Decision tree in decision analysis
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This document discusses decision tree analysis. It provides definitions and examples of decision trees. A decision tree is a graphical representation of decision making that uses nodes to represent decisions, chances, and outcomes. It can be used to identify the strategy most likely to reach a goal. The document includes an example problem where a glass factory is considering three courses of action based on future demand. A decision tree is drawn, expected monetary values are calculated for each alternative, and the alternative with the highest value, constructing a new facility, is identified as the most preferred decision.
Decision tree in decision analysis
- 1. Decision tree in decision analysis BY Dr.Ammara Omer Khakwani
- 2. Decision tree analysis • A decision tree is a graphic device of decision making process. • It is a graphical presentation of the various alternatives. • It is also known as tree-diagram
- 3. Decision tree A decision tree is a decision support tool that uses a tree-like graph or model of decisions and their possible consequences, including chance, event outcomes, resource costs, and utility. It is one way to display an algorithm. Decision trees are commonly used in Operations Research, specifically in Decision Analysis, to help identify a strategy most likely to reach a goal.
- 4. Types of nodes A decision Tree consists of 3 types of nodes:- 1. Decision nodes - commonly represented by squares. 2. Chance nodes - represented by circles. 3. End nodes - represented by triangles. A decision tree has burst nodes (splitting paths) no sink nodes (converging paths).
- 5. Example Problem:- A glass factory that specializes in crystal is developing a substantial back-log and for this the firm’s management is considering three courses of action ; the correct choice depends largely upon the future demand, which may be low , medium, or high. 1. Show this decision situation in the form of a decision tree. 2. Indicate the most preferred decision 3. Its corresponding expected value.
- 6. Demand Course of action Probabilities S1 S2 S3 Low 0.10 10 -20 -150 Medium 0.50 50 60 20 high 0.40 50 100 200 S1=Sub-contracting S2=being-overtime S3=construct new facility
- 7. Expected monetary value • EMV(S1)= (0.10x10)+(0.50x50)+(0.40x50) =46 • EMV(S2)= (0.10x-20)+(0.50x60)+(0.40x100) =68 • EMVS3 = (0.10x-150)+(0.50x20)+(0.40x200) =75 Highest EMV will be selected so, S3 will be selected.
- 8. Decision tree As per decision tree analysis S3 is selected=75 D 2 3 0.10x10=1 0.50x50=25 0.40x50=20 =46 0.10x20=-2 0.50x60=30 0.40x100=40 =40 0.10x-150=-15 0.50x20=10 0.40x200=80 =75 S2=being-overtime 1 node Alternatives EMV
- 9. To find out Most preferred Alternative • • Always find out • EMV
- 10. Expected value of Sample information • way of measuring market information. • Is increase in expected value resulting from the sample information. • EVSI=(EV with SI + Cost ) – (EV without SI) • = (75+200) – (46) • = 229 • = $229 are need for market study Where – EVSI= Expected value of sample information – EV with SI = expected value with sample information. – EV without SI = expected value without sample information.
- 11. Efficiency of sample information • Efficiency of sample information= • if the sample information was perfect then the efficiency would be 100% %100 EVPI EVSI %100 EVPI EVSI
- 12. Sensitivity analysis • EMV (node 1) • =(-150)P – (1-P)10 • =-150P+10P-10 • =-140P-10 • -140P=10 • P=10/-140=-0.0714