Quantitative Analysis for Management
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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

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Quantitative Analysis for Management

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Quantitative analysis for management

Quantitative Analysis for Management

Chapter 3

Fundamentals of Decision Theory Models

3-1


Chapter outline

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

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

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

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

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

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

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 lumber1

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

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


Expected value with perfect information ev pi

Expected Value With Perfect Information (EV|PI)

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

Expected Value of Perfect Information

  • EVPI = EV|PI - maximum EMV

3-12


Expected value of perfect information1

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 information2

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

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


Computing eol the opportunity loss table

Computing EOL - The Opportunity Loss Table

3-16


The opportunity loss table continued

The Opportunity Loss Table continued

3-17


The opportunity loss table continued1

The Opportunity Loss Table continued

3-18


Sensitivity analysis

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

Sensitivity Analysis - continued

EMV (Small Plant)

EMV(Large Plant)

3-20


Decision making under uncertainty

Decision Making Under Uncertainty

  • Maximax

  • Maximin

  • Equally likely (Laplace)

  • Criterion of Realism

  • Minimax

3-21


Decision making under uncertainty1

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 uncertainty2

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 uncertainty3

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 uncertainty4

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 uncertainty5

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

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

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


Caf du donut example

Café du Donut Example

3-29


Caf du donut example continued

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


Caf du donut example continued1

Café du Donut Example continued

3-31


Marginal analysis normal distribution

Marginal AnalysisNormal Distribution

  •  = average or mean sales

  •  = standard deviation of sales

  • MP = marginal profit

  • ML = Marginal loss

3-32


Marginal analysis discrete distributions1

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

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

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


Joe s newsstand example a continued1

Joe’s Newsstand Example A continued

3-36


Joe s newsstand example b

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

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


Joe s newsstand example b continued1

Joe’s Newsstand Example B continued

3-39


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