Chapter 3
Structuring Decisions
Dr. Greg Parnell
Department of Mathematical Sciences
Virginia Commonwealth University
1
Overview
• Problem structuring
• Decision basis
• Structuring Objectives
– Value Hierarchy
– Means-Objectives Network
• Influence Diagram
• Decision Tree
2
Decision Analysis Is a Systematic Process
What do we want?
What do we know?
Questions:
What can we do?
What are the
relationships?
What is important?
Problem
Structuring
Are we ready to
What are the possible
decide OR how much
outcomes?
What are the probabilities more information
would we be willing
of those outcomes?
to pay for?
How much could
we gain/lose?
Iteration
Initial
Situation
Decision
Problem
Structure
Deterministic
Analysis
Probabilistic
Analysis
Evaluation
Values
Value Model
Value Hierarchy
Sensitivity Analysis Probability Distributions Value of Information
Deliverables: Information
Dominated Alternatives Value of Control
Critical
Uncertainties
Alternatives
Risk Profiles
Influence Diagram
Decision Tree
3
Decision Basis
Values
What do we want?
Information
What do we know?
Alternatives
What can we do?
• Problem structuring focuses on the values,
alternatives, and information.
• We start with values. (We will use single
value, usually NPV, until Chapter 15)
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Structuring Objectives
• Identify objectives
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–
–
–
–
–
–
–
Keeney, R.L., (1994) "Creativity in Decision Making
with Value-Focused Thinking," Sloan Management
Review, Summer, 33-41.
Develop a wish list
Identify alternatives
Consider problems and shortcomings
Predict consequences
Identify, goals, constraints, and guidelines
Consider different perspectives
Determine strategic objectives
Determine generic objectives
• Sort or organize objectives into
logical groups
First we identify, then we group the objectives.
5
Definitions
• fundamental objective(s): the decision-makers
ultimate objective(s)
• objectives: the essential reasons for our interest in
the decision situation
• objectives (value) hierarchy: a hierarchy that
identifies what aspects of the higher level objective
are important (Keeney/Clemen call this a
fundamental-objectives hierarchy)
• means: specific approach to achieve our objectives
• means-objectives network: network whose
purpose is to help generate alternatives by
identifying the means to obtain our objectives
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Example: Virginia Science Museum
• Experiencing queuing problems at the major exhibits
– Why?
• Long lines, people leaving
– What?
• Getting patrons into the museum
– How?
• Cashiers with computer hardware and software
– Who?
• Patrons, cashiers, managers
– When?
• During the most popular exhibits
– Where?
• Entrance to the museum
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Objectives Hierarchy
Science Museum of Virginia
Improve patron processing at
the museum
Minimize patron waiting
and procesing time
Minimize patron
processing cost
Minimize time
in queue
Museum
Employees
Minimize processing
time
Hardware
Costs
Software
Costs
Fundamental Objective
Objectives
Subobjectives
Visitor
good will
The objectives define the fundamental objective
& subobjectives define the objectives.
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Means-Objectives Network
Improve patron processing at
the museum
Minimize patron waiting
and procesing time
Minimize time
in queue
Provide
incentives to
arrive at nonpeak times
Minimize processing
time
Provide
entertainment
Minimize patron
processing cost
Museum
Employees
Cashier
training
Recruit
members
Hardware
Costs
Improved
hardware
Software
Costs
Improved
software
Visitor
good will
Separate
processing
for
members
• Add more means
• Connect the means to the subobjectives
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Influence Diagrams - Node Types
Chance
Value
Decision
Deterministic
• ID captures the DM’s state of information
– Technique for decision structuring
– Algorithms also exist to solve IDs
– IDs have no cycles [IDs are not flow diagrams]
• Arrows are used for two purposes
– Relevance: knowledge of the outcome of a predecessor node is useful to
determine the outcome of a successor node
– Sequence: the outcome of a predecessor node is known before the outcome of
a successor node
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Venture Capitalist's Decision
Venture
Suceeds
or Fails
Invest?
Return on
Investment
Questions:
1. What does the arc from Invest to Return on Investment mean?
2. What does the arc from Venture to Return on Investment mean?
3. Why is there no arc from Invest to Venture?
4. Why is there no arc from Venture to Invest?
5. How could the DM obtain additional information about the Venture?
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Influence Diagram Modeling
Market
Activity
Investment
Choice
ALTERNATIVES:
Savings account
Mutual fund
MARKET OUTCOMES:
Market up
Market down
Payoff
ALTERNATIVE MARKET
Savings Account Up
Savings Account Down
Mutual Fund
Up
Mutual Fund
Down
PAYOFF
100
100
400
-100
QUESTIONS
1. Describe how the two arrows model sequence and relevance?
2. What determines the number of possible consequences?
3. If we had three decision alternatives and four Market Activity outcomes,
how many consequences would we have?
• This approach would be very cumbersome for large problems, fortunately, in
many cases, we can use functions to simplify modeling.
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Imperfect Information - Very Common
Actual
Market
Market
Survey
New Product
Decision?
Payoff
QUESTIONS
1. Would you expect the Market Survey to be perfect or imperfect information?
Why?
2. What is the effect of number of outcomes of the Market Survey have on the
number of Payoff outcomes? Why?
3. Describe how the arrows model sequence and relevance?
4. Why do we draw the arrow from Actual Market to Market Survey versus the
other direction?
5. What would an arrow from New Product to Actual Market mean?
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Wildcat Oil ID
WILDCAT OIL DRILLING PROBLEM
Drill
Amount
of Oil
Seismic
Structure
Test
Revenues
Drilling
Costs
Profits
• Some Common Influence
Diagram Mistakes
- IDs are not flow charts
- NO CYCLES!
Sequential decisions
• DPL Note: Read DPL Users
Guide, pp. 244-247
- Color of the arrows is the
key!!!!
Exp
Seismic
Test
Interpret this ID
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Probabilistic Modeling with IDs
Software
Completion
Time
Program
Software
Beta-test
Software
Revise
Manual
Design
Software
Manual
Completion
Time
Write
Manual
Time to
Shipment
Manual
Printing
Time
Packaging
Completion
Time
Design
Packaging
Packaging
Printing
Time
What is missing from this ID?
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Decision Trees
• IDs are good for problem structuring since they
suppress detail
• Decision trees - identify the sequence of
decisions/events and have a branch for each decision
alternative and each uncertain event outcome
• Decision tree must identify all paths
• Each outcome space must be ME & CE !
Venture
Suceeds
or Fails
Invest?
Yes
No
Low
Return_on_Investment
Nominal
Return_on_Investment
High
Return_on_Investment
Develop the
decision tree for
each of the IDs we
have developed
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New Product Decision
Market
Survey
Actual
Market
Low
Low
Nominal
Nominal
High
High
New Product
Decision?
Yes
Payoff
No
Payoff
How many outcomes (at the end of the DT) are there?
How many Payoffs need to be calculated?
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Decision Tree
WILDCAT OIL DRILLING PROBLEM
Drilling
Costs
Drill
Yes
None
Test
a
No
Amount
of Oil
Low
Drilling_Costs
Med
Drilling_Costs
High
Drilling_Costs
Dry
Revenues
Wet
Revenues
Soaking
Revenues
Seismic
No
Structure
Core Sample
Open
Test
a
Closed
Exp
Seismic No
Test
Exp Seismic
Open
Test
a
Closed
How many outcomes (at the end of the DT) are there?
How many Payoffs need to be calculated?
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Probability Tree
Design
Software
Program
Software
Beta-test
Software
Write
Manual
Revise
Manual
Design
Packaging
Major Changes
Easy
Smooth
Easy
Major changes
Fancy
Minor Changes
Hard
Buggy
Hard
Minor changes
Time_to_Shipment
Simple
Time_to_Shipment
What node type is missing?
How many outcomes (at the end of the DT) are there?
How many Payoffs need to be calculated?
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Decision Trees Versus
Influence Diagrams
• Influence diagrams
• Good for problem structuring
• Good for communicating with management
- suppress details
• Decision trees
• Show details
- better for asymmetric problems
• Complementary
- DPL uses both representations
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Clarity Test
• Elements of a decision must be
clearly defined
• DM, DM's staff, decision
analyst
• Clairvoyant = access to all future
information
• Clarity Test (Howard, 1988)
Your model passes the clarity test
if a clairvoyant would be able to
unequivocally tell you the outcome of any
event in the ID/decision tree
EXAMPLE: Does the following
uncertain variable pass the clarity
test?
Saturn (SC)
Sales in
2000
Low
Nominal
High
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Summary
• Problem structuring
• Decision basis
• Structuring objectives
– Value hierarchy
– Means-objectives network
• Influence diagram
– Types of nodes
• Decision tree
– Types of nodes
• Comparison
– Advantages of each problem structuring method
• Clarity test
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