return. none of the above

The following is a payoff table giving profits for various situations. Alternatives Alternative 1 Alternative 2 Alternative 3

States of Nature A B C 120 140 120 200 100 50 100 120 180

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Fundamentals of Decision Theory Models l CHAPTER 3

Do Nothing

0

0

0

What decision would an optimist make? (a) (b) (c) (d) (e)

Alternative 1 Alternative 2 Alternative 3 Do Nothing none of the above

ANSWER: b 3.64

The following is a payoff table giving profits for various situations. Alternatives Alternative 1 Alternative 2 Alternative 3 Do Nothing

States of Nature A B C 120 140 120 200 100 50 100 120 180 0 0 0

What decision would a pessimist make? (a) (b) (c) (d) (e)

Alternative 1 Alternative 2 Alternative 3 Do Nothing none of the above

72

Fundamentals of Decision Theory Models l CHAPTER 3

3.65

Daily sales of a perishable food product are known to be 8, 9, 10, or 11 cases with probabilities 0.1, 0.3, 0.4, and 0.2, respectively. The cost of producing one of these is $4 while the selling price is $7. Cases not sold during the day are sold to a food processing plant for $1 each, but cases can only be produced in the morning before the store opens. If you wish to maximize expected profit, how many cases should be produced each day? (a) (b) (c) (d) (e)

3.66

8 9 10 11 none of the above

The following is a payoff table giving profits for various situations. Alternatives Alternative 1 Alternative 2 Alternative 3 Do Nothing

States of Nature A B C 100 120 180 120 140 120 200 100 50 0 0 0

The probabilities for states of nature A, B, and C are 0.3, 0.5, and 0.2, respectively. If a person selected Alternative 1, what would the expected profit be? (a) (b) (c) (d) (e) 3.67

120 133.33 126 180 none of the above

The following is a payoff table giving profits for various situations. Alternatives Alternative 1 Alternative 2 Alternative 3 Do Nothing

States of Nature A B C 100 120 180 200 100 50 120 140 120 0 0 0

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Fundamentals of Decision Theory Models l CHAPTER 3

The probabilities for states of nature A, B, and C are 0.3, 0.5, and 0.2, respectively. If a perfect forecast of the future were available, what would the expected profits be? (a) 130 (b) 160 (c) 166 (d) 36 (e) none of the above 3.68

The following is a payoff table giving profits for various situations. Alternatives Alternative 1 Alternative 2 Alternative 3 Do Nothing

States of Nature A B C 100 120 180 200 100 50 120 140 120 0 0 0

The probabilities for states of nature A, B, and C are 0.3, 0.5, and 0.2, respectively. If a perfect forecast of the future were available, how much would expected profits increase over the current best EMV? (a) (b) (c) (d) (e) 3.69

166 0 36 40 none of the above

Joel Turner distributes newspapers in a small town. Daily sales of the newspapers are approximately normally distributed with a mean of 500 and a standard deviation of 40. The cost of producing these is 15 cents each, and they are sold for 35 cents each. Joel plans to use a marginal analysis based on the normal distribution to make a decision. How many newspapers should Joel produce? (a) (b) (c) (d) (e)

500.0 520.8 500.6 524.7 none of the above

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Fundamentals of Decision Theory Models l CHAPTER 3

*3.70

The following is an opportunity loss table. Alternatives Alternative 1 Alternative 2 Alternative 3

States of Nature B C 0 90 85 50 0 110 75 80 0

A

What decision should be made based on the minimax regret criterion? (a) (b) (c) (d) (e) 3.71

Alternative 1 Alternative 2 Alternative 3 doesn’t matter none of the above

The following is an opportunity loss table. Alternatives Alternative 1 Alternative 2 Alternative 3

States of Nature A B C 20 100 0 150 0 50 0 40 160

What decision should be made based on the minimax regret criterion? (a) (b) (c) (d) (e) 3.72

Alternative 1 Alternative 2 Alternative 3 State of Nature A none of the above

The following is an opportunity loss table. Alternatives Alternative 1 Alternative 2 Alternative 3

States of Nature A B C 30 0 10 5 20 0 0 20 25

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Fundamentals of Decision Theory Models l CHAPTER 3

What decision should be made based on the minimax regret criterion? (a) (b) (c) (d) (e) 3.73

Alternative 1 Alternative 2 Alternative 3 State of Nature C none of the above

The following is an opportunity-loss table. Alternatives Alternative 1 Alternative 2 Alternative 3

State of Nature A B C 20 100 0 100 0 25 0 40 90

The probabilities for the states of nature A, B, and C are 0.3, 0.5, and 0.2, respectively. If a person were to use the expected opportunity loss criterion, what decision would be made? (a) (b) (c) (d) (e) 3.74

Alternative 1 Alternative 2 Alternative 3 State of Nature C none of the above

Katie Hammond is paying her way through college by working at various odd jobs. She contracted with the school to produce and sell programs at football games. The cost of producing these is 50 cents each and they sell for $1.25 each. Any not sold at the game are worthless. Demand for programs at each game is normally distributed with a mean of 2,500 and a standard deviation of 200. How many should Katie produce for the upcoming game (round off to the nearest unit)? (a) (b) (c) (d) (e)

2,550 2,580 2,500 2,700 none of the above

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Fundamentals of Decision Theory Models l CHAPTER 3

3.75

Consider the following payoff table. Alternatives Alternative 1 Alternative 2 Probability

States of Nature A B 100 150 200 100 0.4 0.6

Based upon these probabilities, a person would select Alternative 2. Suppose there is concern about the accuracy of these probabilities. It can be stated that Alternative 2 will remain the best alternative as long as the probability of A is at least (a) (b) (c) (d) (e) 3.76

0.33. 0.50. 0.40. 0.60. none of the above

Consider the following payoff table. Alternatives Alternative 1 Alternative 2 Probability

States of Nature A B 100 150 200 100 0.4 0.6

How much should be paid for a perfect forecast of the state of nature? (a) (b) (c) (d) (e) 3.77

170 30 10 100 none of the above

Mickey sells newspapers on a corner every day. He pays 10 cents for each of these and sells them for 25 cents. He knows that the demand is always for 30, 40, or 50 papers, but he doesn't know ahead of time which of these will occur. Any left at the end of the day are worthless. If he decides to purchase 40 of these but demand is only for 30, what would his profits be? (a) (b) (c) (d) (e)

7.50 4.00 4.50 3.50 none of the above

3.78 Mickey sells newspapers on a corner every day. He pays 10 cents for each of these and sells them for 25 cents. He knows that the demand is always for 30, 40, or 50 papers, but he doesn't know ahead of time which of these will occur. Any left at the end of the day are sold to a paper company for 2 cents each. If he decides to purchase 40 of these but demand is only for 30, what would his profits be? 77

Fundamentals of Decision Theory Models l CHAPTER 3

(a) (b) (c) (d) (e)

3.79

J. Tom Ball has developed plans for a therapy clinic for stressed-out chemical plant workers. He has estimated that demand for services (measured in hours) will be normally distributed with a mean of 120 hours (per month) and a standard deviation of 20. J. Tom foresees fixed monthly expenses of $3,000. He plans to contract the work to unemployed Ph.D.s in psychology. He will pay them $50 per hour for their time, and this is his variable cost of providing service. He will charge $80 per hour to his clients. If J. Tom is to break even on this venture, how many hours per month of therapy time must be demanded? (a) (b) (c) (d) (e)

3.80

3.50 3.70 7.50 4.00 none of the above

100 600 1,200 60 none of the above

Nick has plans to open some pizza restaurants, but he is not sure how many to open. He has prepared a payoff table to help analyze the situation. Alternatives Open 1 Open 2 Do Nothing

States of Nature Good Fair Poor Market Market Market 380,000 70,000 400,000 200,000 80,000 200,000 0 0 0

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Fundamentals of Decision Theory Models l CHAPTER 3

As Nick does not know how his product will be received, he assumes that all three states of nature are equally likely to occur. If he uses the equally likely criterion, what decision would he make? (a) (b) (c) (d) (e) 3.81

open 1 open 2 good market fair market poor market

Nick has plans to open some pizza restaurants, but he is not sure how many to open. He has prepared a payoff table to help analyze the situation. Alternatives Open 1 Open 2 Do Nothing

States of Nature Good Fair Poor Market Market Market 380,000 70,000 400,000 200,000 80,000 200,000 0 0 0

Nick believes that there is a 40 percent chance that the market will be good, a 30 percent chance that it will be fair, and a 30 percent chance that it will be poor. A market research firm will analyze the market conditions and will provide a perfect forecast of the future (they provide a money back guarantee). What is the most that should be paid for this forecast? (a) (b) (c) (d) (e) 3.82

$ 44,000 $ 53,000 $123,000 $176,000 none of the above

Harry Lender is making his first visit to Las Vegas and plans to try a new blackjack strategy. He believes that he has a 51 percent chance of winning each hand and a 49 percent chance of losing each hand based on this strategy. If he bets $10 on each hand, what would his expected profit (EMV) be? Assume that, on each hand, he will either win $10 or lose $10. (a) 4.90 (b) 5.10 (c) 0 (d) 0.20 (e) none of the above

79

Fundamentals of Decision Theory Models l CHAPTER 3

3.83

An optimistic decision-making criterion is (a) (b) (c) (d) (e)

3.84

If product demand follows a normal distribution and we want to apply marginal analysis, which of the following do we not need to know? (a) (b) (c) (d) (e)

3.85

the mean sales estimate the standard deviation of the sales estimate the marginal profit the marginal loss the standard deviation of the profit estimate

A good decision always implies that we (a) (b) (c) (d) (e)

3.86

maximax. equally likely. maximin. decision-making under certainty. minimax.

will obtain the best final results. have used appropriate quantitative analysis. have considered all alternatives. have based the decision on all available appropriate information. have followed a logical process.

Daily sales for submarine sandwiches are known to be 28, 29, 30, or 31 sandwiches with probabilities of 0.2, 0.3, 0.4, and 0.1, respectively. Sandwiches not sold during the day are worthless, and sandwiches can only be produced in the morning before the store opens. The cost of producing one of these is $2 while the selling price is $3.50. If you wish to maximize expected profit, how many sandwiches should be produced each day? (a) (b) (c) (d) (e)

31 30 29 28 none of the above

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Fundamentals of Decision Theory Models l CHAPTER 3

3.87

Daily sales for submarine sandwiches are known to be 28, 29, 30, or 31 sandwiches with probabilities of 0.2, 0.3, 0.4, and 0.1, respectively. Sandwiches not sold during the day are worthless, and sandwiches can only be produced in the morning before the store opens. The cost of producing one of these is $2 while the selling price is $3.50. If you choose to produce 29 sandwiches in the morning to sell, what is the probability that you will have some sandwiches left over when the store closes? (a) (b) (c) (d) (e)

3.88

Daily sales of submarine sandwiches are known to be 28, 29, 30, or 31 sandwiches with probabilities of 0.1, 0.3, 0.4, and 0.2, respectively. The cost of producing one of these is $2 while the selling price is $3.50. Sandwiches not sold during the day are given to a local homeless shelter, and you believe that you will receive $0.40 in "goodwill" for each sandwich given to the shelter. Sandwiches can only be produced in the morning before the store opens. If you wish to maximize expected profit, how many sandwiches should be produced each day? (a) (b) (c) (d) (e)

3.89

0.20 0.30 0.40 0.50 0.90

28 29 30 31 none of the above

Daily sales of submarine sandwiches are known to be 28, 29, 30, or 31 sandwiches with probabilities of 0.1, 0.3, 0.4, and 0.2, respectively. The cost of producing one of these is $2 while the selling price is $3.50. Sandwiches not sold during the day are given to a local homeless shelter, and you believe that you will incur some goodwill for each sandwich given to the shelter. Sandwiches can only be produced in the morning before the store opens. If you wish to maximize expected profit, for what value of "goodwill" would you produce 30 sandwiches? (a) (b) (c) (d) (e)

$0.30 $0.40 $0.50 $0.60 none of the above

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Fundamentals of Decision Theory Models l CHAPTER 3

3.90

Consider the following payoff table. Alternatives Alternative 1 Alternative 2 Probability

States of Nature A B 100 150 200 100 0.4 0.6

Based upon these probabilities, a person would select Alternative 2. Suppose there is concern about the accuracy of these probabilities. For what probability of B would one select Alternative 1? (a) (b) (c) (d) (e) 3.91

0.33 0.50 0.40 0.60 none of the above

Consider the following payoff table. Alternatives Alternative 1 Alternative 2 Probability

States of Nature A B 100 150 200 100 0.4 0.6

Based upon these probabilities, a person would select Alternative 2. Suppose there is concern about the accuracy of the payoff for Alternative 2 under state of nature A. For what payoff of Alternative 2 under state of nature A would one be indifferent between the two alternatives? (a) (b) (c) (d) (e) 3.92

160 170 175 185 none of the above

Consider the following payoff table. Alternatives Alternative 1 Alternative 2 Probability

States of Nature A B 100 150 175 100 0.4 0.6

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Fundamentals of Decision Theory Models l CHAPTER 3

How much should be paid for a perfect forecast of the state of nature? (a) (b) (c) (d) (e) 3.93

Mickey sells newspapers on a corner every day. He pays 10 cents for each of these and sells them for 25 cents. He knows that the demand is always for 30, 40, or 50 papers, but he doesn't know ahead of time which of these will occur. Any left at the end of the day are worthless. He purchased 40 of the papers, and at the end of the day finds that he has made a profit of $3.50. What was demand? (a) (b) (c) (d) (e)

3.94

160 130 30 100 none of the above

30 40 50 There is insufficient information to solve this problem. none of the above

Mickey sells newspapers on a corner every day. He pays 10 cents for each of these and sells them for 25 cents. He knows that the demand is always for 30, 40, or 50 papers, but he doesn't know ahead of time which of these will occur. Any left at the end of the day are sold to a paper company. If he decides to purchase 40 of these but demand is only for 30, at what price must he sell the remaining papers to the paper company to earn a profit of $3.70? (a) (b) (c) (d) (e)

$0.05 $0.04 $0.03 $0.02 none of the above

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Fundamentals of Decision Theory Models l CHAPTER 3

3.95

J. Tom Ball has developed plans for a therapy clinic for stressed-out chemical plant workers. He has estimated that demand for services (measured in hours) will be normally distributed with a mean of 120 hours (per month) and a standard deviation of 20. J. Tom foresees fixed monthly expenses of $3,000. He will charge $80 per hour to his clients. He plans to contract the work to unemployed Ph.D.s in psychology. What must he pay them per hour if he wants the break-even point to be 100 hours per month? (a) (b) (c) (d) (e)

*3.96

$40/hr $50/hr $60/hr $70/hr none of the above

Dr. Mac, a surgeon, must decide what mode of treatment to use on Mr. Samuels. There are three modes of treatment, Mode A, B, and C; and three possible states of nature: 1.Treatment succeeds and patient leads a normal life, 2. Patient survives treatment but is permanently disabled, and 3. Patient fails to survive treatment. Dr. Mac has prepared the decision table below. What mode of treatment maximizes the expected value? Treatment Mode Normal Life A $1,000,000 P(outcome) .5 B $3,000,000 P(outcome) .5 C $10,000,000 P(outcome) .4 (a) (b) (c) (d) (e)

Outcome Disability -$2,000,000 .2 -$2,500,000 .3 -$5,000,000 .4

Mode A Mode B Mode C All three treatments are equally desirable. none of the above

84

Non-Survival -$500,000 .3 -$500,000 .2 -$600,000 .2

Fundamentals of Decision Theory Models l CHAPTER 3

PROBLEMS 3.97

A concessionaire for the local ballpark has developed a table of conditional values for the various alternatives (stocking decision) and states of nature (size of crowd).

Alternatives Large Inventory Average Inventory Small Inventory

STATES OF NATURE (size of crowd) Large Average Small $22,000 $12,000 $2,000 $15,000 $12,000 $6,000 $ 9,000 $ 6,000 $5,000

If the probabilities associated with the states of nature are 0.30 for a large crowd, 0.50 for an average crowd, and 0.20 for a small crowd, determine: (a) the alternative that provides the greatest expected monetary value (EMV) (b) the expected value of perfect information (EVPI)

3.98

A concessionaire for the local ballpark has developed a table of conditional values for the various alternatives (stocking decision) and states of nature (size of crowd).

Alternatives Large Inventory Average Inventory Small Inventory

States of Nature (size of crowd) Large Average Small $22,000 $12,000 $2,000 $15,000 $12,000 $6,000 $ 9,000 $ 6,000 $5,000

If the probabilities associated with the states of nature are 0.30 for a large crowd, 0.50 for an average crowd, and 0.20 for a small crowd, determine: (a) the opportunity loss table (b) minimum expected opportunity loss (EOL)

85

Fundamentals of Decision Theory Models l CHAPTER 3

3.99

Given the following conditional value table, determine the appropriate decision under uncertainty using: (a) (b) (c) (d)

maximax maximin equally likely minimax Alternatives Large Plant Small Plant Overtime Do Nothing

States of Nature Very Favorable Average Unfavorable Market Market Market $275,000 $100,000 $150,000 $200,000 60,000 $ 10,000 $100,000 $ 40,000 $ 1,000 0 0 0

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Fundamentals of Decision Theory Models l CHAPTER 3

3.100

The ABC Co. is considering a new consumer product. They believe that there is a probability of 0.4 that the XYZ Co. will come out with a competitive product. If ABC adds an assembly line for the product and XYZ does not follow with a competitive product, their expected profit is $40,000; if they add an assembly line and XYZ does follow, they still expect $10,000 profit. If ABC adds a new plant addition and XYZ does not produce a competitive product, they expect a profit of $600,000; if XYZ does compete for this market, ABC expects a loss of $100,000. (a) (b) (c) (d)

3.101

determine the EMV of each decision determine the EOL of each decision compare the results of a and b calculate the EVPI

The ABC Co. is considering a new consumer product. They have no idea whether or not the XYZ Co. will come out with a competitive product. If ABC adds an assembly line for the product and XYZ does not follow with a competitive product, their expected profit is $40,000; if they add an assembly line and XYZ does follow, they still expect $10,000 profit. If ABC adds a new plant addition and XYZ does not produce a competitive product, they expect a profit of $600,000; if XYZ does compete for this market, ABC expects a loss of $100,000. Calculate Hurwicz’s criterion of realism using ’s of 0.7, 0.3, and 0.1.

*3.102 Barbour Electric is considering the introduction of a new product. This product can be produced in one of several ways: (a) using the present assembly line at a cost of $25 per unit, (b) using the current assembly line after it has been overhauled (at a cost of $10,000) with a cost of $22 per unit; and (c) on an entirely new assembly line (costing $30,000) designed especially for the new product with a per unit cost of $20. Barbour is worried, however, about the impact of competition. If no competition occurs, they expect to sell 15,000 units the first year. With competition, the number of units sold is expected to drop to 9,000. At the moment, their best estimate is that there is a 40% chance of competition. They have decided to make their decision based on the first year sales. (a) develop the decision table (EMV) (b) develop a decision table (EOL) (c) what should they do? 3.103

A company is considering expansion of its current facility to meet increasing demand. A major expansion would cost $500,000, while a minor expansion would cost $200,000. If demand is high in the future, the major expansion would result in an additional profit of $800,000, but if demand is low then there would be a loss of $500,000. If demand is high, the minor expansion will result in an increase in profits of $200,000, but if demand is low then there is a loss of $100,000. The company has the option of not expanding. If there is a 50 percent chance the demand will be high, what should the company do to maximize the long-run average profits?

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3.104

The following payoff table provides profits based on various possible stocking decisions and various demand situations.

Alternatives Stock 12 Stock 13 Stock 14

States of Nature Demand Low Medium High 800 800 800 700 900 900 600 800 1000

Based on current information, it is believed that the probabilities of the three demand states are each 1/3. If you wished to minimize the expected opportunity loss, what decision should be made and what would the minimum expected opportunity loss be?

3.105

The following payoff table provides profits based on various possible decision alternatives and various levels of demand. States of Nature Demand Alternatives Low Medium High Alternative 1 80 120 140 Alternative 2 90 90 90 Alternative 3 50 70 150 The probability of a low demand is 0.4, while the probability of a medium and high demand is each 0.3. (a) (b) (c) (d)

What decision would an optimist make? What decision would a pessimist make? What is the highest possible expected monetary value? Calculate the expected value of perfect information for this situation.

EVPI = 117  110 = 7 3.106

Norman L. Flowers holds the exclusive university contract for donut sales. The demand (based on historical records) appears to follow the following distribution: Daily Demand (Dozens) 4 5 6 7 8

Probability 0.15 0.25 0.30 0.25 0.05

The cost of producing these is $1.20 per dozen while the selling price is $4.20 per dozen. Based on a marginal analysis of this situation, how many donuts should Norman produce each day?

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3.107

Orders for clothing from a particular manufacturer for this year’s Christmas shopping season must be placed in February. The cost per unit for a particular dress is $20 while the anticipated selling price is $50. Anything not sold during the season can be sold for $15 to a discount store. Demand is projected to be either 50, 60, or 70 units. There is a 40 percent chance that demand will be 50 units, a 50 percent chance that demand will be 60 units, and a 10 percent chance that demand will be 70 units. If the company decides to use the EMV criterion, how many units should be ordered in February?

3.108

A concessionaire for the local ballpark has developed a table of conditional values for the various alternatives (stocking decision) and states of nature (size of crowd).

Alternatives Large Inv. Average Inv. Small Inv.

States of Nature (size of crowd) Large Average Small $22,000 $12,000 X $15,000 $12,000 $6,000 $ 9,000 $ 6,000 $5,000

The probabilities associated with the states of nature are 0.30 for a large crowd, 0.50 for an average crowd, and 0.20 for a small crowd. For what payoff, X, would one choose to make the Average Investment? 3.109

The ABC Co. is considering a new consumer product. They believe that the XYZ Co. may come out with a competing product. If ABC adds an assembly line for the product and XYZ does not follow with a competitive product, their expected profit is $40,000; if they add an assembly line and XYZ does follow, they still expect $10,000 profit. If ABC adds a new plant addition and XYZ does not produce a competitive product, they expect a profit of $600,000; if XYZ does compete for this market, ABC expects a loss of $100,000. For what value of probability that XYZ will offer a competing product will ABC be indifferent between the alternatives?

3.110

A company is considering expansion of its current facility to meet increasing demand. A major expansion would cost $500,000, while a minor expansion would cost $200,000. If demand is high in the future, the major expansion would result in an additional profit of $800,000, but if demand is low, then there would be a loss of $500,000. If demand is high, the minor expansion will result in an increase in profits of $200,000, but if demand is low, then there is a loss of $100,000. The company has the option of not expanding. For what probability of a high demand will the company be indifferent between the two expansion alternatives?

3.111

Orders for clothing from a particular manufacturer for this year’s Christmas shopping season must be placed in February. The cost per unit for a particular dress is $20 while the anticipated selling price is $50. Demand is projected to be 50, 60, or 70 units. There is a 40 percent chance that

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demand will be 50 units, a 50 percent chance that demand will be 60 units, and a 10 percent chance that demand will be 70 units. The company believes they can sell any leftover goods to a discount store, but they are uncertain as to the price the discount store will pay. For what price to be paid by the discount store would they order 70 cases of dresses in February?

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SHORT ANSWER/ESSAY 3.112

List the six steps in decision-making.

3.113

Briefly describe decision theory.

3.114

Describe what is meant by a good decision.

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3.115

Describe what is meant by a bad decision.

3.116

Briefly describe decision-making under certainty.

3.117

Briefly describe decision-making under risk.

3.118

Briefly describe decision-making under uncertainty.

3.119

List the five decision criteria for making decisions under uncertainty.

*3.120 Briefly discuss why we distinguish between decision-making under risk and decision-making under uncertainty (in neither case are we able to predict the outcome). .

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