Chapter 13 – Decision Analysis
True / False
1. Sample information with an efficiency rating of 100% is perfect information.
a.
True
b.
False
True
Efficiency of sample information
2. States of nature should be defined so that one and only one will actually occur.
a.
True
b.
False
True
Structuring the decision process
3. Decision alternatives are structured so that several could occur simultaneously.
a.
True
b.
False
4. Square nodes in a decision tree indicate that a decision must be made.
a.
True
b.
False
True
Decision trees
5. Circular nodes in a decision tree indicate that it would be incorrect to choose a path from the node.
a.
True
b.
False
True
Decision trees
6. Risk analysis helps the decision maker recognize the difference between the expected value of a decision alternative
and the payoff that may actually occur.
a.
True
b.
False
True
Risk analysis
7. The expected value of an alternative can never be negative.
Chapter 13 – Decision Analysis
a.
True
b.
False
False
8. Expected value is the sum of the weighted payoff possibilities at a circular node in a decision tree.
a.
True
b.
False
True
9. EVPI is always greater than or equal to EVSI.
a.
True
b.
False
True
10. After all probabilities and payoffs are placed on a decision tree, the decision maker calculates expected values at state
of nature nodes and makes selections at decision nodes.
a.
True
b.
False
True
11. A decision strategy is a sequence of decisions and chance outcomes, where the decisions chosen depend on the yet to
be determined outcomes of chance events.
a.
True
b.
False
True
12. EVPI equals the expected regret associated with the minimax decision.
a.
True
b.
False
True
13. The expected value approach is more appropriate for a one-time decision than a repetitive decision.
a.
True
Chapter 13 – Decision Analysis
b.
False
False
14. Maximizing the expected payoff and minimizing the expected opportunity loss result in the same recommended
decision.
a.
True
b.
False
True
15. The expected value of sample information can never be less than the expected value of perfect information.
a.
True
b.
False
False
16. The minimum expected opportunity loss provides the best decision, regardless of whether the decision analysis
involves minimization or maximization.
a.
True
b.
False
True
17. The primary value of decision trees is as a useful way of organizing how operations managers think about complex
multiphase decisions.
a.
True
b.
False
True
18. A high efficiency rating indicates that the sample information is almost as good as perfect information.
a.
True
b.
False
True
19. When the expected value approach is used to select a decision alternative, the payoff that actually occurs will usually
have a value different from the expected value.
a.
True
Chapter 13 – Decision Analysis
b.
False
True
20. The decision alternative with the best expected monetary value will always be the most desirable decision.
a.
True
b.
False
False
21. When monetary value is not the sole measure of the true worth of the outcome to the decision maker, monetary value
should be replaced by utility.
a.
True
b.
False
True
22. The outcome with the highest payoff will also have the highest utility.
a.
True
b.
False
True
23. Expected utility is a particularly useful tool when payoffs stay in a range considered reasonable by the decision maker.
a.
True
b.
False
False
24. To assign utilities, consider the best and worst payoffs in the entire decision situation.
a.
True
b.
False
True
25. A risk avoider will have a concave utility function.
a.
True
b.
False
True
Chapter 13 – Decision Analysis
26. The expected utility is the utility of the expected monetary value.
a.
True
b.
False
False
27. The risk premium is never negative for a conservative decision maker.
a.
True
b.
False
True
28. The risk neutral decision maker will have the same indications from the expected value and expected utility
approaches.
a.
True
b.
False
True
29. The utility function for a risk avoider typically shows a diminishing marginal return for money.
a.
True
b.
False
True
30. The expected monetary value approach and the expected utility approach to decision making usually result in the same
decision choice unless extreme payoffs are involved.
a.
True
b.
False
True
31. A risk neutral decision maker will have a linear utility function.
a.
True
b.
False
True
Chapter 13 – Decision Analysis
32. Given two decision makers, one risk neutral and the other a risk avoider, the risk avoider will always give a lower
utility value for a given outcome.
a.
True
b.
False
False
Developing utilities for monetary payoffs
33. When the payoffs become extreme, most decision makers are satisfied with the decision that provides the best
expected monetary value.
a.
True
b.
False
False
Meaning of utility
Multiple Choice
34. The options from which a decision maker chooses a course of action are
a.
called the decision alternatives.
b.
under the control of the decision maker.
c.
not the same as the states of nature.
d.
All of the alternatives are true.
35. States of nature
a.
can describe uncontrollable natural events such as floods or freezing temperatures.
b.
can be selected by the decision maker.
c.
cannot be enumerated by the decision maker.
d.
All of the alternatives are true.
36. A payoff
a.
is always measured in profit.
b.
is always measured in cost.
c.
exists for each pair of decision alternative and state of nature.
d.
exists for each state of nature.
c
Developing utilities for monetary payoffs
Chapter 13 – Decision Analysis
37. Making a good decision
a.
requires probabilities for all states of nature.
b.
requires a clear understanding of decision alternatives, states of nature, and payoffs.
c.
implies that a desirable outcome will occur.
d.
All of the alternatives are true.
Decision making without probabilities
38. A decision tree
a.
presents all decision alternatives first and follows them with all states of nature.
b.
presents all states of nature first and follows them with all decision alternatives.
c.
alternates the decision alternatives and states of nature.
d.
arranges decision alternatives and states of nature in their natural chronological order.
Decision trees
39. Which of the methods for decision making best protects the decision maker from undesirable results?
a.
the optimistic approach
b.
the conservative approach
c.
minimum regret
d.
minimax regret
Conservative approach
40. Sensitivity analysis considers
a.
how sensitive the decision maker is to risk.
b.
changes in the number of states of nature.
c.
changes in the values of the payoffs.
d.
changes in the available alternatives.
Sensitivity analysis
41. To find the EVSI,
a.
use the EVPI to calculate sample information probabilities.
b.
use indicator probabilities to calculate prior probabilities.
c.
use prior and sample information probabilities to calculate revised probabilities.
d.
use sample information to revise the sample information probabilities.
Payoff tables
Chapter 13 – Decision Analysis
42. If P(high) = .3, P(low) = .7, P(favorable | high) = .9, and P(unfavorable | low) = .6, then P(favorable) =
a.
.10
b.
.27
c.
.30
d.
.55
Conditional probability
43. The efficiency of sample information is
a.
EVSI*(100%)
b.
EVSI/EVPI*(100%)
c.
EVwoSI/EVwoPI*(100%)
d.
EVwSI/EVwoSI*(100%)
Efficiency of sample information
44. Decision tree probabilities refer to
a.
the probability of finding the optimal strategy
b.
the probability of the decision being made
c.
the probability of overlooked choices
d.
the probability of an uncertain event occurring
Decision trees
45. For a maximization problem, the conservative approach is often referred to as the
a.
minimax approach.
b.
maximin approach.
c.
maximax approach.
d.
minimin approach.
Decision making without probabilities
46. For a minimization problem, the optimistic approach is often referred to as the
a.
minimax approach
b.
maximin approach
c.
maximax approach
d.
minimin approach
Expected value of sample information
Chapter 13 – Decision Analysis
47. For a maximization problem, the optimistic approach is often referred to as the
a.
minimax approach
b.
maximin approach
c.
maximax approach
d.
minimin approach
c
Decision making without probabilities
48. For a minimization problem, the conservative approach is often referred to as the
a.
minimax approach
b.
maximin approach
c.
maximax approach
d.
minimin approach
a
Decision making without probabilities
49. In an influence diagram, decision nodes are represented by
a.
circles or ovals
b.
squares or rectangles
c.
diamonds
d.
triangles
Influence diagram
50. Which of the following approaches to decision making requires knowledge of the probabilities of the states of nature?
a.
minimax regret
b.
maximin
c.
expected value
d.
conservative
c
Decision making with probabilities
51. Decision tree probabilities refer to the probability of
a.
an uncertain event occurring.
b.
the decision being made.
c.
finding an optimal value.
d.
overlooked choices.
a
Decision making without probabilities
Chapter 13 – Decision Analysis
52. Which of the following is not an advantage of using decision tree analysis?
a.
the ability to see clearly what decisions must be made
b.
the ability to see clearly in what sequence the decisions must occur
c.
the ability to see clearly the interdependence of decisions
d.
the ability to see clearly the future outcome of a decision
Decision making with probabilities
53. A decision tree provides
a.
a heuristic method for analyzing decisions.
b.
a deterministic approach to decision analysis.
c.
the absolute value of the decision.
d.
an objective way of determining the relative value of each decision alternative.
Decision trees
54. The approach to determining 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.
Decision strategy
55. 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.
information sensitivity.
b.
expected value of sample information.
c.
expected value of perfect information.
d.
efficiency of sample information.
Expected value of sample information
56. When consequences are measured on a scale that reflects a decision maker’s attitude toward profit, loss, and risk,
payoffs are replaced by
a.
utility values.
b.
multicriteria measures.
c.
sample information.
d.
opportunity loss.
Decision making with probabilities
Chapter 13 – Decision Analysis
a
Meaning of utility
57. The purchase of insurance and lottery tickets shows that people make decisions based on
a.
expected value.
b.
sample information.
c.
utility.
d.
maximum likelihood.
c
Meaning of utility
58. The expected utility approach
a.
does not require probabilities.
b.
leads to the same decision as the expected value approach.
c.
is most useful when excessively large or small payoffs are possible.
d.
requires a decision tree.
c
Expected utility approach
59. Utility reflects the decision maker’s attitude toward
a.
probability and profit.
b.
profit, loss, and risk.
c.
risk and regret.
d.
probability and regret.
Meaning of utility
60. Values of utility
a.
must be between 0 and 1.
b.
must be between 0 and 10.
c.
must be nonnegative.
d.
must increase as the payoff improves.
Utility functions
61. If the payoff from outcome A is twice the payoff from outcome B, then the ratio of these utilities will be
a.
2 to 1.
b.
less than 2 to 1.
c.
more than 2 to 1.
d.
unknown without further information.
Chapter 13 – Decision Analysis
d
1
Utility functions
62. The probability for which a decision maker cannot choose between a certain amount and a lottery based on that
probability is
a.
the indifference probability.
b.
the lottery probability.
c.
the uncertain probability.
d.
the utility probability.
a
1
Utility functions
63. A decision maker has chosen .4 as the probability for which he cannot choose between a certain loss of 10,000 and the
lottery p(−25000) + (1 − p)(5000). If the utility of −25,000 is 0 and of 5000 is 1, then the utility of −10,000 is
a.
.5
b.
.6
c.
.4
d.
4
b
1
Utility functions
64. When the decision maker prefers a guaranteed payoff value that is smaller than the expected value of the lottery, the
decision maker is
a.
a risk avoider.
b.
a risk taker.
c.
an optimist.
d.
an optimizer.
a
1
Risk avoiders versus risk takers
65. A decision maker whose utility function graphs as a straight line is
a.
conservative.
b.
a risk taker.
c.
risk neutral.
d.
a risk avoider.
c
1
Risk avoiders versus risk takers
66. When the utility function for a risk-neutral decision maker is graphed (with monetary value on the horizontal axis and
utility on the vertical axis), the function appears as
Chapter 13 – Decision Analysis
a.
a convex curve.
b.
a concave curve.
c.
an ‘S’ curve.
d.
a straight line.
Risk avoiders versus risk takers
Subjective Short Answer
67. Jim has been employed at Gold Key Realty at a salary of $2,000 per month during the past year. Because Jim is
considered to be a top salesman, the manager of Gold Key is offering him one of three salary plans for the next year: (1) a
25% raise to $2,500 per month; (2) a base salary of $1,000 plus $600 per house sold; or, (3) a straight commission of
$1,000 per house sold. Over the past year, Jim has sold up to 6 homes in a month.
a. Compute the monthly salary payoff table for Jim.
b. For this payoff table find Jim’s optimal decision using: (1) the conservative approach, (2) minimax regret
approach.
c. Suppose that during the past year the following is Jim’s distribution of home sales. If one assumes that this a
typical distribution for Jim’s monthly sales, which salary plan should Jim select?
Home Sales
Number of Months
0
1
1
2
2
1
3
2
4
1
5
3
6
2
Decision making with and without probabilities
Chapter 13 – Decision Analysis
68. East West Distributing is in the process of trying to determine where they should schedule next year’s production of a
popular line of kitchen utensils that they distribute. Manufacturers in four different countries have submitted bids to East
West. However, a pending trade bill in Congress will greatly affect the cost to East West due to proposed tariffs, favorable
trading status, etc.
After careful analysis, East West has determined the following cost breakdown for the four manufacturers (in $1,000’s)
based on whether or not the trade bill passes:
Bill Passes
Bill Fails
Country A
260
210
Country B
320
160
Country C
240
240
Country D
275
210
a.
If East West estimates that there is a 40% chance of the bill passing, which country should
they choose for manufacturing?
b.
Over what range of values for the “bill passing” will the solution in part (a) remain optimal?
Country B.
1
Decision making with probabilities
69. Transrail is bidding on a project that it figures will cost $400,000 to perform. Using a 25% markup, it will charge
$500,000, netting a profit of $100,000. However, it has been learned that another company, Rail Freight, is also
considering bidding on the project. If Rail Freight does submit a bid, it figures to be a bid of about $470,000. Transrail
really wants this project and is considering a bid with only a 15% markup to $460,000 to ensure winning regardless of
whether or not Rail Freight submits a bid.
a.
Prepare a profit payoff table from Transrail’s point of view.
b.
What decision would be made if Transrail were conservative?
c.
If Rail Freight is known to submit bids on only 25% of the projects it considers, what
Chapter 13 – Decision Analysis
decision should Transrail make?
d.
Given the information in (c), how much would a corporate spy be worth to Transrail to find
out if Rail Freight will bid?
a.
Bid $500,000
Bid $460,000
b. Bid $460,000
c. Bid $500,000
d. $15,000
Decision making with and without probabilities
70. The Super Cola Company must decide whether or not to introduce a new diet soft drink. Management feels that if it
does introduce the diet soda it will yield a profit of $1 million if sales are around 100 million, a profit of $200,000 if sales
are around 50 million, or it will lose $2 million if sales are only around 1 million bottles. If Super Cola does not market
the new diet soda, it will suffer a loss of $400,000.
a.
Construct a payoff table for this problem.
b.
Construct a regret table for this problem.
c.
Should Super Cola introduce the soda if the company: (1) is conservative; (2) is optimistic;
(3) wants to minimize its maximum disappointment?
d.
An internal marketing research study has found P(100 million in sales) = 1/3; P(50 million in
sales) = 1/2; P(1 million in sales) = 1/6. Should Super Cola introduce the new diet soda?
e.
A consulting firm can perform a more thorough study for $275,000. Should management
have this study performed?
a.
PAYOFF
Do Not
b.
REGRET
c. (1) do not introduce; (2) introduce; (3) do not introduce
d. Yes
e. No
Decision making with and without probabilities
71. Super Cola is also considering the introduction of a root beer drink. The company feels that the probability that the
product will be a success is .6. The payoff table is as follows:
Success (s1)
Failure (s2)
Chapter 13 – Decision Analysis
Produce (d1)
$250,000
−$300,000
Do Not Produce (d2)
−$ 50,000
−$ 20,000
The company has a choice of two research firms to obtain information for this product. Stanton Marketing has market
indicators, I1 and I2 for which P(I1 | s1) = .7 and P(I1 | s2) = .4. New World Marketing has indicators J1 and J2 for which
P(J1 | s1) = .6 and P(J1 | s2) = .3.
a.
What is the optimal decision if neither firm is used? Over what probability of success range
is this decision optimal?
b.
What is the EVPI?
c.
Find the EVSIs and efficiencies for Stanton and New World.
d.
If both firms charge $5,000, which firm should be hired?
e.
If Stanton charges $10,000 and New World charges $4,000, which firm should Super Cola
hire? Why?
a.
Introduce root beer; p ≤ .483
b.
EVPI = $112,000
The answers to (c)-(e) are very sensitive to roundoff error.
Figures in parentheses are for two decimal places only.
c.
Stanton: EVSI = $13,200 ($11,862)
Efficiency = .118 (.106)
Efficiency = .057 (.057)
d.
Hire Stanton (Stanton)
e.
Hire New World (Stanton)
1
Computing branch probabilities
72. Dollar Department Stores has just acquired the chain of Wenthrope and Sons Custom Jewelers. Dollar has received an
offer from Harris Diamonds to purchase the Wenthrope store on Grove Street for $120,000. Dollar has determined
probability estimates of the store’s future profitability, based on economic outcomes, as: P($80,000) = .2, P($100,000) =
.3, P($120,000) = .1, and P($140,000) = .4.
a.
Should Dollar sell the store on Grove Street?
b.
What is the EVPI?
c.
Dollar can have an economic forecast performed, costing $10,000, that produces indicators
I1 and I2, for which P(I1 | 80,000) = .1; P(I1 | 100,000) = .2; P(I1 | 120,000) = .6; P(I1 |
140,000) = .3. Should Dollar purchase the forecast?
a.
b.
EVPI = $8,000
c.
No; survey cost exceeds EVPI
1
Computing branch probabilities
73. An appliance dealer must decide how many (if any) new microwave ovens to order for next month. The ovens cost
$220 and sell for $300. Because the oven company is coming out with a new product line in two months, any ovens not
sold next month will have to be sold at the dealer’s half price clearance sale. Additionally, the appliance dealer feels he
suffers a loss of $25 for every oven demanded when he is out of stock. On the basis of past months’ sales data, the dealer
estimates the probabilities of monthly demand (D) for 0, 1, 2, or 3 ovens to be .3, .4, .2, and .1, respectively.
The dealer is considering conducting a telephone survey on the customers’ attitudes towards microwave ovens. The results
of the survey will either be favorable (F), unfavorable (U) or no opinion (N). The dealer’s probability estimates for the
Chapter 13 – Decision Analysis
survey results based on the number of units demanded are:
P(F | D = 0) = .1
P(F | D = 2) = .3
P(U | D = 0) = .8
P(U | D = 2) = .1
P(F | D = 1) = .2
P(F | D = 3) = .9
P(U | D = 1) = .3
P(U | D = 3) = .1
a.
What is the dealer’s optimal decision without conducting the survey?
b.
What is the EVPI?
c.
Based on the survey results what is the optimal decision strategy for the dealer?
d.
What is the maximum amount he should pay for this survey?
Ovens Ordered
a.
Order one oven: EV = $25.00
b.
EVPI = $63.00
c.
Favorable: order 2; Unfavorable: order 0; No opinion: order 1
d.
EVSI = $9.10
Computing branch probabilities
74. Lakewood Fashions must decide how many lots of assorted ski wear to order for its three stores. Information on
pricing, sales, and inventory costs has led to the following payoff table, in thousands.
Demand
Order Size
Low
Medium
High
1 lot
12
15
15
2 lots
9
25
35
3 lots
6
35
60
a.
What decision should be made by the optimist?
b.
What decision should be made by the conservative?
c.
What decision should be made using minimax regret?
a.
3 lots
b.
1 lot
c.
3 lots
1 lot
Decision making without probabilities
75. The table shows both prospective profits and losses for a company, depending on what decision is made and what
state of nature occurs. Use the information to determine what the company should do.
State of Nature
Chapter 13 – Decision Analysis
Decision
s1
s2
s3
d1
30
80
−30
d2
100
30
−40
d3
−80
−10
120
d4
20
20
20
a.
if an optimistic strategy is used.
b.
if a conservative strategy is used.
c.
if minimax regret is the strategy.
Decision making without probabilities
76. A payoff table is given as
State of Nature
Decision
s1
s2
s3
d1
10
8
6
d2
14
15
2
d3
7
8
9
a.
What decision should be made by the optimistic decision maker?
b.
What decision should be made by the conservative decision maker?
c.
What decision should be made under minimax regret?
d.
If the probabilities of s1, s2, and s3 are .2, .4, and .4, respectively, then what decision should
be made under expected value?
e.
What is the EVPI?
c.
a three way tie
e.
EVPI = 12.4 − 9.6 = 2.8
Chapter 13 – Decision Analysis
77. A payoff table is given as
State of Nature
Decision
s1
s2
s3
d1
250
750
500
d2
300
−250
1200
d3
500
500
600
a.
What choice should be made by the optimistic decision maker?
b.
What choice should be made by the conservative decision maker?
c.
What decision should be made under minimax regret?
d.
If the probabilities of d1, d2, and d3 are .2, .5, and .3, respectively, then what choice should
be made under expected value?
e.
What is the EVPI?
e.
EVPI = 925 − 695 = 230
Decision making with and without probabilities
78. A decision maker has developed the following decision tree. How sensitive is the choice between N and P to the
probabilities of states of nature U and V?
Choose N if p ≤ .78.
Sensitivity analysis
79. If p is the probability of Event 1 and (1 − p) is the probability of Event 2, for what values of p would you choose A?
B? C? Values in the table are payoffs.
Choice/Event
Event 1
Event 2
A
0
20
B
4
16
C
8
0
Choose A if p ≤ .5, choose B is .5 ≤ p ≤ .8, and choose C if p ≥ .8.
Decision making with and without probabilities