Decision Trees for Decision Making1

8/6/2019 Decision Trees for Decision Making1

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Prof. Anjali M. Kulkarni

Decision Trees for Decision Making


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Decision Tree

y A graphical depiction of the sequences of event/ action

combinations in a systematic manner.

y Used for sequential decisions, rather than a single decision.

yA tree is composed of squares, circles and lines.

y Squares indicate decision points and circles represent chance

events.

y The lines or branches emanating from a square indicates

alternatives while those emanating from circles indicatestates of nature.


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Decision Tree Format

a1

a1

a1

s1

s1

s1

s2

s2

s2

s3

s3

S3

Payoff 1,1

Payoff 1,2

Payoff 1,3Payoff2,1

Payoff2,2

Payoff2,3

Payoff3,1

Payoff3,2

Payoff3,3


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Exampley Unicom Inc. is adding a new product. In order to accommodate the anticipated capacity

need of the new product, the firm believes that a new plant must be built. The firm has

to make a decision to build a large plant or a small plant. In either case, demand will be

either favourable or unfavourable with probabilities of 0.55 and 0.45 resp. If a large

plant is built and demand is favourable, the NPV of returns is estimated at Rs.

15,00,000. if demand is unfavourable, the net loss with the large plant is estimated to beRs. 50,000.

y If a small plant is built and demand is unfavourable, the NPV is Rs. 70,000. if demand

proves to be favourable, the firm can either maintain the small plant or expand it.

Maintaining the small plant has a NPV of Rs. 950,000. if the firm decides to expand, the

firm can expect a high return or a low return. There is a 40% chance of earning a NPV

of Rs. 1330,000 (high return) and a 60% chance of earning Rs. 720,000 (low return).y Draw a decision tree for this problem.

y Calculate all of the necessary expected values and determine the best course of action for

management.


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Decision Tree

5

3

4

2

1

700,000

950,000

1330,000

720,000

1500,000

-50,000


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Solutiony Starting from Node 1, expected return is given by

y EMV1 = 0.4 x 1330,000 + 0.6 x 720,000 = Rs. 964000

y Since the expected monetary value of expansion is greaterthan the EMV of maintaining the current size, we choose toexpand.

y At node 3,

y EMV3 = 0.45 x 700,000 + 0.55 x 964000 = Rs. 845,200

y At node 4,

y EMV4= 0.55 x 1500,000 + 0.45 x (-50000) = Rs. 802,500


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Decision Tree

5

3

4

2

1

700,000

950,000

1330,000

720,000

1500,000

-50,000

964000

964000


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Decision Tree

5

3

4

2

1

700,000

950,000

1330,000

720,000

1500,000

-50,000

964000

964000

845,200


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Solution

y When we compare node 3 and 4, EMV of building a small

plant is higher. Therefore we conclude that Unicom Inc.

should choose to build a small plant, and if the demand is

favourable, the company should choose to expand. The

overall net return for the company is Rs. 845,000.


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Question 1

y A businessman has two independent investments A & B

available to him but he lacks the capital to undertake both

simultaneously. He can choose to take A first and then stop or

if A is successful then take B or vice versa. The probability of

success of A is 0.7 while for B it is 0.4. both investments

require an initial capital outlay of Rs. 200000 and both return

nothing if unsuccessful. Successful completion of A will

return Rs. 30000 over cost and the successful completion of

B will return Rs. 15000 over cost . Draw the decision treeand determine best strategy.


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Question 2y Sanchar Ltd. Is dealing with a newly invented telephone device, is faced

with the problem of selecting from the following courses of action:

(a) Manufacture the device themselves

(b) Manufacture by another party on royalty basis

(c) Sell the rights of the invention for a lump sum

y The expected profits in Rs. Lacs at different levels are as below-

Outcome Probability Option a Option b Option c

High sales 0.1 75 35 15

Medium sales 0.3 25 20 15

Low sales 0.6 -10 10 15


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Q. 2 Continuedy Represent the companys problem in the form of a decision

tree. Give your decision on this.

y Redraw the tree with following further information:

(a) If the company manufactures the product ands sales aremedium or high then the company has opportunity ofdeveloping a new version of the telephone.

(b) From past experience, the company estimates that there isa 50% chance of successful development.

(c) The cost of development is Rs. 15 lacs and the returns afterdeducting the development costs are Rs. 30 lacs and Rs. 10lacs for high and medium sales resp.

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