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# Quantitative Analysis for Management PowerPoint PPT Presentation

Quantitative Analysis for Management. Chapter 3 Fundamentals of Decision Theory Models. Chapter Outline. 3.1 Introduction 3.2 The Six Steps in Decision Theory 3.3 Types of Decision-Making Environments 3.4 Decision Making Under Risk 3.5 Decision Making Under Uncertainty

Quantitative Analysis for Management

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#### Presentation Transcript

Quantitative Analysis for Management

Chapter 3

Fundamentals of Decision Theory Models

3-1

### Chapter Outline

3.1 Introduction

3.2 The Six Steps in Decision Theory

3.3 Types of Decision-Making Environments

3.4 Decision Making Under Risk

3.5 Decision Making Under Uncertainty

3.6 Marginal Analysis with a Large Number of Alternatives and States of Nature

3-2

### Learning Objectives

Students will be able to:

• List the steps of the decision-making process

• Describe the types of decision-making environments

• Use probability values to make decisions under risk

• Make decisions under uncertainty where there is risk but probability values are not known

• Use computers to solve basic decision-making problems

3-3

### Introduction

• Decision theory is an analytical and systematic way to tackle problems

• A good decision is based on logic.

3-4

### The Six Steps in Decision Theory

• Clearly define the problem at hand

• List the possible alternatives

• Identify the possible outcomes

• List the payoff or profit of each combination of alternatives and outcomes

• Select one of the mathematical decision theory models

• Apply the model and make your decision

3-5

### Decision Table for Thompson Lumber

Favorable Market (\$)

Unfavorable Market (\$)

Construct a

large plant

200,000

-180,000

Construct a small plant

-20,000

100,000

Do nothing

0

0

3-6

### Types of Decision-Making Environments

• Type 1: Decision-making under certainty

• decision-maker knows with certainty the consequences of every alternative or decision choice

• Type 2: Decision-making under risk

• The decision-maker knows the probabilities of the various outcomes

• Decision-making under uncertainty

• The decision-maker does not know the probabilities of the various outcomes

3-7

### Decision-Making Under Risk

n

=

å

EMV(Altern

ative

i)

(Payoff

*

P(S

))

j

S

j

=

j

1

=

where

j

1

to

the

number

of

states

of

nature,

n

Expected Monetary Value:

3-8

### Decision Table for Thompson Lumber

Favorable Market (\$)

Unfavorable Market (\$)

Construct a

large plant

200,000

-180,000

10,000

Construct a small plant

100,000

-20,000

40,000

Do nothing

0

0

0

0.50

0.50

EMV

3-9

### Expected Value of Perfect Information (EVPI)

• EVPI places an upper bound on what one would pay for additional information

• EVPI is the expected value with perfect information minus the maximum EMV

3-10

n

=

å

EV

|

PI

(

best

outcome

for

state

of

nature

j)

*

P(S

)

j

=

1

j

=

where

j

1

to

the

number

of

states

of

nature,

n

3-11

### Expected Value of Perfect Information

• EVPI = EV|PI - maximum EMV

3-12

### Expected Value of Perfect Information

Favorable Market (\$)

Unfavorable Market (\$)

Construct a

large plant

200,000

Construct a small plant

40,000

Do nothing

0

0.50

0.50

EMV

3-13

### Expected Value of Perfect Information

EVPI = expected value with perfect information - max(EMV)

= \$200,000*0.50 + 0*0.50 - \$40,000

= \$60,000

3-14

### Expected Opportunity Loss

• EOL is the cost of not picking the best solution

• EOL = Expected Regret

We want to maximize EMV or

minimize EOL

3-15

3-16

3-17

3-18

### Sensitivity Analysis

EMV(Large Plant) = \$200,000P - (1-P)\$180,000

EMV(Small Plant) = \$100,000P - \$20,000(1-P)

EMV(Do Nothing) = \$0P + 0(1-P)

3-19

### Sensitivity Analysis - continued

EMV (Small Plant)

EMV(Large Plant)

3-20

### Decision Making Under Uncertainty

• Maximax

• Maximin

• Equally likely (Laplace)

• Criterion of Realism

• Minimax

3-21

### Decision Making Under Uncertainty

Favorable Market (\$)

Unfavorable Market (\$)

200,000

-180,000

Construct a

large plant

100,000

-20,000

Construct a small plant

0

0

Do nothing

Maximax - Choose the alternative with the maximum output

3-22

### Decision Making Under Uncertainty

Favorable Market (\$)

Unfavorable Market (\$)

200,000

-180,000

Construct a

large plant

100,000

-20,000

Construct a small plant

0

0

Do nothing

Maximin - Choose the alternative with the maximum minimum output

3-23

### Decision Making Under Uncertainty

Favorable Market (\$)

Unfavorable Market (\$)

200,000

-180,000

EMV

Construct a

large plant

10,000

100,000

-20,000

Construct a small plant

40,000

0

0

Do nothing

0

0.50

0.50

Equally likely (Laplace) - Assume all states of nature to be equally likely, choose maximum EMV

3-24

### Decision Making Under Uncertainty

Favorable Market (\$)

Unfavorable Market (\$)

200,000

-180,000

CR

Construct a

large plant

124,000

100,000

-20,000

Construct a small plant

76,000

0

0

0

Do nothing

0.50

0.50

Criterion of Realism (Hurwicz):

CR = *(row max) + (1-)*(row min)

3-25

### Decision Making Under Uncertainty

Favorable Market (\$)

Unfavorable Market (\$)

Max in row

Construct a

large plant

0

180,000

180,000

Construct a small plant

100,000

20,000

100,000

Do nothing

200,000

0

200,000

0.50

0.50

Minimax - choose the alternative with the minimum maximum Opportunity Loss

3-26

### Marginal Analysis

• P = probability that demand is greater than or equal to a given supply

• 1-P = probability that demand will be less than supply

• MP = marginal profit ML = marginal loss

• Optimal decision rule is: P*MP  (1-P)*ML

• or

3-27

### Marginal Analysis -Discrete Distributions

• Steps using Discrete Distributions:

• Determine the value forP

• Construct a probability table and add a cumulative probability column

• Keep ordering inventory as long as the probability of selling at least one additional unit is greater than P

3-28

3-29

### Café du Donut Example continued

ML

³

P

+

ML

MP

4

4

=

=

=

0

66

.

4

+

2

6

• Marginal profit = selling price - cost

= \$6 - \$4 = \$2

• Marginal loss = cost

• Therefore:

3-30

3-31

### Marginal AnalysisNormal Distribution

•  = average or mean sales

•  = standard deviation of sales

• MP = marginal profit

• ML = Marginal loss

3-32

### Marginal Analysis -Discrete Distributions

ML

=

P

+

ML

MP

*

-

m

X

=

Z

s

• Steps using Normal Distributions:

• Determine the value forP.

• Locate P on the normal distribution. For a given area under the curve, we find Zfrom thestandard Normal table.

• Using we can now solve for X*

3-33

### Joe’s Newsstand Example A

• ML = 4

• MP = 6

• = Average demand = 50 papers per day

•  = Standard deviation of demand = 10

3-34

### Joe’s Newsstand Example A continued

4

ML

=

=

=

0

40

P

.

+

4

+

6

ML

MP

*

-

50

X

0

25

=

10

*

=

10

0

25

+

50

=

52

5

53

X

*

.

.

or

newspapers

• Step 1:

• Step 2: Look on the Normal table for

P = 0.6 (i.e., 1 - .04)  Z = 0.25,

and

or:

.

3-35

3-36

### Joe’s Newsstand Example B

• ML = 8

• MP = 2

•  = Average demand = 100 papers per day

•  = Standard deviation of demand = 10

3-37

### Joe’s Newsstand Example B continued

8

ML

=

=

=

0

80

P

.

+

8

+

2

ML

MP

*

-

1000

X

-

0

84

=

10

*

=

-

8

4

+

100

=

91

6

92

X

.

.

or

newspapers

• Step 1:

• Step 2:

Z = -0.84 for an area of 0.80

and

or:

.

3-38

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