1decision trees 1 enma 6010: decision trees 1 based on examples from: decision trees – a primer...
TRANSCRIPT
1Decision Trees 1
ENMA 6010:
Decision Trees 1
Based on examples from:Decision Trees – A Primer for Decision-Making Professionalsby Rafael Olivas
©2010 ~ Mark PolczynskiAll rights reserved
Decision Trees 1 2
Where are we now?
•At this point, we have investigated a numberof approaches to create as-is and to-besystem models.
•Now, we need to examine mechanisms toactually decide which approaches to take.
•Further, it may be that a system itself contains adecision-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…
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 ~$400K in revenue,
And has an ~80% chance of success.
Which project, if either, should you do?
Let’s solve this problem using adecision tree…
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…OR…
Decision Trees 1 4
Decision Tree Elements
Choice nodes – Show the decisions to be made with choice costs.
Outcome nodes – Show probability of decision choices.
Endpoint nodes – Show payoffs for benefits of decisions.
Choice 1$ Cost
Choice 2$ Cost
Outcome 1% Prob.
Outcome 2% Prob.
Payoff 1$ Benefit
Payoff 2$ Benefit
Note:Cost and Benefit not necessarily $.
Decision?
5Decision Trees 1
Decision Tree Generation Methodology
1. Identify Decision and Alternatives• What is the decision you are making? (Choice nodes)• What are the alternatives available to you and what are the costs? (Branches)
2. Determine Outcomes and Probabilities• What are the outcomes for each alternative? (Outcome nodes)• What is the probability of each outcome?
3. Calculate Endpoints and Payoffs (Endpoint nodes)• Payoff = Benefit – Cost
4. Calculate Endpoint Expected Value• For each Endpoint: Expected Value = Payoff * Probability
5. Calculate Outcome Expected Value• For each Outcome node: Expected Value = Sum( Endpoint Expected Value)
6.Make Decision• Choose decision with highest Outcome Expected Value
7. Go to Next Decision
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Product ACost 100$ Rev 1,000$ Succ 50%
Product BCost 10$ Rev 400$ Succ 80%
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-$0K
Product?• What is the decision you
are making? (Choice nodes)
• What are the alternatives available to you and what are the costs? (Branches)
• What is the decision you are making? (Choice nodes)
• What are the alternatives available to you and what are the costs? (Branches)
2. Outcomes and Probabilities
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Product ACost 100$ Rev 1,000$ Succ 50%
Product BCost 10$ Rev 400$ Succ 80%
Product A-$100K
Product B-$10K
Neither-$0K
Success0.5
Failure0.5
Success0.8
Failure0.2
Product?
• What are the outcomes for each alternative? (Outcome nodes)
• What is the probability of each outcome?
• What are the outcomes for each alternative? (Outcome nodes)
• What is the probability of each outcome?
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3. Endpoints and Payoffs
Product ACost 100$ Rev 1,000$ Succ 50%
Product BCost 10$ Rev 400$ Succ 80%
Product A-$100K
Product B-$10K
Neither-$0K
Success0.5
Failure0.5
Success0.8
Failure0.2
$1M - $100K$900K
-$100K
$400K - $10K$390K
-$10K
$0
Product?
Payoff = Benefit - CostPayoff = Benefit - Cost
Payoff = Benefit -
Cost
Payoff = Benefit -
Cost
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4. End Point Expected Values
Product A-$100K
Product B-$10K
Neither-$0K
Success0.5
Failure0.5
Success0.8
Failure0.2
$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
For each Endpoint:Expected Value =Payoff * Probability
Expected Value =Payoff *
Probability
Expected Value =Payoff *
Probability
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5. Outcome Expected Values
Product A-$100K
Product B-$10K
Neither-$0K
Success0.5
Failure0.5
Success0.8
Failure0.2
$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)
For each Outcome node:Expected Value =Sum( Endpoint Expected Values)
Expected Value =Sum( Endpoint Expected
Values)
Expected Value =Sum( Endpoint Expected
Values)
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6. Make Decision
Product A-$100K
Product B-$10K
Neither-$0K
Success0.5
Failure0.5
Success0.8
Failure0.2
$900K * 0.5 =$450K
-$100K * 0.5 =-$50K
$390K * 0.8 =
$312K
-$10K * 0.2 =-$2K
$0
$400K
$310K
$0
Product?
Choose branch with highest Outcome Expected Value Choose branch with highest Outcome Expected Value
Highest Outcome Expected Value
Highest Outcome Expected Value
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Alternatives Cost Outcomes Benefit Prob Payoff
Endpoint Expected
Value
Outcome Expected
ValueSucceed 1,000$ 0.5 900$ 450$
Product A 100$ 400$ Fail -$ 0.5 (100)$ (50)$
Succeed 400$ 0.8 390$ 312$ Product B 10$ 310$
Fail -$ 0.2 (10)$ (2)$
Decision Tree in Spreadsheet Form:
Looks like you should do Product A
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
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Expected value = $400K
Expected value = $400K
Expected value = $300K
Expected value = $300K
Expected value = $0K
Expected value = $0K
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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?
Nothing changes for Product B or “Neither” branches, but we have anew decision for Product A , whether or not to submit for UL certification.
Product A-$100K
Product B-$10K
Neither-$0K
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Success0.5
Failure0.5
Success0.8
Failure0.2
-$100K * 0.5 =-$50K
$390K * 0.8 =
$312K
-$10K * 0.2 =-$2K
$0
$310K
$0
Product?
Submit?
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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
Product A-$100K
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Success0.5
Failure0.5
Submit-$5K
Don’t Submit$0K
1. Decision and Alternatives
Submit?
CommercialCost 5$ Rev 1,000$ Succ 30%
ResidentialCost $5Rev $800Succ 60%
• What is the decision you are making? (Choice nodes)
• What are the alternatives available to you and what are the costs? (Branches)
• What is the decision you are making? (Choice nodes)
• What are the alternatives available to you and what are the costs? (Branches)
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2. Outcomes and Probabilities
CommercialCost 5$ Rev 1,000$ Succ 30%
ResidentialCost $5Rev $800Succ 60%
Product A-$100K
Success0.5
Failure0.5
Submit-$5K
Don’t Submit$0K
Commercial0.3
Residential0.6
None0.1
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?
Product A-$100K
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Success0.5
Failure0.5
Submit-$5K
Don’t Submit$0K
Commercial0.3
Residential0.6
None0.1
$800K-$100K-$5K$695
$1M-$100K-$5K$895K
-$100K-$5K-$105K
-$100K
-$100K
3. End Points and Payoffs
CommercialCost 5$ Rev 1,000$ Succ 30%
ResidentialCost $5Rev $800Succ 60%
Submit?
Payoff = Benefit - CostPayoff = Benefit - Cost
4. End Point Expected Values
Product A-$100K
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Success0.5
Failure0.5
Submit-$5K
Don’t Submit$0K
Commercial0.3
Residential0.6
None0.1
0.6 x $695$417K
0.3 x $895$268.5K
0.1 x -$105-$10.5K
-$100K
-$100K
Submit?
For each Endpoint:Expected Value =Payoff * Probability
For each Endpoint:Expected Value =Payoff * Probability
Product A-$100K
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Success0.5
Failure0.5
Submit-$5K
Don’t Submit$0K
Commercial0.3
Residential0.5
None0.1
$417K
$268.5K
-$10.5K
-$100K
-$100K
$268.5K + $417K - $10.5K $675K
$268.5K + $417K - $10.5K $675K
5. Outcome Expected Values
-$100K
Submit?
For each Outcome node:Expected Value =Sum( Endpoint Expected Values)
For each Outcome node:Expected Value =Sum( Endpoint Expected Values)
$675K
$675K
Product A-$100K
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Success0.5
Failure0.5
Submit-$5K
Don’t Submit$0K
Commercial0.3
Residential0.5
None0.1
$417K
$268.5K
-$10.5K
-$100K
-$100K
6. Make Decision
Submit?
-$100K
Here, we choose to submit Product A for UL testing - obviously!
Choose branch with highest Outcome Expected Value Choose branch with highest Outcome Expected Value
Product A-$100K
Product B-$10K
Neither-$0K
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Success0.5
Failure0.5
Success0.8
Failure0.2
$675K * 0.5 =$337.5K
-$100K * 0.5 =-$50K
$390K * 0.8 =
$312K
-$10K * 0.2 =-$2K
$0
$287.5K
$310K
From previous decision
From previous decision
7. Go on to Next Decision
$0
Note: We now have a new value forthe Expected Value for Product A
New valueNew value
Decision Trees 1 24
Scenario 1 Scenario 2UL Not
Required UL RequiredProduct A 400$ 288$ Product B 310$ 310$
Neither -$ -$
Decision: Develop Product A, Product B, or Neither?
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Submit?
Alternatives CostTotal Cost Outcomes Benefit Prob Payoff
Endpoint Expected
Value
Outcome Expected
ValueCommercial 1,000$ 0.3 895$ 268.5$
Submit A 5$ 105$ Residential 800$ 0.6 695$ 417.0$ 675.0$ None -$ 0.1 (105)$ (10.5)$
Don't Submit -$ 100$ -$ (100)$ (100.0)$ (100.0)$
Product?
Alternatives Cost Outcomes Benefit Prob Payoff
Endpoint Expected
Value
Outcome Expected
ValueSucceed 1,000$ 0.5 675$ 338$
Product A 100$ 287.5$ Fail -$ 0.5 (100)$ (50)$
Succeed 400$ 0.8 390$ 312$ Product B 10$ 310.0$
Fail -$ 0.2 (10)$ (2)$
Scenario 2 Decision Tree in Spreadsheet Form:
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Submit?
Alternatives CostTotal Cost Outcomes Benefit Prob Payoff
Endpoint Expected
Value
Outcome Expected
ValueCommercial 1,000$ 0.3 895$ 268.5$
Submit A 5$ 105$ Residential 800$ 0.6 695$ 417.0$ 675.0$ None -$ 0.1 (105)$ (10.5)$
Don't Submit -$ 100$ -$ (100)$ (100.0)$ (100.0)$
Product?
Alternatives Cost Outcomes Benefit Prob Payoff
Endpoint Expected
Value
Outcome Expected
ValueSucceed 1,000$ 0.5 675$ 338$
Product A 100$ 287.5$ Fail -$ 0.5 (100)$ (50)$
Succeed 400$ 0.8 390$ 312$ Product B 10$ 310.0$
Fail -$ 0.2 (10)$ (2)$
This is difficult to follow on a spreadsheet.
Best develop the graphical tree first, then play “What If?” games.
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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.
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?
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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?