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OPERATIONS RESEARCH

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Decision Theory

Decision Theory provides an analytical and systematic approach to the study of decision making wherein data concerning the occurrence of different outcomes may be evaluated to enable the decision maker to identify suitable alternative

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Coverage• Types of decision making environment.

• Characteristics: Decision Alternatives State of Nature Pay-Off

• Criterion for evaluating various courses of actions.

• Decision tree analysis304/21/23

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Types of Decision Making Environment

• Decision making under certainty.

• Decision making under risk.

• Decision making under uncertainty.

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Decision making under Certainty

• Decision maker has the complete knowledge of consequences of every decision choice with one state of nature(future).

• Example:- Decision to purchase NSC, or Indira Vikas patra, or NSS. Complete information of the schemes are known.

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Decision making under Risk

• There are more than one state of nature.

• Decision maker has less than complete knowledge with certainty of the consequences of each decision choice.

• Each state of nature is associated with probability.• E.g.: probability of getting a tail in a toss is 0.5

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Decision making under Uncertainity

• Decision maker is unable to specify the probability with which the various states of nature will occur.

• Less information than decision under risk

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Criterion for Evaluating various Courses of Actions

• Expected monetary value.

• Expected opportunity loss.

• Expected value of perfect information.

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Decision Tree• Decision tree analysis involves

construction of diagram showing all possible courses of action, states of nature and probabilities associated with states of nature.

• Diagram looks much like a tree.

• A Decision tree consists of nodes, branches probability estimates and payoffs.

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NodesNodes are of two types, Decision node and chance nodeDecision node is represented by a square and indicates places where a decision maker must make a decision.Chance node is represented by a circle and indicates a point at which the decision maker will discover the response to his decision i.e. different possible outcomes occurred from a chosen course of action.

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Branches• Branches emanate from and connect various

nodes and are state of nature• Branches are of two types, decision branches

and chance branches.• Decision branch is a branch leading away from

decision node and represents a course of action or strategy that can be chosen at a decision point.

• Chance branch is a branch leading away from a chance node and represents the state of nature of a set of chance factors.

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• Associated probabilities are indicated along each chance branch.

• Probabilities are likelihoods that the chance outcome will assume the value assigned to the particular branch.

• A branch that is not followed by a chance or a deciosion node is a terminal branch. It may be a course of action or a chance outcome.

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Payoffs• The payoff can be positive ( revenue or

sales) or negative ( expenditure or cost ) and they can be associated with either decision or chance branches.

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Which decision to be chosen ?• The optimal sequence of decisions in a

tree is found by starting at the right hand side and rolling backward.

• At each node of the decision tree, an expected return is calculated for each of the branches and the decision corresponding to highest return is selected.

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Decision Tree Analysis – A Case A glass factory specializing in crystal is developing

a substantial backlog and the firm’s management is considering three courses of action; arrange for sub-contracting (S1), begin overtime production (S2), and construct new facilities (S3). The correct choice depends largely upon future demand which may be low, medium, or high. Management ranks the respective probabilities as 0.10, 0.50, 0.40. A cost analysis reveals effect upon the profit that is shown in next slide:

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Decision Tree Analysis – A CaseDemand Probability S1 S2 S3

Low (L) 0.10 10 -20 -150

Medium (M) 0.50 50 60 20

High (H) 0.40 50 100 200

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Decision Tree Analysis – A Case

• Show this decision situation in the form of decision tree.

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