© 2008 Prentice-Hall, Inc. Decision Analysis. © 2009 Prentice-Hall, Inc. 3 – 2 Decision Trees...

© 2008 Prentice-Hall, Inc.

Decision Analysis

© 2009 Prentice-Hall, Inc. 3 – 2

Decision Trees Any problem that can be presented in a

decision table can also be graphically represented in a decision treedecision tree

Decision trees are most beneficial when a sequence of decisions must be made

All decision trees contain decision pointsdecision points or nodesnodes and state-of-nature pointsstate-of-nature points or nodesnodes A decision node from which one of several

alternatives may be chosen A state-of-nature node out of which one state

of nature will occur


Five Steps toDecision Tree Analysis

1. Define the problem2. Structure or draw the decision tree3. Assign probabilities to the states of

nature4. Estimate payoffs for each possible

combination of alternatives and states of nature

5. Solve the problem by computing expected monetary values (EMVs) for each state of nature node


Structure of Decision Trees

Trees start from left to right Represent decisions and outcomes in

sequential order Squares represent decision nodes Circles represent states of nature nodes Lines or branches connect the decisions

nodes and the states of nature

© 2008 Prentice-Hall, Inc.

Each chance node must have branches that correspond

to a set of mutually exclusive and collectively

exhaustive outcomes.

Two outcomes are mutually exclusive (or disjoint) if the

occurrence of one of the outcomes precludes the

simultaneous occurrence of the other.

If you make a list of the outcomes which can occur when

you adopt a particular course of action then this list is said to

be exhaustive if your list includes every possible outcome.


Double-Risk Dilemma

Assume that you have a ticket that will let you participate in a game of chance (a lottery) that will pay off $10 with a 45% chance (or a 55% chance of nothing).

Your friend has a ticket to a different lottery that has a 20% chance of paying $25 (or an 80% chance of nothing).

Your friend has offered to let you have his ticket if you will give him your ticket plus $1.

Should you agree to the trade and play to win $25, or should you keep your ticket?


Keep Ticket

Trade Ticket

Lose (0.55)

Win (0.45)

Max Profit

$24

$10

$0

Lose (0.80)

Win (0.20)

-$1

$25

$0-$1

$10

$0

$0

EMV=$4

EMV=$4.5

EMV=$4.5

Keep Ticket

Trade Ticket

Lose (0.55)

Win (0.45)

Max Profit

$24

$10

$0

Lose (0.80)

Win (0.20)

-$1

$25

$0-$1

$10

$0

$0

EMV=$4

EMV=$4.5

EMV=$4.5

Keep Ticket

Trade Ticket

Lose (0.55)

Win (0.45)

Max Profit

$24

$10

$0

Lose (0.80)

Win (0.20)

-$1

$25

$0-$1

$10

$0

$0

y Pr(Y=y) y*Pr(Y=y)$24.00 0.2 $4.80-$1.00 0.8 -$0.80

$4.00 =EMV

y Pr(Y=y) y*Pr(Y=y)$10.00 0.45 $4.50$0.00 0.55 $0.00

$4.50 =EMV

EMV=$4

EMV=$4.5

EMV=$4.5

Keep Ticket

Trade Ticket

Lose (0.55)

Win (0.45)

Max Profit

$24

$10

$0

Lose (0.80)

Win (0.20)

-$1

$25

$0-$1

$10

$0

$0

EMV=$4

EMV=$4.5

EMV=$4.5


Thompson Lumber Company

STATE OF NATURE

ALTERNATIVEFAVORABLE MARKET ($)

UNFAVORABLE MARKET ($)

Construct a large plant 200,000 –180,000

Construct a small plant 100,000 –20,000

Do nothing 0 0

Table 3.1


Thompson’s Decision Tree

Favorable Market

Unfavorable Market

Favorable Market

Unfavorable Market

Do Nothing

Construct

Large P

lant

1

Construct

Small Plant2

A Decision Node

A State-of-Nature Node


Thompson’s Decision Tree

Favorable Market

Unfavorable Market

Favorable Market

Unfavorable Market

Do Nothing

Construct

Large P

lant

1

Construct

Small Plant2

Alternative with best EMV is selected

EMV for Node 1 = $10,000

= (0.5)($200,000) + (0.5)(–$180,000)

EMV for Node 2 = $40,000

= (0.5)($100,000) + (0.5)(–$20,000)

Payoffs

$200,000

–$180,000

$100,000

–$20,000

$0

(0.5)

(0.5)

(0.5)

(0.5)


Texaco vs. Pennzoil

• In early 1984, Pennzoil and Getty Oil agreed to the terms of a merger. But before any formal documents could be signed, Texaco offered Getty Oil a substantially better price.

• Getty Oil agreed and sold to Texaco.

• In 1985, Pennzoil filed a lawsuit against Texaco. And won the case…awarded $11.0 billion.

• Texaco appealed ----- court $10.3 billion.

• Texaco threat to file for bankruptcy if Pennzoil secured the judgment.


• In 1987, Texaco offered to pay Pennzoil $2billion to settle the case.

• Pennzoil chairman indicated that a settlement between $2 and $5 billion would be fair.

Should Pennzoil accepts or refuses and make a counteroffer of $5billion?

Texaco Might

1- Accepts to pay $5 billion

2- Refuses and counteroffer of $3 billion

3- Refuses and goes to court


Low (0.30)

High (0.20)10.3

0

Medium (0.50) 5Final CourtDecision

Accept $3 Billion

Refuse

Low (0.30)

High (0.20)10.3

0


5

2

Max Result

3

Accept $2 Billion

Counteroffer

$5 Billion

Texaco Accepts $5 Billion (0.17)

Texaco Refuses (0.50)

Counteroffer

TexacoCounter -offers $3 Billion

(0.33)


Step 1

y Pr(Y=y) y*Pr(Y=y)10.300 0.2 $2.065.000 0.5 $2.500.000 0.3 $0.00

$4.56 =EMVLow (0.30)

High (0.20)10.3

0



Low (0.30)

High (0.20)10.3

0


Accept $3 Billion

Refuse

Low (0.30)

High (0.20)10.3

0


5

2

Max Result

3

Accept $2 Billion

Counteroffer

$5 Billion



Counteroffer


(0.33)

EMV = 4.56

EMV = 4.56


Low (0.30)

High (0.20)10.3

0


Accept $3 Billion

Refuse

3

EMV=4.56

EMV=4.56


Low (0.30)

High (0.20)10.3

0


Accept $3 Billion

Refuse

Low (0.30)

High (0.20)10.3

0


5

2

Max Result

3

Accept $2 Billion

Counteroffer

$5 Billion



Counteroffer


(0.33)

EMV = 4.56

EMV = 4.56


5

2

Max Result

Accept $2 Billion

Counteroffer

$5 Billion



Counteroffer


(0.33)

EMV=4.56

EMV=4.56

EMV=4.63

5

2

Max Result

Accept $2 Billion

Counteroffer

$5 Billion



Counteroffer


(0.33)

EMV=4.56

EMV=4.56

y Pr(Y=y) y*Pr(Y=y)5.000 0.17 $0.854.560 0.5 $2.284.560 0.33 $1.50

$4.63 =EMV

EMV=4.63


2

Max Result

Accept $2 Billion

Counteroffer

$5 Billion

EMV=4.63


Decision Path: A path starting at the left most node up to the values at the end of a branch by selecting one alternative from a decision node or by following one outcome from uncertainty nodes.

Decision Strategy: The collection of decision paths connected to a branch of the left most node by selecting one alternative from each decision node along these paths.

Optimal Decision Strategy: That Decision Strategy which results in the highest EMV if we maximize profit and the lowest EMV if we minimize cost.


Low (0.30)

High (0.20)10.3

0


Accept $3 Billion

Refuse

Low (0.30)

High (0.20)10.3

0


5

2

Max Result

3

Accept $2 Billion

Counteroffer

$5 Billion



Counteroffer


(0.33)

EMV=4.56

EMV=4.56

EMV=4.56

EMV=4.63

EMV=4.63


2Accept $2 Billion

D1 =“Accept 2 Billion”


Low (0.30)

High (0.20)10.3

0


Refuse

Low (0.30)

High (0.20)10.3

0


5

Counteroffer

$5 Billion



Counteroffer


(0.33)

D2 = “Counter 5 Billion, Refuse Counter of $3 Billion”


Accept $3 Billion

Low (0.30)

High (0.20)10.3

0


5

3

Counteroffer

$5 Billion



Counteroffer


(0.33)

D3 = “Counter 5 Billion, Accept $3 Billion”


OPTIMAL DECISION STRATEGY

Counteroffer $5 Billion.

Next, if Texaco Counteroffers

$3 Billion, refuse the counteroffer.

Number of Decision Strategies in Decision Tree above: 3

© 2008 Prentice-Hall, Inc. Decision Analysis. © 2009 Prentice-Hall, Inc. 3 – 2 Decision Trees...

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