# Application of Decision Analysis

Written by Dinesh Thakur

The decision theory (decision analysis) refers to the techniques for analysis decisions under risk and uncertainty. In the process of decision-making the decision –maker wants to achieve something, which may be called his goal, purpose or objective. The decision –maker may choose one particular alternative, which is called strategy of the decision maker,from among various alternatives.

All alternative and outcomes are assumed to be known. There are certain factors, which affect the outcome for different strategies. But these factors or conditions, also called 'states of nature, are beyond the control of the decision-maker. The strategy (alternative) along with the state of nature determines the degree to which the goal is actually achieved. A measure of achievement of the goal is called the 'Pay-off'

The pay-off matrix is used as method of presenting data in decision – analysis. Each cell, which is an intersection of a strategy and a state of nature, contains the pay-off.

 Strategies States of nature N1 N2 N3 N4 S1 S2 S3

If the state of nature is known with certainty, the decision –maker is required only to select the strategy that provides him the highest pay-off.

Let us explain the concept of the pay-off matrix by taking an example.

Assume that a marketing manager of a computer manufacturer is to choose from three alternatives.

1)      Modify the existing PC to improve its design and processing power.

2)      Launch a new PC having latest technology.

3)      Do nothing, i.e. leave the PC as it is.

There are three states of nature that affect the pay-off from each of the alternative strategies.

These states of nature are:

i)        A competitor may launch a new PC with latest technology.

i)        The government may impose high-excise duty on the manufacture of PCs and reduce excise to minimum on laptops to encourage the use of laptops.

iii) Condition will remain the same as they are.

The various pay-offs (profit or loss) from the combination of a strategy and a state of nature are given in the pay-off matrix in fig.

 Strategies States of nature Same condition New Competitor 0.40 Govt. Ban 0.20 S1 Modify 7 5 -5 S2New product 10 3 -13 S3Do nothing 5 1 -2

It can be seen that there are three states of nature whose probabilities of occurrence is know. This problem situation is called decision under risk. The probabilities represent the likelihood of occurrence of the specific states of nature, either based on historical data or on personal judgment of the decision-maker. In the above example, the expected value (EV) of each strategy is:

EV of S1= (7)  (0.40)+(5)(0.40)+(-5)(0.20)

=2.8+2.0-1.0=3.8

EV of S2= (10)(0.40)+(3)(0.40)+(-13)(0.20)

=4.0+1.2-2.6=2.6

EV of S3= (5)(0.40)+(1)(0.40)+(-2)(0.20)

=2.0+0.4-0.4=2.0

The maximum expected value 3.8 lakhs is found to be of the option to modify and if the decision is made based on the expected value objective function, the strategy S1 i.e. to modify the existing PC will be selected.