3. decision making payoff matrix_tree analysis.ppt

8/14/2019 3. Decision making Payoff Matrix_Tree Analysis.ppt

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Decision Making


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Sales Price Relationship Analysis

A workshop making lampshades finds that the number it

can sell varies depending on selling price.

It can sell 10 per week if the price is set at Rs. 80, but 50

per week if the price is reduced to Rs. 40. The cost of

production is Rs. 20 for each lampshade and there are

overheads of Rs. 60 per week.

Assume linear relationship between price and sales.

What should be the price to maximize his profit.


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Sales Price Relationship Analysis

0

500

1000

1500

2000

2500

0 20 40 60 80

Sales

R

upees

Revenue Cost Profit


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Inverse Costs

Maintenance department of a foundry wants to plan itsannual expenditure on equipment maintenance.

Currently it has a crew of 10 people. It costs the company

Rs. 20000 per month per crew member.

If department increases its crew size, it can make

maintenance operations more efficient. As a result

breakdown costs will come down.

Data analysis showed that size of maintenance crew and

breakdown loss have a inverse relation as follows.


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Inverse Costs

Crew size 10 11 12 13 14 15

Ependiture 2400000 2640000 2880000 3120000 3360000 3600000

Breakdown loss 12000000 6000000 4000000 3000000 2400000 2000000

Total cost 14400000 8640000 6880000 6120000 5760000 5600000

Crew size 16 17 18 19 20

Ependiture 3840000 4080000 4320000 4560000 4800000

Breakdown loss 1900000 1800000 1700000 1600000 1500000

Total cost 5740000 5880000 6020000 6160000 6300000


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Inverse Costs

0

2000000

4000000

60000008000000

10000000

12000000

14000000

16000000

8 9 10 11 12 13 14 15 16 17 18 19 20 21

Crew size

Cost

Expenditure Breakdown loss Total cost


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Inventory Costs

Annualcost

Lot Size (Q)

Holding cost (HC)

Ordering (setup) cost (OC)

Total cost = HC+ OC


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Replacement Decisions


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Depreciation

Any equipment we use at work reduces in value year by

year, which is called as depreciation.

Calculation of depreciation is needed for many decision

making situations and one of them is replacement

analysis.

There are two basic methods of depreciation calculation.

1. Straight line analysis

2. Declining Balance method


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Depreciation and Replacement Analysis

A machine tool costs Rs. 300,000 when new.

Lets calculate the written down value after 1,2 and 3 years using

1. Straight line method with annual depreciation of Rs. 50,000

2. By declining Balance method with annual depreciation of 20 %

Approach 1: Straight line method

Capital cost = 3,00,000

Annual depreciation = 50,000Value after 1st year = 2,50,000

Value after 2nd year = 2,00,000

Value after 3rd year = 1,50,000


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Depreciation and Replacement Analysis

A machine tool costs Rs. 300,000 when new.

Lets calculate the written down value after 1,2 and 3 years using

1. Straight line method with annual depreciation of Rs. 50,000

2. By declining Balance method with annual depreciation of 20 %

Approach 2: Declining balance method

Capital cost = 3,00,000

Annual depreciation = 20%Value after 1st year = 30,00,000 - 0.2 x 3,00,000 = 2,40,000

Value after 2nd year = 2,40,0000.2 x 2,40,000 = 1,92,000

Value after 3rd year = 1,92,0000.2 x 1,92,000 = 1,53,600


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Equipment Replacement Decisions

Suppose a factory has a permanent need for an

equipment, that wears out over a period of several

years. In the initial period of use, the depreciation is

likely to be high but maintenance costs will be low.

Towards the end of its useful life, the rate of

depreciation may be slow but maintenance costs will

be high.

When will it be better to sell off the existing equipment

and purchase a new one ?


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When will it be better to sell off the existing equipment

and purchase a new one ?

Year Depreciation maintenance

Cost

1 50000 6000

2 45000 75003 40000 12000

4 35000 20000

5 30000 34000

6 25000 50000

7 20000 700008 15000 90000


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0

20000

40000

60000

80000

100000

120000

0 2 4 6 8 10

Year

Rupees

Depreciation Maintenence Total Cost


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Decision making Under Uncertainty


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A set of quantitative decision-making techniques for

decision situations where uncertainty exists

States of nature

events that may occur in the future

decision maker is uncertain which state of nature

will occur

decision maker has no control over the states of

nature

Decision making Under Uncertainty


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Payoff Table

A method of organizing & illustrating the payoffs

from different decisions given various states ofnature

A payoff is the outcome of the decision


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Payoff Table

States Of Nature

Decision a b1 Payoff 1a Payoff 1b

2 Payoff 2a Payoff 2b


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Decision making Criteria

Maximax criterion (optimistic)

choose decision with the maximum of the maximum

payoffs

Maximin criterion (Pessimist)

choose decision with the maximum of the minimum

payoffs

Minimax regret criterion

choose decision with the minimum of the maximum

regrets for each alternative


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Hurwicz criterion

choose decision in which decision payoffs are

weighted by a coefficient of optimism,

coefficient of optimism () is a measure of a decision

makers optimism, from 0 (completely pessimistic) to 1

(completely optimistic)

Equal likelihood (Laplace) criterion

choose decision in which each state of nature is

weighted equally

Decision making Criteria


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A B C D

X 8 0 -10 6

Y -4 12 18 -2

Z 14 6 0 8

Pay-Offs in Thousands of rupeesAlternative

X -10 8Y -4 18

Z 0 14

Alternative Minimum Pay-off Maximum Pay-off

Decision Making Example


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A B C D

X 8 0 -10 6

Y -4 12 18 -2

Z 14 6 0 8

Pay-Offs in Thousands of rupeesAlternative

X -10 8Y -4 18

Z 0 14

Alternative Minimum Pay-off Maximum Pay-off

Maximin Maximax

Decision Making Example


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Minimax Regret Example

A B C

S1 700 300 150

S2 500 450 200

S3 300 300 100

Events and Pay-offsStrategic

Altenatives

A B C

S1 0 150 50

S2 200 0 0

S3 400 150 100

Strategic

Altenatives

Events and Regrets


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A B C

S1 700 300 150

S2 500 450 200

S3 300 300 100


Altenatives

A B C

S1 0 150 50 150

S2 200 0 0 200

S3 400 150 100 400

Maximum

Regret

Strategic

Altenatives

Events and Regrets


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A B C

S1 700 300 150

S2 500 450 200

S3 300 300 100


Altenatives

A B C

S1 0 150 50 150

S2 200 0 0 200

S3 400 150 100 400

Maximum

Regret

Strategic

Altenatives

Events and Regrets


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Hurwicz Criterion

Step 1:Choose alfa and (1-alfa)

Step 2:Determine for each alternative,

h = (alfa) (max pay off) + (1-alfa) (minimum pay off)

Step 3:Select the alternative with maximum value of h

alfa is the coefficient of optimism. It is a measure of a

decision makers optimism, from 0 to 1 (completelyoptimistic)

(1-alfa) is the degree of pessimism


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Hurwicz Criterion Example

Take degree of optimism as 0.6

A B C

S1 8000 4500 2000

S2 3500 4500 5000

S3 5000 5000 4000

Strategic

Altenativ

Events and Pay-offs

For alternative S1,

h = 0.6(8000)+0.4(2000) = 5600


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A B C

S1 8000 4500 2000 5600

S2 3500 4500 5000 4400

S3 5000 5000 4000 4600

Strategic

Altenative

Events and Pay-offsh


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A B C

S1 8000 4500 2000 5600

S2 3500 4500 5000 4400

S3 5000 5000 4000 4600

Strategic

Altenativ

Events and Pay-offsh


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Laplace Criterion Example

In this method we each state of nature is weighted equally.

In other words, likelihood of occurrence of events is

considered to be equal.

Step 1:Assign equal weights to each pay off of an

alternative or strategy.

Step 2:Estimate the expected pay off for each alternative

Step 3:Select the alternative which has the maximum

expected pay off


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A B C D

1 4 0 -5 32 -2 6 9 1

3 7 3 2 4

Events and Pay offsAlternative

Expected Pay off for Alternative 1:

0.25 (4) + 0.25 (0) +0.25 (-5) + 0.25 (3) = 0.5


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A B C D

1 4 0 -5 3 0.52 -2 6 9 1 3.5

3 7 3 2 4 4.0


Expected

Pay off


0.25 (4) + 0.25 (0) +0.25 (-5) + 0.25 (3) = 0.5


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A B C D

1 4 0 -5 3 0.52 -2 6 9 1 3.5

3 7 3 2 4 4.0


Expected

Pay off


0.25 (4) + 0.25 (0) +0.25 (-5) + 0.25 (3) = 0.5


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Decision making With Probabilities


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Decision making With Probabilities

Probabilities need to be assigned to events

Expected Value is a weighted average of decision

outcomes.

EV x p ix ixi

n

whereix outcome i

p ix probability of outco

( )

1

me i


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Expected payoff Criterion

A store keeper stocks a perishable item. Shelf life of thisitem is one month. Store keeper wants to determine the

number of items he should stock at the beginning of the

month.

He buys the item for Rs. 30 and sells at Rs. 50.He analyzes the trend for last two years i.e. 24 months.

The following table gives the sales during last 24 months.

Sales 10 11 12 13

Frequency 3 5 10 6


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Sales 10 11 12 13

Frequency 3 5 10 6

Probability 0.125 0.208 0.417 0.250



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10 11 12 1310 200 170 140 110

11 200 220 190 160

12 200 220 240 210

13 200 220 240 260

StockDemand


Expected Demand is derived from the sales of the past


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10 11 12 13

10 25.00 21.25 17.50 13.7511 41.67 45.83 39.58 33.33

12 83.33 91.67 100.00 87.50

13 50.00 55.00 60.00 65.00

EMV 200.00 213.75 217.08 199.58

Stock and conditional pay offDemand


EMV = Expected Monetary Value


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10 11 12 13

10 25.00 21.25 17.50 13.7511 41.67 45.83 39.58 33.33

12 83.33 91.67 100.00 87.50

13 50.00 55.00 60.00 65.00

EMV 200.00 213.75 217.08 199.58

Stock and conditional pay offDemand



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Expected Regret Criterion

10 11 12 13

10 0 30 60 90

11 20 0 30 60

12 40 20 0 30

13 60 40 20 0

Stock and Regret

Demand

10 11 12 13

10 0.00 3.75 7.50 11.25

11 4.17 0.00 6.25 12.50

12 16.67 8.33 0.00 12.50

13 15.00 10.00 5.00 0.00

ER 35.83 22.08 18.75 36.25

Stock and Conditional RegretDemand

D i i T


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Decision Trees

Decision Trees


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Decision Trees

Bharat Oil Company (BOC) owns a land that may

contain oil.

Geologist report shows a 25% chance of oil

Another company is offering to buy the land for Rs.90 Cr

If BOC decides to drill, it will earn a profit of Rs. 700

Cr if oil is found.

However, it will incur a loss of Rs. 100 Cr if oil is notfound.

Should BOC drill or sell ?

Decision Trees


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Decision Trees

Oil

Oil

Dry

Dry

(0.25)

(0.25)

(0.75)

(0.75)

700 Cr

-100 Cr

90 Cr

90 Cr

Drill

Sell

decision

Expected

pay off is

100 Cr

Expected

pay off is

90 Cr

Value of Perfect Information


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In many decision making exercises it is possible

to get more or extra information about the events

or state of nature.

But it will cost extra money.

Question : Is additional information worth the

cost ?



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Continuing with the previous example,

A sesmic survey can tell whether the land is fairly

likely or fairly unlikely to have oil.Cost of the survey is Rs. 30 Cr

Should BOC do the survey ?



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Expected pay off with perfect information is

= 0.25 (700) + 0.75 (90) = 242.5 Cr

Expected value of perfect information is

= Expected pay off with perfect information - Expected pay

off without perfect information

= 242.5100 = 142.5 Cr.

If EVPI is less than the cost of survey, then dont do thesurvey. Its not worth it.

In this case, 142.5 Cr. >> 30 Cr.

It is worthwhile doing the survey.

Decision Trees


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Decision Trees

A firm is adding a new product line and must build a new plant. Demand

will either be favourable or unfavourable, with probabilities of 0.6 and 0.4,

respectively. If a large plant is built and demand is favourable the pay off is

estimated to be Rs. 1520 Cr. If the demand is unfavourable, the loss with

larger plant will be Rs. 20 Cr

If a medium sized plant is built and demand is unfavourable, the pay off is

Rs. 760 Cr. If the demand proves to be favourable, the firm can maintain the

medium sized facility or expand it. Maintaining medium sized facility will

result in to a pay off of Rs. 950 Cr and expanding it will give a pay off of Rs

570 Cr in the next period.

Draw a decision tree for this problem

What should the management do to achieve the highest expected pay off ?

Decision Trees


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Decision Trees

Fav

Un Fav

(0.6)

(0.6)

(0.4)

(0.4)

1520 Cr

-20 Cr

760 Cr

Large

Small

decision Fav

Un Fav

Expand

Continue

570 Cr

950 Cr

0.6 (1520) 0.4 (20) = 904 Cr

0.6 (950) + 0.4 (760) = 874 Cr

Build a large Plant

3. decision making payoff matrix_tree analysis.ppt

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