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 exp ected 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 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.
outcome. Maximax is the optimistic criterion. It maximizes the maximum outcome.
10.
outcome. Maximin is the pessimistic criterion. It maximizes the minimum outcome.
END-OF-MODULE PROBLEMS
States of Nature
.1
Alternatives
Very Favorable Market
Large plant
$275,000
Small plant Overtime
Unfavorable Market
Row Minimum
Row Maximum
$100,000
$150,000 – $150,000
150,000 – 150,000
275,000
75,000
$200,000
$60,000
$10,000 – $10,000
10,000 – 10,000
200,000
83,333
$100,000
$40,000
$1,000 – $1,000
1,000 – 1,000
100,000
46,333
$0
$0
$0
0
0
0
Do nothing
Average Market
maximin
(a) (b) (c) .2
(a)
equally likely
Large plant Do nothing nothin g Small plant Market Size of First Station
Good Market
Fair Market
Poor Market
50,000
20,000
10,000 – 10,000
–10,000
50,000
20,000
Medium Large
80,000 100,000
30,000 30,000
20,000 – 20,000 – 40,000 40,000
20,000 – 20,000 – 40,000 40,000
Very large
300,000
25,000
– 160,000 160,000
– 160,000 160,000
80,000 100,000 300,000
30,000 30,000 55,000
maximin
maximax
equally likely
Small
(b)
maximax
Row Average
Row Row Minimum Maximum
Row Average
Maximax decision: very large station
Quantitative Module A: Decision-Making Tools
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(c) (d)
Maximin decision: decision: small station Equally likely decision: very large lar ge station
A.3
EMV (large stock) 0.322 + 0.512 12 + 0.22 12.2 EMV (average stock) 0.314 14 0.510 10 0.26 10.4 EMV (small stock) 0.39 0.58 0.24 7. 5 Maximum EMV is large stock $12,200
A.4
EVPI $13,800 12,20 200 $1,600 where: $13,800 0.322 + 0.512 12 + 0.26
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) .8
EMV (Alt. 1) 0.4 80 0.312 120 0.314 140 32 36 42 110 max. EMV 90 0.390 0.390 36 27 27 90 EMV (Alt. 2) 0.4 EMV (Alt. 3) 0.450 0.370 0.315 150 20 21 45 86 EVPI 117 110 7
Expected cost of hiring full-t l-timer 0.2300 + 0.5500 + 03 . 700 $60 + 250 250 + 210 210 $520
Expected cost of part-t t-timer 0.2 0 + 0.5350 + 0.31,00 0 00 175 + 300 300 $475 $0 + 175
Thus, use part-time part -time lawyers. A.9
Large has EMV = $75,000 $75,000;; Small has EMV EMV = $83,333 $83,333;; Overtime EMV = $46,333 $46,333;; and $0 . Do nothing EMV $0. Small plant i s 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. .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
385
420
455
$341.25
112 273
56
56 329
Stoc Stock k 13 cas cases es
*
2
364
The recommended recommended course of action, based on the expected monetary value criterion, is to stock 11 cases.
Instructor’s Solutions Solutions Manual t/a Operations Operations Ma nagement
(b)
It should be intuitively intuit ively obvious obvious that if no loss loss due to overstocking is involved, one 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 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
P 0.1
6
7
300
300
Demand (Cases) 7 8 0 . 3 0.5 P P 300 30 0 300
9 300
EMV $300.00
P 0.1
350
350
350
$340.50
300
350
400
400
$352.50
90
45
210
305
300
350
400
450
$317.00
135
90
45
165
260
355
45 255
8
9
*
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)
Work (0.9) $171
– 10
190 Fail (0.1) –$16
$155
200
Do not build
–150 – 10 –160 –10
$72.5 Try pilot
Build –$90
Pilot fails (0.5)
–$10
Work (0.2) $38
190 Fail (0.8) –$128
Do not build Decide now $0
$0 Do not build
–150 – 10 –160 –10
Work (0.4) $80 –$10
200 – 10
Fail (0.6) –$90
$200
–$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. utility.
4
Instructor’s Solutions Solutions Manual t/a Operations Operations Ma nagement
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
–$0
(b) (c)
Based on the expected monetary monetar y value criterion, criter ion, Penny should elect to build a small plant. We can find the EVPI from the following: Expected Expected value under certainty certainty = (0.4) (400,000) (400,000)+ + 0.6 (0) (0) = $160,000 $160,000 Maximum EMV = $26,000 EVPI EV PI = $160,0 $160,000 00 $26,00 $26,000 0 = $134,0 $134,000 00 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
.15 (a)
Buy from A –90 –90
(b)
Switches should be purchased purcha sed from supplier A.
Quantitative Module A: Decision-Making Tools
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A.16 (a) (b)
Maximum EMV = $11,700 EVPI EV PI = 13,200 13,200 11,700 11,700 = 1,500 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 – 85 – 45 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 – 85 – 45 60 45 0 0
(c)
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 la rge wing. (d) Build large wing Build small wing Do not build
Population Trend Growth P 0.6 Stable P 0.4 150 85 – 85 – 45 60 45 0 0
EMV $56.00 $18.00 $0.00
Based on the expected monetary value criterion, she should build the large wing.
6
Instructor’s Solutions Solutions Manual t/a Operations Operations Ma nagement
Favorable
.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
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Favorable
.19 Small shop
(0.9)
$21
Unfavorable (0.1) Survey says favorable market (0.6) +$45
Favorable Large shop
(0.9)
$45
Unfavorable (0.1) No shop
Use survey $25
Small shop
–$10.2
Unfavorable (0.88) Survey says unfavorable market (0.4)
Large shop
Favorable (0.12) –$33
Unfavorable (0.88)
–$5
No shop (0.5)
$10
Unfavorable (0.5) Favorable Decide now $10
Large shop
(0.5)
$10
Unfavorable (0.5) No shop
60 – 5 = 55 –40 – 5 = –45
30 – 5 = 25 –10 – 5 = –15 60 – 5 = 55 –40 – 5 = –45 0 – 5 = –5
Favorable Small shop
–10 – 5 = –15
0 – 5 = –5
Favorable (0.12)
$25
30 – 5 = 25
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 favorable market, then th en do nothing.
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Instructor’s Solutions Solutions Manual t/a Operations Operations Ma nagement
.20
(0.9)
8,500
(0.1)
Info favorable (0.5) 8500
12000 –23000
(0.9)
500 50 0
(0.1)
2000 –13000 –3000
Gather more information 2750
(0.4)
–9,0 00
(0.6)
Info unfavorable (0.5)
12000 –23000 –23000
(0.4)
–7,0 00
(0.6)
–3000
2000 –13000 –13000 –3000
(0.7)
4,500
(0.3) Do not gather more information 4500
15000 –20000 –20000
(0.7)
500 50 0
(0.3)
5000 –10000 –10000
0
Your advice should be to not gather additional information and to build a large video section. .21 (a)
5,000
Major 10,000
Minor 10,000
Market favorable
(0.5)
Market unfavorable
(0.5)
Market favorable
(0.5)
Market unfavorable
(0.5)
Do nothing
(b)
100,000 –90,000
40,000 –20,000
0
EMV (major renovation) renovation ) 5,000 EMV (minor renovation) renovation) 10,000* * best decision is minor renovation
Quantitative Module A: Decision-Making Tools
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Good (1/3)
.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) (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 Solutions Manual t/a Operations Operations Ma nagement
