11. decision tree

7/28/2019 11. Decision Tree

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Decision TreeDecision Tree


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Decision Tree

Representation of sequence of alternative decisions and

their results

Benefits of decision tree: Pictorial representation of sequential decision process

which helps clear understanding of process

Makes expected value computation easier

More than one alternative decisions can be considered

and compared in single diagram


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Decision Tree

3

D1BC

A

D1

HIGH SALES

LOW SALES


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Problem - 1

Sales

Units Probability Unit Cost Probability

10,000 0.8 Rs 6 0.7

15,000 0.2 Rs 8 0.3

4

A company can choose to launch a new product

XYZ or not. If the product is launched expected

sales and expected unit cost are shown in the

table


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Problem - 1

5

D1

Do not launch

Launch

1

Sales, 10000 (0.8)

Sales, 15000 (0.2)

2

3

Cost 6 (0.7)

Cost 8 (0.3)

Cost 6 (0.7)

Cost 8 (0.3)


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Problem - 1

6

D1

Do not launch

Launch

1

Sales, 10000, Cost Rs 6 (0.56)

Sales, 10000, Cost Rs 8 (0.24)

Sales, 15000, Cost Rs 6 (0.14)

Sales, 15000, Cost Rs 8 (0.6)


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Problem - 2

A co has an investable surplus of Rs 100 cr, Investing

this in existing business can give areturn of 8%.

Alternatively there is an opportunity of diversification

which if successful is expected to bring a return of 17%.

However if diversification is not successful expectedreturn will be only 2%. What must be the probabilities of

two outcomes of diversification for it to be worthwhile.

Let probability of success be X, so probability of failurewill be 1-X

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Problem - 2

8

D1

Existing business Rs 8 cr

Diversification1

Success X% - 17 cr

Failure (1-X)% - 2 cr


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Problem - 2

Evaluation of diversification should be atleast 8cr.

Hence,

8 = 17X + 2(1-X)

8 = 17X + 2 2XX = 0.4

Probability of success in diversification should atleast be

40%

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Problem - 3

A mfg co has to select one of the two products A & B. A

requires investment of Rs 20000 and B requires 40000.

Market research survey shows high, medium and low

demands with corresponding probabilities and return

from sales. Construct an appropriate decision tree. Whatdecision the company should take.

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Problem - 3

Market Probability Return from Sales

A B A B

HIGH 0.4 0.3 50000 80000

MEDIUM 0.3 0.5 30000 60000

LOW 0.3 0.2 10000 50000

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Problem - 3

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D1

Product A

Product B2

HIGH, 80000 (0.3)

LOW, 50000 (0.2)

1

HIGH, 50000 (0.4)

LOW, 10000 (0.3)

MED, 30000 (0.3)

MED, 60000 (0.5)


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Problem - 3

Roll Back technique to evaluate decision tree

We need to calculate earnest monetory value (EMV) for

each alternate

EMV at 1 (50000 x 0.4) + (30000 x 0.3) + (10000 x 0.3)

= 32,000

EMV at 2 (80000 x 0.3) + (60000 x 0.5) + (50000 x 0.2)

= 64,000

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Problem - 3

Net profit from product A 32000 20000 = Rs 12,000

Net profit from product B 64000 40000 = Rs 24000

Optimum decision at D1 is product B

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Problem 4 (Practice)

Alfa industries has to decide whether to set up a alarge

plant or a small plant for its new range of refrigerators. A

large plant will cost the company Rs 25 lakhs while the

small plant will cost Rs 12 lakhs. An extensive market

survey and a cost profit volume analysis carried ou bythe company reveal:

High demand probability = 0.5

Medium demand probability = 0.3 Low demand probability = 0.2

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Problem 4 (Practice)

A large plant with high demand will yield an annual profit

of Rs 100 lakhs

A large plant with moderate demand will yield an annual

profit of Rs 60 lakhs

A large plant with low demand will loose Rs 20 lakhs

annually due to production inefficiencies

A small plant with high demand will yield an annual profit

of Rs 25 lakhs

A small plant with moderate demand will yield an annual

profit of Rs 35 lakhs

A small plant with low demand will yield an annual profit

of Rs 45 lakhs16


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Problem - 5

A company has an opportunity of marketing a new

package of computer games. It has two possible courses

of action: to test market on a limited scale or to

completely give up the project. A test market would cost

Rs 1,60,000 and current evidence suggest thatconsumer reaction is equally likely to be positive or

negetive. If the reaction to the test marketing were to be

positive the company could either market the games

nationally or still give up the project.

Research suggest that the national launch might result in

following sales:

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Problem - 5

SALES CONTRIBUTION(Million)

Probability

HIGH 0.25

MEDIUM 0.3 0.50

LOW -0.24 0.25

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If the test marketing were to yield negetive results the

company would give up the project. Giving up the

project at any point would result in a contribution of

Rs 60000 from sale of patents and copyrights.


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Problem - 5

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D1

Give up the project, Contribution = Rs 60000

Test Market

Cost = Rs

160000

1

Negative, Contribution Rs 60000 (0.5)

Positive (0.5) D2

Give up the project,

Contribution = Rs

60000

2

High, 12,00,000(0.25)

Low, -2,40,000(0.25)

Moderate, 3,00,000(0.5)Market


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Problem - 5

EMV at 2 (1200000 x 0.25) + (300000 x 0.5) + (-240000 x 0.25)

= 3,90,000

Decision at D2 is to market the product

EMV at 1

390000 x 0.5 = 1,95,000 for positive For negative contribution is 60000

Choose positive i.e 1,95,000

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Decision at D1 If we test market = 195000 160000 = 35,000

If we drop the project = Rs 60000

Select dropping the project

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11. decision tree

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