Decision Analysis-Decision Trees

1. 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).

2. Decision Analysis-Decision Trees General Form of a Decision Tree

3. 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.

4. 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.

5. Decision Analysis-Decision Trees Case Problem - (A) p. 38 (continued)

6. Decision Analysis-Decision Trees

7. 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, .....)

8. 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

9. Decision Analysis-Decision Trees

10. Decision Analysis-Decision Trees Case Problem (A) p. 64

11. Decision Analysis-Decision Trees

12. Decision Analysis-Decision Trees

13. Decision Analysis-Decision Trees

14. Decision Analysis - Treeplan Ctrl-t activates Treeplan

15. Decision Analysis - Treeplan

16. Decision Analysis - Probability

17. Decision Analysis Conditional Probability

18. Decision AnalysisPerfect Information

19. Decision AnalysisNo Information

20. Decision AnalysisPerfect Information

21. Decision AnalysisNo Information

22. Decision AnalysisImperfect Information

23. Decision Analysis Bayes Theorem

24. 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’

25. Decision Analysis-Decision TreesModified Case Problem - Imperfect Information

26. Decision Analysis-Decision TreesModified Case Problem - Imperfect Information

27. 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

28. Decision Analysis-Decision Trees Modified Case Problem - Imperfect Information Next Page

29. Decision Analysis-Decision TreesModified Case Problem- Imperfect Information Previous Page

30. 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

31. Decision Analysis-Decision TreesImperfect Information-Sensitivity Analysis Next Page

32. Decision Analysis-Decision TreesImperfect Information-Sensitivity Analysis Previous Page