1. 1Decision Trees 1 ENMA 6010: Decision Trees 1 Based on examples from: Decision Trees – A Primer for Decision-Making Professionals by Rafael Olivas ©2010 ~ Mark Polczynski All rights reserved

2. Decision Trees 12 Where are we now? At this point, we have investigated a number of approaches to create as-is and to-be system models. Now, we need to examine mechanisms to actually decide which approaches to take. Further, it may be that a system itself contains a decision-making element. Thus, it is beneficial for us to add decision-making models to our growing list of system modeling tools. Here, we will be introduced to the concept of decision trees. We will start with a typical business decision…

3. Scenario 1: Which Product to Develop? Your new product development team has presented you with proposals for two new products, A and B. Product A will cost ~ $100K to develop, Will generate a revenue of ~$1,000K, And has a ~50% chance of succeeding Product B will cost ~$10K to develop, Will generate ~$400K in revenue, And has an ~80% chance of success. Which project, if either, should you do? Let’s solve this problem using a decision tree… 3Decision Trees 1 …OR…

4. Decision Trees 14 Decision Tree Elements Choice nodes – Show the decisions to be made with choice costs. Outcome nodes – Show probability of decision choices. Endpoint nodes – Show payoffs for benefits of decisions. Choice 1 $ Cost Choice 2 $ Cost Outcome 1 % Prob. Outcome 2 % Prob. Payoff 1 $ Benefit Payoff 2 $ Benefit Note: Cost and Benefit not necessarily $. Decision?

5. 5Decision Trees 1 Decision Tree Generation Methodology 1. Identify Decision and Alternatives What is the decision you are making? (Choice nodes) What are the alternatives available to you and what are the costs? (Branches) 2. Determine Outcomes and Probabilities What are the outcomes for each alternative? (Outcome nodes) What is the probability of each outcome? 3. Calculate Endpoints and Payoffs (Endpoint nodes) Payoff = Benefit – Cost 4. Calculate Endpoint Expected Value For each Endpoint: Expected Value = Payoff * Probability 5. Calculate Outcome Expected Value For each Outcome node: Expected Value = Sum( Endpoint Expected Value) 6.Make Decision Choose decision with highest Outcome Expected Value 7. Go to Next Decision

6. Decision Trees 16 1. Decision and Alternatives Decision: Which product to develop? Alternatives: Product A @ $100K Or Product B @ $10K Or Neither product @ $0 Product A -$100K Product B -$10K Neither -$0K Product? What is the decision you are making? (Choice nodes) What are the alternatives available to you and what are the costs? (Branches) What is the decision you are making? (Choice nodes) What are the alternatives available to you and what are the costs? (Branches)

7. 2. Outcomes and Probabilities 7Decision Trees 1 Product A -$100K Product B -$10K Neither -$0K Success 0.5 Failure 0.5 Success 0.8 Failure 0.2 Product? What are the outcomes for each alternative? (Outcome nodes) What is the probability of each outcome? What are the outcomes for each alternative? (Outcome nodes) What is the probability of each outcome?

8. 8Decision Trees 1 3. Endpoints and Payoffs Product A -$100K Product B -$10K Neither -$0K Success 0.5 Failure 0.5 Success 0.8 Failure 0.2 $1M - $100K $900K -$100K $400K - $10K $390K -$10K $0 Product? Payoff = Benefit - Cost

9. 9Decision Trees 1 4.End Point Expected Values Product A -$100K Product B -$10K Neither -$0K Success 0.5 Failure 0.5 Success 0.8 Failure 0.2 $900K * 0.5 = $450K -$100K * 0.5 = -$50K $390K * 0.8 = $312K -$10K * 0.2 = -$2K $0 Product? For each Endpoint: Expected Value = Payoff * Probability Expected Value = Payoff * Probability

10. 10Decision Trees 1 5.Outcome Expected Values Product A -$100K Product B -$10K Neither -$0K Success 0.5 Failure 0.5 Success 0.8 Failure 0.2 $900K * 0.5 = $450K -$100K * 0.5 = -$50K $390K * 0.8 = $312K -$10K * 0.2 = -$2K $0 $400K $310K $0 Product? For each Outcome node: Expected Value = Sum( Endpoint Expected Values) Expected Value = Sum( Endpoint Expected Values)

11. 11Decision Trees 1 6. Make Decision Product A -$100K Product B -$10K Neither -$0K Success 0.5 Failure 0.5 Success 0.8 Failure 0.2 $900K * 0.5 = $450K -$100K * 0.5 = -$50K $390K * 0.8 = $312K -$10K * 0.2 = -$2K $0 $400K $310K $0 Product? Choose branch with highest Outcome Expected Value Highest Outcome Expected Value

12. Decision Trees 112 Decision Tree in Spreadsheet Form: Looks like you should do Product A

13. Scenario 1: Which Product to Develop? Your new product development team has presented you with proposals for two new products, A and B. Product A will cost ~ $100K to develop, Will generate a revenue of ~$1,000K, And has a ~50% chance of succeeding Product B will cost ~$10K to develop, Will generate ~$400K in revenue, And has an ~80% chance of success. Neither product 13Decision Trees 1 Expected value = $400K Expected value = $300K Expected value = $0K

14. 14Decision Trees 1 Scenario 2: Which Product to Develop? New information just came in from marketing: Product A requires UL safety certification. UL certification can be for a commercial grade or a residential grade unit. Marketing estimates the revenues for commercial and residential units as: $1M = Commercial grade $800K = Residential grade The development team estimates the probability of passing UL testing as: 30% = Probability of passing commercial grade testing. 60% = Probability of passing residential grade test. 10% = Probability of failing UL testing. There is a $5K cost for UL certification. Now which product should we develop?

15. Nothing changes for Product B or “Neither” branches, but we have a new decision for Product A, whether or not to submit for UL certification. Product A -$100K Product B -$10K Neither -$0K 15Decision Trees 1 Success 0.5 Failure 0.5 Success 0.8 Failure 0.2 -$100K * 0.5 = -$50K $390K * 0.8 = $312K -$10K * 0.2 = -$2K $0 $310K $0 Product? Submit?

16. 16Decision Trees 1 Decision Tree Generation Methodology 1. Identify Decision and Alternatives What is the decision you are addressing (decision node)? What are the alternatives available to you (branches)? 2. Determine Outcomes and Probabilities What are the outcomes for each alternative (chance nodes)? What is the probability of each outcome? 3. Calculate Endpoints and Payoffs Payoff = Benefit – Cost 4. Calculate Endpoint Expected Value For each Endpoint: Expected Value = Payoff * Probability 5. Calculate Outcome Expected Value For each Outcome node: Expected Value = Sum( Endpoint Expected Value) 6.Make Decision Choose decision with highest Outcome Expected Value 7. Go to Next Decision

17. Product A -$100K 17Decision Trees 1 Success 0.5 Failure 0.5 Submit -$5K Don’t Submit $0K 1. Decision and Alternatives Submit? What is the decision you are making? (Choice nodes) What are the alternatives available to you and what are the costs? (Branches) What is the decision you are making? (Choice nodes) What are the alternatives available to you and what are the costs? (Branches)

18. 18Decision Trees 1 2. Outcomes and Probabilities Product A -$100K Success 0.5 Failure 0.5 Submit -$5K Don’t Submit $0K Commercial 0.3 Residential 0.6 None 0.1 Submit? What are the outcomes for each alternative? (Outcome nodes) What is the probability of each outcome? What are the outcomes for each alternative? (Outcome nodes) What is the probability of each outcome?

19. Product A -$100K 19Decision Trees 1 Success 0.5 Failure 0.5 Submit -$5K Don’t Submit $0K Commercial 0.3 Residential 0.6 None 0.1 $800K-$100K-$5K $695 $1M-$100K-$5K $895K -$100K-$5K -$105K -$100K 3. End Points and Payoffs Submit? Payoff = Benefit - Cost

20. 4.End Point Expected Values Product A -$100K 20Decision Trees 1 Success 0.5 Failure 0.5 Submit -$5K Don’t Submit $0K Commercial 0.3 Residential 0.6 None 0.1 0.6 x $695 $417K 0.3 x $895 $268.5K 0.1 x -$105 -$10.5K -$100K Submit? For each Endpoint: Expected Value = Payoff * Probability

21. Product A -$100K 21Decision Trees 1 Success 0.5 Failure 0.5 Submit -$5K Don’t Submit $0K Commercial 0.3 Residential 0.5 None 0.1 $417K $268.5K -$10.5K -$100K $268.5K + $417K - $10.5K $675K 5.Outcome Expected Values -$100K Submit? For each Outcome node: Expected Value = Sum( Endpoint Expected Values) $675K

22. Product A -$100K 22Decision Trees 1 Success 0.5 Failure 0.5 Submit -$5K Don’t Submit $0K Commercial 0.3 Residential 0.5 None 0.1 $417K $268.5K -$10.5K -$100K 6. Make Decision Submit? -$100K Here, we choose to submit Product A for UL testing - obviously! Choose branch with highest Outcome Expected Value

23. Product A -$100K Product B -$10K Neither -$0K 23Decision Trees 1 Success 0.5 Failure 0.5 Success 0.8 Failure 0.2 $675K * 0.5 = $337.5K -$100K * 0.5 = -$50K $390K * 0.8 = $312K -$10K * 0.2 = -$2K $0 $287.5K $310K From previous decision 7. Go on to Next Decision $0 Note: We now have a new value for the Expected Value for Product A New value

24. Decision Trees 124 Decision: Develop Product A, Product B, or Neither?

25. 25Decision Trees 1 Scenario 2 Decision Tree in Spreadsheet Form:

26. 26Decision Trees 1 This is difficult to follow on a spreadsheet. Best develop the graphical tree first, then play “What If?” games.

27. 27Decision Trees 1 So What? This concludes our first look at decision trees. This overview has focused on using this tool to provide quantitative “proof” for qualitative decisions. A future lecture will demonstrate how these scenarios can be made more realistic by incorporating Monte Carlo simulation to account for uncertainty.

28. Scenario 1: Which Product to Develop? Your new product development team has presented you with proposals for two new products, A and B. Product A will cost ~ $100K to develop, Will generate a revenue of ~$1,000K, And has a ~50% chance of succeeding Product B will cost ~$10K to develop, Will generate ~$400K in revenue, And has an ~80% chance of success. Which project, if either, should you do? Well, what are the spreads? 28Decision Trees 1

29. 29 What Next? Well, this works great if you have just one goal, like develop the product that has the greatest probability of making lots of money. But what if you have other simultaneous goals like: Keep you biggest customer happy, Create a green image for stockholders, etc… We saw how to use causal loop diagrams to model interdependencies among multiple simultaneous goals. Now, how can we model decision-making for systems with multiple simultaneous goals?