Decision Trees for Decision Making1
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Transcript of 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.