Description
concept of Decision Tree and it contains topics like decision tree, representation, sequence of alternative decisions, benefits of decision tree
Decision Tree
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
2
Decision Tree
A B
D1
C
D
1
HIGH SALES
LOW SALES
3
Problem - 1
Sales
Units
10,000 15,000
Probability
0.8 0.2
Unit Cost
Rs 6 Rs 8
Probability
0.7 0.3
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
4
Problem - 1
Do not launch
D1
Sales, 10000 (0.8) Launch 1 3 Sales, 15000 (0.2) 2
Cost 6 (0.7) Cost 8 (0.3) Cost 6 (0.7) Cost 8 (0.3)
5
Problem - 1
Do not launch
D1
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)
6
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 expected return 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 failure will be 1-X
7
Problem - 2
Existing business – Rs 8 cr
D1
Success X% - 17 cr
Diversification
1 Failure (1-X)% - 2 cr
8
Problem - 2
• Evaluation of diversification should be atleast 8cr. Hence, 8 = 17X + 2(1-X) 8 = 17X + 2 – 2X X = 0.4 Probability of success in diversification should atleast be 40%
9
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. What decision the company should take.
10
Problem - 3
Market HIGH MEDIUM LOW
Probability A 0.4 0.3 0.3 B 0.3 0.5 0.2
Return from Sales A 50000 30000 10000 B 80000 60000 50000
11
Problem - 3
HIGH, 50000 (0.4)
Product A
1
MED, 30000 (0.3) LOW, 10000 (0.3)
D1
HIGH, 80000 (0.3)
Product B
2
MED, 60000 (0.5)
LOW, 50000 (0.2)
12
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
?
13
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
14
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 by the company reveal:
? ? ?
High demand probability = 0.5 Medium demand probability = 0.3 Low demand probability = 0.2
15
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 lakhs 16
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 that consumer 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:
17
Problem - 5
SALES HIGH MEDIUM CONTRIBUTION (Million) 1.2 0.3 Probability 0.25 0.50
LOW
-0.24
0.25
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.
18
Problem - 5
Give up the project, Contribution = Rs 60000
D1
Test Market Cost = Rs 160000 1 Positive (0.5)
Negative, Contribution Rs 60000 (0.5) Give up the project, Contribution = Rs 60000 High, 12,00,000(0.25)
D2
Market
2
Moderate, 3,00,000(0.5) Low, -2,40,000(0.25)
19
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
20
• Decision at D1
? ? ?
If we test market = 195000 – 160000 = 35,000 If we drop the project = Rs 60000 Select dropping the project
21
doc_794920488.ppt
concept of Decision Tree and it contains topics like decision tree, representation, sequence of alternative decisions, benefits of decision tree
Decision Tree
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
2
Decision Tree
A B
D1
C
D
1
HIGH SALES
LOW SALES
3
Problem - 1
Sales
Units
10,000 15,000
Probability
0.8 0.2
Unit Cost
Rs 6 Rs 8
Probability
0.7 0.3
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
4
Problem - 1
Do not launch
D1
Sales, 10000 (0.8) Launch 1 3 Sales, 15000 (0.2) 2
Cost 6 (0.7) Cost 8 (0.3) Cost 6 (0.7) Cost 8 (0.3)
5
Problem - 1
Do not launch
D1
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)
6
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 expected return 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 failure will be 1-X
7
Problem - 2
Existing business – Rs 8 cr
D1
Success X% - 17 cr
Diversification
1 Failure (1-X)% - 2 cr
8
Problem - 2
• Evaluation of diversification should be atleast 8cr. Hence, 8 = 17X + 2(1-X) 8 = 17X + 2 – 2X X = 0.4 Probability of success in diversification should atleast be 40%
9
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. What decision the company should take.
10
Problem - 3
Market HIGH MEDIUM LOW
Probability A 0.4 0.3 0.3 B 0.3 0.5 0.2
Return from Sales A 50000 30000 10000 B 80000 60000 50000
11
Problem - 3
HIGH, 50000 (0.4)
Product A
1
MED, 30000 (0.3) LOW, 10000 (0.3)
D1
HIGH, 80000 (0.3)
Product B
2
MED, 60000 (0.5)
LOW, 50000 (0.2)
12
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
?
13
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
14
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 by the company reveal:
? ? ?
High demand probability = 0.5 Medium demand probability = 0.3 Low demand probability = 0.2
15
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 lakhs 16
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 that consumer 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:
17
Problem - 5
SALES HIGH MEDIUM CONTRIBUTION (Million) 1.2 0.3 Probability 0.25 0.50
LOW
-0.24
0.25
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.
18
Problem - 5
Give up the project, Contribution = Rs 60000
D1
Test Market Cost = Rs 160000 1 Positive (0.5)
Negative, Contribution Rs 60000 (0.5) Give up the project, Contribution = Rs 60000 High, 12,00,000(0.25)
D2
Market
2
Moderate, 3,00,000(0.5) Low, -2,40,000(0.25)
19
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
20
• Decision at D1
? ? ?
If we test market = 195000 – 160000 = 35,000 If we drop the project = Rs 60000 Select dropping the project
21
doc_794920488.ppt