set 7 due april 11 set 8 due apr 18 c-3 due apr 18
Post on 21-Dec-2015
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Set 7 due April 11
• Set 8 due Apr 18
• C-3 due Apr 18
DECISION ANALYSIS:Ch 12
I. Probabilities Given A. Expected Value
B. Opportunity Loss II. Probabilities NOT Given
A. Maximax B. Maximin
C. Minimax
I.A. Expected Value
)()( xxPxE
Expected Value
x P(x) xP(x)
2 .7 1.4
3 .3 0.9
SUM 1 2.3=E(x)
Excel
Previous table as computer spreadsheet
Probability
Here: given Real life: Calculate using formulas in
previous section
Decision Example
Should we build a new plant?
Source: Render,B. and Stair,R.,
Quantitative Analysis (6th ed)
Prentice-Hall, 1997, p 100
Alternative Actions
Act 1: Build large plant Act 2:Build small plant
Act 3:Do not build new plant
OBJECTIVE: Maximize Profit
Outcomes (States of Nature)
P(x)
(1) Favorable demand .5 (2)Unfavorable
demand .5
Payoff Table
Action Favorable
Demand
Un-
Favorable
Large plant $ 200,000 -180,000
Small plant 100,000 -20,000
No plant 0 0
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
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
Summary
Act E(x)
Large plant 10,000
Small plant 40,000=MAX E(x)
No plant 0
Objective: MAX E(x)
Build small plant
DECISION TREE
Alternative Graphical Tool to re-do
same problem
Symbols in tree
Decision Node
Outcome Node
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
IB: Opportunity Loss
OL = Best payoff for each outcome
- Actual
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
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
Economic Interpretation
Loss resulting from wrong decision
Different Example
Quit job to start new business.
OL= Loss of current salary
+loss of interest income if you withdraw from savings
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
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
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
Summary
Act EOL
Large plant 90,000
Small plant 60,000=MIN EOL
No plant 100,000
Summary
Build Small Plant to MIN EOL
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
EVPI = $60,000
Suppose consultant bid $70,000>EVPI, so reject bid
CAUTION
No consultant has perfect information, so bid should be much
less than $60,000
II. Probabilities Not Given
Some managers do not trust subjective probabilities
IIA. MAXIMAX
Same example as before, but without probabilities Note: Go back to
original payoff table
MAXIMAX
Step 1: For each act, find the outcome with maximum payoff
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
Maximax Step 2
Choose the act with maximum of maximum values
Maximax
Act Maximum
Large plant 200,000= MAX of MAX
Small plant 100,000
No plant 0
Maximax Decision
Build large plant
What personality type is Maximax?
Maximax personality
• Optimistic
• Aggressive
• Risk seeker (gambler)
• Entrepreneur
II B. Maximin
Step 1: For each act, find minimum payoff
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
Maximin Step 2
Choose act with MAXImum of MINimum values
Maximin
Act Minimum
Large plant -180,000
Small plant -20,000
No plant 0=MAX
Maximin Decision
No plant
What personality type is maximin?
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
II C. Minimax
Step 1: Opportunity Loss Table
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
Minimax Step 2
For each act, find maximum opportunity loss
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
Minimax Step 3
Find MINImum of MAXimum OL
MINIMAX Step 3
Act MAX OL
Large 180,000
Small 100,000=MIN
No plant 200,000
Minimax Decision
Build small plant