Post on 11-Oct-2020
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
Yan Liu, Department of BIE, Wright State University
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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
Yan Liu, Department of BIE, Wright State University
15
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
Yan Liu, Department of BIE, Wright State University
16
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.
Yan Liu, Department of BIE, Wright State University
17Influence Diagram of the Investment Decision Problem
Basic Influence Diagrams
Yan Liu, Department of BIE, Wright State University
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Basic Influence Diagrams
• 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.
Yan Liu, Department of BIE, Wright State University
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ForecastHurricane
Path
Decision Consequence
Basic Influence Diagrams
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
Yan Liu, Department of BIE, Wright State University
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Basic Influence Diagrams
• 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.
Yan Liu, Department of BIE, Wright State University
21
ForecastHurricane
Path
Evacuate? Consequence
Wait for
Forecast?
Basic Influence Diagrams
Influence Diagram of the Sequential Evacuation Decision Problem
sequence
Yan Liu, Department of BIE, Wright State University
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Basic Influence Diagrams
• 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
Yan Liu, Department of BIE, Wright State University
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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
Basic Influence Diagrams
Yan Liu, Department of BIE, Wright State University
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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
Yan Liu, Department of BIE, Wright State University
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Constructing an Influence Diagram
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)
Yan Liu, Department of BIE, Wright State University
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Constructing an Influence Diagram
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.
Yan Liu, Department of BIE, Wright State University
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Usage
Decision?
Lab
TestSurvey
Carcinogenic
Potential
Net Value
Economic
Value
Cancer
CostExposure
Rate
Constructing an Influence Diagram
EPA Example
Influence Diagram of the EPA Decision Problem
Net Value
Economic
Value
Cancer
Cost
Yan Liu, Department of BIE, Wright State University
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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)
Constructing an Influence Diagram
Yan Liu, Department of BIE, Wright State University
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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
Yan Liu, Department of BIE, Wright State University
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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)
Yan Liu, Department of BIE, Wright State University
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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
Yan Liu, Department of BIE, Wright State University
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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.
Yan Liu, Department of BIE, Wright State University
33
Decision Tree of the Politician’s Basic Risk Decision
Basic Decision Trees
Running
Decision
Election
Result
Yan Liu, Department of BIE, Wright State University
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• Double-Risk Decision Dilemma
– Decide between two risky prospects
Basic Decision Trees
The Politician’s Double- Risk Decision Dilemma
Running
Decision
Election
Result
Election
Result
Yan Liu, Department of BIE, Wright State University
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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.
Basic Decision Trees
Decision Tree of the
Insurance Example
Court
Result
Yan Liu, Department of BIE, Wright State University
36
Basic Decision Trees
• 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
Yan Liu, Department of BIE, Wright State University
37
Basic Decision Trees
• 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
Yan Liu, Department of BIE, Wright State University
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Basic Decision Trees
• Schematic Representation of Sequential Decisions
– In problems with many decisions involved, the sizes of full-blown
decision trees can increase exponentially
Yan Liu, Department of BIE, Wright State University
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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
Yan Liu, Department of BIE, Wright State University
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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
Yan Liu, Department of BIE, Wright State University
41
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.
Yan Liu, Department of BIE, Wright State University
42
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
Yan Liu, Department of BIE, Wright State University
43
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)
Yan Liu, Department of BIE, Wright State University
44
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