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Chapter 27—Decision analysis
MULTIPLE CHOICE
1. The expected value of perfect information is the same as:
A.
the expected monetary value for the best alternative.
B.
the expected monetary value for worst alternative.
C.
the expected opportunity loss for the best alternative.
D.
the expected opportunity loss for the worst alternative.
2. In most business situations, the choice of the best alternative will be made under conditions of:
A.
ignorance.
B.
uncertainty.
C.
risk.
D.
business cycles.
3. Which of the following statements is correct?
A.
The expected value of perfect information (EVPI) equals the largest expected monetary
value (EMV*).
B.
The expected value of perfect information (EVPI) equals the smallest expected
opportunity loss (EOL*).
C.
The expected value of perfect information (EVPI) equals the expected payoff with perfect
information (EPPI).
D.
All of the above are correct statements.
4. Which of the following statements is correct?
A.
The EMV criterion selects the act with the smallest expected monetary value.
B.
The EOL criterion selects the act with the smallest expected opportunity loss.
C.
The expected value of perfect information (EVPI) equals the largest expected opportunity
loss.
D.
All of the above are correct statements.
5. Which of the following would be considered a state of nature for a business firm?
A.
Inventory levels.
B.
Salaries for employees.
C.
Site for new plant.
D.
Worker safety laws.
6. A payoff table lists the monetary values for each possible combination of:
A.
mean and median.
B.
mean and standard deviation.
C.
event (state of nature) and act (alternative).
D.
None of the above are correct.
7. Decision trees are composed of:
A.
branches and nodes.
B.
nodes and probabilities.
C.
probabilities and branches.
D.
success nodes and failure nodes.
8. Which of the following would not be considered a state of nature for a business firm?
A.
ASIC regulations.
B.
OH&S regulations.
C.
The number of employees to hire
D.
Minimum wage regulations.
9. The expected value of sample information (EVSI) is the difference between:
A.
the posterior probabilities and the prior probabilities of the states of nature.
B.
the expected payoff with perfect information (EPPI) and the expected monetary value for
the best decision (EMV*).
C.
the expected monetary value with additional information (EMV´) and the expected
monetary value for the best decision (EMV*).
D.
the expected value of perfect information (EVPI) and the smallest expected opportunity
loss (EOL*).
TRUE/FALSE
1. The payoff table is a table in which the rows are states of nature, the columns are decision alternatives,
and the entry at each intersection of a row and column is a numerical payoff such as a profit or loss.
2. The expected monetary value (EMV) of a decision alternative is the sum of the products of the payoffs
and the state-of-nature probabilities.
3. We calculate the expected payoff with perfect information (EPPI) by multiplying the probability of
each state of nature by the largest payoff associated with that state of nature, and then summing the
products.
4. The expected monetary value (EMV) decision is always the same as the expected opportunity loss
(EOL) decision, simply because the opportunity loss table is produced directly from the payoff table.
5. The expected value of perfect information (EVPI) equals the smallest expected opportunity loss
(EOL*).
6. The expected value of perfect information (EVPI) is always the same as the expected opportunity loss
for the best alternative. That is, EVPI = EOL*.
7. The expected value of perfect information (EVPI) is the difference between the expected payoff with
perfect information (EPPI) and the expected monetary value (EMV*). That is,
EVPI = EPPI – EMV*.
8. In most business situations, the choice of the best alternative will be made under conditions of risk and
ignorance.
9. The number of secretaries to hire would be considered a state of nature for a business firm.
10. Salaries for employees would be considered a state of nature for a business firm.
11. In decision analysis, the alternatives are referred to as events and the states of nature are referred to as
acts.
12. Incentive programs for sales staff would be considered a state of nature for a business firm.
13. Worker safety laws would be considered a state of nature for a business firm.
14. The expected value of sample information (EVSI) is the difference between the expected monetary
value with additional information (EMV´)and the expected monetary value without additional
information (EMV*). That is, EVSI = EMV´ – EMV*.
15. In general, the expected monetary values (EMV) represent possible payoffs.
16. If EMV(
1
a
) = $50 000, EMV(
2
a
) = $65 000, and EMV(
3
a
) = $45 000, then EMV* = $160 000.
17. If EOL(
1
a
) = $13 000, EOL(
2
a
) = $25 000 and EOL(
3
a
) = $20 000, then EOL* = $25 000.
18. An opportunity loss is the difference between what the decision maker’s profit for an act (alternative)
is and what the profit could have been had the best decision been made.
19. In making decisions, we choose the decision with the largest expected monetary value, or the smallest
expected opportunity loss.
20. In general, the branches of a decision tree represent the states of nature.
21. The expected payoff with perfect information (EPPI) represents the maximum amount a decision
maker would be willing to pay for perfect information.
22. Since the expected monetary value decision is always the same as the expected opportunity loss
decision, then EMV*(
i
a
) = EOL*(
i
a
), for any alternative
i
a
.
23. The objective of a preposterior analysis is to determine whether the value of the prediction is greater or
less than the cost of the information.
24. All entries of any opportunity loss table are negative values since they represent losses.
25. We can use the payoff table to calculate the expected monetary value (EMV) and the expected
opportunity loss (EOL) of each act (alternative).
26. The preposterior analysis determines whether or not sample information should be purchased to revise
the prior probabilities associated with the states of nature.
SHORT ANSWER
1. Define the term payoff table.
2. Define the expected monetary value (EMV) of a decision alternative.
3. Define the expected payoff with perfect information (EPPI).
4. Define the expected value of perfect information (EVPI).
5. A high-school student who started doing photography as a hobby is considering going into the
photography business. The anticipated payoff table is:
Alternative
State of Nature
Start
new business
Do not start
new business
Poor
–$12 000
0
Fair
$10 000
0
Super
$15 000
0
The following prior probabilities are assigned to the states of nature:
P(poor) = 0.4, P(fair) = 0.4 , P(super) = 0.2.
a. Calculate the expected monetary value for each act with present information. What decision
should be made using the EMV criterion?
b. Convert the payoff table to an opportunity loss table.
c. Calculate the expected opportunity loss for each act with present information. What decision
should be made using the EOL criterion?
d. Review the decisions made in a. and c. Is this a coincidence? Explain.
e. What is the expected payoff with perfect information?
f. What is the expected value of perfect information? What does it mean?
6. A payoff table is shown below.
Alternative
State of Nature
1
a
2
a
3
a
1
s
21
8
–3
2
s
12
12
7
3
s
–15
9
13
The following prior probabilities are assigned to the states of nature:
P(
1
s
) = 0.2, P(
2
s
) = 0.7, P(
3
s
) = 0.1.
a. Determine the EMV decision.
b. Set up the opportunity loss table.
c. Determine the EOL decision.
d. What is the expected payoff with perfect information?
e. What is the expected value of perfect information?
7. A payoff table is shown below:
Alternative
State of Nature
1
a
2
a
3
a
4
a
1
s
7
0
4
6
2
s
2
4
3
5
The following prior probabilities are assigned to the states of nature:
P(
1
s
) = 0.3, P(
2
s
) = 0.7.
a. Calculate the expected monetary value for each act with present information. What decision
should be made using the EMV criterion?
b. Convert the payoff table to an opportunity loss table.
c. Calculate the expected opportunity loss for each act with present information. What decision
should be made using the EOL criterion?
d. What is the expected payoff with perfect information?
e. What is the expected value of perfect information?
8. Three different designs are being considered for a new refrigerator, and profits will depend on the
combination of the refrigerator design and market condition. The following payoff table summarises
the decision situation, with amounts in millions of dollars.
Alternative (Design)
State of Nature
(Market condition)
1
a
2
a
3
a
1
s
$30
$20
$10
2
s
$19
$21
$15
3
s
$11
$23
$35
Assume that the following probabilities are assigned to the three market conditions:
P(
1
s
) = 0.2, P(
2
s
) = 0.4, P(
3
s
) = 0.4.
a. Calculate the expected monetary value for each design with present information. Which design
should be selected in order to maximise the firm’s expected profit?
b. Convert the payoff table to an opportunity loss table.
c. Calculate the expected opportunity loss for each design with present information. Which design
should be selected in order to minimise the firm’s expected loss?
d. Determine the expected payoff that would be realised if perfect information were available.
e. What is the most the firm would be willing to pay for a research study designed to reduce its
uncertainty about market conditions?
9. A payoff table, the prior probabilities for two states of nature, and the likelihood probabilities are
shown below.
Payoff Table:
Alternative
State of Nature
1
a
2
a
3
a
1
s
20
28
33
2
s
32
29
25
Prior Probabilities:
P(
1
s
) = 0.4, P(
2
s
) = 0.6.
Likelihood Probabilities:
1
I
2
I
1
s
0.95
0.05
2
s
0.08
0.92
a. Determine the EMV decision.
b. Set up the opportunity loss table.
c. Determine the EOL decision.
d. What is the expected payoff with perfect information?
e. What is the expected value of perfect information?
10. A payoff table, the prior probabilities for two states of nature, and the likelihood probabilities are
shown below.
Payoff Table:
Alternative
State of Nature
1
a
2
a
3
a
1
s
20
28
33
2
s
32
29
25
Prior Probabilities:
P(
1
s
) = 0.4, P(
2
s
) = 0.6.
Likelihood Probabilities:
1
I
2
I
1
s
0.95
0.05
2
s
0.08
0.92
a. Use the prior and likelihood probabilities to calculate the posterior probabilities for the
experimental outcome
1
I
.
b. Use the posterior probabilities from a. to recalculate the expected monetary value of each act, then
determine the optimal act and the EMV*.
c. Use the prior and likelihood probabilities to calculate the posterior probabilities for the
experimental outcome
2
I
.
d. Use the posterior probabilities from c. to recalculate the expected monetary value of each act, then
determine the optimal act and the
EMV
.
e. Use your answers to parts a. to d. to calculate the expected monetary value with additional
information.
f. Calculate the expected value of sample information.
11. A company must decide whether or not to change its packaging to a more environmentally safe
material. The impact of the decision on profits depends on which of the following three possible
scenarios develops in the future.
Scenario 1:
The media do not focus heavily on concerns about packaging, and no new laws requiring changes in
packaging are passed. Under this scenario, the company will make $35 million if they change their
packaging now, but will make $75 million if they do not change their packaging now.
Scenario 2:
The media focus heavily on concerns about packaging, and no new laws requiring changes in
packaging are passed. Under this scenario, the company will make $50 million if they change their
packaging now, but will make $55 million if they do not change their packaging now.
Scenario 3:
The media focus heavily on concerns about packaging, and new laws requiring changes in packaging
are passed. Under this scenario, the company will make $60 million if they change their packaging
now, but will make only $15 million if they do not change their packaging now.
The prior probabilities of the three scenarios are 0.3, 0.5 and 0.2, respectively.
a. Develop a payoff table for this decision situation.
b. What decision will be made to maximise expected payoff?
c. What is the most the company should be willing to pay for a research study designed to reduce its
uncertainty about media and legal developments concerning packaging?
d. Set up the opportunity loss table.
e. Which decision has the minimum expected opportunity loss?
12. The following table displays the payoffs (in thousands of dollars) for five different decision
alternatives under three possible states of nature:
Alternative (Decision)
State of Nature
1
a
2
a
3
a
4
a
5
a
1
s
$100
$80
$35
$20
$0
2
s
$70
$75
$55
$50
$15
3
s
–$30
$0
$35
$55
$60
The prior probabilities of the states of nature are:
P(
1
s
) = 0.2, P(
2
s
) = 0.3, P(
3
s
) = 0.5
a. Calculate the expected monetary value for each alternative with present information. What
decision should be made using the EMV criterion?
b. Calculate the expected payoff with perfect information.
c. Calculate the expected value of perfect information.
d. Convert the payoff table to an opportunity loss table.
e. Calculate the expected opportunity loss for each act with present information. What decision
should be made using the EOL criterion?
13. A payoff table, the prior probabilities for three states of nature and the likelihood probabilities are
shown below.
Payoff Table:
Alternative
State of Nature
1
a
2
a
3
a
1
s
80
120
90
2
s
60
130
170
3
s
200
140
100
Prior Probabilities:
P(
1
s
) = 0.4, P(
2
s
) = 0.5, P(
3
s
) = 0.1.
Likelihood Probabilities:
1
I
2
I
3
I
1
s
0.5
0.3
0.2
2
s
0.2
0.6
0.2
3
s
0.1
0.2
0.7
a. Determine the EMV decision.
b. Set up the opportunity loss table.
c. Determine the EOL decision.
d. What is the expected payoff with perfect information?
e. What is the expected value of perfect information?
14. A payoff table, the prior probabilities for three states of nature and the likelihood probabilities are
shown below.
Payoff Table:
Alternative
State of Nature
1
a
2
a
3
a
1
s
80
120
90
2
s
60
130
170
3
s
200
140
100
Prior Probabilities:
P(
1
s
) = 0.4, P(
2
s
) = 0.5, P(
3
s
) = 0.1.
Likelihood Probabilities:
1
I
2
I
3
I
1
s
0.5
0.3
0.2
2
s
0.2
0.6
0.2
3
s
0.1
0.2
0.7
a. Use the prior and likelihood probabilities to calculate the posterior probabilities for the
experimental outcome
1
I
.
b. Use the posterior probabilities from a. to recalculate the expected monetary value of each act, then
determine the optimal act and the EMV*.
c. Use the prior and likelihood probabilities to calculate the posterior probabilities for the
experimental outcome
2
I
.
d. Use the posterior probabilities from c. to recalculate the expected monetary value of each act, then
determine the optimal act and the EMV*.
e. Use the prior and likelihood probabilities to calculate the posterior probabilities for the
experimental outcome
3
I
.
f. Use the posterior probabilities from e. to recalculate the expected monetary value of each act, then
determine the optimal act and the EMV*.
g. Use your answers to parts a. to f. to calculate the expected monetary value with additional
information.
h. Calculate the expected value of sample information.
