1. -73- HMP654 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. -74- HMP654 Decision Analysis-Decision Trees General Form of a Decision Tree

3. -75- HMP654 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. Alternative A Alternative B Alternative C Decision Node

4. -76- HMP654 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. State of Nature 1 State of Nature 2 State of Nature 3 Event Node

5. -77- HMP654 Decision Analysis-Decision Trees Case Problem - (A) p. 38 (continued)

6. -78- HMP654 Decision Analysis-Decision Trees

7. -79- HMP654 Decision Analysis-Decision Trees In a maximization problem, the value assigned to a decision node is the maximum of the values of the adjacent nodes. Evaluation of Nodes V1 V2 V3 V4 V4 = MAX(V1, V2, V3,.....)

8. -80- HMP654 Decision Analysis-Decision Trees The value assigned to an event node is the expectation of the values that correspond to adjacent nodes. Evaluation of Nodes V1 V2 V3 V4 p1 p2 p3 V4 = V1 x p1 + V2 x p2 + V3 x p3

9. -81- HMP654 Decision Analysis-Decision Trees

10. -82- HMP654 Decision Analysis-Decision Trees Case Problem (A) p. 64

11. -83- HMP654 Decision Analysis-Decision Trees

12. -84- HMP654 Decision Analysis-Decision Trees

13. -85- HMP654 Decision Analysis-Decision Trees

14. -86- HMP654 Decision Analysis - Treeplan Ctrl-t activates Treeplan

15. -87- HMP654 Decision Analysis - Treeplan

16. -88- HMP654 Decision Analysis - Probability

17. -89- HMP654 Decision Analysis Conditional Probability

18. -90- HMP654 Decision Analysis Perfect Information

19. -91- HMP654 Decision Analysis No Information

20. -92- HMP654 Decision Analysis Perfect Information

21. -93- HMP654 Decision Analysis No Information

22. -94- HMP654 Decision Analysis Imperfect Information

23. -95- HMP654 Decision Analysis Bayes Theorem

24. -96- HMP654 Decision Analysis-Decision Trees Modified 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. -97- HMP654 Decision Analysis-Decision Trees Modified Case Problem - Imperfect Information

26. -98- HMP654 Decision Analysis-Decision Trees Modified Case Problem - Imperfect Information

27. -99- HMP654 Decision Analysis-Decision Trees Modified Case Problem - Imperfect Information SF RS RF 0.720.28 0.318 0.682 Probabilities of “report outcome” given “actual outcome” p(S)p(F) p(RS) p(RF) SF RS RF Probabilities of “actual outcome” given “report outcome”

28. -100- HMP654 Decision Analysis-Decision Trees Next Page Modified Case Problem - Imperfect Information

29. -101- HMP654 Decision Analysis-Decision Trees Modified Case Problem- Imperfect Information Previous Page

30. -102- HMP654 Decision Analysis-Decision Trees Imperfect Information-Sensitivity Analysis SF RS RF 0.720.28 0.31 0.69 Probabilities of “report outcome” given “actual outcome” p(S)p(F) p(RS) p(RF) SF RS RF Probabilities of “actual outcome” given “report outcome”

31. -103- HMP654 Decision Analysis-Decision Trees Imperfect Information-Sensitivity Analysis Next Page

32. -104- HMP654 Decision Analysis-Decision Trees Imperfect Information-Sensitivity Analysis Previous Page