Quantitative Analysis for Management, 11e (Render)

1. 3-1
Quantitative AnalysisQuantitative Analysis
for Managementfor Management
Chapter 3Chapter 3
Fundamentals ofFundamentals of
Decision Theory ModelsDecision Theory Models

2. 3-2
Chapter OutlineChapter 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. 3-3
Learning ObjectivesLearning 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

4. 3-4
IntroductionIntroduction
♦Decision theory is an analytical and
systematic way to tackle problems
♦A good decision is based on logic.

5. 3-5
The Six Steps in DecisionThe Six Steps in Decision
TheoryTheory
♦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

6. 3-6
Decision TableDecision Table
for Thompson Lumberfor Thompson Lumber
State of Nature
Alternative
200,000 -180,000
100,000 -20,000
0 0
Construct a
large plant
Construct a
small plant
Do nothing
Favorable
Market ($)
Unfavorable
Market ($)

7. 3-7
Types of Decision-MakingTypes of Decision-Making
EnvironmentsEnvironments
♦Type 1: Decision-making under certainty
♣decision-maker knows with certaintyknows with certainty the
consequences of every alternative or decision
choice
♦Type 2: Decision-making under risk
♣The decision-maker knowsknows the probabilities
of the various outcomes
♦Decision-making under uncertainty
♣The decision-maker does not knowdoes not know the
probabilities of the various outcomes

8. 3-8
Decision-Making Under RiskDecision-Making Under Risk
nnature,ofstatesofnumbertheto1jwhere
))P(S*(Payoffi)ativeEMV(Altern
n
1j
jSj
=
∑=
=
Expected Monetary Value:Expected Monetary Value:

9. 3-9
Decision TableDecision Table
for Thompson Lumberfor Thompson Lumber
State of Nature
Alternative
Probabilities
200,000 -180,000
100,000 -20,000
0 0
Construct a
large plant
Construct a
small plant
Do nothing
Favorable
Market ($)
Unfavorable
Market ($)
0.50 0.50
EMV
10,000
40,000
0

10. 3-10
Expected Value of PerfectExpected Value of Perfect
Information (Information (EVPI))
♦EVPIEVPI places an upper bound on what one
would pay for additional information
♦EVPIEVPI is the expected value with perfect
information minus the maximum EMV

11. 3-11
Expected Value With PerfectExpected Value With Perfect
Information (Information (EV|PI))
nnature,ofstatesofnumbertheto1j
)P(S*j)natureofstateforoutcomebest j
=
∑=
=
where
(PI|EV
n
j 1

12. 3-12
Expected Value of PerfectExpected Value of Perfect
InformationInformation
♦EVPIEVPI = EV|PIEV|PI - maximum EMVEMV

13. 3-13
Expected Value of PerfectExpected Value of Perfect
InformationInformation
State of Nature
Alternative
Probabilities
200,000
0
Construct a
large plant
Construct a
small plant
Do nothing
Favorable
Market ($)
Unfavorable
Market ($)
0.50 0.50
EMV
40,000

14. 3-14
Expected Value of PerfectExpected Value of Perfect
InformationInformation
EVPIEVPI = expected value with perfect
information - max(EMVEMV)
= $200,000*0.50 + 0*0.50 - $40,000
= $60,000

15. 3-15
Expected Opportunity LossExpected Opportunity Loss
♦EOLEOL is the cost of not picking the best
solution
♦EOLEOL = Expected Regret
We want to maximize EMV or
minimize EOL

16. 3-16
Computing EOL - TheComputing EOL - The
Opportunity Loss TableOpportunity Loss Table
State of Nature
Alternative Favorable Market
($)
Unfavorable
Market ($)
Large Plant 200,000 - 200,000 0 - (-180,000)
Small Plant 200,000 - 100,000 0 -(-20,000)
Do Nothing 200,000 - 0 0-0
Probabilities 0.50 0.50

17. 3-17
The Opportunity Loss TableThe Opportunity Loss Table
continuedcontinued
State of Nature
Alternative Favorable Market
($)
Unfavorable
Market ($)
Large Plant 0 180,000
Small Plant 100,000 20,000
Do Nothing 200,000 0
Probabilities 0.50 0.50

18. 3-18
The Opportunity Loss TableThe Opportunity Loss Table
continuedcontinued
Alternative EOL
Large Plant (0.50)*$0 +
(0.50)*($180,000)
$90,000
Small Plant (0.50)*($100,000)
+ (0.50)(*$20,000)
$60,000
Do Nothing (0.50)*($200,000)
+ (0.50)*($0)
$100,000

19. 3-19
Sensitivity AnalysisSensitivity Analysis
EMV(Large Plant) = $200,000PP - (1-P1-P)$180,000
EMV(Small Plant) = $100,000PP - $20,000(1-P1-P)
EMV(Do Nothing) = $0PP + 0(1-P1-P)

20. 3-20
Sensitivity Analysis -Sensitivity Analysis -
continuedcontinued
-200000
-150000
-100000
-50000
0
50000
100000
150000
200000
250000
0 0.2 0.4 0.6 0.8 1
Values of P
EMVValues
Point 1
Point 2
EMV (Small Plant)
EMV(Large Plant)

21. 3-21
Decision MakingDecision Making
Under UncertaintyUnder Uncertainty
♦Maximax
♦Maximin
♦Equally likely (Laplace)
♦Criterion of Realism
♦Minimax

22. 3-22
Decision MakingDecision Making
Under UncertaintyUnder Uncertainty
Maximax - Choose the alternative with the
maximum output
State of Nature
Alternative
Probabilities
200,000 -180,000
100,000 -20,000
0 0
Construct a
large plant
Construct a
small plant
Do nothing
Favorable
Market ($)
Unfavorable
Market ($)

23. 3-23
Decision MakingDecision Making
Under UncertaintyUnder Uncertainty
Maximin - Choose the alternative with the
maximum minimum output
State of Nature
Alternative
Probabilities
200,000 -180,000
100,000 -20,000
0 0
Construct a
large plant
Construct a
small plant
Do nothing
Favorable
Market ($)
Unfavorable
Market ($)

24. 3-24
Decision MakingDecision Making
Under UncertaintyUnder Uncertainty
Equally likely (Laplace) - Assume all states
of nature to be equally likely, choose
maximum EMV
State of Nature
Alternative
Probabilities
200,000 -180,000
100,000 -20,000
0 0
Construct a
large plant
Construct a
small plant
Do nothing
Favorable
Market ($)
Unfavorable
Market ($)
0.50 0.50
EMV
10,000
40,000
0

25. 3-25
Decision MakingDecision Making
Under UncertaintyUnder Uncertainty
Criterion of Realism (Hurwicz):
CR = α*(row max) + (1-α)*(row min)
State of Nature
Alternative
Probabilities
200,000 -180,000
100,000 -20,000
0 0
Construct a
large plant
Construct a
small plant
Do nothing
Favorable
Market ($)
Unfavorable
Market ($)
0.50 0.50
CR
124,000
76,000
0

26. 3-26
Decision MakingDecision Making
Under UncertaintyUnder Uncertainty
Minimax - choose the alternative with the
minimum maximum Opportunity Loss
State of Nature
Alternative
Probabilities
0 180,000
100,000 20,000
200,000 0
Construct a
large plant
Construct a
small plant
Do nothing
Favorable
Market ($)
Unfavorable
Market ($)
0.50 0.50
Max in row
180,000
100,000
200,000

27. 3-27
Marginal AnalysisMarginal Analysis
♦PP = probability that demand is greater than
or equal to a given supply
♦1-P1-P = probability that demand will be less
than supply
♦MPMP = marginal profit MLML = marginal loss
♦Optimal decision rule is: P*MPP*MP ≥≥ (1-P)*ML(1-P)*ML
♦or
MLMP
ML
P
+
≥

28. 3-28
Marginal Analysis -Marginal Analysis -
Discrete DistributionsDiscrete Distributions
♦Steps using Discrete Distributions:
♣Determine the value for PP
♣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 PP

29. 3-29
Café du Donut ExampleCafé du Donut Example
Daily Sales
(Cartons)
Probability of Sales
at this Level
Probability that Sales
Will Be at this Level
or Greater
4 0.05 1.00
5 0.15 0.95
6 0.15 0. 80
7 0.20 0.65
8 0.25 0.45
9 0.10 0.20
10 0.10 0.10
1.00

30. 3-30
Café du Donut ExampleCafé du Donut Example
continuedcontinued
♦Marginal profit = selling price - cost
= $6 - $4 = $2
♦Marginal loss = cost
♦Therefore:
66
6
0
24
44
.
MPML
ML
P
=
+
==
+
≥

31. 3-31
Café du Donut ExampleCafé du Donut Example
continuedcontinued
Daily
Sales
(Cartons)
Probability of
Sales at this Level
Probability that
Sales Will Be at this
Level or Greater
4 0.05 1.00 ≥0.66
5 0.15 0.95 ≥0.66
6 0.15 0. 80 ≥0.66
7 0.20 0.65
8 0.25 0.45
9 0.10 0.20
10 0.10 0.10
1.00

32. 3-32
Marginal AnalysisMarginal Analysis
Normal DistributionNormal Distribution
♦µµ = average or mean sales
♦σσ = standard deviation of sales
♦MPMP = marginal profit
♦MLML = Marginal loss

33. 3-33
Marginal Analysis -Marginal Analysis -
Discrete DistributionsDiscrete Distributions
♦Steps using Normal Distributions:
♣Determine the value for P.
♣Locate P on the normal distribution. For a
given area under the curve, we find Z from the
standard Normal table.
♣ Using we can now solve for X*
MPML
ML
P
+
=
σ
µ−
=
*
X
Z

34. 3-34
Joe’s Newsstand Example AJoe’s Newsstand Example A
♦MLML = 4
♦MPMP = 6
♦µµ = Average demand = 50 papers per day
♦σσ = Standard deviation of demand = 10

35. 3-35
Joe’s Newsstand Example AJoe’s Newsstand Example A
continuedcontinued
♦Step 1:
♦Step 2: Look on the Normal table for
PP = 0.6 (i.e., 1 - .04) ∴ ZZ = 0.25,
and
or:
400
64
4
.
MPML
ML
P =
+
=
+
=
10
50
250
−
=
*
X
.
newspapersor535525025010 ..*X*
=+=

36. 3-36
Joe’s Newsstand Example AJoe’s Newsstand Example A
continuedcontinued

37. 3-37
Joe’s Newsstand Example BJoe’s Newsstand Example B
♦MLML = 8
♦MPMP = 2
♦µµ = Average demand = 100 papers per
day
♦σσ = Standard deviation of demand = 10

38. 3-38
Joe’s Newsstand Example BJoe’s Newsstand Example B
continuedcontinued
♦Step 1:
♦Step 2:
ZZ = -0.84 for an area of 0.80
and
or:
800
8 2
8
.
MPML
ML
P =
+
=
+
=
10
1000
840
−
=−
*
X
.
newspapersor9269110048 ..X*
=+−=

39. 3-39
Joe’s Newsstand Example BJoe’s Newsstand Example B
continuedcontinued