1. OPERATION RESEARCH
DECISION THEORY
PRESENTED BY: ANASUYA BARIK
OPERATION RESEARCH 1

2. DECISION THEORY
Steps involved in decision theory approach:
•Determine the various alternative courses of actions from which the final
decision has to be made.
•Identify the possible outcomes, called the states of nature or events
for the decision problem.
•Construct a pay off table.
•The decision maker chooses the criterion which results in largest pay off.
OPERATION RESEARCH 2

3. Decision making environments:
•Decision under certainty
Whenever there exists only one outcome for a decision, we are
dealing with this category
•Decisions under uncertainty:
When more than one outcome can result from any single
decision i.e. more than one state of nature exists.
•Decision under risk:
The decision maker chooses from among several possible
outcomes where the probability of occurrence can be stated
objectively from the past data.
•Decision under conflict:
Neither states of nature are completely known nor are they
completely uncertain.
OPERATION RESEARCH 3

4. DECISION UNDER UNCERTAINTY:
There are five criterion on the basis of which rules for making a decision is
Formulated:
Criterion of pessimism:
• Minimax or Maximin
• Maximin is a conservative approach to assume worst possible outcomes
• Steps involved:
Find minimum assured pay off for each alternative
Choose the maximum of minimum values.
• Minimax involves two steps:
Determine maximum possible cost for each alternative
Choose the alternative minimum of above costs
OPERATION RESEARCH 4

5. Criterion of optimism:
•Mimimin or maximax
•Two extreme optimism
•Decision makes ensures that he should not miss the opportunity to achieve the
the greatest possible pay off or lowest possible cost
•Steps involved:
Determine maximum possible payoff
Select a alterative which corresponds to maximum of above
maximum pay off
•Minimin of cost is done in similar manner
OPERATION RESEARCH 5

6. Laplace criterion:
• It is assumed that all states of nature will occur with equal probability
•Probabilities of each state of nature is given by 1/( number of states of nature)
•Steps involved:
i. Assign equal probabilities to each payoff of a strategy
ii. Determine the expected pay off value for each alternative.
iii. Select the alternative which corresponds to the maximum payoff or
minimum cost
OPERATION RESEARCH 6

7. Criterion of realism or Hurwicz criterion:
•Coefficient of optimism α
•0<α<1 where o signifies total pessimism and 1 total optimism
•Steps involved:
i. Decide the coefficient of optimism and the coefficient of pessimism
ii. Determine the maximum as well as minimum pay off for each alterative
h= α x maximum for each alterative + (1-α) x minimum for each alterative
iii. Select the alternative with highest value of h.
OPERATION RESEARCH 7

8. Example:
A farmer wants to decide which of the three crops he should plant on his 100
Acre farm. The profit from each is dependent on the rainfall during the growing
seasons. The farmer has categorized the amount of rainfall as high, medium,
low. His estimated profit for each is show in the table:
Rainfall Crop A Crop B Crop C
High 8000 3500 5000
Medium 4500 4500 5000
Low 2000 5000 4000
If the farmer wishes to plant only one crop, decide which will be his choice using
•Maximax criterion
•Maximin criterion
•Hurwicz criterion
•Laplace criterion
OPERATION RESEARCH 8

9. Rainfall Crop A Crop B Crop C
High 8000 3500 5000
Medium 4500 4500 5000
Low 2000 5000 4000
i. Maximax criterion:
From table we observe that maximum pay off for each alternative are
8000, 5000 ad 5000 respectively. Maximum among these is 8000
corresponding to crop A. So this strategy chooses crop A .
ii. Maximin criterion selects crop C
iii. Hurwicz criterion:
Assuming degree of optimism α = 0.6 ad therefore 1-α = 0.4 , the value of
h is calculated in the table:
Alternativ
e
Maximum
pay off
Minimum
pay off
OPERATION RESEARCH 9
h
Crop A 8000 2000 5600
Crop B 5000 3500 4400
Crop C 5000 4000 4600

10. The maximum value is 5600 so this criterion selects crop A.
iv. Laplace criterion:
Assign equal probabilities i.e. 1/3. The expected pay off is calculated
for each alterative:
E (Crop A)=1/3(8000)+1/3(4500)+1/3(2000)= 4833
E (Crop B)=4333
E (Crop C)=4666
Hence this criterion also selects crop A.
OPERATION RESEARCH 10

11. Thank you!
OPERATION RESEARCH 11