CHAPTER 20—DECISION ANALYSIS
MULTIPLE CHOICE
1. A tabular representation of the payoffs for a decision problem is a
a.
decision tree
b.
payoff table
c.
matrix
d.
sequential matrix
2. The uncontrollable future events that can affect the outcome of a decision are known as
a.
alternatives
b.
decision outcome
c.
payoff
d.
states of nature
3. An intersection or junction point of a decision tree is called a (n)
a.
junction
b.
intersection
c.
intersection point
d.
node
4. A line or arc connecting the nodes of a decision tree is called a(n)
a.
junction
b.
intersection
c.
branch
d.
node
5. A decision criterion which weights the payoff for each decision by its probability of occurrence is
known as the
a.
payoff criterion
b.
expected value criterion
c.
probability
d.
expected value of perfect information
6. For a decision alternative, the weighted average of the payoffs is known as
a.
the expected value of perfect information
b.
the expected value
c.
the expected probability
d.
perfect information
7. The expected opportunity loss of the best decision alternative is the
a.
expected value
b.
payoff
c.
expected value of perfect information
d.
None of the answers are correct.
8. In computing an expected value (EV), the weights are
a.
decision alternative probabilities
b.
in pounds or some unit of weight
c.
in dollars or some units of currency
d.
the state-of-nature probabilities
9. The probability of the states of nature, after use of Bayes’ theorem to adjust the prior probabilities
based upon given indicator information, is called
a.
marginal probability
b.
conditional probability
c.
posterior probability
d.
None of the answers are correct.
10. Experts in problem solving agree that the first step in solving a complex problem is to
a.
decompose it into a series of smaller subproblems
b.
acquire the best software available for solving it
c.
assign several teams to work on it simultaneously
d.
recognize your staff’s limitations and hire expert consultants
11. Future events which cannot be controlled by the decision maker are called
a.
indicators
b.
states of nature
c.
prior probabilities
d.
posterior probabilities
12. A tabular presentation of the expected gain from the various options open to a decision maker is called
a.
a payoff table
b.
a decision tree
c.
the expected opportunity loss
d.
the expected value of perfect information
13. A graphic presentation of the expected gain from the various options open to the decision maker is
called
a.
a payoff table
b.
a decision tree
c.
the expected opportunity loss
d.
the expected value of perfect information
14. The expected value of information that would tell the decision maker exactly which state of nature is
going to occur is
a.
the expected value of sample information
b.
the expected value of perfect information
c.
the maximum information
d.
the expected value
15. Prior probabilities are the probabilities of the states of nature
a.
after obtaining sample information
b.
prior to obtaining of perfect information
c.
prior to obtaining sample information
d.
after obtaining perfect information
16. The probabilities of states of nature after revising the prior probabilities based on given indicator
information are
a.
the expected probabilities
b.
the posterior probabilities
c.
the prior probabilities
d.
None of the answers are correct.
17. Information about a state of nature is known as
a.
natural information
b.
states information
c.
a sampling method
d.
an indicator
18. The process of revising prior probabilities to create posterior probabilities based on sample
information is a
a.
revision process
b.
sampling revision
c.
Bayesian revision
d.
posterior revision
19. The difference between the expected value of an optimal strategy based on sample information and the
“best” expected value without any sample information is called the
a.
optimal information
b.
expected value of sample information
c.
expected value of perfect information
d.
efficiency of information
Exhibit 20-1
Below you are given a payoff table involving two states of nature and three decision alternatives.
Decision
States of Nature
Alternative
S1
S2
A
5
8
B
10
12
C
20
6
The probability of occurrence of S1 = 0.2.
20. Refer to Exhibit 20-1. The expected value of the best alternative is
a.
8.8
b.
9.6
c.
22.0
d.
None of the answers are correct.
21. Refer to Exhibit 20-1. The recommended decision alternative based on the expected value is
a.
A
b.
B
c.
C
d.
All alternatives are the same.
22. Refer to Exhibit 20-1. The expected value of alternative A is
a.
7.4
b.
11.6
c.
8.8
d.
13
23. Refer to Exhibit 20-1. The expected value of perfect information is
a.
6.2
b.
2.0
c.
13.6
d.
4.8
Exhibit 20-2
Below you are given a payoff table involving three states of nature and two decision alternatives.
Decision
States of Nature
Alternative
S1
S2
S3
A
80
45
-20
B
40
50
15
The probability that S1 will occur is 0.1; the probability that S2 will occur is 0.6; and the probability
that S3 will occur is 0.3.
24. Refer to Exhibit 20-2. The recommended decision based on the expected value criterion is
a.
A
b.
B
c.
Both alternatives are the same.
d.
None of the answers are correct.
25. Refer to Exhibit 20-2. The expected value of the best alternative equals
a.
29
b.
105
c.
12
d.
38.5
26. Refer to Exhibit 20-2. The expected value of perfect information equals
a.
12
b.
4
c.
37
d.
29
Exhibit 20-3
Below you are given a payoff table involving two states of nature and three decision alternatives.
Decision
States of Nature
Alternative
S1
S2
A
50,000
-10,000
B
10,000
15,000
C
25,000
10,000
The probability of the occurrence of state of nature S1 is 0.4.
27. Refer to Exhibit 20-3. The recommended decision based on the expected value criterion is
a.
A
b.
B
c.
C
d.
All alternatives are the same.
28. Refer to Exhibit 20-3. The expected value of the best alternative equals
a.
13,000
b.
14,000
c.
15,000
d.
16,000
29. Refer to Exhibit 20-3. The expected value of perfect information equals
a.
13,000
b.
14,000
c.
15,000
d.
16,000
Exhibit 20-4
Below you are given a payoff table involving two states of nature and three decision alternatives.
Decision
States of Nature
Alternative
S1
S2
A
15
12
B
16
12
C
20
6
The probability of occurrence of S1 = 0.3.
30. Refer to Exhibit 20-4. The expected value of the best alternative is
a.
10.2
b.
13.2
c.
28.0
d.
51.0
31. Refer to Exhibit 20-4. The recommended decision alternative based on the expected value is
a.
A
b.
B
c.
C
d.
All alternatives are the same.
32. Refer to Exhibit 20-4. The expected value of alternative C is
a.
10.2
b.
13.2
c.
12.9
d.
26
33. Refer to Exhibit 20-4. The expected value of perfect information is
a.
1.5
b.
1.2
c.
1.0
d.
4.8
Exhibit 20-5
Below you are given a payoff table involving three states of nature and three decision alternatives.
Decision
States of Nature
Alternative
S1
S2
S3
A
-20
10
15
B
16
-5
8
C
15
25
-10
The probability of occurrence of S1 is 0.2 and the probability of occurrence of S2 is 0.3.
34. Refer to Exhibit 20-5. The expected value of the best alternative is
a.
5.0
b.
6.5
c.
7.5
d.
9.0
35. Refer to Exhibit 20-5. The recommended decision alternative based on the expected value is
a.
A
b.
B
c.
C
d.
All of the answers are correct.
36. Refer to Exhibit 20-5. The expected value of alternative C is
a.
30
b.
6.5
c.
5.7
d.
5.5
37. Refer to Exhibit 20-5. The expected value of perfect information is
a.
18.2
b.
11.7
c.
51
d.
37
38. The probability of both sample information and a particular state of nature occurring simultaneously is
a.
joint probability
b.
unconditional probability
c.
marginal probability
d.
conditional probability
39. The probability of one event given the known outcome of a (possibly) related event is known as
a.
unconditional probability
b.
joint probability
c.
marginal probability
d.
conditional probability
40. New information obtained through research or experimentation that enables an updating or revision of
the state-of-nature probabilities is
a.
population information
b.
sampling without replacement
c.
sample information
d.
conditional information
41. Nodes indicating points where an uncertain event will occur are known as
a.
decision nodes
b.
chance nodes
c.
marginal nodes
d.
conditional nodes
42. The result obtained when a decision alternative is chosen and a chance event occurs is known as
a.
happenstance
b.
consequence
c.
alternative probability
d.
conditional probability
43. A sequence of decisions and chance outcomes that provide the optimal solution to a decision problem
is called
a.
a payoff table
b.
the expected value approach
c.
a decision strategy
d.
a contingency plan
44. The approach to determine the optimal decision strategy involves
a.
a forward (left to right) pass through the decision tree
b.
a backward (right to left) pass through the decision tree
c.
choosing the outcome of a chance event with the greatest probability
d.
choosing the outcome of a chance event with the greatest payoff
45. Application of Bayes’ theorem enables us to compute
a.
the prior probability of each state of nature
b.
the posterior probability of each sample outcome
c.
the conditional probability of the sample outcomes given each state of nature
d.
the conditional probability of the states of nature given each sample outcome
46. A posterior probability associated with sample information is of the form
a.
P(a state of nature | a sample outcome)
b.
P(a sample outcome | a state of nature)
c.
P(a decision alternative | a sample outcome)
d.
P(a sample outcome | a decision alternative)
47. When working backward through a decision tree, the analyst should
a.
compute the expected value at each chance node
b.
select the best chance branch at each chance node
c.
select the best chance branch at each decision node
d.
compute the expected value at each decision node
PROBLEM
1. Suppose we are interested in investing in one of three investment opportunities: d1, d2, or d3. The
following profit payoff table shows the profits (in thousands of dollars) under each of the 3 possible
economic conditions: Sl, S2, and S3. The probability of the occurrence of S1 is 0.1, and the probability
of the occurrence of S2 is 0.3.
Decision
States of Nature
Alternative
S1
S2
S3
d1
18
28
30
d2
19
17
-5
d3
3
40
16
Determine the expected value of each alternative and indicate which decision alternative is the
best.
Determine the expected value with perfect information about the states of nature.
Determine the expected value of perfect information.
2. Assume you are faced with the following decision alternatives and two states of nature. The
probability of the occurrence of state of nature 1 is 0.35. The payoff table is shown below:
Decision
States of Nature
Alternative
S1
S2
d1
20
40
d2
60
20
d3
10
50
Determine the expected value of each alternative and indicate which decision alternative is the
best.
Determine the expected value with perfect information about the states of nature.
Determine the expected value of perfect information.
33, 34, 36, d3
53.5
17.5
3. Suppose we are interested in investing in one of three investment opportunities: d1, d2, or d3. The
following profit payoff table shows the profits (in thousands of dollars) under each of the 3 possible
economic conditions⎯S1, S2, and S3:
28.2, 4, 21.9, d1
b.
31.9
3.7
Decision
States of Nature
Alternative
S1
S2
S3
d1
38
28
18
d2
60
50
-10
d3
15
40
16
Assume the states of nature have the following probabilities of occurrence: P(S1) = 0.2 P(S2) = 0.3
P(S3) = 0.5
Determine the expected value of each alternative and indicate which decision alternative is the
best.
Determine the expected value with perfect information about the states of nature.
Determine the expected value of perfect information.
4. Assume you are faced with the following decision alternatives and two states of nature. The payoff
table is shown below.
Decision
States of Nature
Alternative
S1
S2
d1
9
18
d2
0
30
d3
20
5
Assume the states of nature have the following probabilities: P(S1) = 0.4, P(S2) = 0.6
Determine the expected value of each alternative and indicate which decision alternative is the
best.
Determine the expected value of perfect information.
14.4, 18, 11, d2
8
5. You are given the following payoff table:
Decision
States of Nature
Alternative
S1
S2
d1
100
200
d2
50
300
d3
500
0
25, 22, 23, d1
b.
36
c.
11
Assume the following probability information is given:
P(S1) = 0.3
P(I1 | S1) = 0.9
P(I2 | S1) = 0.1
P(S2) = 0.7
P(I1 | S2) = 0.2
P(I2 | S2) = 0.8
Find the values of P(I1) and P(I2).
What are the values of P(S1 | I1), P(S2 | I1), P(S1 | I2), and P(S2 | I2)?
Use the decision tree approach and determine the optimal decision strategy. What is the
expected value of the solution?
Determine the expected value of sample information.
6. You are given the following payoff table:
Decision
States of Nature
Alternatives
S1
S2
d1
1,000
3,000
d2
4,000
500
Assume the following probability information is given:
P(S1) = 0.45
P(I1 | S1) = 0.7
P(I2 | S1) = 0.3
P(S2) = 0.55
P(I1 | S2) = 0.6
P(I2 | S2) = 0.4
Find the values of P(I1) and P(I2).
Determine the values of P(S1 | I1), P(S2 | I1), P(S1 | I2), and P(S2 | I2).
Use the decision tree approach and determine the optimal strategy. What is the expected value
of your solution?
0.645, 0.355
0.488, 0.512, 0.380, 0.620
If I1, select d2; If I2, select d1; EV = $2,219.36
7. A group of investors wants to open up a jewelry store in a new shopping center. The investors are
trying to decide whether to stock the store with inexpensive jewelry, medium-priced jewelry, or
expensive jewelry. The probability of their choice depends upon the economic conditions. The payoff
table below gives the anticipated profits for different states of the economy. The probability of
prosperity is 0.5.
Decision
States of Nature
Alternatives
Prosperity
Recession
a.
0.41, 0.59
b.
0.6585, 0.3415, 0.0508, 0.9492
c.
If I1, select d3; If I2, select d2; EV = 304.5