Module 4
Modeling Decisions:
MAKING CHOICES
Topics:
• Creating case study
decision tree
• Solving a decision tree
• Risk profiles
• Dominance of alternatives
• Attributes and scales
• Using multiple objectives
1
Introduction
• Module 3:
– Structure values and objectives
– Identify performance measures
– Structure decision tree and influence diagram models
• Module 4:
– Solve decision trees
– Approach for multiple objectives
• Module 4 software tutorial
2
Making Choices
Learning Objectives
• Create decision tree from case study
• Solve a decision tree
– Expected value preference criterion
• Create and interpret
– Risk profiles
– Cumulative risk profiles
• Concept of dominance
– Definition and identification
– Decision problem simplification
3
Making Choices
Learning Objectives
• Develop
– Constructed attributes
– Constructed scales
• Formulate multiple objectives problems
– Common scales
– Trade–off weights
– Composite consequences
4
Making Choices
• Analysis of structured problems
– graphing
– calculating
– examining results
5
“Texaco versus Pennzoil”
• Pennzoil and Getty Oil agreed to a merger
• Texaco made better offer to Getty
• Getty reneged on Pennzoil and sold to
Texaco
• Pennzoil sued Texaco for interference
• Pennzoil won and was awarded the $11.1
billion
6
“Texaco versus Pennzoil”
• Texaco appealed; award reduced to $10.3
billion
• Texaco threatened bankruptcy if Pennzoil
filed liens
• Texaco also threatened to take case to
Supreme Court
7
“Texaco versus Pennzoil”
• Texaco offered to settle out of court by
paying Pennzoil $2 billion
• Pennzoil believed fair settlement between
$3 and $5 billion
8
“Texaco versus Pennzoil”
• What should Pennzoil do?
– Accept $2 billion settlement
– Make counteroffer
• Assume objective is to maximize settlement
9
Decision Trees and Expected
Monetary Value
• Expected Monetary Value (EMV); i.e.,
select alternative with highest expected
value
• “Folding back the tree” or “rolling back”
procedure
10
Decision Trees and Expected
Monetary Value
Folding Back:
• Start at the endpoints of the branches on the
far right-hand-side and move to the left
• Calculate expected values at a chance node
• Choose the branch with the highest value
or expected value at a decision node.
11
Expected Monetary Value
• Weighted average of outcomes at chance
node
• Sum of the product of each outcome and its
probability
12
Pennzoil’s Decision Tree
• Pennzoil’s final decision tree
figure 4.7
• What has been decided?
– Pennzoil should reject Texaco’s offer and make
a $5 billion counteroffer
– If Texaco then makes a $3 billion counteroffer,
Pennzoil should take its chances in court
13
Solving Influence Diagrams
• More cumbersome than decision trees
• Conversion to symmetric decision tree
• Software packages used
14
Risk Profiles
• Graph illustrating chances of possible
payoffs or consequences
• One profile for each strategy
graph 4.18
15
Risk Profiles
• Creation is straightforward process, but
tedious
• Can create for strategies and specific
sequences
• Only strategies for first one or two decisions
examined
16
Risk Profiles
• Three steps to follow:
1.Determine probabilities of paths
2.Determine probabilities of payoffs
3.Create charts for strategies
17
Dominance
• Dominating alternative always preferred
over another alternative
• Dominating alternative always has higher
EV than other alternative
18
Dominance
• May enable elimination of alternatives early
in the process
• Elimination simplifies and reduces cost of
the process
19
Dominance
Approaches:
• Inspection
• Cumulative distribution function
– Cumulative risk profile
• Sensitivity analysis
– Tornado diagram
20
Attributes and Scales
Measurement of fundamental objectives
• Measurement crucial to evaluation of
consequences
• Methods must be consistent with objectives
• Attributes and attribute scales define
measurement
• Different types of attributes
21
Attributes and Scales
• Purpose:
Explore attributes and scales
that measure achievement of
objectives
• Major field of study and in-depth
exploration beyond scope of cource
22
Attributes and Scales
• Attribute: measure of performance or
merit
• Scale:
defined graduated series or
specified scheme
• Scale frequently implicit in attribute
definition
23
Types of Attributes
Keeney identifies three types of attributes:
• Natural attributes
– generally known and have common meaning
– for example, centimeters
• Constructed attributes
– created when no natural attributes exists
– for example, qualitative ratings
• Proxy attributes
– indirect measures (either natural or constructed) when no direct
measures exist
– for example, use “sulphur dioxide concentration” for “acid rain
damage to sculptures”
24
Constructed Attributes
• Intellectually challenging and demanding
• Requires depth of knowledge and
understanding of decision situation and
objectives
• Three properties
– measurable: define objective in detail
– operational: describe possible consequences
– understandable: no ambiguity
25
Constructed Attributes
• Frequently needed and most challenging
• A constructed attribute of site biological
impact
26
Constructed Attributes
• Implied scale may not reflect measures
needed
• Nominal values in rank order may not
correspond to rational scale
• For example
(level 2 – level 1) ?≠? (level 4 – level 3)
• Use subjective judgment to rate nominal
values on rational scale
27
Constructed Attributes
• Define constructed attributes from natural
attributes
• Need to compare or combine constructed
and natural attributes
• Convert natural attributes to constructed
scale using proportions
28
Multiple Objectives
Problems require:
• Common scale for measurement of
consequences
• Trade–off weights for objectives
• Single composite consequence
29
Multiple Objectives
Common scale for consequences:
• Select common scale
–
–
–
–
May be one used for an objective
May be one not already used
May be natural or constructed
Tendency toward constructed with utility values
• Convert consequence measures for each objective
to common scale
30
Multiple Objectives
Trade–offs weights:
• Value between zero and one
• Sum to unity
• Consider consequence range
• Reflect relative importance of objectives
• Consistent with objectives hierarchy
31
Multiple Objectives
Composite consequence for final outcomes:
• Linear combination of individual
consequences
• Trade–off weights are coefficients
32
Summary
•
•
•
•
•
Creation of decision tree from case study
Solution of case study decision tree
Construction and use of risk profiles
Definition and use of dominance
Attributes and attribute scales, particularly
constructed attributes
• Formulation and solution of a multiple
objectives problem
33