set 7 due april 11 set 8 due apr 18 c-3 due apr 18
Post on 21-Dec-2015
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TRANSCRIPT
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Set 7 due April 11
• Set 8 due Apr 18
• C-3 due Apr 18
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DECISION ANALYSIS:Ch 12
I. Probabilities Given A. Expected Value
B. Opportunity Loss II. Probabilities NOT Given
A. Maximax B. Maximin
C. Minimax
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I.A. Expected Value
)()( xxPxE
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Expected Value
x P(x) xP(x)
2 .7 1.4
3 .3 0.9
SUM 1 2.3=E(x)
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Excel
Previous table as computer spreadsheet
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Probability
Here: given Real life: Calculate using formulas in
previous section
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Decision Example
Should we build a new plant?
Source: Render,B. and Stair,R.,
Quantitative Analysis (6th ed)
Prentice-Hall, 1997, p 100
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Alternative Actions
Act 1: Build large plant Act 2:Build small plant
Act 3:Do not build new plant
OBJECTIVE: Maximize Profit
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Outcomes (States of Nature)
P(x)
(1) Favorable demand .5 (2)Unfavorable
demand .5
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Payoff Table
Action Favorable
Demand
Un-
Favorable
Large plant $ 200,000 -180,000
Small plant 100,000 -20,000
No plant 0 0
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Expected Value: Large Plant
Outcome x=payoff P(x) xP(x)
Favorable 200,000 .5 100,000
Un-favorable
-180,000 .5 -90,000
E(x) 10,000
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Expected Value: Small Plant
Outcome x= payoff P(x) xP(x)
Favorable 100,000 .5 50,000
Un-favorable
-20,000 .5 -10,000
E(x) 40,000
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Summary
Act E(x)
Large plant 10,000
Small plant 40,000=MAX E(x)
No plant 0
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Objective: MAX E(x)
Build small plant
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DECISION TREE
Alternative Graphical Tool to re-do
same problem
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Symbols in tree
Decision Node
Outcome Node
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40,000
10,000
40,000
200,000
-180,000
100,000
-20,000
0
Large
Small
No
Fav
Fav
Unfav
Unfav
.5
.5
.5
.5
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IB: Opportunity Loss
OL = Best payoff for each outcome
- Actual
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Payoff Table
Action Favorable
Demand
Un-
Favorable
Large plant $ 200,000=
BEST IN COL
-180,000
Small plant 100,000 -20,000
No plant 0 0 = BEST IN
COLUMN
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OL Table
Action Favorable
Demand
Un-
Favorable
Large plant $ 200,000
-200,000= 0
0-(-180,000)=
180,000
Small plant 200,000
-100,000=
100,000
0-(-20,000)=
20,000
No plant 200,000
-0=200,000
0-0=0
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Economic Interpretation
Loss resulting from wrong decision
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Different Example
Quit job to start new business.
OL= Loss of current salary
+loss of interest income if you withdraw from savings
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EOL=Expected OL: Large Plant
Outcome OL P(OL) OL(P(OL))
Favorable 0 .5 0
Un-favorable
180,000 .5 90,000
EOL 90,000
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EOL=Expected OL: Small Plant
Outcome OL P(OL) OL(P(OL))
Favorable 100,000 .5 50,000
Un-favorable
20,000 .5 10,000
EOL 60,000
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EOL=Expected OL: No Plant
Outcome OL P(OL) OL(P(OL))
Favorable 200,000 .5 100,000
Un-favorable
0 .5 0
EOL 100,000
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Summary
Act EOL
Large plant 90,000
Small plant 60,000=MIN EOL
No plant 100,000
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Summary
Build Small Plant to MIN EOL
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Compare and Contrast
• Both E(x) and EOL give same optimal decision (Build small plant)
• Both E(x) and EOL have same arithmetic differences between optimal and alternatives
• EOL better than E(x) to interpret “do nothing” alternative
• MINIMUM EOL = EVPI = Expected Value of Perfect Information = Most you would pay someone to tell you if demand favorable or unfavorable
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EVPI = $60,000
Suppose consultant bid $70,000>EVPI, so reject bid
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CAUTION
No consultant has perfect information, so bid should be much
less than $60,000
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II. Probabilities Not Given
Some managers do not trust subjective probabilities
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IIA. MAXIMAX
Same example as before, but without probabilities Note: Go back to
original payoff table
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MAXIMAX
Step 1: For each act, find the outcome with maximum payoff
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Maximax Step 1
Action Favorable
Demand
Un-
Favorable
Large plant $ 200,000=MAX IN ROW
-180,000
Small plant 100,000= MAX IN ROW
-20,000
No plant 0= MAX IN ROW
0
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Maximax Step 2
Choose the act with maximum of maximum values
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Maximax
Act Maximum
Large plant 200,000= MAX of MAX
Small plant 100,000
No plant 0
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Maximax Decision
Build large plant
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What personality type is Maximax?
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Maximax personality
• Optimistic
• Aggressive
• Risk seeker (gambler)
• Entrepreneur
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II B. Maximin
Step 1: For each act, find minimum payoff
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Maximin Step 1
Action Favorable
Demand
Un-
Favorable
Large plant $ 200,000 -180,000=MIN OF ROW
Small plant 100,000 -20,000= MIN OF ROW
No plant 0 0=MIN OF ROW
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Maximin Step 2
Choose act with MAXImum of MINimum values
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Maximin
Act Minimum
Large plant -180,000
Small plant -20,000
No plant 0=MAX
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Maximin Decision
No plant
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What personality type is maximin?
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Maximin
• Pessimistic• Cautious• In 1961 would have advised against Moon
landing project• In 1965 would have advised against US
troops in Viet Nam• In 1996 would have advised against
deregulation of electricity companies
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II C. Minimax
Step 1: Opportunity Loss Table
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OL Table
Action Favorable
Demand
Un-
Favorable
Large plant $ 200,000
-200,000= 0
0-(-180,000)=
180,000
Small plant 200,000
-100,000=
100,000
0-(-20,000)=
20,000
No plant 200,000
-0=200,000
0-0=0
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Minimax Step 2
For each act, find maximum opportunity loss
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OL Table: Step 2
Action Favorable
Demand
Un-
Favorable
Large plant 0 180,000=MAX IN ROW
Small plant 100,000=MAX IN ROW
20,000
No plant 200,000=MAX IN ROW
0
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Minimax Step 3
Find MINImum of MAXimum OL
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MINIMAX Step 3
Act MAX OL
Large 180,000
Small 100,000=MIN
No plant 200,000
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Minimax Decision
Build small plant