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Decision Analysis

Y. lker TOPCU, Ph.D.www.ilkertopcu.info

www.yoneylem.itu.edu.tr

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Outline

Introduction

What is Decision Analysis?

Decision Making under Certainty

Decision Making under Uncertainty

Decision Making under Risk

Utility Theory

Decision Trees

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Introduction

One dimensional (single criterion) decisionmaking

Single stage vs. multi stage decision making

Decision analysis is an analytical and

systematic way to tackle problems

A good decision is based on logic (rationaldecision maker)

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Components ofDecision Analysis

Astate of nature is an actual event that may occurin the future.

Apayoff matrix (decision table) is a means of

organizing a decision situation, presenting thepayoffs from different decisions/alternatives given

the various states of nature.

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Basic Steps inDecision Analysis

1) Clearly define the problem at hand2) List the possible alternatives

3) Identify the possible state of natures (outcomes)

4) List the payoff or profit/cost of alternatives withrespect to state of natures

5) Select one of the mathematical decision analysis

models6) Apply the model and make your decision

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Types of Decision-MakingEnvironments

Type 1: Decision-making under certainty The decision-makerknows with certainty the

consequences of every alternative or decision choice

Type 2: Decision-making under uncertainty

The decision-makerdoes not know the probabilities of

the various outcomes. Actually s/he knows nothing!

Type 3: Decision-making under risk

The decision-makerdoes know the probabilities of the

various outcomes

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Decision MakingUnder Certainty

Instead of state of natures, a true state is known to

the decision maker before s/he has to make decision

The optimal choice is to pick an alternative with the

highest payoff

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Decision MakingUnder Uncertainty

Maximax

Maximin

Criterion of Realism

Equally likelihood

Minimax

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Payoff Matrix

STATES OF NATURE

ALTERNATIVES

Favorable

market

Unfavorable

marketConstruct large plant $200,000 ($180,000)

Construct small plant $100,000 ($20,000)

Do nothing $0 $0

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Maximax

Choose the alternative with the maximumoptimistic level

ok = {oi} = { {vij}}

STATES OF NATURE

ALTERNATIVES

Favorable

market

Unfavorable

market

Maximum in

row (ok)

Construct large plant $200,000 ($180,000) $200,000

Construct small plant $100,000 ($20,000) $100,000

Do nothing $0 $0 $0

m

i 1max

m

i 1max

m

j 1max

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Maximin

Choose the alternative with the maximumsecurity level

sk

= {si

} = { {vij

}}m

i 1

max

m

i 1

max

m

j 1

min

STATES OF NATURE

ALTERNATIVES

Favorable

market

Unfavorable

market

Minimum in

row (sk)Construct large plant $200,000 ($180,000) ($180,000)

Construct small plant $100,000 ($20,000) ($20,000)

Do nothing $0 $0 $0

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Criterion of Realism

Hurwicz suggested to use the optimism-pessimismindex (a)

Choose the alternative with the maximum weightedaverage of optimistic and security levels

{a oi + (1a) si} where 0

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Criterion of Realism

120a

-20 = 0

a

= 0.1667380a-180 = 120a-20 a = 0.6154

0Z>X).

X

Y

Z

p

1p

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Risk Premium

Risk Premium (RP) of a lottery is the differencebetween the EV of the lottery and the CE of the

lottery

If the DM is risk averse, RP>0S/he prefers to receive a sum of money equal to expected

value of a lottery than to enter the lottery itself

If the DM is risk prone, RP