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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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Decision analysis decision trees
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.

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


Decision analysis decision trees1
Decision Analysis-Decision Trees

General Form of a Decision Tree


Decision analysis decision trees2

Alternative A

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.


Decision analysis decision trees3

State of Nature 1

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.


Decision analysis decision trees4
Decision Analysis-Decision Trees

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



Decision analysis decision trees6
Decision Analysis-Decision Trees

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, .....)


Decision analysis decision trees7
Decision Analysis-Decision Trees

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



Decision analysis decision trees9
Decision Analysis-Decision Trees

Case Problem (A) p. 64





Decision analysis treeplan
Decision Analysis - Treeplan

Ctrl-t activates Treeplan




Decision analysis conditional probability
Decision Analysis Conditional Probability


Decision analysis perfect information
Decision AnalysisPerfect Information


Decision analysis no information
Decision AnalysisNo Information


Decision analysis perfect information1
Decision AnalysisPerfect Information


Decision analysis no information1
Decision AnalysisNo Information


Decision analysis imperfect information
Decision AnalysisImperfect Information


Decision analysis bayes theorem
Decision Analysis Bayes Theorem


Decision analysis decision trees modified case problem imperfect information
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 trees modified case problem imperfect information1
Decision Analysis-Decision TreesModified Case Problem - Imperfect Information


Decision analysis decision trees modified case problem imperfect information2
Decision Analysis-Decision TreesModified Case Problem - Imperfect Information


Decision analysis decision trees modified case problem imperfect information3
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


Decision analysis decision trees13
Decision Analysis-Decision Trees

Modified Case Problem - Imperfect Information

Next Page


Decision analysis decision trees modified case problem imperfect information4
Decision Analysis-Decision TreesModified Case Problem- Imperfect Information

Previous Page


Decision analysis decision trees imperfect information sensitivity analysis
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 trees imperfect information sensitivity analysis1
Decision Analysis-Decision TreesImperfect Information-Sensitivity Analysis

Next Page


Decision analysis decision trees imperfect information sensitivity analysis2
Decision Analysis-Decision TreesImperfect Information-Sensitivity Analysis

Previous Page