MODULE A
DISCUSSION QUESTIONS
4.
EMV is defined as the expected monetary value. The EMV is the expected or average return that we
would realize if we were to repeat the decision an infinite number of times.
“Expected value under certainty” is the expected or average return that we would realize if we
were to repeat the decision an infinite number of times, each time having “perfect” or complete
information and making the “best” possible decision based on that information. EVPI is defined as
the expected value of perfect information. EVPI is equal to the difference between EMV (the
expected or average return given that we were to make the decision based on current or available
information) and “expected value under certainty” and is the maximum amount 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.
9.
Maximax is the optimistic criterion. It maximizes the maximum outcome.
10.
Maximin is the pessimistic criterion. It maximizes the minimum outcome.
END-OF-MODULE PROBLEMS
A.1
States of Nature
Alternatives
Very
Favorable
Market
Average
Market
Large plant
$275,000
Small plant
Overtime
Unfavorable
Market
Row
Minimum
Row
Maximum
$100,000
–$150,000
–150,000
275,000
75,000
$200,000
$60,000
–$10,000
–10,000
200,000
83,333
$100,000
$40,000
–$1,000
–1,000
100,000
46,333
$0
$0
$0
0
0
0
Do nothing

maximin
A.2
(a)
(b)
(c)
Large plant
Do nothing
Small plant
(a)
Market
Size
of First
Station
Good
Market
Fair
Market
Poor
Market
Small
Medium
Large
50,000
80,000
100,000
20,000
30,000
30,000
–10,000
–20,000
–40,000
–10,000
Very large
300,000
25,000
–160,000
(b)

maximax
Row
Row
Minimum Maximum
Row
Average

equally likely
Row
Average
–160,000
50,000
80,000
100,000
300,000
20,000
30,000
30,000
55,000

maximin

maximax

equally likely
–20,000
–40,000
Maximax decision: very large station
Quantitative Module A: Decision-Making Tools
1
(c)
(d)
Maximin decision: small station
Equally likely decision: very large station
A.3
EMV (large stock)  0.322 + 0.512 + 0.22  12.2
EMV (average stock)  0.314  0.510  0.26  10.4
EMV (small stock)  0.39  0.58  0.24  7.5
Maximum EMV is large stock  $12,200
A.4
EVPI  $13,800  12,200  $1,600 where: $13,800  0.322 + 0.512 + 0.26
A.5
EMV (assembly line)   0.4$10,000   0.6$40,000  $28,000
EMV (new plant)   0.4 $100,000   0.6$600,000  $320,000
EMV (nothing)  0
Select the new plant option.
A.6
EVPI  $364,000  $320,000  $44,000
A.7
(a)
(b)
A.8
EMV (Alt. 1)  0.480  0.3120  0.3140  32  36  42  110  max. EMV
EMV (Alt. 2)  0.490  0.390  0.390  36  27  27  90
EMV (Alt. 3)  0.450  0.370  0.3150  20  21  45  86
EVPI  117  110  7
Expected cost of hiring full-timer  0.2300  + 0.5500  + 0.3 700 
 $60 + 250 + 210  $520
Expected cost of part-timer  0.2 0  + 0.5350  + 0.31,000 
 $0 + 175 + 300  $475
Thus, use part-time lawyers.
A.9
Large has EMV = $75,000 ;
Small has EMV = $83,333 ;
Overtime EMV = $46,333 ; and
Do nothing EMV  $0 .
Small plant is best decision.
A.10 EMV (major expansion)  150,000*
EMV (minor expansion)  50,000
EMV (do nothing)  0
* Therefore, the company should do the major expansion.
A.11 (a)
Stock 11 cases
Demand
11 Cases
P  0.45
385
Demand
12 Cases
P  0.35
385
Demand
13 Cases
P  0.20
385
EMV
$385.00
Stock 12 cases
385
420
420
$379.05
420
455
$341.25
56
329
Stock
*
2
13 cases
385
112
56
273
364
The recommended course of action, based on the expected monetary value criterion, is to stock 11 cases.
Instructor’s Solutions Manual t/a Operations Management
(b)
It should be intuitively obvious that if no loss due to overstocking is involved, one should
always carry the maximum stock. This observation is confirmed by the following table.
Demand
11 Cases
P  0.45
385
385
385
Stock 11 cases
Stock 12 cases
Stock 13 cases
*
Demand
12 Cases
P  0.35
385
420
420
Demand
13 Cases
P  0.20
385
420
455
EMV
$385.00
$404.25
$411.25
The recommended course of action, based on the expected monetary value criterion, is to stock the maximum of
13 cases.
A.12 Profit from each case sold: $95  $45  $50 . Loss from each case produced but not sold: $45.
Production
(Cases)
6
6
P  0.1
300
7
300
Demand (Cases)
7
8
P  0.3
P  0.5
300
300
9
P  0.1
300
EMV
$300.00
350
350
350
$340.50
350
400
400
$352.50
400
450
$317.00
 45
255
8
9
*
300
90
 45
210
305
300
135
350
90
 45
165
260
355
She should manufacture eight cases per month
Quantitative Module A: Decision-Making Tools
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A.13 Note: All dollar values in 1,000s
Build
$155
Pilot works (0.5)
$155
Work (0.9)
$171
200
– 10
190
Fail (0.1)
–$16
–150
– 10
–160
–10
Work (0.2)
$38
200
– 10
190
–150
– 10
–160
Do not build
$72.5
Try
pilot
Build
–$90
Pilot fails (0.5)
–$10
Fail (0.8)
–$128
Do not build
Decide
now
–$10
$0
$0
Do not build
–10
Work (0.4)
$80
$200
Fail (0.6)
–$90
–$150
$0
The recommended strategy (EMV = 72.5) is

Try pilot

If pilot is success: build plant
If pilot is failure: do not build plant
Note: All costs/revenues have been entered at the end of the branches of the tree. Although this
procedure is not required in this example due to an implicit assumption of linear utility, it is required
when using a more general representation of utility.
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Instructor’s Solutions Manual t/a Operations Management
A.14 Note: All dollar values are in 1,000s.
Favorable (0.4)
$160
(a)
Build large
–20
400
–$20
Unfavorable (0.6)
–$180
–300
Favorable (0.4)
$32
Build small
26
80
$26
Unfavorable (0.6)
–$6
–10
Favorable (0.4)
$0
Do not build
0
0
$0
Unfavorable (0.6)
–$0
(b)
(c)
Based on the expected monetary value criterion, Penny should elect to build a small plant.
We can find the EVPI from the following:
Expected value under certainty = (0.4) (400,000) + 0.6 (0) = $160,000


Maximum EMV = $26,000
EVPI = $160,000  $26,000 = $134,000

1% Defective
(0.7)
–50
3% Defective
(0.2)
–150
5% Defective
(0.1)
–250
–113
1% Defective
(0.3)
–50
+37 saving
Buy from B
–150
3% Defective
(0.4)
–150
5% Defective
(0.3)
–250
A.15 (a)
Buy from A
–90
–90
(b)
0
Switches should be purchased from supplier A.
Quantitative Module A: Decision-Making Tools
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A.16 (a)
(b)
Maximum EMV = $11,700
EVPI =13,200  11,700 =1,500
A.17 Note: All dollar values are in 1,000s.
Grow
(a)
150
Build large
Stable
–85
Grow
60
Build small
Stable
–45
Grow
0
Do not build
Stable
(b)
0
Build large wing
Build small wing
Do not build
Population Trend
Growth
Stable
150
–85
60
–45
0
0
Build large wing
Build small wing
Do not build
Population Trend
Growth P  0.5
Stable P  0.5
150
–85
60
–45
0
0
(c)
a
f
a
f
EMV
$32.50
$7.50
$0.00
Based on the expected monetary value criterion with the assumption that the states of nature
are equally likely, she should build the large wing.
(d)
Population Trend
Growth P  0.6
Stable P  0.4
150
–85
60
–45
0
0
a
Build large wing
Build small wing
Do not build
f
a
f
EMV
$56.00
$18.00
$0.00
Based on the expected monetary value criterion, she should build the large wing.
6
Instructor’s Solutions Manual t/a Operations Management
Favorable
A.18
Small shop
Unfavorable
Favorable
Survey says favorable
Large shop
Unfavorable
No shop
Use survey
Favorable
Small shop
Unfavorable
Favorable
Survey says unfavorable
Large shop
Unfavorable
No shop
Favorable
Small shop
Unfavorable
Favorable
Decide now
Large shop
Unfavorable
No shop
Quantitative Module A: Decision-Making Tools
7
A.19
Small shop
Survey says
favorable market (0.6)
+$45
Large shop
Favorable (0.9)
$21
Unfavorable (0.1)
Favorable (0.9)
$45
Unfavorable (0.1)
No shop
Use survey
$25
$25
Survey says
unfavorable market (0.4)
–$5
Small shop
Large shop
Decide now
$10
Large shop
No shop
–10 – 5 = –15
60 – 5 = 55
–40 – 5 = –45
0 – 5 = –5
Favorable (0.12)
–$10.2
Unfavorable (0.88)
Favorable (0.12)
–$33
Unfavorable (0.88)
No shop
Small shop
30 – 5 = 25
30 – 5 = 25
–10 – 5 = –15
60 – 5 = 55
–40 – 5 = –45
0 – 5 = –5
Favorable (0.5)
$10
Unfavorable (0.5)
Favorable (0.5)
$10
Unfavorable (0.5)
30
–10
60
–40
0
The optimal strategy is to use the survey. If the survey indicates a favorable market, then build a
large shop. If the survey does not indicate a favorable market, then do nothing.
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Instructor’s Solutions Manual t/a Operations Management
A.20
(0.9)
8,500
(0.1)
Info favorable (0.5)
8500
12000
–23000
(0.9)
500
(0.1)
2000
–13000
–3000
Gather
more information
2750
(0.4)
–9,000
(0.6)
Info unfavorable (0.5)
–3000
12000
–23000
(0.4)
–7,000
(0.6)
2000
–13000
–3000
(0.7)
4,500
(0.3)
Do not gather
more information
4500
15000
–20000
(0.7)
500
(0.3)
5000
–10000
0
Your advice should be to not gather additional information and to build a large video section.
A.21 (a)
5,000
Minor
10,000
Market favorable
(0.5)
Market unfavorable (0.5)
Do nothing
(b)
(0.5)
Market unfavorable (0.5)
Major
10,000
Market favorable
100,000
–90,000
40,000
–20,000
0
EMV (major renovation)  5,000
EMV (minor renovation)  10,000*
* best decision is minor renovation
Quantitative Module A: Decision-Making Tools
9
Good (1/3)
A.22
Small
Fair (1/3)
20,000
Poor (1/3)
Good (1/3)
Medium
Fair (1/3)
30,000
Poor (1/3)
50,000
20,000
–10,000
80,000
30,000
–20,000
55,000
Good (1/3)
Large
Fair (1/3)
30,000
Poor (1/3)
Good (1/3)
Very large
Fair (1/3)
55,000
Poor (1/3)
10
100,000
30,000
–40,000
300,000
25,000
–160,000
Instructor’s Solutions Manual t/a Operations Management