Module 4 Topics: Creating case study decision tree Solving a decision tree Risk profiles Dominance of alternatives Attributes and scales Using multiple objectives Module 4 Modeling Decisions: MAKING CHOICES

Introduction Module 3: Module 4: Module 4 software tutorial 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

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

Making Choices Learning Objectives Develop Constructed attributes Constructed scales Formulate multiple objectives problems Common scales Trade–off weights Composite consequences

Making Choices Analysis of structured problems graphing calculating examining results

“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

“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

“Texaco versus Pennzoil” Texaco offered to settle out of court by paying Pennzoil $2 billion Pennzoil believed fair settlement between $3 and $5 billion

“Texaco versus Pennzoil” What should Pennzoil do? Accept $2 billion settlement Make counteroffer Assume objective is to maximize settlement

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

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.

Expected Monetary Value Weighted average of outcomes at chance node Sum of the product of each outcome and its probability

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

Solving Influence Diagrams More cumbersome than decision trees Conversion to symmetric decision tree Software packages used

Risk Profiles Graph illustrating chances of possible payoffs or consequences One profile for each strategy graph 4.18

Risk Profiles Creation is straightforward process, but tedious Can create for strategies and specific sequences Only strategies for first one or two decisions examined

Risk Profiles Three steps to follow: Determine probabilities of paths Determine probabilities of payoffs Create charts for strategies

Dominance Dominating alternative always preferred over another alternative Dominating alternative always has higher EV than other alternative

Dominance May enable elimination of alternatives early in the process Elimination simplifies and reduces cost of the process

Dominance Approaches: Inspection Cumulative distribution function Cumulative risk profile Sensitivity analysis Tornado diagram

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

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

Attributes and Scales Attribute: measure of performance or merit Scale: defined graduated series or specified scheme Scale frequently implicit in attribute definition

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”

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

Constructed Attributes Frequently needed and most challenging A constructed attribute of site biological impact

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

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

Multiple Objectives Problems require: Common scale for measurement of consequences Trade–off weights for objectives Single composite consequence

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

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

Multiple Objectives Composite consequence for final outcomes: Linear combination of individual consequences Trade–off weights are coefficients

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