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Operations Research - Meaning of Decision Theory | 12th Business Maths and Statistics : Chapter 10 : Operations Research

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

Meaning of Decision Theory

The decision maker refers to individual or a group of individual responsible for making the choice of an appropriate course of action amongst the available courses of action.

Meaning

The decision maker: The decision maker refers to individual or a group of individual responsible for making the choice of an appropriate course of action amongst the available courses of action.

Acts (or courses of action): Decision making problems deals with the selection of a single act from a set of alternative acts. If two or more alternative courses of action occur in a problem, then decision making is necessary to select only one course of action. Let the acts or action be a1, a2, a3,… then the totality of all these actions is known as action space denoted by A. For three actions a1, a2 a3; A = action space = (a1, a2, a3) or A = (A1, A2, A3). Acts may be also represented in the following matrix form.


Events (or States of nature): The events identify the occurrences, which are outside of the decision maker’ s control and which determine the level of success for a given act. These events are often called ‘ States of nature’ or outcomes. An example of an event or states of nature is the level of market demand for a particular item during a stipulated time period.

A set of states of nature may be represented in any one of the following ways:

S = {S1, S2, …,Sn} or E = {E1, E2, …,En} or Ω = {θ1, θ2, θ3}

For example, if a washing powder is marketed, it may be highly liked by outcomes (outcome θ1) or it may not appeal at all (outcome θ2) or it may satisfy only a small fraction, say 25% (outcome θ3)

Ω = {θ1 , θ2, θ3}

In a tree diagram the places are next to acts. We may also get another act on the happening of events as follows:


In a matrix form, they may be represented as either of the two ways.


Pay-off: The result of combinations of an act with each of the states of nature is the outcome and monetary gain or loss of each such outcome is the pay-off. This means that the expression pay-off should be in quantitative form.

Pay -off may be also in terms of cost saving or time saving. In general, if there are k alternatives and n states of nature, there will be k × n outcomes or pay-offs. These k × n payoffs can be very conveniently represented in the form of a k × n pay -off table.


Where aij = conditional outcome (pay-off) of the i th event when j th alternative is chosen. The above pay-off table is called pay-off matrix.


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


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