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