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Chapter 3

Structuring Decisions

Dr. Greg ParnellDepartment of Mathematical Sciences

Virginia Commonwealth University

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Overview

• Problem structuring

• Decision basis

• Structuring Objectives– Value Hierarchy– Means-Objectives Network

• Influence Diagram

• Decision Tree

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Decision Analysis Is a Systematic Process

Questions:

Deliverables:

What do we want?What do we know?What can we do?

ValuesValue HierarchyInformationAlternativesInfluence DiagramDecision Tree

Value ModelSensitivity AnalysisCritical Uncertainties

What are the relationships?What is important?

What are the possible outcomes?What are the probabilities of those outcomes?How much could we gain/lose?

Probability DistributionsDominated AlternativesRisk Profiles

Are we ready to decide OR how much more information would we be willing to pay for?

Value of InformationValue of Control

Iteration

ProblemStructure

DeterministicAnalysis

Probabilistic Analysis

Evaluation

DecisionInitial

Situation

Problem Structuring

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Decision Basis

ValuesWhat do we want?

InformationWhat do we know?

AlternativesWhat 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– 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

Keeney, R.L., (1994) "Creativity in Decision Making with Value-Focused Thinking," Sloan Management Review, Summer, 33-41.

First we identify, then we group the objectives.

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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 HierarchyScience Museum of Virginia

M in im ize t im ein q u eu e

M in im ize p rocess in gtim e

M in im ize p a tron w a it in gan d p roces in g t im e

M u seu mE m p loyees

H ard w areC os ts

S o ftw areC os ts

V is ito rg ood w ill

M in im ize p a tronp rocess in g cos t

Im p rove p a tron p rocess in g a tth e m u seu m Fundamental Objective

Objectives

Subobjectives

The objectives define the fundamental objective & subobjectives define the objectives.

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Means-Objectives Network

M in im ize t im ein q u eu e

M in im ize p rocess in gtim e

M in im ize p a tron w a it in gan d p roces in g t im e

M u seu mE m p loyees

H ard w areC os ts

S o ftw areC os ts

V is ito rg ood w ill

M in im ize p a tronp rocess in g cos t

Im p rove p a tron p rocess in g a tth e m u seu m

Provide incentives to arrive at non-peak times

Improved software

Improved hardware

Cashiertraining

Provideentertainment

Separate processing for members

Recruitmembers

• Add more means• Connect the means to the subobjectives

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Influence Diagrams - Node Types

• 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

Chance

Deterministic

ValueDecision

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Venture Capitalist's Decision

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?

Return onInvestment

Venture Suceeds or Fails

Invest?

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Influence Diagram Modeling

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.

Payoff

MarketActivity

InvestmentChoice

ALTERNATIVES:Savings account

Mutual fund

MARKET OUTCOMES:Market up

Market down

ALTERNATIVE MARKET PAYOFFSavings Account Up 100Savings Account Down 100Mutual Fund Up 400Mutual Fund Down -100

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Imperfect Information - Very Common

QUESTIONS1. 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?

Payoff

Market Survey

ActualMarket

New ProductDecision?

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Wildcat Oil ID

ProfitsRevenues

SeismicStructure

ExpSeismic

Test

Amountof Oil

DrillingCosts

TestDrill

WILDCAT OIL DRILLING PROBLEM

Interpret this ID

• 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!!!!

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Probabilistic Modeling with IDs

Time to Shipment

ManualPrinting

Time

PackagingPrinting

Time

ManualCompletion

Time

PackagingCompletion

Time

SoftwareCompletion

Time

DesignSoftware

Beta-testSoftware

ProgramSoftware

WriteManual

ReviseManual

Design Packaging

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 !

Low

Return_on_Investment Nominal

Return_on_Investment High

Return_on_Investment

Yes

Venture Suceeds or Fails

No

Invest? Develop the decision tree for each of the IDs we have developed

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New Product Decision

Yes

Payoff No

Payoff

Low

Nominal

High

New ProductDecision?

Low

Nominal

High

ActualMarket

Market Survey

How many outcomes (at the end of the DT) are there?How many Payoffs need to be calculated?

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Decision Tree

Dry

Revenues Wet

Revenues Soaking

Revenues

Low

Drilling_Costs Med

Drilling_Costs High

Drilling_Costs

Amountof Oil

Yes

DrillingCosts

No None

a

Drill

No

Open

Closed

a Core Sample

Test

SeismicStructure

No

Open

Closed

a Exp Seismic

Test

ExpSeismic

Test

Test

WILDCAT OIL DRILLING PROBLEM

How many outcomes (at the end of the DT) are there?How many Payoffs need to be calculated?

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Probability Tree

Fancy

Time_to_Shipment Simple

Time_to_Shipment

Major changes

Minor changes

Design Packaging

Easy

Hard

ReviseManual

Smooth

Buggy

WriteManual

Easy

Hard

Beta-testSoftware

Major Changes

Minor Changes

ProgramSoftware

DesignSoftware

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?

Low

Nominal

High

Saturn (SC)Sales in

2000

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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