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# Decision Theory: Maximin and Minimax strategy

This criterion is the decision to take the course of action which maximizes the minimum possible pay-off.

Maximin and Minimax strategy

## Maximin criteria

This criterion is the decision to take the course of action which maximizes the minimum possible pay-off. Since this decision criterion locates the alternative strategy that has the least possible loss, it is also known as a pessimistic decision criterion. The working method is:

(i) Determine the lowest outcome for each alternative.

(ii) Choose the alternative associated with the maximum of these.

## Minimax criteria

This criterion is the decision to take the course of action which minimizes the maximum possible pay-off. Since this decision criterion locates the alternative strategy that has the greatest possible gain. The working method is:

(i) Determine the highest outcome for each alternative.

(ii) Choose the alternative associated with the minimum of these.

Example 10.10

Consider the following pay-off (profit) matrix Action States Determine best action using maximin principle.

Solution: Example 10.11

A business man has three alternatives open to him each of which can be followed by any of the four possible events. The conditional pay offs for each action - event combination are given below: Determine which alternative should the businessman choose, if he adopts the maximin principle.

Solution: Max (â€“10,â€“4, 0) = 0. Since the maximum payoff is 0, the alternative Z is selected by the businessman.

Example 10.12

Consider the following pay-off matrix Using minmax principle, determine the best alternative.

Solution: min( 27, 25, 23, 32) = 23. Since the minimum cost is 23, the best alternative is E3 according to minimax principle.

Tags : Operations Research , 12th Business Maths and Statistics : Chapter 10 : Operations Research
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