Unit-I-2-DT

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Operations Research

MBA-024

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DECISION-MAKINGENVIRONMENTS/DECISION THEORY

UNITI

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Decision Theory: Introduction

The managerial activity includes broadly four

phases, namely, planning, organising, directing

and controlling.

In performing all of these activities the

management has to face several such

situations where they have to make a choice

of the best among a number of alternativecourses of action.

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This choice making is technically termed as

decision-making.

A decision is simply a selection from two or

more courses of action.

Decision theory provides a rich set of conceptsand techniques to aid the decision maker in

dealing with complex decision problems.

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Decision Theory: Definition

A process which results in the selection from a

set of alternative courses of action, that

course of action which is considered to meet

the objectives of the decision problem more

satisfactorily than others as judged by the

decision maker.

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Decision Theory: Applications

Select the best from among several job offers.

Select the most profitable investment portfolio.

Determine whether or not to expand amanufacturing facility.

Determine whether a large plant, a small plant, orno plant should be built.

D

ecide whether to invest in a new plant,equipment, research programme, marketingfacilities, etc.

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Decision Theory: Steps

Clearly identify and define the problem at

hand.

Specify objectives and the decision criteria. Identify and evaluate the possible

alternatives.

Formulate (or select) one of the mathematical

decision theory models.

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Decision Theory: Steps

Apply the model and select the best

alternative.

Conduct a sensitivity analysis of the solution. Communication and implementation of

decision.

Follow-up and feedback of results of decision.

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Decision Theory: Concepts

Decision Maker. An individual or a group of

individuals responsible for making the choice

of an appropriate course of action amongst

the available courses of action.

Courses of Action. The alternative courses of

actions or strategies are the acts that are

available to the decision maker.

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States of Nature. The events or occurrences

which are outside the control of the decision

maker, but which determine the level of

success for a given decision.

Payoff. Each combination of a strategy andevent is associated with a payoff, which

measures the net benefit to the decision

maker.

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Payoff Table. For a given problem, payoff table

lists the payoffs for each combination of eventand strategy.

Regret/Opportunity Loss Table. Anopportunity loss is the loss incurred due tofailure of not adopting the best possiblestrategy. For a given state of nature theopportunity loss of possible strategy is thedifference between the payoff for thatstrategy and the payoff for the best possiblestrategy that could have been selected.

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Types ofDecision-Making

Environments Certainty. Complete and accurate knowledge

of the outcome of each alternative. There isonly one outcome for each alternative.

Risk. Multiple possible outcomes for eachalternative. A probability of occurrenceattached to each possible outcome.

Uncertainty. Multiple outcomes for eachalternative. But no knowledge of the

probability of their occurrence.

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Decision-Making under Certainty

The consequence of selecting each course of

action known with certainty.

It is presumed that only one state of nature isrelevant for the purpose of the decision

maker.

He identifies this state of nature, takes it for

granted and presumes complete knowledge as

to its occurrence.

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Decision-Making under Certainty

Some techniques used:

System of equations.

Linear programming.

Integer programming.

Dynamic programming.

Queuing models.

I

nventory models. Capital budgeting analysis.

Break even analysis.

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Decision-Making under Risk

The decision maker faces several states ofnature.

He is supposed to have believable evidentialinformation, knowledge, experience or

judgement to enable him to assign probabilityvalues to the likelihood of occurrence of eachstate of nature.

The course of action which has the largestexpected payoff value is selected.

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Decision-Making under Risk

The most widely used decision criterion is the

expected monetary value (EMV) or expected

payoff.

The objective of decision making is to

optimise expected payoff.

It means maximisation of expected profit or

minimisation of expected regret.

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EMV

Given a payoff table with payoffs and

probability assessments for all states of

nature, it is possible to determine EMV for

each course of action if the decision is

repeated a large number of times.

The EMV for a given course of action is the

sum of possible payoffs of the alternatives,each weighted by the probability of that

payoff occurring.

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Steps for Calculating EMV

Construct payoff table along with the

probabilities of the occurrence of each state of

nature.

Calculate EMV for each course of action, as

shown earlier.

Select the course of action that yields the

optimal EMV.

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Expected Value with Perfect

Information The expected value with perfect information is

the expected or average return, in the long

run, if we have perfect information before a

decision has to be made.

It is calculated by choosing the best

alternative for each state of nature and

multiplying its payoff with the probability ofthat state of nature.

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Expected value with perfect information =

(Best outcome for 1st state of nature) x

(Probability of 1st state of nature) + (Best

outcome for 2nd state of nature) x (Probability

of 2nd

state of nature) + + (Best outcome forlast state of nature) x (Probability of last state

of nature)

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Expected Value of Perfect

Information (EVPI) EVPI is the expected value with perfect

information minus the expected value without

perfect information, namely the maximum

EMV.

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Expected Opportunity Loss (EOL)

An alternative approach to maximising EMV is

to minimise EOL or expected value of regrets.

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Decision-Making under Uncertainty

The probabilities are not known.

No historical data available.

Expected payoff cannot be calculated.

Example: Introduction of a new product in the

market.

T

he choice of a course of action dependslargely upon the personality of the decision-

maker or policy of the organisation.

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Decision Criteria under condition

ofUncertainty Maximin.

Maximax.

Minimax Regret.

Hurwicz Criterion.

Bayes/Lapalces Criterion.

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Criterion of Pessimism (Maximin)

Also called Waldian Criterion.

Determine the lowest outcome for each

alternative. Choose the alternative associated with the

best of these.

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Criterion of Optimism (Maximax)

Suggested by Leonid Hurwicz.

Determine the best outcome for each

alternative. Select the alternative associated with the best

of these.

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Minimax Regret Criterion

Attributed to Leonard Savage.

For each state, identify the most attractivealternative.

Place a zero in those cells.

Compute opportunity loss for other alternatives.

Identify the maximum opportunity loss for eachalternative.

Select the alternative associated with the lowestof these.

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Criterion of Realism (Hurwicz

Criterion) A compromise between maximax and

maximin criteria.

A coefficient of optimism (01) isselected.

When is close to 1, the decision-maker is

optimistic about the future.

When is close to 0, the decision-maker is

pessimistic about the future.

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Hurwicz Criterion

Select the strategy which maximises:

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Laplace Criterion

Assign equal probabilities to each state.

Compute the expected value for each

alternative. Select the alternative with the highest

alternative.

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Decision Tree Approach

Using a decision tree the decision problem,

alternative courses of action, states of nature

and the likely outcomes are diagrammatically

depicted.

A decision tree consists of a network of nodes,

branches, probability estimates and payoffs.

Nodes are of two types: decision-node(square) and chance node (circle).

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Alternative courses of action originate from

decision nodes as main branches (decisionbranches).

At the terminal of each decision branch, there is achance node.

Chance events emanate from chance nodes in theform of sub-branches (chance branches).

The respective payoffs and the probabilitiesassociated with the alternative courses andchance events are shown alongside the chance

branches. At the terminal of the chance branches expected

payoffs are shown.

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Types ofDecision Trees

Deterministic.

Probabilistic.

These can further be subdivided into singlestage and multistage trees.

A single stage deterministic decision tree

involves making only one decision under

conditions of certainty (no chance events).

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In a multi stage deterministic tree a sequence

or chain of decisions are to be made.

A problem involving only one decision to be

made under conditions of risk or uncertainty

(more than one chance events) can berepresented using a single stage probabilistic

decision tree.

In the above problem, if a sequence of

decisions is required, a multi stage

probabilistic decision tree is required.

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Drawing a Decision Tree:

Conventions Identifyall decisions (and their alternatives) to

be made and the order in which they must be

made.

Identifythe chance events or states of nature

that might occur as a result of each decision

alternative.

Develop a tree diagram showing the sequenceof decisions and chance events.

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Estimate probabilities that the possible events

will occur as a result of the decisionalternatives.

Obtain outcomes (usually expressed ineconomic terms) of the possible interactions

among decision alternatives and events.

Calculate the expected value of all possibledecision alternatives.

Selectthe decision alternative (or course ofaction) offering the most attractive expected

value.

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Roll-Back Technique

Used for analysing a decision tree.

Proceeds from the last decision in the sequenceand works back to the first for each of the

possible decisions. Two rules concerning this technique:

If branches emanate from a circle, the total expectedpayoff may be calculated by summing up the expectedvalues of all the branches.

If branches emanate from a square, we calculate thetotal expected payoff for each branch emanating fromthat square and the branch with the highest expectedbenefit gives the solution.

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Decision Tree: Advantages

Useful for portraying the interrelated, sequential andmultidimensional aspects of a decision problem.

Focuses attention on the critical elements in a decisionproblem.

Especially useful in cases where an initial decision andits outcome affect the subsequent decisions.

Enables the decision maker to see the various elementsof the decision problem in a systematic way.

Complex managerial problems can be explicitlydefined.

Can be applied in various fields.

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Decision Tree Approach: Applications

Introduction of a new product.

Marketing strategy.

Make or buy decisions. Pricing assets acquisition.

Investment decisions.

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A company owns a lease on a property. It may

sell the lease for Rs.12000 or it may drill the saidproperty for oil. Various possible drilling results

are as under along with the probabilities of

happening and rupee consequences:

Possible Result Probability Rupee Consequence

Dry well 0.10 -100000

Gas well 0.40 45000

Oil & gas well 0.30 98000

Oil well 0.20 199000