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

**Maximin
and Minimax strategy**

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.

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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12th Business Maths and Statistics : Chapter 10 : Operations Research : Decision Theory: Maximin and Minimax strategy | Operations Research

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