Prentice-Hall, Inc.1 Chapter 8 The Home and Automobile Decision.
© 2008 Prentice-Hall, Inc. Decision Analysis. © 2009 Prentice-Hall, Inc. 3 – 2 Decision Trees...
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Transcript of © 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
© 2009 Prentice-Hall, Inc. 3 – 3
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
© 2009 Prentice-Hall, Inc. 3 – 4
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.
© 2009 Prentice-Hall, Inc. 3 – 6
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?
© 2009 Prentice-Hall, Inc. 3 – 7
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=$4.5
© 2009 Prentice-Hall, Inc. 3 – 8
Thompson Lumber Company
STATE OF NATURE
ALTERNATIVEFAVORABLE MARKET ($)
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
© 2009 Prentice-Hall, Inc. 3 – 9
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
© 2009 Prentice-Hall, Inc. 3 – 10
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)
© 2009 Prentice-Hall, Inc. 3 – 11
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.
© 2009 Prentice-Hall, Inc. 3 – 12
• 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
© 2009 Prentice-Hall, Inc. 3 – 13
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
Medium (0.50) 5Final CourtDecision
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)
© 2009 Prentice-Hall, Inc. 3 – 14
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
Medium (0.50) 5Final CourtDecision
© 2009 Prentice-Hall, Inc. 3 – 15
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
Medium (0.50) 5Final CourtDecision
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)
EMV = 4.56
EMV = 4.56
© 2009 Prentice-Hall, Inc. 3 – 16
Low (0.30)
High (0.20)10.3
0
Medium (0.50) 5Final CourtDecision
Accept $3 Billion
Refuse
3
EMV=4.56
EMV=4.56
© 2009 Prentice-Hall, Inc. 3 – 17
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
Medium (0.50) 5Final CourtDecision
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)
EMV = 4.56
EMV = 4.56
© 2009 Prentice-Hall, Inc. 3 – 18
5
2
Max Result
Accept $2 Billion
Counteroffer
$5 Billion
Texaco Accepts $5 Billion (0.17)
Texaco Refuses (0.50)
Counteroffer
TexacoCounter -offers $3 Billion
(0.33)
EMV=4.56
EMV=4.56
EMV=4.63
5
2
Max Result
Accept $2 Billion
Counteroffer
$5 Billion
Texaco Accepts $5 Billion (0.17)
Texaco Refuses (0.50)
Counteroffer
TexacoCounter -offers $3 Billion
(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
© 2009 Prentice-Hall, Inc. 3 – 19
2
Max Result
Accept $2 Billion
Counteroffer
$5 Billion
EMV=4.63
© 2009 Prentice-Hall, Inc. 3 – 20
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.
© 2009 Prentice-Hall, Inc. 3 – 21
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
Medium (0.50) 5Final CourtDecision
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)
EMV=4.56
EMV=4.56
EMV=4.56
EMV=4.63
EMV=4.63
© 2009 Prentice-Hall, Inc. 3 – 22
2Accept $2 Billion
D1 =“Accept 2 Billion”
© 2009 Prentice-Hall, Inc. 3 – 23
Low (0.30)
High (0.20)10.3
0
Medium (0.50) 5Final CourtDecision
Refuse
Low (0.30)
High (0.20)10.3
0
Medium (0.50) 5Final CourtDecision
5
Counteroffer
$5 Billion
Texaco Accepts $5 Billion (0.17)
Texaco Refuses (0.50)
Counteroffer
TexacoCounter -offers $3 Billion
(0.33)
D2 = “Counter 5 Billion, Refuse Counter of $3 Billion”
© 2009 Prentice-Hall, Inc. 3 – 24
Accept $3 Billion
Low (0.30)
High (0.20)10.3
0
Medium (0.50) 5Final CourtDecision
5
3
Counteroffer
$5 Billion
Texaco Accepts $5 Billion (0.17)
Texaco Refuses (0.50)
Counteroffer
TexacoCounter -offers $3 Billion
(0.33)
D3 = “Counter 5 Billion, Accept $3 Billion”
© 2009 Prentice-Hall, Inc. 3 – 25
OPTIMAL DECISION STRATEGY
Counteroffer $5 Billion.
Next, if Texaco Counteroffers
$3 Billion, refuse the counteroffer.
Number of Decision Strategies in Decision Tree above: 3