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OM5 Test Bank Supplementary Chapter E 1
Supplementary Chapter E — Decision Analysis
TRUE/FALSE
1. Making decisions in an emergency room of a hospital is an example of a decision analysis
situation.
2. Decision analysis situations often have multiple objectives.
ANS: T
3. Risk is a form of uncertainty associated with an unexpected good.
ANS: F
4. With an unstable economy, it is difficult to predict actual demand for a product.
5. For decisions that are repeated over and over, managers can choose decisions based on the
expected payoff that might occur.
ANS: T
6. An aggressive or risk-taking approach to one-time decisions without event probabilities is
called maximin.
7. With some modification, the decision rules for one-time decisions without event probabilities
can be applied to situations where the payoff is cost.
ANS: T
8. The minimax-regret approach to one-time decisions without event probabilities is neither
aggressive nor conservative.
9. Decision problems can be depicted graphically using the expected-value approach.
10. The expected-value concept weighs each payoff for an alternative in proportion to the
likelihood that the payoff will occur.
11. Irrespective of its quality, the expected value of perfect information represents the maximum
amount a company should be willing to pay for any information about events.
OM5 Test Bank Supplementary Chapter E 2
12. A numerical value associated with a decision coupled with some event is called a decision
tree.
MULTIPLE CHOICE
1. Which of the following is NOT a characteristic of management decisions for which decision
analysis techniques apply?
a. They must be important.
b. They are probably unique.
c. They are usually deterministic.
d. They are complex.
2. Uncertainty refers to not knowing what will happen in the future. Which of the following
LEAST applies to uncertainty?
a. There is no sequence of decisions.
b. Little or no data is available.
c. Some data are very expensive.
d. Some data are time-consuming to obtain.
3. _____ represent a future outcome that can occur after a decision is made that are not under the
control of the decision maker.
a. Decision alternatives
b. Events
c. Payoffs
d. Probabilities
4. A conservative or risk-averse approach to one-time decisions without event probabilities is
known as _____.
a.
maximax
b.
maximin
c.
minimax regret
d.
expected value
5. Opportunity loss or ill-feeling that people often have after making a nonoptimal decision is best
related to _____.
a.
maximax
b.
maximin
c.
minimax regret
d.
expected value
OM5 Test Bank Supplementary Chapter E 3
6. The decision criterion, for a one-time decision without event probabilities, which is neither
aggressive nor conservative, is known as _____.
a. maximax
b. maximin
c. minimax regret
d. expected value
7. Which of the following is NOT a similarity between the elements of a decision problem and a
decision tree?
a. Time
b. States of nature
c. Alternatives
d. Probabilities
8. Which of the following statements is TRUE of the expected-value approach to selecting
decision alternatives?
a.
It mostly applies to one-time decisions.
b.
It knows the state of nature in advance.
c.
It is best suited for repeated decisions.
d.
It is independent of probability estimates for events.
9. Which of the following statements is TRUE of expected value of perfect information (EVPI)?
a.
EVPI mostly applies to situations that require one-time decisions.
b.
EVPI is a numerical value associated with a decision coupled with some event.
c.
EVPI is calculated by adding the expected payoff under perfect information to the
expected payoff of the optimal decision without perfect information.
d.
EVPI can be computed by determining the best decision and payoff if each event occurs.
10. In a decision tree, event nodes are denoted by _____.
a.
rectangles
b.
ovals
c.
squares
d.
circles
11. For _____, managers must take into account the risk associated with making the wrong
decision.
a.
recurrent payoffs
b.
expected payoffs
c.
one-time decisions
d.
repeated decisions
OM5 Test Bank Supplementary Chapter E 4
12. Which of the following statements is TRUE of a decision tree?
a.
The number at each endpoint of a decision tree represents the probability associated with a
particular chain of events.
b.
A decision tree cannot be used for complex business decisions.
c.
In a decision tree, event nodes are represented by squares, while decision nodes are
represented by circles.
d.
Expected value calculations can be made directly on a decision tree to arrive at the best
decision strategy.
13. A model that starts with the future-most point and moves toward the current time period is
called a _____.
a.
payoff table
b.
maximax decision
c.
decision tree
d.
satisficing matrix
SHORT ANSWERS
1. Discuss the five characteristics of management decisions when decision analysis techniques
should be utilized.
2. Differentiate between uncertainty and risk.
3. List the four elements of a decision problem.
4. Describe how the following criteria are applied to a decision problem in which the object is
maximization.
a.
Maximax
b.
Maximin
c.
Minimax regret
OM5 Test Bank Supplementary Chapter E 5
5. Describe how the following criteria are applied to a decision problem in which the payoff is
cost.
a.
Minimin
b.
Minimax
c.
Minimax regret
6. In what type of situation would the expected value criterion be useful? In what type of
situation would it not be useful?
7. Explain the concept of expected value of perfect information (EVPI). How does it help a
decision maker?
8. Explain the structure and purpose of a decision tree.
NUMERICALS
1. A company is expanding its production capacity. The decision will depend upon whether the
increase in demand is low, medium, or high. The company's choices for expansion are small,
medium, large, or very large. The following table provides an estimate of profits over the next two
years.
Demand Values
Decision
Low (S1)
Medium (S2)
High (S3)
Small Expansion (d1)
$5,000
$10,000
$10,000
OM5 Test Bank Supplementary Chapter E 6
Medium Expansion (d2)
$2,000
$12,000
$14,000
Large Expansion (d3)
0
$6,000
$13,000
Very Large Expansion (d4)
$5,000
$8,000
$20,000
a. Which decision variable would be selected using maximax?
b. Which decision variable would be selected using maximin?
c. Which decision variable would be selected using minimax-regret criteria?
d. Suppose the decision maker assigns the probability of low demand as 0.2, medium demand as
0.5, and high demand as 0.3. Which decision variable would be selected using the expected value
criterion?
2. The following table shows cost payoffs for four decision variables and four states of nature.
S1
S2
S3
S4
d1
16
8
15
4
d2
12
12
10
6
d3
10
12
16
10
d4
9
14
20
12
a. Which decision variable would be selected using minimin criteria?
b. Which decision variable would be selected using minimax?
c. Which decision variable would be selected using minimax-regret criteria.
d. Suppose the decision maker assigns the probability for S1 = 0.10; S2 = 0.25; S3 = 0.45; and S4
= 0.20, which decision variable would be selected using the expected value criterion?
3. In the following profit table, di represents decision variables and Si represents states of nature.
S1
S2
S3
S4
d1
15.00
15.00
15.00
15.00
d2
10.00
5.00
25.00
25.00
d3
35.00
0
40.00
60.00
d4
60.00
20.00
50.00
90.00
a. If management assigns probabilities as follows: S1 = 0.15; S2 = 0.25; S3 = 0.40; and S4 = 0.20,
determine the expected value for d2.
b. Determine the expected value for d3.
c. Assuming the largest expected value for a decision variable is 24.00; determine the value of
perfect information.
OM5 Test Bank Supplementary Chapter E 7
4. Jumbo James sells hotdogs out of a cart for $3.00 each. The cost to purchase and prepare the
hotdog is $1.15 each. James operates the small business with very few capital assets and has no
place to store unsold hotdogs. For this reason, every evening he sells the unsold hotdogs to a local
homeless shelter for $0.50 each. Jumbo James will choose one of the following options as a
standard stocking plan: d1 = 100; d2 = 150; or d3 = 200 hotdogs. On any weekday, the demand for
hotdogs and the probability of selling them is estimated as follows:
Demand Per Day
Probability
100
0.50
200
0.30
300
0.20
a. Determine the expected value if Jumbo James stocks 200 hotdogs every day.
b. Determine the expected value if Jumbo James decides to stock 150 hotdogs every day.
5. Given the following table, calculate the expected value of perfect information.
Low
Demand
Medium
Demand
High
Demand
Expected
Value
Small d1
$400
$400
$400
$400
Medium d2
$100
$600
$600
$500
Large d3
$300
$300
$900
$450
Probability
0.20
0.35
0.45
6. Elizabeth, a decision maker has decided to expand her operations and become more efficient.
She uses 3 decision variables—d1 is to do nothing; d2 is a moderate expansion; and d3 is a
major expansion.
a. Determine the expected value of d2 if the states of nature are S1 = 0.25; S2 = 0.60; and S3 =
0.15.
b. Determine the expected value for d3 if the states of nature are S1 = 0.25; S2 = 0.60; and S3 =
0.15.
7. A regional fast-food restaurant is considering an expansion program. The major factor influenc-
ing the success of such a program is the future level of interest rates. It is estimated that there is a
20 per-cent chance that interest rates will increase by 2 percentage points, a 50 percent chance that
they will remain the same, and a 30 percent chance that they will decrease by 2 percentage points.
The alternatives they are considering and possible payoffs are shown in the following table:
Rates Up
Rates
Rates Down
2 Percent
Unchanged
2 Percent
Build 50 new places
-$200,000
$50,000
$150,000
Build 25 new places
-$115,000
$26,000
$ 80,000
Do nothing
-$ 70,000
0
$ 5,000
a. Using decision tree analysis, what is the expected value (EV) for building 50 new restaurants?
b. Using decision tree analysis, what is the expected value (EV) for building 25 new restaurants?
c. What is the action and corresponding expected value EV for this overall decision tree problem?
8. A Pacific Northwest lumber company is considering the expansion of one of its mills. The ques-
tion is whether to do it now, or wait for one year and re-consider. If they expand now, the major
factors of importance are the state of the economy and the level of interest rates. The combination
of these two factors results in five possible situations. If they do not expand now, only the state of
the economy is important, and three conditions characterize the possibilities. The following table
summarizes the situation:
Expand
Probabilities
Revenues
very favorable
0.2
$80,000
favorable
0.2
$60,000
neutral
0.1
$20,000
unfavorable
0.3
-$20,000
very unfavorable
0.2
-$30,000
Don’t expand
expansion
0.2
$50,000
steady
0.5
$30,000
contraction
0.3
$10,000
a. Using decision tree analysis, what is the expected value (EV) for expanding?
b. Using decision tree analysis, what is the expected value (EV) for not expanding?
c. Based on expected value (EV), what should the company’s decision(s) be?
9. A major retail clothing store is considering whether to open a new store on the other side of
town or wait for one year and then open the store. In the meantime, they have paid $10,000 for
one year option on a building. If they open the store now it will cost $140,000 to refurbish it, but it
will cost $160,000 if they wait one year. They expect sales to depend on the economy in the area
at the time they open the store. If they go ahead now, there is a 50% chance the economy will go
up, 30% it will stay the same, and 20% it will go down. They then expect the following returns: if
the economy goes up $200,000; stays the same $160,000; and goes down -$20,000.
If they wait one year, they can either open the store then or not open the store and let the option
expire. If the option expires, they will lose the $10,000. One year from now they expect there is a
40% chance the economy will go up, 30% stay the same, and 30% go down. The returns they ex-
pect to get would then be: if the economy goes up $180,000; stays the same $160,000; and goes
down -$30,000.
a. Using decision tree analysis, what is the expected value (EV) of opening the store now?
b. Using decision tree analysis, what is the expected value (EV) of waiting one year to open the
store?
c. What should the company do and what is the expected value (EV) of that decision?
OM5 Test Bank Supplementary Chapter E 11
10. A chemical company is trying to decide whether to build a pilot plant now for a new chemical
process or to build the full plant now. If they build a pilot plant now, they could expand it later to
a full plant or license the plant to another company. It would cost them $2 million to build the pi-
lot plant and another $2 million later to expand it. If they build the full plant now it would cost
$3.5 million to construct. The returns they expect to get from the full production plant depend up-
on the market.
They estimate there is a 60% chance the market will be robust, a 30% chance it will remain stable,
and a 10% chance it will become stagnant. The returns are estimated to be $5 million if it is ro-
bust, $3 million if it is stable, and $1 million if it is stagnant.
Before they expand the pilot plant, they plan to conduct a comprehensive study. Based on past
experience, they expect the study to report a 60% chance of favorable outcome for expansion and
a 40% unfavorable chance. In either case, they should decide whether to expand to a full plant or
license the pilot plant. If the report is favorable and they license it, they expect to get $3 million.
However, if the report is unfavorable and they license it, they will only get $1 million.
a. Using decision tree analysis, what is the expected value for building the full plant now?
b. Using decision tree analysis, what is the value of the decision on expanding the pilot plant as-
suming the report is favorable?
c. What should the company do, and what is the expected value of that decision?
OM5 Test Bank Supplementary Chapter E 12
11. A paint company has three sources for buying bright red pigment for their paints: Vietnam,
Taiwan, or Thailand. Unfortunately, the pigment is made from a bush whose annual growth is
heavily dependent upon the amount of rainfall during the growing season. The tables below show
probabilities and prices for wet, dry, and normal growing seasons:
Probabilities
Wet
Dry
Normal
Vietnam
0.5
0.2
0.3
Taiwan
0.6
0.3
0.1
Thailand
0.4
0.4
0.2
Price/Pound ($)
Wet
Dry
Normal
Vietnam
0.95
1.10
1.00
Taiwan
0.85
1.20
.98
Thailand
0.90
1.15
1.05
a. Using decision tree analysis, what is the expected value (price) for Thailand?
b. What country should the company select, and what is the expected value (price) associated
with it?
