Introduction
• It is a statistical tool or
technique which is used to select the best way of doing any work.
• It helps in taking the best decision
by subtracting (avoiding/skipping) useless alternative.
Types of
Decision Problems
- Decision making under
certainty.
- Decision making under
uncertainty.
- Decision making under
risk/conflict.
NOTE: IT IS
ALSO KNOWN AS DECISION MAKING ENVIRONMENT.
METHODS
STEPS IN
DECISION MAKING
- Determine various approaches or
strategies.
- To know the effect of decision.
- To determine pay off.
- Construction of pay off table.
|
States
of nature (event) |
Alternatives
(or payoff) |
|||
|
E1 |
A1 |
A2 |
A3 |
….. |
|
E2 |
||||
|
…. |
||||
Laplace
criterion
The
following matrix gives the pay off of different strategies (alternatives)
S1,S2,S3 and S4 against conditions (events) N1,N2,N3 and N4.
SELECT BEST
ALTERNATIVE
|
N1 |
N2 |
N3 |
N4 |
|
|
S1 |
1000 |
1500 |
750 |
0 |
|
S2 |
250 |
2000 |
3750 |
3000 |
|
S3 |
-500 |
1250 |
3000 |
4750 |
|
S4 |
-1250 |
500 |
2250 |
4000 |
EXPECTED PAY OFF =
= no. of events
Let P1, P2,
….., Pn represent the pay off value of
each and every alternative
Calculation
of expected pay
EXPECTED
PAY OFF =
now for the
1st strategy S1,
= 812.5
For S2,
= 2250
Expected
Pay off
|
812.5
2250
2125
1375
2250 is the
maximum value of the expected pay off which means 2nd alternative
will be best alternative.
If in the
given question will give cost not pay off then minimum of them will be the best
alternative for that case S1 would be the best alternative.
That’s how
decision is taken under Laplace criterion.
OPTIMISM
CRITERION
A).
MAXIMAX CRITERION (applicable for pay
off matrix)
|
N1 |
N2 |
N3 |
N4 |
|
|
S1 |
1000 |
1500 |
750 |
0 |
|
S2 |
250 |
2000 |
3750 |
3000 |
|
S3 |
-500 |
1250 |
3000 |
4750 |
|
S4 |
-1250 |
500 |
2250 |
4000 |
Maximum pay off
|
3750
4750
4000
Here 4750
is maximum so S3 is the best alternative
B).
MINIMIN CRITERION (applicable for cost
matrix)
|
N1 |
N2 |
N3 |
N4 |
|
|
S1 |
1000 |
1500 |
750 |
0 |
|
S2 |
250 |
2000 |
3750 |
3000 |
|
S3 |
-500 |
1250 |
3000 |
4750 |
|
S4 |
-1250 |
500 |
2250 |
4000 |
Minimum cost
|
250
-500
-1250
Here -1250
is minimum so S4 is the best alternative
PESSIMISM
CRITERION
A).
MAXIMIN CRITERION (applicable for pay
off matrix)
|
N1 |
N2 |
N3 |
N4 |
|
|
S1 |
1000 |
1500 |
750 |
0 |
|
S2 |
250 |
2000 |
3750 |
3000 |
|
S3 |
-500 |
1250 |
3000 |
4750 |
|
S4 |
-1250 |
500 |
2250 |
4000 |
Minimum pay off
|
250
-500
-1250
Here 250 is
maximum so S2 is the best alternative
B).
MINIMAX CRITERION (applicable for cost
matrix)
|
N1 |
N2 |
N3 |
N4 |
|
|
S1 |
1000 |
1500 |
750 |
0 |
|
S2 |
250 |
2000 |
3750 |
3000 |
|
S3 |
-500 |
1250 |
3000 |
4750 |
|
S4 |
-1250 |
500 |
2250 |
4000 |
Minimum cost
|
3750
4750
4000
Here 1500
is minimum so S1 is the best alternative
Question
1.
Pay
off table
|
Strategies |
States
of nature |
||
|
N1 |
N2 |
N3 |
|
|
S1 |
7,00,000 |
3,00,000 |
1,50,000 |
|
S2 |
5,00,000 |
4,50,000 |
0 |
|
S3 |
3,00,000 |
3,00,000 |
3,00,000 |
Which
strategies should we choose on the basis of:
a). Maximin
Criterion
B). Maximax
Criterion
C). Laplace
Criterion
A). Maximin
criterion
|
Strategies |
States
of nature |
||
|
N1 |
N2 |
N3 |
|
|
S1 |
7,00,000 |
3,00,000 |
1,50,000 |
|
S2 |
5,00,000 |
4,50,000 |
0 |
|
S3 |
3,00,000 |
3,00,000 |
3,00,000 |
Minimum Pay
off
1,50,000
0
3,00,000
Here
3,00,000 is maximum so S3 is the best alternative
B). Maximax
Criterion
|
Strategies |
States
of nature |
||
|
N1 |
N2 |
N3 |
|
|
S1 |
7,00,000 |
3,00,000 |
1,50,000 |
|
S2 |
5,00,000 |
4,50,000 |
0 |
|
S3 |
3,00,000 |
3,00,000 |
3,00,000 |
|
7,00,000
5,00,000
3,00,000
Here
7,00,000 is maximum so S1 is the best alternative
c). Laplace
Criterion
|
Strategies |
States
of nature |
||
|
N1 |
N2 |
N3 |
|
|
S1 |
7,00,000 |
3,00,000 |
1,50,000 |
|
S2 |
5,00,000 |
4,50,000 |
0 |
|
S3 |
3,00,000 |
3,00,000 |
3,00,000 |
EXPECTED
PAY OFF =
For
S1, = 3,83,333.33
For
S2, =
3,16,666.67
For
S3, = 3,00,000
Expected
Pay off
3,83,333.33
3,16,666.67
3,00,000
Here
3,83,333.33 is maximum expected pay off so S1 is the best alternative
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