Yan Liu, Department of BIE, Wright State University ...nbaloian/DSS-DCC/Temas/Structuring...

Yan Liu, Department of BIE, Wright State University

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Influence Diagrams

Invest?Venture

Succeeds

or Fails

Return on

InvestmentComputer

Industry

Growth

Overall

Satisfaction

Decision

Node

Chance

Node

Computation

Node

Payoff

Node

Influence Diagram of a Venture Capitalist’s Decision Problem


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Influence Diagrams

Relationships between nodes are symbolized with arrows or directed arcs

Distinctions are made here between sequence and dependence arcs only for teaching purposes.

Once you are familiar with the differences, you can use solid arcs throughout the influence

diagram like the convention used in the textbook


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Influence Diagrams

• Influence Diagrams and Fundamental-Objectives Hierarchy

– The Payoff node corresponds to the most general objective (located at the

upper-most level) in the fundamental-objectives hierarchy

– The computation nodes correspond to the objectives at the lower levels

in the hierarchy


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Basic Influence Diagrams

• Basic Risky Decision

– Whether the potential gain in the risky choice is worth the risk

Investment Example

You have $2,000 to invest and the objective is to earn as high a return on your

investment as possible. There are two alternatives: investing in a friend’s business or

keeping the money in a savings account with a fixed interests rate. If you invest in the

business, your return depends on the success of the business. You figure there could be

two possible outcomes: the business is either widely successful earning you $3,000

beyond your initial investment (hence leaving you $5,000 in total) or a total flop, in

which case you will lose all your money. On the other hand, if you put your money into

a saving account, you will earn $200 in interest regardless of your friend’s business.


17Influence Diagram of the Investment Decision Problem



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• Imperfect Information– Imperfect information about some uncertain event (such as forecast and

estimate) will affect the eventual payoff

Evacuation Example

Suppose you live in Miami. A hurricane near the Bahama Islands threatens to cause severe

damage. As a result, the authorities recommend everyone to evacuate. Although the

evacuation is costly, you would be safe. On the other hand, staying is risky. You could be

injured or even killed if the storm comes ashore within 10 miles of your home. If the

hurricane’s path changes, however, you would be safe without having incurred the cost of

evacuating. The two fundamental objectives are to maximize your safety and to minimize

your costs.

Undoubtedly, you will pay close attention to the weather forecasters who would predict

the course of the storm. However, the weather forecasters are not perfect predictors

because not everything is known about hurricanes.


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ForecastHurricane

Path

Decision Consequence


Stay

Evacuate

Choices

Misses Miami

Hits Miami

Outcomes

“Will miss Miami”

“Will hit Miami”

Forecasts

Safety, Low CostMisses Miami

Danger, Low CostHits MiamiStay

Safety, High CostMisses Miami

Safety, High CostHits MiamiEvacuate

ConsequencesOutcomes Choices

Influence Diagram of the Evacuation Decision Problem

sequence

dependence


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• Sequential Decisions

– Two or more decisions that need to be made in sequence

Evacuation Example

Suppose in the example of hurricane-evacuation decision, you are waiting anxiously for

the forecast as the hurricane is bearing down. Should you keep waiting for the forecast

or leave immediately? In this case, you are facing a sequential decision situation. If you

decide to wait for the forecast, then your next decision is whether you should evacuate or

stay based on the forecast information.


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ForecastHurricane

Path

Evacuate? Consequence

Wait for

Forecast?


Influence Diagram of the Sequential Evacuation Decision Problem

sequence


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• Computation Nodes (Intermediate Calculations )

– Emphasizing the structure of the influence diagram, especially when a node

receives inputs from many other nodes

– Used in the same way as a payoff node

• The values of the nodes can be calculated directly from inputs of predecessor nodes

Product Example

Suppose a firm is considering introducing a product, and its fundamental objective is to

maximize the profit.

Revenue Cost

Introduce

Product?Profit

1st Version


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Units Sold Fixed Cost

Introduce

Product?Profit

Price?Variable Cost

2nd Version

Units Sold Fixed Cost

Introduce

Product?Profit

Price?Variable Cost

3rd Version

Revenue Cost



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Constructing an Influence Diagram

• No set strategy is given; a good approach is to put together a simple version of the diagram first and then add details as necessary

The following are the steps that can be followed when constructing an influence diagram:

1. Identify the decisions to be made. If there are more than one decision, determine their time sequence and draw sequence arcs to connect the decision nodes

2. Structure fundamental-objective hierarchy and represent them as payoff and intermediate computation nodes in the influence diagram

3. Identify relevance relationships between the decision nodes and computation nodes or payoff node and draw dependence arcs to connect them

4. Identify all the uncertain events


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5. Identify the sequence relationships between the chance nodes and decision nodes and draw corresponding arcs between them

6. Identify the relevance relationships between the chance nodes and draw corresponding arcs between them

7. Identify the relevance relationships between the chance nodes and computation nodes or payoff node and draw corresponding arcs between them

8. Check the appropriateness of the influence diagram (any missing and/or irrelevant information)


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EPA Example

The Environmental Protection Agency (EPA) often must decide whether to permit the use

of an economically beneficial chemical that may induce cancer (carcinogenic).

Furthermore, the decision often must be made without perfect information about either

the long-term benefits or health hazards. Alternative courses of actions are to permit

the use of the chemical, restrict its use, or to ban it all together. Tests can be run to

learn something about the carcinogenic potential, and survey data can give an

indication of the extent to which people are exposed when they do use the chemical.

These pieces of information are both important in making the decision. For example, if

the chemical is only mildly toxic and the exposure rate is minimal, then restricted use

may be reasonable. On the other hand, if the chemical is only mildly toxic but the

exposure rate is high, then banning its use may be imperative.


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Usage

Decision?

Lab

TestSurvey

Carcinogenic

Potential

Net Value

Economic

Value

Cancer

CostExposure

Rate


EPA Example

Influence Diagram of the EPA Decision Problem

Net Value

Economic

Value

Cancer

Cost


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Usage

Decision?

Lab

TestSurvey

Carcinogenic

Potential

Net Value

Economic

Value

Cancer

Cost

Exposure

Rate

Cancer

Risk

EPA Example

Influence Diagram of the EPA Decision Problem

(adding a computation node)



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Comments on Influence Diagrams

• NOT a flowchart of the decision process

– A snapshot of the decision situation at a particular time

– Sequencing is implied

• Should NEVER contain cycles (no feedbacks)

• Very compact notations that hide lots of information

• Interpreting an influence diagram is generally easy

– Good for conveying model design to others

• Creating influence diagrams can be difficult


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Decision Trees

• Decision trees display more details of a decision problem than

influence diagrams

– Decision trees explicitly identify the sequence of decisions/events (from

left to right)

– Decision trees represent all possible future scenarios

• One branch for each decision alternative

• One branch for each outcome of an uncertain event (outcomes must be mutually

exclusive and collectively exhaustive)


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Investment

Choice

Savings

Business

Business

Result

Widely

Success

Flop

$3,000

$0

$200

Decision

Node

Chance

Node

ConsequenceDecision

Alternative

Outcome of

Uncertain Event

Decision Tree of the Investment Decision Problem

Decision Trees


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Basic Decision Trees

• Basic Risky Decision

Politician Example

The fundamental objective of a politician is to have a career that provides

leadership for the country and representation for her constituency. She can do so to

a varying degrees by serving in Congress. She might have two options: 1) running

for reelection to her U.S. House of Representatives seat, in which case her

reelection is virtually assured; and 2) running for a Senate seat, in which case

there is a chance of losing. If she loses, she could return to her old job as a lawyer

(the worst possible outcome). The best possible outcome is to win the Senate place

in terms of her objective of providing leadership and representation.


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Decision Tree of the Politician’s Basic Risk Decision


Running

Decision

Election

Result


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• Double-Risk Decision Dilemma

– Decide between two risky prospects


The Politician’s Double- Risk Decision Dilemma

Running

Decision

Election

Result

Election

Result


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• Range-of-Risk Decision Dilemma

– The outcomes of the chance events are a range of values

Insurance Example

An individual has sued for damages of $450,000 because of injury. The insurance

company has offered to settle for $100,000. The plaintiff must decide whether to accept

the settlement or go to court.


Decision Tree of the

Insurance Example

Court

Result


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• Imperfect Information

– Placing the corresponding chance node prior to the decision that it affects

Decision Tree of the Evacuation Decision Problem

Forecast

Evacuation

Decision

Evacuation

Decision


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• Sequential Decisions

– Order decisions in decision trees from left to right

Decision Tree of the Sequential Evacuation Decision Problem

Wait

Decision

Evacuation

Decision

Evacuation

Decision


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• Schematic Representation of Sequential Decisions

– In problems with many decisions involved, the sizes of full-blown

decision trees can increase exponentially


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Compare Influence Diagrams and

Decision TreesBoth influence diagrams and decision trees have strength and weakness and can complement each other

The size of the tree increases fast

as the decision problems become

more complicated

Display many details of the decision

problem; Useful during careful reflection

and sensitivity analysis on specific

probability and value inputs

Decision Tree

Hide many details

Compact representation and easy to

understand; Particularly valuable for

the structuring phase of problem solving

and representing large problems

Influence Diagram

ConsProsTools


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Decision Details

• Define Elements of the Decision Clearly

In the Environmental Protection Agency example.

Fundamental Objective: Minimize the social cost of cancer. How will the cancer cost

be measured? Incremental lives cost? Incremental cases of cancer, both treatable

and fatal?

Uncertain Event: Rate of exposure. What are the possible outcomes? How to

measure? The number of people exposed to the chemical per day or per hour?

• Every Element of the Decision Model Needs to Pass the Clarity Test

– Various people involved in the decision think about the decision elements in

exactly the same way; no misunderstandings regarding the definitions of the

basic decision elements


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Decision Details

• Cash Flows and Probabilities

– Specific chances associated with each outcome of uncertain events

– Specific cash flows at different times

Research-and-Development Example

A company needs to decide whether to spend $2M to continue with a particular

research project. The success of the project (measured by obtaining a patent) is

not assured. At this point, the decision maker judges only a 70% chance of

getting the patent. If the patent is awarded, the company can either license the

patent for an estimated $25M or invest an additional $10M to create a production

and marketing system to sell the product directly. If the company chooses the

latter, it faces uncertainty of demand and associated profit from sales.


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Demands High

Development

DecisionStop

Development

Continue

Development

Development

Result

Patent

Awarded

No Patent

License

Technology

$0

-$2M

Develop Production and

Marketing to Sell Product

$23M

Demands Med.

Demands Low

(p=0.3)

(p=0.7)

$25M

-$2M-$10M

(p=0.25) $55M

(p=0.55) $33M

(p=0.20) $15M

$43M

$21M

$3M

A Decision Tree Representation (With Cash Flows and Probabilities Specified)

of the Research-and-Development Decision Problem

Decision Details

Production

DecisionMarket

Result


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Decision Details

• Defining Measurement Scales for Fundamental Objectives

– Objectives with natural attribute scales can be measured objectively

• e.g. monetary values, time, length, weight, etc.

– Objectives without natural attribute scales

• e.g. public image, quality of life, etc.

• Measured indirectly with proxies

– GPA as a measure of a person’s intelligence

• Measured subjectively using an attribute rating scale

– The quality of life can be measured using a five-point Likert scale questionnaire

(best, better, satisfactory, worse, and worst)


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Exercise

3.9 in the textbook

A dapper young decision maker has just purchased a new suit for $200. On the

way out the door, the decision maker considers taking an umbrella. With the

umbrella on hand, the suit will be protected in the event of rain. Without the

umbrella, the suit will be ruined if it rains. On the other hand, if it does not

rain, carrying the umbrella is an unnecessary inconvenience.

1. Draw a decision tree of this situation

2. Draw an influence diagram of this situation

3. Before deciding, the decision maker considers listening to the weather

forecast on the radio. Draw an influence diagram that takes into account

the weather forecast

Yan Liu, Department of BIE, Wright State University ...nbaloian/DSS-DCC/Temas/Structuring...

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