Answers to Homework Chapter 3
BSBN2120, J. Wang, 100 pts
Decision
Alternatives
Page 101 3-17 (7 pts).
(a) The type of the decision making is decision making under uncertainty, because the
probability of each state of nature is not known.
(b) Since he is a ‘very optimistic decision maker, Ken should use Maximax as his
decision criterion.
(c) The row maximums:
States of Nature
Favorable
Unfavorable
Row
Market
Market
Maximums
Sub 100
$300,000
-$200,000
$300,000
Oiler J
$250,000
-$100,000
$250,000
Texan
$ 75,000
-$ 18,000
$ 75,000
The maximum of the row maximums is $300,000 that is associated with Sub 100.
Therefore, the decision with the Maximax criterion is Sub 100.
Decision
Alternatives
3-18 (7 pts).
Since Bob enjoys his pessimistic attitude about business and oil industry, he
should use Maximin as the decision criterion.
The row minimums:
States of Nature
Favorable
Unfavorable
Row
Market
Market
Minimums
Sub 100
$300,000
-$200,000
-$200,000
Oiler J
$250,000
-$100,000
-$100,000
Texan
$ 75,000
-$ 18,000
-$ 18,000
The maximum of the row minimums is -$18,000 that is associated with Texan.
Therefore, the decision with the Maximin criterion is Texan.
3-19 (7 pts).
(a) Since the probability for each state of nature is given, the decision making model is
decision making under risk, and EMV (expected monetary value) is used as the criterion.
(b) The EMV for each decision alternative:
1
State of Nature
Favorable
Market
Unfavorable
Market
0.7
0.3
Sub 100
$300,000
-$200,000
Oiler J
$250,000
-$100,000
Texan
$ 75,000
-$ 18,000
Alternatives
Probability
EMV
300,0000.7 + (-200,000)0.3
= 150,000
250,0000.7 + (-100,000)0.3
= 145,000
75,0000.7 + (-18,000)0.3
= 47,100
The highest EMV is $150,000 that is associated with Sub 100. Therefore, the
optimal decision is Sub 100.
3-22 (12 pts)
(a) Payoff (net gain) Table and EMV’s:
Investment
Alternatives
Stock market
CD
Probability
Good
$1,400
$900
0.4
Market Condition
Fair
$800
$900
0.4
Poor
$0
$900
0.2
EMV
880
900
(b) Since 900>880, the best decision is to deposit the money in CD with expected gain of
$900.
3-23 (12 pts)
(a) The column maximums:
Investment
Alternatives
Good
Stock market
$1,400
Bank deposit
$900
Probability
0.4
Column Max
$1,400
Market Condition
Fair
$800
$900
0.4
$900
Poor
$0
$900
0.2
$900
EMV
880
900
$1,100
The expected value with perfect information, EVwPI, is:
EVwPI = $1,400*0.4 + $900*0.4 + 900*0.2 = $1,100.
The best expected value without the information, EVw/oPI, from the newsletter is
$900 as we have calculated in 3-21 (b). That is, EVw/oPI = 900.
Therefore, the expected value of perfect information, EVPI, is
EVPI = EVwPI - EVw/oPI = $1,100 - $900 = $200.
So, Allen would be willing to pay at most $200 for the newsletter.
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(b) Yes, the annual return rate change would change the amount Allen is willing to pay.
The expected value with perfect information is now changing to:
EVwPI = $1,100*0.4 + $900*0.4 + 900*0.2 = $980.
EMV for alternative “stock market” is: 1,100*0.4+800*0.4+0*0.2=$760. EMV
for alternative “bank deposit” is 900*0.4+900*0.4+900*0.2=$900. The max EMV=$900,
which is also Vw/oPI.
The expected value of perfect information is :
EVPI = EVwPI - EVw/oPI = $980 - $900 = $80.
So, Allen would be willing to pay at most $80 for a newsletter.
3-24. (11 pts)
(a) The given payoff (profit) table, and column maximums.
Decision
Alternatives
States of Nature
Strong market
Large facility
550,000
Medium facility
300,000
Small facility
200,000
No facility
0
Column maximum
550,000
Fair market
110,000
129,000
100,000
0
129,000
Poor market
-310,000
-100,000
-32,000
0
0
The opportunity loss table of the above payoff table:
Decision
Alternatives
States of Nature
Large facility
Medium facility
Small facility
No facility
Strong market
0
250,000
350,000
550,000
Fair market
19,000
0
29,000
129,000
Poor market
310,000
100,000
32,000
0
(b) The row maximums of the above opportunity loss table:
Row
Strong market Fair market Poor market Maximum
Large facility
0
19,000
310,000
310,000
Medium facility
250,000
0
100,000
250,000
Small facility
350,000
29,000
32,000
350,000
No facility
550,000
129,000
0
550,000
The minimum of the row maximums is 250,000. So, the minimax regret decision
is Medium facility.
Decision
Alternatives
States of Nature
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3-25. (16 pts)
Decision:
How many cases of BC-6 to order and stock every week.
Decision alternatives: Stocking 11 cases, 12 cases, or 13 cases.
States of nature:
Weekly demand of 11 cases, 12 cases, or 13 cases.
Given:
Net Profit = $35/case; Cost = $56/case.
So, revenue from selling a case is: $35+$56=$91/case sold.
Note: There is no penalty cost in terms of ($ out of pocket) for shortage, though there is
opportunity cost of shortage due to lost sales.
Payoff is in terms of net profit:
Profit = $in - $out = Revenue – Cost, that is,
Profit = $91*(number of cases sold) - $56*(number of cases ordered/stocked).
to order
(a) Payoff Table:
11 cases
12 cases
13 cases
11 cases
Prob=0.45
91*11-56*11 =385
91*11-56*12 =329
91*11-56*13 =273
Weekly Demand
12 cases
Prob=0.35
91*11-56*11 =385
91*12-56*12 =420
91*12-56*13 =364
to order
(b) EMV for each decision alternative:
Weekly Demand
11 cases
12 cases
13 cases
Prob=0.45 Prob=0.35 Prob=0.2
11 cases
12 cases
13 cases
385
329
273
385
420
364
385
420
455
13 cases
Prob=0.2
91*11-56*11 =385
91*12-56*12 =420
91*13-56*13 =455
EMV
385*0.45+385*0.35+385*0.3=
385*
329*0.45+420*0.35+420*0.2=
379.05
273*0.45+364*0.35+455*0.2=
341.25
The maximum EMV is 385 that is associated with 11 cases. So, the best decision
is stocking 11 cases.
to order
(c) If the unsold cases can be sold later, then the new payoff table would be:
Weekly Demand (States of Nature)
11 cases
12 cases
13 cases
Decision
Alternatives
Prob=0.45
Prob=0.35
Prob=0.2
11 cases
385
385
385
12 cases
420
420
420
13 cases
455
455
455
So, stocking 13 cases is the best alternative.
EMV
385
420
455
Or, without needing to generate the above payoff table, it is pretty obvious that
stocking 13 cases that is the largest possible weekly demand is the best decision, since
there is no penalty of overstocking but there is penalty of under-stocking of losing sales.
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3-30. (28 pts)
(a) Payoff table
Decision
alternatives
Size of 1st Station
Small
Medium
Large
Very large
(b) Maximax (5 pts)
Row maximums:
Good
Size of 1st Station
Market
Small
$50,000
Medium
$80,000
Large
$100,000
Very large
$300,000
States of Nuture
Good
Fair
Poor
Market
Market
Market
$50,000
$20,000 $10,000
$80,000
$30,000 $20,000
$100,000
$30,000 $40,000
$300,000
$25,000 $160,000
Fair
Poor
Market
Market
$20,000 $10,000
$30,000 $20,000
$30,000 $40,000
$25,000 $160,000
Row Maximums
$50,000
$80,000
$100,000
$300,000
The maximum of the four row maximums is $300,000, and the decision is
therefore Very Large.
(c) Maximin (5 pts)
Row minimums:
Size of 1st Station
Small
Medium
Large
Very large
Good
Market
$50,000
$80,000
$100,000
$300,000
Fair
Poor
Market
Market
$20,000 $10,000
$30,000 $20,000
$30,000 $40,000
$25,000 $160,000
Row
Minimums
$10,000
$20,000
$40,000
$160,000
The maximum of the four row minimums is $10,000, and the decision is
therefore Small.
(d) Equally Likely (6 pts)
Good
Fair
Poor
Market
Market
Market
Small
$50,000
$20,000 $10,000
Medium
$80,000
$30,000 $20,000
Large
$100,000
$30,000 $40,000
Very large
$300,000
$25,000 $160,000
For example, for alternative ‘Small’:
Size of 1st Station
Averages
$20,000
$30,000
$30,000
$55,000
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Average = ($50,000 + $20,000 + (-$10,000)) / 3
= $60,000 / 3
= $20,000.
The maximum of row averages is $55,000, and the decision is therefore Very
Large.
(e) Realism (Hurwicz), =0.8 (6 pts)
Good
Fair
Poor
Hurwicz
Market
Market
Market
Values
Small
$50,000
$20,000 $10,000
$38,000
Medium
$80,000
$30,000 $20,000
$60,000
Large
$100,000
$30,000 $40,000
$72,000
Very large
$300,000
$25,000 $160,000
$208,000
For example, for the row of alternative ‘Small’:
Hurvicz value = (row maximum)   + (row minimum)  (1-)
= $50,000  0.8 + (-$10,000)  (1-0.8)
= $50,000  0.8 + (-$10,000)  0.2
= $40,000 - $2,000
= $38,000.
Size of 1st Station
The maximum of the row Hurwicz values is $208,000, and the decision is
therefore Very Large.
(f) and (g). (8 pts)
The column maximums:
Size of 1st Station
Small
Medium
Large
Very large
Column Maximum
Good
Market
$50,000
$80,000
$100,000
$300,000
$300,000
Fair
Poor
Market
Market
$20,000 $10,000
$30,000 $20,000
$30,000 $40,000
$25,000 $160,000
$30,000 $10,000
The Opportunity Loss (Regret) Table and the row maximum are:
Good
Fair
Poor
Row
Size of 1st Station
Market
Market
Market
Maximums
Small
$250,000
$10,000
$0
$250,000
Medium
$220,000
$0
$10,000
$220,000
Large
$200,000
$0
$30,000
$200,000
Very large
$0
$5,000
$150,000
$150,000
For examples, the opportunity cost for alternative ‘Small’ in ‘Good market’ is
$300,000  $50,000 = $250,000; the opportunity cost for alternative ‘Medium’ in ‘Good
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market’ is $300,000  $80,000 = $220,000; the opportunity cost for alternative ‘Very
large’ in ‘Poor market’ is ($10,000)  ($160,000) = $150,000;
The minimum of row maximums in the opportunity loss table is $150,000, and
the decision therefore is Very Large.
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