Decsion Theory

8/7/2019 Decsion Theory

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Presented by:Shikha AgarwalPurva Dhadich

Shahina


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2.Events:-events are also called states of nature or outcomes .The various events symbolized by E1, E2, E3 ..etc. examples or

events are sales of a product, demand of a product in market etc.

3 pay off:- each combination of a course of action and an eventsis associated wit h a pay-off. Thus pay-off measure the net

benefit to the decision-maker that results from a givencombination of decision alternative and events.

4.pay off table-various:-various pay-off can be put in the shape ofa table to from a pay-off table. A pay-off table shows the relation

between all possible states of nature, all possible acts and thevalues associated with the consequences.


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A specimen of pay-off table is given below-

Pay off Table

Events

Acts

A1 A2 A3 An

E1 P11 P12 P13 P1n

E2 P21 P22 P23 P24

. . . . .

. . . . .

. . . . .

Em Pm1 Pm2 Pm3 Pmn


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5.Opportunity Loss Or Regret:-The opportunity Loss or regret isthe difference pay- off realised and the maximum pay off

which could have been realised if another strategy was chosen.This loss is incurred because of failure to adopt the bestpossible outcome.

Regret(opportunity Loss) table

EventsActs

a a a a

E1 M1 - P 11 M1 P12 M1 P13 M1 P 14

E2 M2 - P 21 M2 - P 22 M2- P 23 M2 - P 24

. . . . .

. . . . .

E3 Mm - P m1 Mm - P m2 Mm - P m3 M1 - P mn


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Decision- Making Under Risk

Under this the following decision criterions are used forevaluating the alternative strategies:

1. Expected monetary Value(EMV) Criterion

2. Expected Opportunity Loss (EOL) Criterion3. Expected Value Of perfectInformation(EVPI)


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Illustration

A newspaper boy has the following probabilities of selling amagazine:

No. of Copies Sold probability

10 0.10

11 0.15

12 0.20

13 0.25

14 0.30

Cost of copy is Rs. 3, and sale price is Rs. 5. He cannotunsold copies. How many copies should he order?


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Solution:The number of copies for purchases and for sales

range between 10 and 14. The conditional profit in RS.Is given by

Pay- off= 2*copies sold- 3*copies unsoldhere profit on sale = Rs. (5-3)= Rs. 2Loss on unsold copies= RS.3


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Possible

Demand

(no. of

Copies)

probability Possible Stock Action

10

Copies

11copies 12copies 13copies 14copies

10 0.10 20 17 14 11 8

11 0.15 20 22 1- 16 13

12 0.20 20 22 24 21 18

13 0.25 20 22 24 26 23

14 0.30 20 22 24 26 28

Conditional Profit Table(In Rs.)

Now , expected profit table can be calculated multiplying the

probability with the possible stock action.


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Expected Profit table

Possible

Demand(no. of

Copies)

probability Expected Profit From Stocking(Rs.)

10

Copies

11

copies

12

copies

13

copies

14

copies

10 0.10 2 1.7 1.40 1.1 0.80

11 0.15 3 3.3 2.85 2.4 1.-5

12 0.20 4 4.4 4.80 4.2 3.60

13 0.25 5 5.5 6.00 6.5 5.75

14 0.30 6 6.6 7.20 7.8 8.40

EMV(Rs.) 20.0 21.6 22.25 22.0 20.50

Hence the boy must order 12 copies to earn the highest

possible average daily profit of Rs. 22.25.


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Opportunity Loss Table

Possible

Demand

(no. ofCopies)

probability Possible Stock

10

Copies

11

copies

12

copies

13

copies

14

copies

10 0.10 0 3 6 - 12

11 0.15 2 0 3 6 -

12 0.20 4 2 0 3 6

13 0.25 6 4 2 0 3

14 0.30 8 6 4 2 0

Now , expected opportunity loss table can be calculated multiplying theprobability with the possible stock action.


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Possible

Demand

(no. of

Copies)

probability Possible Stock(no. of copies)

10

Copies

11

copies

12

copies

13

copies

14

copies

10 0.10 0.0 0.3 0.6 0.- 1.2

11 0.15 0.3 0.0 0.45 0.- 1.35

12 0.20 0.8 0.4 0.0 0.6 1.20

13 0.25 1.5 1.0 0.5 0.0 0.0

14 0.30 2.4 1.8 1.2 0.6

EOL (Rs.) 5.0 3.5 2.75 3.0 4.5

Expected Opportunity Loss Table

The optimum stock level is one which minimizes EOL.

In this case the boy must keep stock of 12 copies


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For calculate the EVPI, first find the expected profit of perfectinformation(EPPI); for this construct profit table under certainty.Under certainty the boy would stock each day the exact number of

copies required that day. For a sale of 10 copies he would stock 10copies and realise a profit of rs. 20. this can be shown as follows:

Conditional Profit Table Under Certainty(Rs.)

Possible

Demand(no. of

Copies)

Possible Stock

10Copies

11copies

12copies

13copies

14copies

10 20 - - - -

11 - 22 - - -

12 - - 24 - -

13 - - - 26 -

14 - - - - 28


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The expected profit under perfect information(EPPI) can now becomputed. This is shown in the table given below:

Expected Profit Table With PerfectI

nformation(Rs.)(1)

Demand

(number of

copies)

(2)

Conditional

profit under

certainty

(3)

Probability of

demand

(4)

Expected

Profit with

information

(2)*(3)

10 20 0.10 2.0

11 22 0.15 3.3

12 24 0.20 4.8

13 26 0.25 6.5

14 28 0.30 8.4

EPPI 25.00


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Thus EVPI= EPPI-EMV;25-22.25=2.75

NOTE: EVPI is equal to minimum EOL.


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Decsion Theory

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