1Decision Trees 1 ENMA 6010: Decision Trees 1 Based on examples from: Decision Trees – A Primer...

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…

3Decision Trees 1

…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

Decision Trees 1 6

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)


2. Outcomes and Probabilities

7Decision Trees 1



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?



8Decision Trees 1

3. Endpoints and Payoffs



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

9Decision Trees 1

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


Expected Value =Payoff *

Probability

Expected Value =Payoff *

Probability

10Decision Trees 1

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)


Expected Value =Sum( Endpoint Expected

Values)

Expected Value =Sum( Endpoint Expected

Values)

11Decision Trees 1

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

Decision Trees 1 12

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







Neither product

13Decision Trees 1

Expected value = $400K






14Decision Trees 1


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

15Decision Trees 1

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?

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

Product A-$100K

17Decision Trees 1

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%





18Decision Trees 1

2. Outcomes and Probabilities



Product A-$100K

Success0.5

Failure0.5

Submit-$5K

Don’t Submit$0K

Commercial0.3

Residential0.6

None0.1

Submit?





Product A-$100K

19Decision Trees 1

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



Submit?

Payoff = Benefit - CostPayoff = Benefit - Cost

4. End Point Expected Values

Product A-$100K

20Decision Trees 1

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?



Product A-$100K

21Decision Trees 1

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?



$675K

$675K

Product A-$100K

22Decision Trees 1

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

23Decision Trees 1

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?

25Decision Trees 1

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?


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:

26Decision Trees 1

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?


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.

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.







Which project, if either, should you do?

Well, what are the spreads?

28Decision Trees 1

Decision Trees 1 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?

1Decision Trees 1 ENMA 6010: Decision Trees 1 Based on examples from: Decision Trees – A Primer...

Documents

Transcript of 1Decision Trees 1 ENMA 6010: Decision Trees 1 Based on examples from: Decision Trees – A Primer...