Decision Analysis

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Decision Analysis OPS 370

description

Decision Analysis. OPS 370. Decision Theory. A. B. a. b. c. d. e. Decision Theory. A. a. b. c. . Decision Theory. Steps: 1. A. B. 2. A. 3. 4. 5. Payoff Table. Shows Expected Payoffs for Various States of Nature. Decision Environments. A. a. B. a. C. - PowerPoint PPT Presentation

Transcript of Decision Analysis

Page 1: Decision Analysis

Decision Analysis

OPS 370

Page 2: Decision Analysis

Decision Theory

• A. • B.

– a.– b.– c.– d.– e.

Page 3: Decision Analysis

Decision Theory

• A.

– a.

– b. – c.

Page 4: Decision Analysis

Decision Theory• Steps:

– 1. • A. • B.

– 2. • A.

– 3.

– 4.

– 5.

Page 5: Decision Analysis

Payoff Table

• Shows Expected Payoffs for Various States of Nature

Low Moderate HighIndoor 500 1200 2000

Drive-In 700 1500 1250Both -2000 -1000 3000

Demand for Ice Cream

Type of Parlor

* Payoffs in Predicted Profit Per Month

Page 6: Decision Analysis

Decision Environments

• A. – a.

• B.– a.

• C. – a.

Page 7: Decision Analysis

Decision Making

• A. – a. – b.

Low Moderate HighIndoor 500 1200 2000

Drive-In 700 1500 1250Both -2000 -1000 3000

Demand for Ice Cream

Type of Parlor

* Payoffs in Predicted Profit Per Month

Page 8: Decision Analysis

Decision Making

• Under Uncertainty– Four Decision Criteria– 1.

• A.

• B. – 2.

• A.

• B.

Page 9: Decision Analysis

Decision Making

• Under Uncertainty– 3.

• A.

• B. – 4.

• A.

• B.

Page 10: Decision Analysis

Example

• Maximin– Indoor – Drive-In – Both – Choose “Best of Worst”

Low Moderate HighIndoor 500 1200 2000

Drive-In 700 1500 1250Both -2000 -1000 3000

Demand for Ice Cream

Type of Parlor

* Payoffs in Predicted Profit Per Month

Page 11: Decision Analysis

Example

• Maximax– Indoor – Drive-In – Both – Choose “Best of Best”

Low Moderate HighIndoor 500 1200 2000

Drive-In 700 1500 1250Both -2000 -1000 3000

Demand for Ice Cream

Type of Parlor

* Payoffs in Predicted Profit Per Month

Page 12: Decision Analysis

Example

• Laplace– Indoor – Drive-In – Both – Choose

Low Moderate HighIndoor 500 1200 2000

Drive-In 700 1500 1250Both -2000 -1000 3000

Demand for Ice Cream

Type of Parlor

* Payoffs in Predicted Profit Per Month

Page 13: Decision Analysis

Decision Making

• Minimax Regret– Criterion for Decision Making Under Uncertainty

• A.

• B.

Page 14: Decision Analysis

Decision MakingLow Moderate High

Indoor 500 1200 2000Drive-In 700 1500 1250

Both -2000 -1000 3000

Demand for Ice Cream

Type of Parlor

Low Moderate HighIndoor

Drive-InBoth

Demand for Ice Cream

Type of Parlor

Page 15: Decision Analysis

Decision Making

• A.– Indoor – Drive-In – Both

• B. – a.

Page 16: Decision Analysis

Decision Making

• Under Risk– A.

– B.

• a. • b.

Page 17: Decision Analysis

Decision Making

• Under Risk

– Expected Payoffs:• Indoor:• Drive-In: (0.3)(700) + (0.5)(1500) + (0.2)(1250) = • Both: (0.3)(-2000) + (0.5)(-1000) + (0.2)(3000) =

– Select

0.3 0.5 0.2Low Moderate High

Indoor 500 1200 2000Drive-In 700 1500 1250

Both -2000 -1000 3000

Type of Parlor

Demand Probabilities

Page 18: Decision Analysis

Expected Value of Perfect Info

• A.

• B.

Page 19: Decision Analysis

Expected Value of Perfect Info

• Steps:– 1. – 2. – 3.

• Example– A.

• a. – B. – C.

Page 20: Decision Analysis

Expected Value of Perfect Info

• NOTE:– A.

Page 21: Decision Analysis

Decision Trees

• Visual tool to represent a decision model• Squares: - Decisions• Circles: - Uncertain Events (Subject to

Probability)• Branches: Potential Actions or Results• Some Branches are Terminal (End) Terminal

Branches Have Payoffs (Payoffs Should Reflect All Costs/Revenues)

Page 22: Decision Analysis

Decision Trees

• Simple Example

No

Yes($1 to Buy)

Buy Raffle Ticket? Win (0.01)

Lose (0.99)

Terminal Branches

Decision

Uncertain Event

$0

$49

-$1

Page 23: Decision Analysis

Decision Trees

• Build Decision Trees from LEFT to RIGHT• Solve Decision Trees from RIGHT to LEFT• Determine Expected Values at Chance Nodes• Choose “Best” Expected Value at Decision

Nodes• Identify “Best” Path of Decisions

Page 24: Decision Analysis

Decision Trees

• Simple Example

No

Yes($1 to Buy)

Buy Raffle Ticket? Win (0.01)

Lose (0.99)

$0

$49

-$1

Expected Value = (0.01)(49) + (0.99)(-1) = 0.49 – 0.99 = -0.5

Page 25: Decision Analysis

Decision Trees

• Simple Example

• Should You Buy a Raffle Ticket?• NO! Your Expected Value is Negative

No

Yes

Buy Raffle Ticket?

$0

-$0.5

Page 26: Decision Analysis

Decision Trees

• More Complex Example

Page 27: Decision Analysis

Decision Trees

Settle?

Settle Now ($?)

Wait

Page 28: Decision Analysis

Decision Trees

Settle?

Settle Now ($?)

Wait

Opp Wins (0.5)

Opp Loses (0.5)

$0

Page 29: Decision Analysis

Decision Trees

Settle?

Settle Now ($?)

Wait

Opp Wins (0.5)

Opp Loses (0.5)

$0

Opp Sues (0.8)

No Suit(0.2)

Page 30: Decision Analysis

Decision Trees

Settle?

Settle Now ($?)

Wait

Opp Wins (0.5)

Opp Loses (0.5)

$0

Opp Sues (0.8)

No Suit(0.2)

$0

Settle ($8)

Contest

ContestSettlement

Page 31: Decision Analysis

Decision Trees

Settle?

Settle Now ($?)

Wait

Opp Wins (0.5)

Opp Loses (0.5)

$0

Opp Sues (0.8)

No Suit(0.2)

$0

Settle ($8)

Contest

ContestSettlement

We Win (0.3) ($0)

We Lose (0.7) ($10)

Low (0.4) ($5)

Win (0.6) ($15)

Page 32: Decision Analysis

Decision Trees

Settle?

Settle Now ($?)

Wait

Opp Wins (0.5)

Opp Loses (0.5)

$0

Opp Sues (0.8)

No Suit(0.2)

$0

Settle ($8)

Contest

ContestSettlement

We Win (0.3) ($0)

We Lose (0.7) ($10)

Low (0.4) ($5)

Win (0.6) ($15)

EV = (0.3)(0) + (0.7)(10) = 7

EV = (0.4)(5) + (0.6)(15) = 11

Page 33: Decision Analysis

Decision Trees

Settle?

Settle Now ($?)

Wait

Opp Wins (0.5)

Opp Loses (0.5)

$0

Opp Sues (0.8)

No Suit(0.2)

$0

Settle ($8)

Contest

ContestSettlement

$7

$11

Page 34: Decision Analysis

Decision Trees

Settle?

Settle Now ($?)

Wait

Opp Wins (0.5)

Opp Loses (0.5)

$0

Opp Sues (0.8)

No Suit(0.2)

$0

$7

Page 35: Decision Analysis

Decision Trees

Settle?

Settle Now ($?)

Wait

Opp Wins (0.5)

Opp Loses (0.5)

$0

Opp Sues (0.8)

No Suit(0.2)$0

$7

EV = (0.8)(7) + (0.2)(0) = 5.6

Page 36: Decision Analysis

Decision Trees

Settle?

Settle Now ($?)

Wait

Opp Wins (0.5)

Opp Loses (0.5)

$0

$5.6

Page 37: Decision Analysis

Decision Trees

Settle?

Settle Now ($?)

Wait

Opp Wins (0.5)

Opp Loses (0.5)$0

$5.6

EV = (0.5)(5.6) + (0.5)(0) = 2.8

Page 38: Decision Analysis

Decision Trees

Settle?

Settle Now ($?)

Wait$2.8