An introduction to decision trees
- 1. AN INTRODUCTION TO DECISION TREES: widely used quantitative technique to make decision
- 2. Duration: 30 minutes Presented by Fahim Muntaha
- 3. Objective/ Learning Outcome • To have a clear idea about decision tree • How to use this tool in making quantitative decisions • Impacts of these decisions in real life
- 4. Content • Define Decision Tree • Steps to make decision trees • Limitations of Decision Tree • Advantage of decision tree
- 5. A-5 The Decision-Making Process Problem Decision Quantitative Analysis Logic Historical Data Marketing Research Scientific Analysis Modeling Qualitative Analysis Emotions Intuition Personal Experience and Motivation Rumors
- 6. Quantitative Decision Making Tools: • Decision Trees, • Payback Analysis & • Simulations
- 7. What is a Decision Tree? • A Visual Representation of Choices, Consequences, Probabilities, and Opportunities. • A Way of Breaking Down Complicated Situations Down to Easier-to-Understand Scenarios. • By applying - Logic - Likely Outcome - Quantitative decision Decision Tree
- 8. Notation Used in Decision Trees • A box is used to show a choice that the manager has to make. (Decision Node) • A circle is used to show that a probability outcome will occur. (Chance Node) • Lines connect outcomes to their choice or probability outcome. • Terminal nodes - represented by triangles (optional)
- 9. Easy Example • A Decision Tree with two choices. Go to Graduate School to get my master in CS. Go to Work “in the Real World”
- 10. Example Decision Tree Decision node Chance node Event 1 Event 2 Event 3
- 11. Decision Trees Solving the tree involves pruning all but the best decisions at decision nodes, and finding expected values of all possible states of nature at chance nodes Works like a flow chart All paths - mutually exclusive
- 12. Mary’s Factory Mary is the CEO of a gadget factory. She is wondering whether or not it is a good idea to expand her factory this year. The cost to expand her factory is $1.5M. If she expands the factory, she expects to receive $6M if economy is good and people continue to buy lots of gadgets, and $2M if economy is bad. If she does nothing and the economy stays good she expects $3M in revenue; while only $1M if the economy is bad. She also assumes that there is a 40% chance of a good economy and a 60% chance of a bad economy.
- 13. Decision Tree Example Expand Factory Cost = $1.5 M Don’t Expand Factory Cost = $0 40 % Chance of a Good Economy Profit = $6M 60% Chance Bad Economy Profit = $2M Good Economy (40%) Profit = $3M Bad Economy (60%) Profit = $1M EVExpand = {.4(6) + .6(2)} – 1.5 = $2.1M EVNo Expand = .4(3) + .6(1) = $1.8M $2.1 > 1.8, therefore you should expand the factory
- 14. Steps are A. Draw the Diagram B. Use quantitative data i. Payoff Table and Probability ii. Decision under uncertainty iii. Expected Return iv. Expected value of perfect information
- 15. Problem: Jenny Lind Jenny Lind is a writer of romance novels. A movie company and a TV network both want exclusive rights to one of her more popular works. If she signs with the network, she will receive a single lump sum, but if she signs with the movie company, the amount she will receive depends on the market response to her movie. What should she do?
- 16. Step A: Jenny Lind Decision Tree Small Box Office Medium Box Office Large Box Office Small Box Office Medium Box Office Large Box Office Sign with Movie Co. Sign with TV Network
- 17. Payouts and Probabilities Movie company Payouts Small box office - $200,000 Medium box office - $1,000,000 Large box office - $3,000,000 TV Network Payout Flat rate - $900,000 Probabilities P(Small Box Office) = 0.3 P(Medium Box Office) = 0.6 P(Large Box Office) = 0.1
- 18. Step B: Use Quantitative Data in Decision Tree: Payoff Small Box Office Medium Box Office Large Box Office Small Box Office Medium Box Office Large Box Office Sign with Movie Co. Sign with TV Network $200,000 $1,000,000 $3,000,000 $900,000 $900,000 $900,000
- 19. A-19 ii. Decision Making Under Uncertainty - Criteria Maximax - Choose alternative that maximizes the maximum outcome for every alternative (Optimistic criterion). Maximin - Choose alternative that maximizes the minimum outcome for every alternative (Pessimistic criterion). Expected Value - Choose alternative with the highest expected value.
- 20. Jenny Lind Decision Tree Small Box Office Medium Box Office Large Box Office Small Box Office Medium Box Office Large Box Office Sign with Movie Co. Sign with TV Network $200,000 $1,000,000 $3,000,000 $900,000 $900,000 $900,000 .3 .6 .1 .3 .6 .1 ER ? ER ? ER ?
- 21. Probability of payoff Decision s States of Nature Probability of payoff Small Box Office Medium Box Office Large Box Office Small Box Office Medium Box Office Large Box Office Sign with Movie Company $200,00 0 $1,000,00 0 $3,000,00 0 200,000 X 0.3 = 60,000 1,000,000 X0.6= 600,000 3000,000 X0.1 = 300,000 Sign with TV Network $900,00 0 $900,000 $900,000 900,000X 0.3 = 270,000 900,000X 0.6 = 540,000 900,000X 0.1 = 90,000 Prior Probabilit ies 0.3 0.6 0.1
- 22. A-22 Expected Value Equation Probability of payoffEV A V P V V P V V P V V P V i i i i N N ( ( ) ( ) ( ) ( ) ) = = * = * + * + + * 1 1 1 2 2 Number of states of nature Value of Payoff Alternative i ... N
- 23. iii. Expected Return Criteria EVmovie=0.3(200,000)+0.6(1,000,000)+0.1(3,000,000) = $960,000 = EVBest EVtv =0.3(900,000)+0.6(900,000)+0.1(900,000) = $900,000 Select alternative with largest expected value (EV). Therefore, using this criteria, Jenny should select the movie contract.
- 24. Jenny Lind Decision Tree - Solved Small Box Office Medium Box Office Large Box Office Small Box Office Medium Box Office Large Box Office Sign with Movie Co. Sign with TV Network $200,000 $1,000,000 $3,000,000 $900,000 $900,000 $900,000 .3 .6 .1 .3 .6 .1 ER 900,000 ER 960,000 ER 960,000
- 25. Something to Remember Jenny’s decision is only going to be made one time, and she will earn either $200,000, $1,000,000 or $3,000,000 if she signs the movie contract, not the calculated EV of $960,000!! Nevertheless, this amount is useful for decision- making, as it will maximize Jenny’s expected returns in the long run if she continues to use this approach.
- 26. A-26 iv. Expected Value of Perfect Information (EVPI) EVPI places an upper bound on what one would pay for additional information. EVPI is the maximum you should pay to learn the future. EVPI is the expected value under certainty (EVUC) minus the maximum EV. EVPI = EVUC - maximum EV
- 27. Expected Value of Perfect Information (EVPI) What is the most that Jenny should be willing to pay to learn what the size of the box office will be before she decides with whom to sign?
- 28. EVPI Calculation EVwPI (or EVc) =0.3(900,000)+0.6(1,000,000)+0.1(3,000,000) = $1,170,000 EVBest (calculated to be EVMovie from the previous page) =0.3(200,000)+0.6(1,000,000)+0.1(3,000,000) = $960,000 EVPI = $1,170,000 - $960,000 = $210,000 Therefore, Jenny would be willing to spend up to $210,000 to learn additional information before making a decision.
- 29. Jenny Lind Decision Tree Small Box Office Medium Box Office Large Box Office Small Box Office Medium Box Office Large Box Office Sign with Movie Co. Sign with TV Network $200,000 $1,000,000 $3,000,000 $900,000 $900,000 $900,000
- 30. Jenny Lind Decision Tree - Solved Small Box Office Medium Box Office Large Box Office Small Box Office Medium Box Office Large Box Office Sign with Movie Co. Sign with TV Network $200,000 $1,000,000 $3,000,000 $900,000 $900,000 $900,000 .3 .6 .1 .3 .6 .1 ER 900,000 ER 960,000 ER 960,000
- 31. Using Decision Trees Scientific analysis to decision making visual aids to structure solve sequential decision problems Especially beneficial when the complexity of the problem grows Useful for operational decision making Encourage clear thinking and planning
- 32. Decision Tree Limitations local optimal solution not global optimal solution Possibility of duplication with the same sub-tree on different paths Possibility of spurious relationships
- 33. Thanks