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# Decision Analysis-Decision Trees - PowerPoint PPT Presentation

Decision Analysis-Decision Trees. A decision tree is a graphical representation of every possible sequence of decision and random outcomes (states of nature) that can occur within a given decision making problem.

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Presentation Transcript

• A decision tree is a graphical representation of every possible sequence of decision and random outcomes (states of nature) that can occur within a given decision making problem.

• A decision tree is composed of a collection of nodes (represented by circles and squares) interconnected by branches (represented by lines).

General Form of a Decision Tree

Alternative B

Alternative C

Decision Node

Decision Analysis-Decision Trees

• A square node is called a decision node because it represents a decision. Branches emanating from a decision node represent the different alternatives for a particular decision.

State of Nature 2

State of Nature 3

Event Node

Decision Analysis-Decision Trees

• A circular node in a decision tree is called an event node because it represents an uncertain event. The branches emanating from an event node correspond to the possible states of nature or the possible outcomes of an uncertain event.

Case Problem - (A) p. 38 (continued)

Evaluation of Nodes

• In a maximization problem, the value assigned to a decision node is the maximum of the values of the adjacent nodes.

V1

V2

V4

V3

V4 = MAX(V1, V2, V3, .....)

Evaluation of Nodes

• The value assigned to an event node is the expectation of the values that correspond to adjacent nodes.

p1

V1

p2

V4

V2

p3

V3

V4 = V1 x p1 + V2 x p2 + V3 x p3

Case Problem (A) p. 64

Ctrl-t activates Treeplan

Decision Analysis Conditional Probability

Decision AnalysisPerfect Information

Decision AnalysisNo Information

Decision AnalysisPerfect Information

Decision AnalysisNo Information

Decision AnalysisImperfect Information

Decision Analysis Bayes Theorem

Decision Analysis-Decision TreesModified Case Problem - Imperfect Information

• Assume that it is possible for the market research report to be wrong. Thus, the content of the report does not provide the decision maker with certain knowledge about the true outcome of the campaign.

Conditional probabilities of ‘report outcomes’ given

‘actual outcomes’

Decision Analysis-Decision TreesModified Case Problem - Imperfect Information

Decision Analysis-Decision TreesModified Case Problem - Imperfect Information

Decision Analysis-Decision TreesModified Case Problem - Imperfect Information

Probabilities of “report outcome” given “actual outcome”

S

F

RS

0.682

p(RS)

RF

0.318

p(RF)

0.72

0.28

p(S)

p(F)

Probabilities of “actual outcome” given “report outcome”

S

F

RS

RF

Modified Case Problem - Imperfect Information

Next Page

Decision Analysis-Decision TreesModified Case Problem- Imperfect Information

Previous Page

Decision Analysis-Decision TreesImperfect Information-Sensitivity Analysis

Probabilities of “report outcome” given “actual outcome”

S

F

RS

0.69

p(RS)

RF

0.31

p(RF)

0.72

0.28

p(S)

p(F)

Probabilities of “actual outcome” given “report outcome”

S

F

RS

RF

Decision Analysis-Decision TreesImperfect Information-Sensitivity Analysis

Next Page

Decision Analysis-Decision TreesImperfect Information-Sensitivity Analysis

Previous Page