A: MODULE DECISION-MAKING TOOLS
TRUE/FALSE
1.
Analytic decision making is based on logic and considers all available data and
possible alternatives.
True (The decision process in operations, easy) {AACSB: Analytic Skills}
2.
The last step in the analytic decision process clearly defines the problem and the
factors that influence it.
False (The decision process in operations, easy) {AACSB: Analytic Skills}
3.
A state of nature is an occurrence of a situation over which the decision maker has
little or no control.
True (Fundamentals of decision making, easy)
4.
In a decision tree, a square symbol represents a state of nature node.
False (Fundamentals of decision making, moderate)
5.
If a decision maker can assign probabilities of occurrence to the states of nature, then the
decision is being made under conditions of uncertainty.
False (Types of decision-making environments, moderate)
6.
An example of a conditional value would be the payoff from selecting a particular
alternative when a particular state of nature occurs.
True (Types of decision-making environments, moderate)
7.
The maximax criterion of decision making requires that all decision alternatives have
an equal probability of occurrence.
False (Types of decision-making environments, easy)
8.
The maximin criterion is pessimistic, while the maximax criterion is optimistic.
True (Types of decision-making environments, easy)
9.
If a decision maker knows for sure which state of nature will occur, he/she is making a
decision under certainty.
True (Types of decision-making environments, moderate)
10. The expected value with perfect information assumes that all states of nature are equally
likely.
False (Types of decision-making environments, easy)
11.
An example of expected monetary value would be the payoff from selecting a particular
alternative when a particular state of nature occurs.
False (Decision tables, moderate)
12.
The expected monetary value of a decision alternative is the sum of all possible payoffs
from the alternative, each weighted by the probability of that payoff occurring.
True (Types of decision-making environments, easy)
478
1 3.
If a decision maker has to make a certain decision only once, expected monetary value
is a good indication of the payoff associated with the decision.
False (Types of decision-making environments, moderate)
14.
The expected value of perfect information is the same as the expected value with
perfect information.
False (Decision tables, moderate)
15.
Decision trees and decision tables can both solve problems requiring a single decision, but
decision tables are the preferred method when a sequence of decisions is involved.
False (Decision trees, easy)
16.
In a decision tree, the expected monetary values are computed by working from right to left.
True (Decision trees, moderate)
MULTIPLE CHOICE
17.
Which of the following is not considered a step in the decision-making process?
a. Clearly identify the
problem. c.
Develop
objectives.
d. Evaluate alternatives.
b. Select the best alternative.
e. Minimize costs whenever possible.
e (The decision process in operations, moderate)
18.
The first step, and a key element, in the decision-making
process is to a. consult a specialist
b. clearly define the
problem c.
develop
objectives
d. monitor the results
e. select the best alternative
b (The decision process in operations, easy)
19.
In terms of decision theory, an occurrence or situation over which the decision
maker has no control is called a(n)
a. decision under uncertainty
b. decision tree
c. state of
nature d.
alternative
e. none of the above
c (Fundamentals of decision making, easy)
479
2 0.
A tabular presentation that shows the outcome for each decision alternative under the
various possible states of nature is called a(n)
a. isoquant table
b. payback period
matrix c.
payoff
table
d. feasible region
e. decision tree
c (Decision tables, easy)
21.
The decision criterion that would be used by an optimistic decision maker solving a
problem under conditions of uncertainty would be the
a. expected monetary value criterion
b. equally likely
criterion c.
maximax
criterion
d. maximin criterion
e. minimin criterion
c (Types of decision-making environments, moderate)
22.
A decision maker who uses the maximin criterion when solving a problem under
conditions of uncertainty is
a. an optimist
b. a pessimist
c. an economist
d. an
optometrist
e. making a serious mistake; maximin is not appropriate for conditions of uncertainty
b (Types of decision-making environments, moderate)
23.
Expected monetary value is most appropriate for problem solving that
takes place a. when conditions are average
b. when all states of nature are equally likely
c. when all alternatives are equally
likely d. under conditions of
uncertainty
e. under conditions of risk
e (Types of decision-making environments, moderate)
24.
The expected value with perfect
information
a. is appropriate when solving problems under conditions of certainty
b. requires that each decision alternative have a known probability of
occurrence c. is an input into the calculation of the expected value of
perfect information
d. is the average of the maximax and the
maximin e.
none of the above
c (Types of decision-making environments, moderate)
480
2 5.
The difference between the expected payoff under perfect information and the maximum
expected payoff under risk is
a. expected monetary value
b. economic order quantity
c. expected value of perfect
information d. PERT
e. expected monetary payoff
c (Types of decision-making environments, moderate)
26.
The outcome of an alternative/state of nature combination is
a(n)
a. price
b. conditional
value c. expected
value
d. conditional probability
e. All of the above are correct.
b (Decision tables, moderate)
27.
The likelihood that a decision maker will ever receive a payoff precisely equal to the
EMV when making any one decision is
a. low (near 0%)
b. high (near 100%)
c. dependent upon the number of alternatives
d. dependent upon the number of states of
nature e.
none of the above
a (Types of decision-making environments, moderate)
28.
The expected value of perfect information (EVPI) is
the a. payoff for a decision made under perfect
information b. payoff under minimum risk
c. average expected payoff
d. difference between the payoff under perfect information and the payoff
under risk e. none of the above
d (Types of decision-making environments, moderate)
481
29.
A decision-maker using the maximax criterion on the problem below would choose
Alternative
because the maximum of the row maximums is
_.
States of
nature
Alternative A
Alternative B
Alternative C
Alternative D
50
30
70
-100
1
2
55
50
80
-10
60
80
70
140
3
a. A; 60
b.
B;
80
c.
C; 70
d. D;
-100 e. D;
140
e (Types of decision-making environments, moderate) {AACSB: Analytic
Skills}
30.
A decision-maker using the maximin criterion on the problem below would choose
Alternative
because the maximum of the row minimums is
_.
States of
nature
Alternative A
Alternative B
Alternative C
Alternative D
50
30
70
-100
1
55
50
80
-10
2
60
80
70
140
3
a. A; 55
b.
B;
30
c.
C; 70
d. D;
140 e. D;
10
c (Types of decision-making environments, moderate) {AACSB: Analytic
Skills}
31.
The highest value for the equally likely criterion is
Alternatives
Option 2
Option 3
S1
$5,000
$-4,000
States of nature
S2
$45,000
$60,000
; this occurs with alternative
.
a. $20,000; Option
1 b.
$25,000;
Option
2
c.
$28,000; Option
3 d.
$32,000;
Option
3
e.
$60,000; Option
3
c (Types of decision-making environments, moderate) {AACSB: Analytic
Skills}
482
3 2.
What is the EMV for Option 1 in the following decision table?
Alternatives
p
Option 1
Option 2
a.
b.
c.
d.
e.
States of nature
S2
.7
20,000
30,000
15,00
17,00
0 ,50
17
0 50
18,
0 ,00
20
0 d (Types of decision-making environments, easy) {AACSB: Analytic Skills}
33.
34.
The expected value with perfect
information is a.
the maximum EMV
for a set of alternatives
b. the same as the expected value of perfect information
c. valuable in situations involving risk
d. the average return obtained when the decision maker knows which state of nature is
going to occur before the decision is made
e. obtained using conditional probabilities
d (Types of decision-making environments, moderate)
What is the EMV for Option 2 in the following decision
table?
Alternatives
p
Option 1
Option 2
a.
b.
c.
d.
e.
S1
.3
15,000
10,000
S1
.3
15,000
10,000
States of nature
S2
.7
20,000
30,000
10,00
16,00
0 ,00
20
0 00
24,
0 ,00
30
0 d (Types of decision-making environments, moderate) {AACSB: Analytic Skills}
483
3 5.
What is the EMV for Option 1 in the following decision table?
Alternatives
p
Option 1
Option 2
Option 3
a.
b.
c.
d.
e.
What is the EMV for Option 2 in the following decision table?
Alternatives
p
Option 1
Option 2
Option 3
S1
.4
10,000
5,000
-4,000
States of nature
S2
.6
30,000
45,000
60,000
5,000
21,00
0 ,00
25
0 00
29,
0 ,00
45
0 d (Types of decision-making environments, moderate) {AACSB: Analytic Skills}
37.
What is the expected value with perfect information of the following decision table?
Alternatives
p
Option 1
Option 2
Option 3
a.
b.
c.
d.
e.
States of nature
S2
.6
30,000
45,000
60,000
10,00
18,00
0 ,00
20
0 00
22,
0 ,00
30
0 d (Types of decision-making environments, moderate) {AACSB: Analytic Skills}
36.
a.
b.
c.
d.
e.
S1
.4
10,000
5,000
-4,000
S1
.4
10,000
5,000
-4,000
States of nature
S2
.6
30,000
45,000
60,000
5,000
10,00
0 ,00
40
0 00
60,
0 ,00
70
0 c (Types of decision-making environments, moderate) {AACSB: Analytic Skills}
484
38.
What is the EMV for Option 1 in the following decision table?
Alternatives
p
Option 1
Option 2
a.
b.
c.
d.
e.
What is the EMV for Option 2 in the following decision table?
Alternatives
p
Option 1
Option 2
S1
.6
200
50
States of nature
S2
.4
300
350
50
100
170
200
350
c (Types of decision-making environments, moderate) {AACSB: Analytic Skills}
40.
What is the expected value with perfect information in the following decision table?
Alternatives
p
Option 1
Option 2
a.
b.
c.
d.
e.
States of nature
S2
.4
300
350
200
240
250
260
300
b (Types of decision-making environments, moderate) {AACSB: Analytic Skills}
39.
a.
b.
c.
d.
e.
S1
.6
200
50
S1
.6
200
50
States of nature
S2
.4
300
350
50
200
260
300
350
c (Types of decision-making environments, moderate) {AACSB: Analytic Skills}
485
4 1.
What is the expected value of perfect information of the following decision table?
Alternatives
p
Option 1
Option 2
S1
.6
200
50
States of nature
S2
.4
300
350
a. 0 b.
20 c.
50
d.
150 e.
200
b (Types of decision-making environments, moderate) {AACSB: Analytic Skills}
42.
A retailer is deciding how many of a certain product to stock. The historical probability
distribution of sales for this product is 0 units, 0.2; 1 unit, 0.3; 2 units, 0.4, and 3 units, 0.1.
The product costs
$8 per unit and sells for $25 per unit. The conditional value for the decision alternative
"Stock 3" and state of nature "Sell 1" is
a. 1.4 units
b. $1 profit
c. $25
profit d. $8 profit
e. none of the above
b (Types of decision-making environments, moderate) {AACSB: Analytic Skills}
43.
A retailer is deciding how many of a certain product to stock. The historical probability
distribution of sales for this product is 0 units, 0.2; 1 unit, 0.3; 2 units, 0.4, and 3 units, 0.1.
The product costs
$8 per unit and sells for $25 per unit. The largest conditional value (profit) in the entire
payoff table
for this scenario
is a.
$-24
profit
b. $-8 profit
c. $17
profit
d.
$51 profit e.
$75
profit
d (Types of decision-making environments, moderate) {AACSB: Analytic Skills}
44.
Decision trees
a. give more accurate solutions than decision
tables b. give less accurate solutions than
decision tables
c. are especially powerful when a sequence of decisions must be made
d. are rarely used because one needs specialized software to graph
them e. are too complex to be used by decision makers
c (Decision trees, moderate)
486
4 5.
A decision tree is a(n)
a. algebraic representation of alternatives and states of
nature b. behavioral representation of alternatives and
states of nature c.
matrix representation of alternatives
and states of nature
d. schematic representation of alternatives and states of
nature e.
tabular representation of alternatives and
states of nature
d (Decision trees, moderate)
46.
All of the following steps are taken to analyze problems with decision trees except
a. define the problem
b. structure or draw a decision tree
c. assign probabilities to the alternatives
d. estimate payoffs for each possible alternative/state of nature combination
e. solve the problem by computing expected monetary values for each state of nature node
c (Decision trees, moderate)
47.
A problem that involves a sequence of decisions
a. cannot be analyzed with expected monetary value
b. can be better analyzed with a decision tree than by a decision
table c. must be analyzed in the same order that the decisions are
made
d. cannot be analyzed with decision tree software
e. can only be analyzed using decision making under certainty
b (Decision trees, moderate)
FILL-IN-THE BLANK
48.
A(n)
is a tabular means of analyzing decision alternatives and states of nature.
decision table (Decision tables, easy)
49.
is the criterion for decision making under uncertainty that finds an
alternative that maximizes the minimum outcome or consequences.
Maximin (Decision tables, moderate)
50.
is the criterion for decision making under certainty that assigns equal
probability to each state of nature.
Equally likely (Decision tables, moderate)
51.
is the expected payout or value of a variable that has different possible
states of nature, each with an associated probability.
Expected monetary value or EMV (Decision tables, moderate)
52.
is the difference between the payoff under perfect information and the payoff
under risk.
Expected value of perfect information or EVPI (Decision tables, moderate)
53.
A(n)
is a graphical means of analyzing decision alternatives and states of nature.
decision tree (Decision trees, easy)
487
5 4.
A(n)
is an occurrence or situation over which the decision maker has little
or no control.
state of nature (Decision trees, easy)
55.
The square symbol used in drawing a decision trees represents a
decision (Decision trees, easy)
56.
A branch of a decision tree that is less favorable than other available options may be
pruned or dropped (Decision trees, easy)
node.
.
SHORT ANSWER
57.
In the context of decision-making, define state of nature.
A state of nature is an occurrence or situation over which the decision maker has
little or no control. (Fundamentals of decision making, moderate)
58.
In the context of decision-making, define alternative.
An alternative is a course of action or a strategy that may be chosen by a decision
maker. (Fundamentals of decision making, moderate)
59.
Identify, in order, the six steps of analytical decision making.
1. Clearly define the problem and factors that influence it.
2. Develop specific and measurable objectives.
3. Develop a modelthat is, a relationship between objectives and variables
(which are measurable quantities).
4. Evaluate each alternative solution based on its merits and drawbacks.
5. Select the best alternative.
6. Implement the decision and set a timetable for
completion. (The decision process in operations,
moderate)
60.
Explain the graphical shapes used in decision tree analysis.
A decision node from which one or several alternatives may be selected is
represented by a square; a state of nature node out of which states of nature will
occur is represented by a circle. (Fundamentals of decision making, moderate)
61.
What are decision tables?
Decision tables are a tabular means of analyzing decision alternatives and states of
nature. (Decision tables, easy)
62.
What is a conditional value?
It is an outcome of a particular alternative/state of nature combination. (Decision
tables, moderate)
63.
How is the expected value of perfect information (EVPI) found?
It is found by taking the expected value with perfect information and
subtracting the maximum expected monetary value (EMV) from it. (Types of
decision-making environments, moderate)
488
64. Identify and describe three methods used for decision making under conditions of
uncertainty.
The three decision rules are maximax, maximin, and equally likely. Maximax is a
criterion that finds an alternative that maximizes the maximum outcome. Maximin
is a criterion that finds an alternative that maximizes the minimum outcome.
Equally likely is a criterion that assigns equal likelihood to each state of nature.
(Types of decision-making environments, moderate)
65.
Which technique results in an optimistic decision? Why?
Maximax is the optimistic criterion. It maximizes the maximum outcome. (Types of
decision- making environments, easy)
66.
If a decision maker is a pessimist, what decision-making criterion is appropriate? Why?
Maximin is the pessimistic criterion. It assumes that the worst state of nature will
happen. The decision making criterion selects the best of all possible worst
outcomes. (Types of decision-making environments, easy)
67.
What limitation(s) do decision trees overcome compared to decision tables?
Decision trees work better when a sequence of decisions must be made.
(Decision trees, moderate)
Define expected monetary value (EMV).
EMV is the expected value or return for an alternative if we were to repeat the
decision a large number of times, each time choosing that alternative. (Types of
decision-making environments, moderate)
68.
69.
Describe the meaning of EVPI. Provide an example in which EVPI can help a manager.
EVPI is defined as the expected value of perfect information. It is found by taking
the expected value with perfect information and subtracting the maximum expected
monetary value (EMV) from it, and it is the maximum amount that we would be
willing to pay for additional (perhaps, perfect) information. Determination of EVPI
is useful any time the manager has the option of expending additional resources to
acquire additional information and making the decision using currently available
information. (Decision trees, moderate)
489
PROBLEMS
70.
The construction manager for Acme Construction, Inc. must decide whether to build
single family homes, apartments, or condominiums. This is not a product-mix an problem,
but all-or nothing decision. He will hire workers and rent equipment appropriate for
one action only. He estimates annual profits (in thousands of dollars) will vary with
population trends as follows:
Dwelling type Population steady Population grows
Population grows
Single family
$100
$90
$70
Apartments
50
170
90
Condominium
-20
100
220
s
a. If he uses the maximin criterion, which type of dwellings will he choose to build?
Show your supporting calculations.
b. If he uses the equally likely criterion, which kind of dwellings will he choose to build?
Show
your supporting calculations.
c. If the construction manager were an optimist, what criterion would he choose? What
would be the choice of dwelling for that criterion? Show your supporting calculations.
(a) The pessimistic maximin criterion assumes the worst state of nature will occur and
selects the action associated with the best of these worst outcomes. For this problem,
the "worsts" for each action are Single family = $70, Apartments = $50, and
Condominiums = -20. The best of the worsts is $70, so the manager should choose to
build single family homes.
(b) The equally likely criterion calculates the simple average of each action; the
results are Single family = $83.3, Apartments = $103.3, and Condominiums = $100.
The manager should select the action associated with the largest of these values, and
build apartments.
(c) The optimistic criterion is maximax, which assumes that the best outcome will
occur for each action. The best outcomes are Single family = $100, Apartments =
$170, and Condominiums = $220. The manager chooses the action associated with
the best of the bests, or Condominiums. (Types of decision-making environments,
moderate) {AACSB: Analytic Skills}
490
7 1.
An operations manager's staff has compiled the information below for four manufacturing
alternatives (A, B, C, and D) that vary by production technology and the capacity of the
machinery. All choices enable the same level of total production and have the same
lifetime. The four states of nature represent four levels of consumer acceptance of the
firm's products. Values in the table are net present value of future profits in millions of
dollars.
States of
nature
Alternative A
Alternative B
Alternative C
Alternative D
50
30
70
-100
1
55
50
80
-10
2
60
80
70
150
3
65
130
65
220
4
a. Assuming a maximax strategy, which alternative would be chosen?
b. If maximin were used, which would be chosen?
c. If the states of nature were equally likely, which alternative should be chosen?
(a) The maximax strategy selects the best of the best, which is $220. This happens
when Alternative D is selected. (b) The maximin strategy selects the best of the
worsts; the worsts are A=50, B=30, C=65, and D=-100. The best of these is 65,
associated with Alternative C. (c) The averages for the four alternatives are A=57.5,
B=72.5, C=71.25, and D=65. The highest of these is 72.5, associated with Alternative
B. (Decision tables, moderate) {AACSB: Analytic Skills}
72.
An operations manager's staff has compiled the information below for four manufacturing
alternatives (E, F, G, and H) that vary by production technology and the capacity of the
machinery. All choices enable the same level of total production and have the same
lifetime. The four states of nature represent four levels of consumer acceptance of the
firm's products. Values in the table are net present value of future profits in millions of
dollars. Forecasts indicate that there is a 0.1 probability of acceptance level 1, 0.2 chance
of acceptance level 2, 0.4 chance of acceptance level
3, and 0.3 change of acceptance level 4.
States of
nature
Alternative E
Alternative F
Alternative G
Alternative H
50
30
70
-140
1
50
50
80
-10
2
70
80
70
150
3
60
130
60
220
4
Using the criterion of expected monetary value, which production alternative should be
chosen?
The expected values are:
E = .1*50 + .2*50 + .4*70 + .3*60 = 5 + 10 + 28 + 18 = 61
F = .1*30 + .2*50 + .4*80 + .3*130 = 3 + 10 + 32 + 39 = 84
G = .1*70 + .2*80 + .4*70 + .3*60 = 7 + 16 + 28 + 18 = 69
H = .1 *-140 + .2*-10 + .4*150 + .3*220 = -10 -2 + 60 + 66 = 110
The highest of these occurs with production alternative H. (Decision tables, moderate)
{AACSB: Analytic Skills}
491
7 3.
A toy manufacturer makes stuffed kittens and puppies which have relatively lifelike
motions. There are three different mechanisms which can be installed in these "pets."
These toys will sell for the same price regardless of the mechanism installed, but each
mechanism has its own variable cost
and setup cost. Profit, therefore, is dependent upon the choice of mechanism and upon the
level of demand. The manufacturer has in hand a forecast of demand that suggests a 0.2
probability of light demand, a 0.45 probability of moderate demand, and a probability of
0.35 of heavy demand. Payoffs for each mechanism-demand combination appear in the
table below.
Demand
Light
Moderate
Heavy
Wind-up action
$250,000
400,000
650,000
Pneumatic action
$90,000
440,000
740,000
Electronic
-$100,000
400,000
780,000
Construct the appropriate decision tree to analyze this problem. Use standard symbols for
the tree. Analyze the tree to select the optimal decision for the manufacturer.
0.2
Li ght demand
250,000
250000
250000
0.45
Moderate demand
W i nd-up
0
457500
400,000
400000
0.35
Heavy demand
650,000
650000
650000
0.2
Li ght demand
90000
90,000
90000
0.45
Moderate demand
Pneumatic
2
475000
400000
440000
0
475000
440,000
440000
0.35
Heavy demand
740,000
740000
0.2
Li ght demand
-100,000
0
-100000
-100000
0.45
Moderate demand
El ectroni c
433000
400,000
400000
400000
0.35
Heavy demand
780,000
740000
780000
780000
The best choice is Pneumatic, $475,000. (Decision trees, moderate) {AACSB: Analytic
Skills}
492
7 4.
A toy manufacturer has three different mechanisms that can be installed in a doll that it
sells. The different mechanisms have three different setup costs (overheads) and variable
costs and, therefore, the profit from the dolls is dependent on the volume of sales. The
anticipated payoffs are as
follows.
Probability
Wind-up action
Pneumatic action
Electrical action
Light Demand
0.25
$325,000
$300,000
-$400,000
Moderate Demand
0.45
$190,000
$420,000
$240,000
Heavy Demand
0.3
$170,000
$400,000
$800,000
a. What is the EMV of each decision alternative?
b. Which action should be selected?
c. What is the expected value with perfect information?
d. What is the expected value of perfect information?
(a) Wind-up=.25*$325,000 + .45*$190,000 + .3*$170,000 = $217,750; Pneumatic
=.25*$300,000 + .45*$420,000 + .3*$400,000 = $384,000; and Electrical = .25*($400,000) +
.45*$240,000 + .3*$800,000 = $248,000. (b) Pneumatic has the best EMV, at
$384,000. (c) EVwPI is .25*$325,000 + .45* $420,000 + .3* $800,000 = $510,250;
(d) EVPI =$510,250 $384,000 = $126,250.
(Types of decision-making environments, moderate) {AACSB: Analytic Skills}
75.
A local business owner is a bit uncertain of the demand forecast, and is timidly
approaching the capacity decision for a business he is about to open. Here's how he
describes the decisions that confront him over the next two years.
"First, I have to choose between building a large plant initially and building a small one
that has room to expand. Or I could stay on the sidelines now, and enter with a business
next year. That one, too, could be the large version or the small. If I build small, then
after one year, I can review
how good business was, and decide whether to expand. If I build large, there is no further
option to enlarge."
Do not concern yourself with probabilities or payoff values .Simply draw the tree that
illustrates the manager's decision alternatives and the chance events that go along with
them. Use standard symbols for decision tree construction, and label all parts of your
diagram carefully. To simplify, assume that business in the first year, and in the second,
can be only "good" or "bad."
SEE SOLUTION ON NEXT PAGE.
493
Second year "good"
0
Business "good"
Second
year
"bad"
Build Large
0
B
u
s
i
n
e
s
s
"
b
a
d
"
Expand
Business "good"
Don't expand
Build small
0
Second
year
"good"
0
Secon
d year
"bad"
0
Second
year
"good"
0
S
e
c
o
n
d
a
r
"
b
a
d
"
0
y
e
Second
year
"good"
0
Expand
Second
year
"good" 0
Don't expand
Second year "bad"
0
Second
year
"good" 0
Build large
Second year "bad"
0
S
econd year
"good"
Business
"good"
0
1
B
u
i
l
d
s
m
a
l
l
Second year "bad"
Wait a
year
B
u
0
0
D
o
Second
year
"good" 0
Second year "bad"
0
econd year
"good"
Business "bad"
0
S
1
B
u
i
l
d
s
m
a
l
l
Second year "bad"
0
Don't
build
(Decision trees, moderate) {AACSB:
Analytic Skills}
494
Second
year
"ba0
d"
Business "bad"
0
7 6.
Steve Gentry, the operations manager of Baja Fabricators, wants to purchase a new
profiling machine (it cuts compound angles on the ends of large structural pipes used in
the fabrication yard). However, because the price of crude oil is depressed, the market for
such equipment is down. Steve believes that the market will improve in the near future
and that the company should expand its capacity. The table below displays the three
equipment options he is currently considering, and the profit he expects each one to yield
over a two-year period. The consensus forecast at Baja is that there is about a 30%
probability that the market will pick up "soon" (within
3 to 6 months) and a 70% probability that the improvement will come "later" (in 9 to 12
months, perhaps longer).
Equipment Option
Manual Machine
NC Machine
CNC Machine
Profit from Capacity Investment (in Dollars)
Market picks up
Market picks up
-120000
210000
140000
160000
200000
-200000
a. Calculate the expected monetary value of each decision
alternative. b. Which equipment option should Steve take?
(a) The expected monetary values are: "Manual machine" $111,000, "NC Machine"
$154,000, and "CNC Machine" -$80,000. (b) Based upon the EMV criterion, Baja
should purchase an NC machine. (Types of decision-making environments, easy)
{AACSB: Analytic Skills}
77.
Miles is considering buying a new pickup truck for his lawn service firm. The economy in
town seems to be growing, and he is wondering whether he should opt for a subcompact,
compact, or full-size pickup truck. The smaller truck would have better fuel economy, but
would sacrifice capacity and some durability. A friend at the Bureau of Economic
Research told him that there is a
30% chance of lower gas prices in his area this year, a 20% chance of higher gas prices,
and a 50%
chance that gas prices will stay roughly unchanged. Based on this information, Miles
has developed a decision table that indicates the profit amount he would end up with
after a year for each combination of truck and gas prices.
Alternatives
probability
Subcompact
Compact
Full size
Lower gas prices
.3
16,000
15,000
18,000
States of
nature
Gas prices unchanged Higher gas prices
.5
.2
21,000
23,000
20,000
22,000
19,000
6,000
Calculate the expected monetary value for each decision alternative. Which decision
yields the highest EMV?
The expected values are: subcompact $19,900, compact $18,900, and full size
$16,100. The highest EMV is that of the subcompact truck. (Types of decisionmaking environments, moderate) {AACSB: Analytic Skills}
495
78.
Earl Shell owns his own Sno-Cone business and lives 30 miles from a beach resort. The
sale of
Sno-Cones is highly dependent upon his location and upon the weather. At the resort, he
will profit
$110 per day in fair weather, $20 per day in foul weather. At home, he will profit $70 in
fair weather, $50 in foul weather. Assume that on any particular day, the weather
service suggests a
60% chance of fair weather.
a. Construct Earl's payoff table.
b. What decision is recommended by the expected value criterion?
c. What is the EVPI?
(a)The payoff table is
Profit
Fair weather
Foul weather
Probability = 0.6 Probability = .
4
Sell at the resort
110
20
Sell at home
70
50
(b) the EMV for sell at the resort = .6*110 + .4*20 = 74; The EMV for sell at home = .
6*70 +
.3*50 = 62. The better value is $74, so Earl should sell at the
resort. (c) EVwPI = .6*110 + .4*50 = $86; EVPI = $86 - $74 =
$12.
(Types of decision-making environments, moderate) {AACSB: Analytic Skills}
79.
The campus bookstore sells stadium blankets embroidered with the university crest. The
blankets must be purchased in bundles of one dozen each. Each blanket in the bundle costs
$65, and will sell for $90. Blankets unsold by homecoming will be clearance priced at $20.
The bookstore estimates that demand patterns will follow the table below.
a. Build the decision table.
b. What is the maximum expected value?
c. How many bundles should be purchased?
Demand level
1 bundle
2 bundles
3 bundles
4 bundles
Probability
10 percent
30 percent
50 percent
10 percent
(a) See the table below; (b) the maximum expected value is $516; (c) the bookstore
should order 2 cases.
Profit
Demand 1 Demand 2 Demand 3 Demand 4
EMV
Probabilit
0.1
0.3
0.5
0.1
Order 1
300
300
300
300
300
Order 2
-240
600
600
600
Maximum 516
Order 3
-780
60
900
900
480
Order 4
-1320
-480
360
1200
24
(Types of decision-making environments, moderate) {AACSB: Analytic Skills}
496
8 0.
Miles is considering buying a new pickup truck for his lawn service firm. The economy in
town seems to be growing, and he is wondering whether he should opt for a subcompact,
compact, or full-size pickup truck. The smaller truck would have better fuel economy, but
would sacrifice capacity and some durability. A friend at the Bureau of Economic
Research told him that there is a
30% chance of lower gas prices in his area this year, a 20% chance of higher gas prices,
and a 50%
chance that gas prices will stay roughly unchanged. Based on this information, Miles
has developed a decision table that indicates the profit amount he would end up with
after a year for each combination of truck and gas prices. Develop a decision tree for
this situation and indicate which type of truck he should select.
Alternatives
probability
Subcompact
Compact
Full size
Lower gas prices
.3
16,000
15,000
24,000
States of
nature
Gas prices unchanged Higher gas prices
.5
.2
19,000
21,000
20,000
22,000
19,000
6,000
The tree appears in the drawing below. The highest expected value decision
alternative is the compact truck, at $18,900, as shown in the POM for Windows
solution.
(Decision trees, easy) {AACSB: Analytic Skills}
497
8 1.
Daily sales of bread by Salvador Monella's Baking Company follow the historical pattern
shown in the table below. It costs the bakery 50 cents to produce a loaf of bread, which
sells for 95 cents. Any bread unsold at the end of the day is sold to the parish jail for 25
cents per loaf. Construct the decision table of conditional payoffs. How many loaves
should Sal bake each day in order to maximize contribution?
Demand
Probability
400
.20
500
.20
600
.40
700
.15
800
.05
The Excel OM decision table and solution appear below. The best expected value
is $228, which occurs with the decision to bake 600 loaves.
EMV
180
211
228
217
Maximum
195.5
(Types of decision-making environments, moderate) {AACSB: Analytic Skills}
82. Earl Shell owns his own Sno-Cone business and lives 30 miles from a beach resort. The
sale of
Sno-Cones is highly dependent upon his location and upon the weather. At the resort, he
will profit
$120 per day in fair weather, $10 per day in bad weather. At home, he will profit $70
in fair weather, $55 in bad weather. Assume that on any particular day, the weather
service suggests a
40% chance of foul weather.
a. Construct Earl's decision tree.
b. What decision is recommended by the expected value criterion?
Resort has a higher EMV ($76) than Home
(Decision trees, moderate) {AACSB: Analytic Skills}
498
8 3.
The campus bookstore sells highlighters that it purchases by the case. Cost per case,
including shipping and handling, is $200. Revenue per case is $350. Any cases unsold will
be discounted and sold at $175. The bookstore has estimated that demand will follow the
pattern below
Demand level
10 cases
11 cases
12 cases
13 cases
14 cases
Probability
20 percent
20 percent
40 percent
15 percent
5 percent
a. Construct the bookstore's payoff table.
b. How many cases should the bookstore stock in order to maximize profit?
c. How would your answer differ if the clearance price were not $175 per case but $225
per case? (It is not necessary to re-solve the problem to answer this.)
(a) The Excel OM table is below. (b) The highest EMV is 1705, from stocking 13
cases. (c) If the clearance price exceeds the case cost, there will be no disincentive to
stocking the maximum demand level, 14 cases.
Profit Demand 10 Demand 11 Demand 12 Demand 13 Demand 14
EMV
Probabilit 0.2
0.
0.
0.15
0.05
y Stock 10
2
4
1500
1500
1500
1500
1500
1500
Stock 11
1475
1650
1650
1650
1650
1615
Stock 12
1450
1625
1800
1800
1800
1695
Stock 13
1425
1600
1775
1950
1950 Maximu
1705
m
Stock 14
1400
1575
1750
1925
2100
1688.7
5
(Types of decision-making environments, moderate) {AACSB: Analytic Skills}
499
8 4.
Bratt's Bed and Breakfast, in a small historic New England town, must decide how to
subdivide (remodel) the large old home that will become their inn. There are three
alternatives: Option A would modernize all baths and combine rooms, leaving the inn
with four suites, each suitable for two to four adults. Option B would modernize only the
second floor; the results would be six suites, four for two to four adults, and two for two
adults only. Option C (the status quo option) leaves all walls intact. In this case, there are
eight rooms available, but only two are suitable for four adults, and four rooms will not
have private baths. Below are the details of profit and demand patterns that will
accompany each option. Which option has the highest expected value?
Annual profit under
various demand patterns
nd
Branch 2, which represents Option B-Modernize 2
value,
floor, has the highest expected
$74,000. This cannot be done as a decision table. POM for Windows solution follows.
(Decision trees, moderate) {AACSB: Analytic Skills}
500