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DECISION THEORY:

1.INTRODUCTION:

Decision theory in a way can be defined as a mathematical study of strategies for optimal

decision-making between options involving different risks or expectations of gain or loss

depending on the outcome.

In decision theory a set of techniques are used for making the decisions in the decision

environment of uncertainty and risk. The success or failure of an individual or an organization

depends on a large extent on the ability of making decisions on time. To arrive at such a

situation, a decision maker needs to enumerate feasible and viable course of action and

measure the effectiveness of all of them to choose the best course of action.

1.1) Basic terminologies in Decision Theory:

Acts: These are alternative course of action or strategies that are available for decision making.

The objective is to choose best alternative from the available.

Events: These are the outcomes that effect the achievement of the objectives. In decision table

rows represent the decision alternatives and columns represent the events.

Payoff table: Decision analysistool that summarizes pros and cons of adecision in

atabularform. It lists payoffs (negative or positivereturns) associated with all

possiblecombinations of alternativeactions (under the decision makerscontrol) andexternalconditions (not under decision maker's control). Alsocalledpayoff matrix.

Utilities: It is an individuals satisfaction level over a risky decision and its outcomes.

1.3) Steps in decision making process:

The decision making process involves the following steps:-

1) Determine the various alternatives or courses of action from which the final decision is to

be made.2) Identify the possible outcomes also called as events.\

3) Tabulate the payoff function for all the decision alternatives with respect to the outcomes

from different combinations.

4) Select the optimum decision criteria which results in the largest payoff.

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2.) Decision making environment:

Decisions are made under three type of environments :-

2.1) Decision making under conditions of certainty:

In this environment there exists only one outcome for a decision as there is complete

certainty about the future. The decision environment is perfect and deterministic. The

decision to restock food supply, for example, when the goods in stock fall below a

determined level is an example of decision making under uncertainty.

2.2) Decision under uncertainty:

If the available information for a decision environment is insufficient, then the decision taken

under such an environment is called decision under uncertainty. This available information

about the decision environment cannot be described in the form of a probability distribution.

Such a situation arises when a new product is launched in the market.

Under conditions of uncertainty there are five criteria available for making a decision:

Maximin gain criteria or Minimax loss criteria.

Maximax gain criteria or Minimin loss criteria.

Laplace criteria.

Savage Minimax regret criteria.

Hurwicz criteria.

2.3) Decision making under conditions of risk:

If the availability of information for a decision environment is partial, then the decision

under such an environment is called decision under risk. The available information will

be given a form of a probability distribution. The probability of various outcomes may be

determined objectively from the past data.

Three approaches can be used to deal with the decision environment with risk:

Expected money value(EMV) criteria.

Expected opportunity loss(EOL) criteria.

Expected value of perfect information(EVPI) criteria.

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3). Decision Tree analysis:

A decision tree is a chronological representation of the decision process. It utilizes a network oftwo types of nodes: decision (choice) nodes (represented by square shapes), and states ofnature (chance) nodes (represented by circles). Construct a decision tree utilizing the logic ofthe problem. For the chance nodes, ensure that the probabilities along any outgoing branch

sum to one. Calculate the expected payoffs by rolling the tree backward (i.e., starting at the rightand working toward the left). You may imagine driving your car; starting at the foot of thedecision tree and moving to the right along the branches. At each square you have control, tomake a decision and then turn the wheel of your car. At each circle, fortune takes over thewheel and you are powerless.

Here is a step-by-step description of how to build a decision tree:

Draw the decision tree using squares to represent decisions and circles to representuncertainty.

Evaluate the decision tree to make sure all possible outcomes are included. Calculate the tree values working from the right side back to the left.

Calculate the values of uncertain outcome nodes by multiplying the value of theoutcomes by their probability (i.e expected values).

On the tree, the value of a node can be calculated when we have the values for all the nodesfollowing it. The value for a choice node is the largest value of all nodes immediately following it.The value of a chance node is the expected value of the nodes following that node, using theprobability of the arcs. By rolling the tree backward, from its branches toward its root, you cancompute the value of all nodes including the root of the tree. Put these numerical results on thedecision tree results in a graph like structure. Determine the best decision for the tree by startingat its root and going forward.

3.1) Advantages and Limitations of decision tree analysis:

Advantages:

It structures the decision process and helps the decision making in a systematic andsequential order.

It helps decision maker to examine all possible outcomes whether desirable or not. It communicates the decision making process to others in an easy and clear manner.

Limitations:

Decision tree diagrams become more complicated as the number of decisionalternatives and variables increases.

It becomes highly complicated when interdependent alternatives and dependentvariables are present in the problem.

It analyzes the expected value and gives an average solution only.