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Module 4Modeling Decisions:MAKING CHOICES

Topics:• Creating case study

decision tree• Solving a decision tree• Risk profiles• Dominance of alternatives• Attributes and scales• Using multiple objectives

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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

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Making ChoicesLearning 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

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Making ChoicesLearning Objectives

• Develop– Constructed attributes– Constructed scales

• Formulate multiple objectives problems– Common scales– Trade–off weights– Composite consequences

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Making Choices

• Analysis of structured problems

– graphing

– calculating

– examining results

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“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

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“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

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“Texaco versus Pennzoil”

• Texaco offered to settle out of court by paying Pennzoil $2 billion

• Pennzoil believed fair settlement between $3 and $5 billion

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“Texaco versus Pennzoil”

• What should Pennzoil do?– Accept $2 billion settlement– Make counteroffer

• Assume objective is to maximize settlement

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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

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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.

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Expected Monetary Value

• Weighted average of outcomes at chance node

• Sum of the product of each outcome and its probability

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Pennzoil’s Decision Tree

• Pennzoil’s final decision treefigure 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

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Solving Influence Diagrams

• More cumbersome than decision trees

• Conversion to symmetric decision tree

• Software packages used

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Risk Profiles

• Graph illustrating chances of possible payoffs or consequences

• One profile for each strategy

graph 4.18

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Risk Profiles

• Creation is straightforward process, but tedious

• Can create for strategies and specific sequences

• Only strategies for first one or two decisions examined

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Risk Profiles

• Three steps to follow:1.Determine probabilities of paths

2.Determine probabilities of payoffs

3.Create charts for strategies

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Dominance

• Dominating alternative always preferred over another alternative

• Dominating alternative always has higher EV than other alternative

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Dominance

• May enable elimination of alternatives early in the process

• Elimination simplifies and reduces cost of the process

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Dominance

Approaches:

• Inspection

• Cumulative distribution function– Cumulative risk profile

• Sensitivity analysis– Tornado diagram

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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

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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

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Attributes and Scales

• Attribute: measure of performance or merit

• Scale: defined graduated series or specified scheme

• Scale frequently implicit in attribute definition

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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”

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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

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Constructed Attributes

• Frequently needed and most challenging

• A constructed attribute of site biological impact

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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

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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

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Multiple Objectives

Problems require:

• Common scale for measurement of consequences

• Trade–off weights for objectives

• Single composite consequence

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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

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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

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Multiple Objectives

Composite consequence for final outcomes:

• Linear combination of individual consequences

• Trade–off weights are coefficients

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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