3. decision making payoff matrix_tree analysis.ppt
TRANSCRIPT
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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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Equipment Replacement Decisions
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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Equipment Replacement Decisions
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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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 50 150
S2 200 0 0 200
S3 400 150 100 400
Maximum
Regret
Strategic
Altenatives
Events and Regrets
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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 50 150
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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Hurwicz Criterion Example
Take degree of optimism as 0.6
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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Hurwicz Criterion Example
Take degree of optimism as 0.6
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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Laplace Criterion Example
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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Laplace Criterion Example
A B C D
1 4 0 -5 3 0.52 -2 6 9 1 3.5
3 7 3 2 4 4.0
Events and Pay offsAlternative
Expected
Pay off
Expected Pay off for Alternative 1:
0.25 (4) + 0.25 (0) +0.25 (-5) + 0.25 (3) = 0.5
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Laplace Criterion Example
A B C D
1 4 0 -5 3 0.52 -2 6 9 1 3.5
3 7 3 2 4 4.0
Events and Pay offsAlternative
Expected
Pay off
Expected Pay off for Alternative 1:
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
Expected payoff Criterion
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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 payoff Criterion
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
Expected payoff Criterion
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
Expected payoff Criterion
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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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Value of Perfect Information
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 ?
Value of Perfect Information
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Value of Perfect Information
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 ?
Value of Perfect Information
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Value of Perfect Information
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