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
E ( x)   xP( x)
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
Large plant
Favorable
Demand
$ 200,000
UnFavorable
-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
Unfavorable
-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
Unfavorable
-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
200,000
.5
Fav
Unfav
Large
.5
10,000
Fav
40,000
-180,000
100,000
.5
Small
40,000
.5
Unfav
No
0
-20,000
IB: Opportunity Loss
OL = Best payoff for each outcome
- Actual
Payoff Table
Action
UnFavorable
-180,000
Small plant
Favorable
Demand
$ 200,000=
BEST IN COL
100,000
No plant
0
0 = BEST IN
COLUMN
Large plant
-20,000
OL Table
Action
Large plant
Small plant
No plant
Favorable
Demand
$ 200,000
-200,000= 0
200,000
-100,000=
100,000
200,000
-0=200,000
UnFavorable
0-(-180,000)=
180,000
0-(-20,000)=
20,000
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
Unfavorable
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
Unfavorable
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
Unfavorable
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
Large plant
Small plant
No plant
Favorable
Demand
$
200,000=MAX
IN ROW
100,000= MAX
IN ROW
UnFavorable
-180,000
0= MAX IN
ROW
0
-20,000
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
Large plant
Favorable
Demand
$ 200,000
UnFavorable
-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
Large plant
Small plant
No plant
Favorable
Demand
$ 200,000
-200,000= 0
200,000
-100,000=
100,000
200,000
-0=200,000
UnFavorable
0-(-180,000)=
180,000
0-(-20,000)=
20,000
0-0=0
Minimax Step 2
For each act, find maximum
opportunity loss
OL Table: Step 2
Action
Favorable
Demand
0
UnFavorable
180,000=MAX
IN ROW
Small plant
100,000=MAX
IN ROW
20,000
No plant
200,000=MAX
IN ROW
0
Large plant
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