Deck 8: Decision Analysis

Question 1

Use this information to answer the following questions.
Consider the following payoff table that represents the profits earned for each alternative (A,B,and C)under the states of nature S1,S2,and S3.

Refer to the payoff table.Using the maximax criterion,what would be the highest expected payoff?

A)$145
B)$124
C)$120
D)$110
E)$100

Answer 1

A

Question 2

The maximin criterion is an optimistic approach to decision making.

Answer 2

False

Question 3

Use this information to answer the following questions.
Consider the following payoff table that represents the profits earned for each alternative (A,B,and C)under the states of nature S1,S2,and S3.

Refer to the payoff table.Using the Laplace criterion,what would be the highest expected payoff?

A)$103.3
B)$108.3
C)$120
D)$125
E)$145

Answer 3

B

Question 4

Use this information to answer the following questions.
Consider the following payoff table that represents the profits earned for each alternative (A,B,and C)under the states of nature S1,S2,and S3.

Refer to the payoff table.Using the criterion of realism and an alpha value of 0.7,what would be the highest expected payoff?

A)$127
B)$119.5
C)$98.5
D)$116
E)$145

Question 5

Use this information to answer the following questions.
Consider the following payoff table that represents the profits earned for each alternative (A,B,and C)under the states of nature S1,S2,and S3.

Refer to the payoff table.Using the maximin criterion,what would be the highest expected payoff?

A)$145
B)$125
C)$85
D)$75
E)$60

Question 6

What is the correct equation for computing the expected value of perfect information (EVPI)?

A)EVPI = expected value under risk for best alternative - expected value under certainty.
B)EVPI = expected value under certainty - expected value under risk for best alternative.
C)EVPI = expected value with sample information - expected value without sample information.
D)EVPI = expected value without sample information - expected value with sample information.
E)none of the above

Question 7

The minimum guaranteed amount you are willing to accept to avoid the risk associated with a gamble is referred to as the ________.

A)risk premium
B)certainty equivalent
C)EVPI
D)EMV
E)EVSI

Question 8

The approach that is used for analyzing decision trees is called:

A)maximax
B)maximin
C)Laplace
D)minimax regret
E)expected monetary value

Question 9

Determining the best payoff for each alternative and choosing the alternative with the "best of the best" is the approach called:

A)maximax
B)maximin
C)Laplace
D)minimax regret
E)expected monetary value

Question 10

In decision making under risk,probabilities associated with future events are usually unknown.

Question 11

The EMV that a person is willing to give up in order to avoid the risk associated with a gamble is referred to as the ________.

A)risk premium
B)certainty equivalent
C)EVPI
D)EVwPI
E)EVSI

Question 12

Use this information to answer the following questions.
Consider the following payoff table that represents the profits earned for each alternative (A,B,and C)under the states of nature S1,S2,and S3.

Refer to the payoff table.Using the expected monetary value (EMV)criterion,what is the highest attainable expected profit? Assume P(S1)= 0.5 and P(S2)= 0.25.

A)$101.25
B)$103.33
C)$108.33
D)$125
E)$145

Question 13

Determining the average payoff for each alternative and choosing the one with the best payoff is the approach called:

A)maximax
B)maximin
C)Laplace
D)minimax regret
E)expected monetary value

Question 14

Determining the worst payoff for each alternative and choosing the alternative with the "best of the worst" is the approach called:

A)maximax
B)maximin
C)Laplace
D)minimax regret
E)expected monetary value

Question 15

Which of the following statements concerning decision trees is False?

A)Decision nodes are represented by a square.
B)Outcome nodes are represented by a circle.
C)EMV is calculated at each outcome.
D)The alternative is chosen with the highest EMV.
E)Decision trees are solved by starting at the first decision node and moving forward.

Question 16

The maximin criterion approach selects the "best of the worst."

Question 17

Use this information to answer the following questions.
Consider the following payoff table that represents the profits earned for each alternative (A,B,and C)under the states of nature S1,S2,and S3.

Refer to the payoff table.Using the minimax regret criterion,which alternative would you choose?

A)A
B)B
C)C
D)A or B
E)B or C

Question 18

Use this information to answer the following questions.
Consider the following payoff table that represents the profits earned for each alternative (A,B,and C)under the states of nature S1,S2,and S3.

Refer to the payoff table.What is the expected value under certainty? Assume P(S1)= 0.5 and P(S2)= 0.25.

A)$101.25
B)$103.33
C)$108.33
D)$116.25
E)$136.25

Question 19

Which of the following statements the use of decision trees in multi-stage decision making problems is False?

A)Multi-stage decision making problems involve a sequence of decisions.
B)EVSI is an upper bound for the EVPI.
C)Multi-stage decision making problems using decision trees are solved moving backward.
D)EVSI measure the value of sample information.
E)The efficiency of sample information is a ratio of EVSI to EVPI.

Question 20

Use this information to answer the following questions.
Consider the following payoff table that represents the profits earned for each alternative (A,B,and C)under the states of nature S1,S2,and S3.

Refer to the payoff table.What is the expected value of perfect information (EVPI)? Assume P(S1)= 0.5 and P(S2)= 0.25.

A)$0
B)$11.25
C)$15
D)$20
E)$35

Question 21

Use this information to answer the following questions.
A bakery must decide how many pies to prepare for the upcoming weekend.The bakery has the option to make 50,100,or 150 pies.Assume that demand for the pies can be 50,100,or 150.Each pie costs $5 to make and sells for $7.Unsold pies are donated to a nearby charity center.Assume that there is no opportunity cost for lost sales.
Refer to the information above.Assume that the bakery (see problem 7)has obtained the following probability information regarding demand for the pies: P(50)= 0.3,P(100)= 0.5,and P(150)= 0.2.
a.Which alternative should be chosen using the expected monetary value (EMV)criterion?
b.What is the expected value under certainty?
c.What is the expected value under perfect information (EVPI)?

Question 22

In a payoff table,the payoff values must always be expressed as profits.

Question 23

The expected value of perfect information (EVPI)places a lower bound on how much a decision maker should be willing to pay to obtain perfect information.

Question 24

Decision trees are typically analyzed from right to left.

Question 25

Use this information to answer the following questions.
A bakery must decide how many pies to prepare for the upcoming weekend.The bakery has the option to make 50,100,or 150 pies.Assume that demand for the pies can be 50,100,or 150.Each pie costs $5 to make and sells for $7.Unsold pies are donated to a nearby charity center.Assume that there is no opportunity cost for lost sales.
Refer to the information above.
a.Which alternative should be chosen based on the maximax criterion?
b.Which alternative should be chosen based on the maximin criterion?
c.Which alternative should be chosen based on the Lapalce criterion?
d.Which alternative should be chosen based on criterion of realism with alpha = 0.8?
e.Which alternative should be chosen based on the minimax regret criterion?

Question 26

In multistage decision trees,it is not possible for one outcome to follow another.

Question 27

Use this information to answer the following questions.
A plant manager is considering buying additional stamping machines to accommodate increasing demand.The alternatives are to buy 1 machine,2 machines,or 3 machines.The profits realized under each alternative are a function of whether their bid for a recent defense contract is accepted or not.The payoff table below illustrates the profits realized (in $000's)based on the different scenarios faced by the manager.

Refer to the information above.Assume that based on historical bids with the defense contractor,the plant manager believes that there is a 65% chance that the bid will be accepted and a 35% chance that the bid will be rejected.
a.Which alternative should be chosen using the expected monetary value (EMV)criterion?
b.What is the expected value under certainty?
c.What is the expected value under perfect information (EVPI)?

Question 28

Use this information to answer the following questions.
A plant manager is considering buying additional stamping machines to accommodate increasing demand.The alternatives are to buy 1 machine,2 machines,or 3 machines.The profits realized under each alternative are a function of whether their bid for a recent defense contract is accepted or not.The payoff table below illustrates the profits realized (in $000's)based on the different scenarios faced by the manager.

Refer to the information above.
a.Which alternative should be chosen based on the maximax criterion?
b.Which alternative should be chosen based on the maximin criterion?
c.Which alternative should be chosen based on the Lapalce criterion?
d.Which alternative should be chosen based on criterion of realism with alpha = 0.8?
e.Which alternative should be chosen based on the minimax regret criterion?

Question 29

Use this information to answer the following questions.
ABC Inc.must make a decision on its current capacity for next year.Estimated profits (in $000s)based on next year's demand are shown in the table below.

Refer to the information above.
a.Which alternative should be chosen based on the maximax criterion?
b.Which alternative should be chosen based on the maximin criterion?
c.Which alternative should be chosen based on the Lapalce criterion?
d.Which alternative should be chosen based on criterion of realism with alpha = 0.7?
e.Which alternative should be chosen based on the minimax regret criterion?

Question 30

Use this information to answer the following questions.
A plant manager is considering buying additional stamping machines to accommodate increasing demand.The alternatives are to buy 1 machine,2 machines,or 3 machines.The profits realized under each alternative are a function of whether their bid for a recent defense contract is accepted or not.The payoff table below illustrates the profits realized (in $000's)based on the different scenarios faced by the manager.

Refer to the information above.Assume that ABC Inc.has hired a marketing research firm that provided additional information regarding next year's demand.Suppose that the probabilities of low and high demand are assessed as follows: P(Low)= 0.4 and P(High)= 0.6.
a.Develop a decision tree for this problem.
b.Analyze the decision tree and determine which alternative should be chosen.
c.Using the expected opportunity loss (EOL)criterion,which alternative should be chosen?

Question 31

The expected opportunity loss (EOL)will always result in the same decision as the maximum expected monetary value (EMV).

Question 32

An individual who is indifferent to risk would have a utility curve that is linear.

Question 33

In a decision tree representation,round nodes represent decision alternatives.

Question 34

Opportunity loss is the difference between the optimal payoff and the actual payoff received.

Question 35

Use this information to answer the following questions.
A bakery must decide how many pies to prepare for the upcoming weekend.The bakery has the option to make 50,100,or 150 pies.Assume that demand for the pies can be 50,100,or 150.Each pie costs $5 to make and sells for $7.Unsold pies are donated to a nearby charity center.Assume that there is no opportunity cost for lost sales.
Refer to the information above.Assume that based on historical bids with the defense contractor,the plant manager believes that there is a 65% chance that the bid will be accepted and a 35% chance that the bid will be rejected.
a.Develop a decision tree for this problem.
b.Analyze the decision tree and determine which alternative should be chosen.
c.Using the expected opportunity loss (EOL)criterion,which alternative should be chosen?

Question 36

The minimax regret criterion minimizes the maximum opportunity loss within each alternative.

Question 37

Bayes' theorem allows decision makers to incorporate additional information to revise their probability estimates of various outcomes.

Question 38

Use this information to answer the following questions.
ABC Inc.must make a decision on its current capacity for next year.Estimated profits (in $000s)based on next year's demand are shown in the table below.

Refer to the information above.Assume that ABC Inc.has hired a marketing research firm that provided additional information regarding next year's demand.Suppose that the probabilities of low and high demand are assessed as follows: P(Low)= 0.4 and P(High)= 0.6.
a.Which alternative should be chosen using the expected monetary value (EMV)criterion?
b.What is the expected value under certainty?
c.What is the expected value under perfect information (EVPI)?

Question 39

The expected monetary value (EMV)approach allows you to incorporate your own attitude toward risk.

Question 40

If the coefficient of realism alpha equals 1,then the criterion of realism will yield the same result as the maximax criterion.

Question 41

A defense contractor has submitted a bid to make new helmets for the army.The defense contractor believes that the odds of winning the bid stand at 50-50 chance.Past history indicates that if the bid is successful,there is a 0.75 probability that the contractor will hear about the status of the bid within one week.There is also a 0.40 probability that the contractor will hear from the army within one week if the bid is unsuccessful.What is the probability that the bid is successful if the contractor hears about the status of the bid within one week? Use Bayes' theorem to compute this posterior probability.

Question 42

Suppose that the utility function for a decision maker is represented as follows:
U(x)= .The potential payoffs that are possible are illustrated below.
Payoff (x)
$100
$200
$300
$400
$500
$600
$700
$800
$900
$1000
Convert these payoffs into utility values using the above function.Plot the utility curve and determine whether the decision maker is a risk avoider,risk indifferent,or a risk seeker.

Question 43

Suppose that the utility function for a decision maker is represented as follows:
U(x)= 2x.The potential payoffs that are possible are illustrated below.
Payoff (x)
$100
$200
$300
$400
$500
$600
$700
$800
$900
$1000
Convert these payoffs into utility values using the above function.Plot the utility curve and determine whether the decision maker is a risk avoider,risk indifferent,or a risk seeker.

Question 44

Use this information to answer the following questions.
A bakery must decide how many pies to prepare for the upcoming weekend.The bakery has the option to make 50,100,or 150 pies.Assume that demand for the pies can be 50,100,or 150.Each pie costs $5 to make and sells for $7.Unsold pies are donated to a nearby charity center.Assume that there is no opportunity cost for lost sales.
Refer to the information above.Assume that the bakery (see problem 7)has obtained the following probability information regarding demand for the pies: P(50)= 0.3,P(100)= 0.5,and P(150)= 0.2.
a.Develop a decision tree for this problem.
b.Analyze the decision tree and determine which alternative should be chosen.
c.Using the expected opportunity loss (EOL)criterion,which alternative should be chosen?

Question 45

Use this information to answer the following questions.
AAA auto supply store sells snow tires which are ordered every Friday to meet next week's demand.The sales price for the most popular size is $50 per tire and its cost for AAA is $35.If too many tires are ordered AAA incurs an inventory carrying cost of $2 per tire.If AAA is out of stock,it forgoes the profits from missed sales.AAA has the option to order 100,150,or 200 tires to meet next week's demand which can be either 100,150,or 200 tires.
Refer to the information above.Based on its historical demand distribution,assume that AAA Inc.has determined the following probability information: P(100)= 0.4,P(150)= 0.3,and P(200)= 0.3.
a.Develop a decision tree for this problem.
b.Analyze the decision tree and determine which alternative should be chosen.
c.Using the expected opportunity loss (EOL)criterion,which alternative should be chosen?

Question 46

A toy store is considering expanding its capacity to meet a growing demand for its products.The options faced by management are to build a new store,expand the existing store,or do nothing.A marketing research firm has projected a 50% probability of a high demand for the toy market,a 30% probability of a low demand,and a 20% probability of an unchanged demand.The following estimates of annual returns (in $000's)are as follows:

a.Develop a decision tree for this problem.
b.Analyze the decision tree and determine which alternative should be chosen.

Question 47

A company must decide whether to build a small,medium,or large grocery store.Marketing research findings indicate a 0.35 probability that demand will be low and a 0.65 probability that demand will be high.If the company builds a small grocery store and demand is low,the net present value will be $150,000.If demand is high the company can buy its additional grocery needs from a wholesaler and realize a net present value of $100,000 or expand and realize a net present value of $120,000.If the company builds a medium grocery store and demand is low,the net present value will be $175,000;if demand turns to be high the company could do nothing and realize a net present value of $100,000,or expand and realize a net present value of $135,000.If the firm builds a large grocery store and demand is low,the net present value will be $50,000;if demand turns out to be high the net present value will be $250,000.
a.Develop a decision tree for this problem.
b.Analyze the decision tree and determine which alternative should be chosen.

Question 48

Use this information to answer the following questions.
AAA auto supply store sells snow tires which are ordered every Friday to meet next week's demand.The sales price for the most popular size is $50 per tire and its cost for AAA is $35.If too many tires are ordered AAA incurs an inventory carrying cost of $2 per tire.If AAA is out of stock,it forgoes the profits from missed sales.AAA has the option to order 100,150,or 200 tires to meet next week's demand which can be either 100,150,or 200 tires.
Refer to the information above.Based on its historical demand distribution,assume that AAA Inc.has determined the following probability information: P(100)= 0.4,P(150)= 0.3,and P(200)= 0.3.
a.Which alternative should be chosen using the expected monetary value (EMV)criterion?
b.What is the expected value under certainty?
c.What is the expected value under perfect information (EVPI)?

Question 49

Dan faces the option to sell his small seafood company to an interested bidder.Assume that if he stays in business for another year,his company will be worth $5 million with 0.7 probability,and $0.5 million with 0.3 probability.If Dan chooses to accept an offer of $2 million for his company,rather than going with the gamble of another year with the company,then what is the risk premium?

Question 50

Limousine Inc.must decide how many new limousines to buy.The owner has narrowed down the decision to two choices: buy one limousine or two limousines.If only one limousine is bought and demand ridership is high,a second limousine can be bought later.The probability of high demand is ridership 0.65,and the probability of low demand ridership is 0.35.The net present value obtained with the purchase of two limousines is $100,000 if demand is high and $65,000 if demand is low.The net present value for one limousine and low demand is $55,000.If demand is high,there are two options.The first option is to buy a second limousine.This option has a net present value of $80,000.The second option is to do nothing,which would have a net present value of $50,000.
a. Develop a decision tree for this problem.
b.Analyze the decision tree and determine how many limousines should be bought initially.

Question 51

Suppose that the utility function for a decision maker is represented as follows:
U(x)= x².The potential payoffs that are possible are illustrated below.
Payoff (x)
$100
$200
$300
$400
$500
$600
$700
$800
$900
$1000
Convert these payoffs into utility values using the above function.Plot the utility curve and determine whether the decision maker is a risk avoider,risk indifferent,or a risk seeker.

Question 52

Strike It Rich is a gold mining company that is attempting to decide whether to invest in a particular site.The probability that the site has gold is 0.50.In order to obtain more information about the potential presence of gold,the company has hired a geologist to analyze the soil.Past history indicates that there is a 60% chance that the geologist's test is positive given the presence of gold and a 35% chance that the test is positive given the absence of any gold.What is the probability of the presence of gold given that the geologist's test yielded a positive result? Use Bayes' theorem to compute this posterior probability.

Question 53

Use this information to answer the following questions.
AAA auto supply store sells snow tires which are ordered every Friday to meet next week's demand.The sales price for the most popular size is $50 per tire and its cost for AAA is $35.If too many tires are ordered AAA incurs an inventory carrying cost of $2 per tire.If AAA is out of stock,it forgoes the profits from missed sales.AAA has the option to order 100,150,or 200 tires to meet next week's demand which can be either 100,150,or 200 tires.
Refer to the information above.
a.Which alternative should be chosen based on the maximax criterion?
b.Which alternative should be chosen based on the maximin criterion?
c.Which alternative should be chosen based on the Lapalce criterion?
d.Which alternative should be chosen based on criterion of realism with alpha = 0.7?
e.Which alternative should be chosen based on the minimax regret criterion?