to accompany quantitative analysis for management, 9e by render/stair/hanna 3-1 © 2006 by prentice...
TRANSCRIPT
To accompany Quantitative Analysis for Management, 9e by Render/Stair/Hanna
3-1 © 2006 by Prentice Hall, Inc. Upper Saddle River, NJ 07458
Prepared by Lee Revere and John LargePrepared by Lee Revere and John Large
Chapter 3Chapter 3
Decision AnalysisDecision Analysis
To accompany Quantitative Analysis for Management, 9e by Render/Stair/Hanna
3-2 © 2006 by Prentice Hall, Inc. Upper Saddle River, NJ 07458
Learning ObjectivesLearning ObjectivesStudents will be able to:
1. List the steps of the decision-making process.
2. Describe the types of decision-making environments.
3. Make decisions under uncertainty.
4. Use probability values to make decisions under risk.
5. Develop accurate and useful decision trees.
6. Revise probabilities using Bayesian analysis.
7. Use computers to solve basic decision-making problems.
8. Understand the importance and use of utility theory in decision theory.
To accompany Quantitative Analysis for Management, 9e by Render/Stair/Hanna
3-3 © 2006 by Prentice Hall, Inc. Upper Saddle River, NJ 07458
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 Uncertainty
3.5 Decision Making under Risk
3.6 Decision Trees
3.7 How Probability Values Are Estimated by Bayesian Analysis
3.8 Utility Theory
To accompany Quantitative Analysis for Management, 9e by Render/Stair/Hanna
3-4 © 2006 by Prentice Hall, Inc. Upper Saddle River, NJ 07458
IntroductionIntroduction
Decision theory is an analytical and systematic way to tackle problems.
A good decision is based on logic.
To accompany Quantitative Analysis for Management, 9e by Render/Stair/Hanna
3-5 © 2006 by Prentice Hall, Inc. Upper Saddle River, NJ 07458
The Six Steps in The Six Steps in Decision TheoryDecision Theory
1. Clearly define the problem at hand.
2. List the possible alternatives.
3. Identify the possible outcomes.
4. List the payoff or profit of each combination of alternatives and outcomes.
5. Select one of the mathematical decision theory models.
6. Apply the model and make your decision.
To accompany Quantitative Analysis for Management, 9e by Render/Stair/Hanna
3-6 © 2006 by Prentice Hall, Inc. Upper Saddle River, NJ 07458
John Thompson’s John Thompson’s Backyard Storage Backyard Storage
ShedsShedsDefine problem To manufacture or market
backyard storage sheds
List alternatives 1. Construct a large new plant
2. A small plant
3. No plant at all
Identify outcomes The market could be favorable or unfavorable for storage sheds
List payoffs List the payoff for each state of nature/decision alternative combination
Select a model Decision tables and/or trees can be used to solve the problem
Apply model and make decision
Solutions can be obtained and a sensitivity analysis used to make a decision
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Decision Table Decision Table for Thompson Lumberfor Thompson Lumber
Alternative
State of Nature
Favorable Market ($)
Unfavorable Market ($)
Construct a large plant
200,000 -180,000
Construct a small plant
100,000 -20,000
Do nothing 0 0
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3-8 © 2006 by Prentice Hall, Inc. Upper Saddle River, NJ 07458
Types of Decision-Types of Decision-Making EnvironmentsMaking 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 does know the
probabilities of the various outcomes.
Decision making under uncertainty.The decision maker does not know the
probabilities of the various outcomes.
To accompany Quantitative Analysis for Management, 9e by Render/Stair/Hanna
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Decision MakingDecision Making under Uncertainty under Uncertainty
Maximax
Maximin
Equally likely (Laplace)
Criterion of realism
Minimax
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Decision Table for Decision Table for Thompson LumberThompson Lumber
Alternative
State of Nature
Favorable Market ($)
Unfavorable Market ($)
Construct a large plant
200,000 -180,000
Construct a small plant
100,000 -20,000
Do nothing 0 0
Maximax: Optimistic Approach Find the alternative that maximizes the maximum
outcome for every alternative.
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Thompson Lumber: Thompson Lumber: Maximax SolutionMaximax Solution
Alternative
State of Nature
Maximax
Favorable Market ($)
Unfavorable Market ($)
Construct a large plant
200,000 -180,000 200,000
Construct a small plant
100,000 -20,000 100,000
Do nothing 0 0 0
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3-12 © 2006 by Prentice Hall, Inc. Upper Saddle River, NJ 07458
Decision Table for Decision Table for Thompson LumberThompson Lumber
Alternative
State of Nature
Favorable Market ($)
Unfavorable Market ($)
Construct a large plant
200,000 -180,000
Construct a small plant
100,000 -20,000
Do nothing 0 0
Maximin: Pessimistic Approach Choose the alternative with maximum
minimum output.
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Thompson Lumber: Thompson Lumber: Maximin SolutionMaximin Solution
Alternative
State of Nature
MaximinFavorable Market ($)
Unfavorable Market ($)
Construct a large plant
200,000 -180,000 -180,000
Construct a small plant
100,000 -20,000 -20,000
Do nothing 0 0 0
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3-14 © 2006 by Prentice Hall, Inc. Upper Saddle River, NJ 07458
Thompson Lumber: Thompson Lumber: HurwiczHurwicz
Criterion of Realism (Hurwicz) Decision maker uses a weighted average based
on optimism of the future.
Alternative
State of Nature
Favorable Market ($)
Unfavorable Market ($)
Construct a large plant
200,000 -180,000
Construct a small plant
100,000 -20,000
Do nothing 0 0
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Thompson Lumber: Thompson Lumber: Hurwicz SolutionHurwicz Solution
CR = α*(row max)+(1- α)*(row min)
Alternative
State of NatureCriterion
of Realism or
Weighted Average (α = 0.8) ($)
Favorable Market ($)
Unfavorable Market ($)
Construct a large plant
200,000 -180,000 124,000
Construct a small plant
100,000 -20,000 76,000
Do nothing 0 0 0
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Decision MakingDecision Making under Uncertainty under Uncertainty
Equally likely (Laplace)Assume all states of nature to be
equally likely, choose maximum Average.
Alternative
State of Nature
Favorable Market ($)
Unfavorable Market ($)
Construct a large plant
200,000 -180,000
Construct a small plant
100,000 -20,000
Do nothing 0 0
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3-17 © 2006 by Prentice Hall, Inc. Upper Saddle River, NJ 07458
Decision MakingDecision Making under Uncertainty under Uncertainty
Alternative
State of Nature
Avg.Favorable Market ($)
Unfavorable Market ($)
Construct a large plant
200,000 -180,000 10,000
Construct a small plant
100,000 -20,000 40,000
Do nothing 0 0 0
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Thompson Lumber;Thompson Lumber;Minimax RegretMinimax Regret
Minimax Regret: Choose the alternative that minimizes the
maximum opportunity loss .
Alternative
State of Nature
Favorable Market ($)
Unfavorable Market ($)
Construct a large plant
200,000 -180,000
Construct a small plant
100,000 -20,000
Do nothing 0 0
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Thompson Lumber:Thompson Lumber:Opportunity Loss Opportunity Loss
TableTable
Alternative
State of Nature
Favorable Market ($)
Unfavorable Market ($)
Construct a large plant
200,000 – 200,000 = 0
0- (-180,000) = 180,000
Construct a small plant
200,000 - 100,000 = 100,000
0- (-20,000) = 20,000
Do nothing 200,000 – 0 = 0 0 – 0 = 0
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3-20 © 2006 by Prentice Hall, Inc. Upper Saddle River, NJ 07458
Thompson Lumber:Thompson Lumber:Minimax Regret Minimax Regret
SolutionSolution
Alternative
State of NatureMaximum
Opportunity LossFavorable
Market ($)Unfavorable Market ($)
Construct a large plant
0 180,000 180,000
Construct a small plant
100,000 20,000 100,000
Do nothing 200,000 0 200,000
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3-21 © 2006 by Prentice Hall, Inc. Upper Saddle River, NJ 07458
In-Class Example 1In-Class Example 1
Let’s practice what we’ve learned. Use the decision table below to compute (1) Mazimax (2) Maximin (3) Minimax regret
Alternative
State of Nature
Good
Market
($)
Average
Market
($)
Poor
Market
($)
Construct a large plant
75,000 25,000 -40,000
Construct a small plant
100,000 35,000 -60,000
Do nothing 0 0 0
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In-Class Example 1:In-Class Example 1:MaximaxMaximax
Alternative
State of Nature
MaximaxGood
Market
($)
Average
Market
($)
Poor
Market
($)
Construct a large plant
75,000 25,000 -40,000 75,000
Construct a small plant
100,000 35,000 -60,000 100,000
Do nothing 0 0 0 0
To accompany Quantitative Analysis for Management, 9e by Render/Stair/Hanna
3-23 © 2006 by Prentice Hall, Inc. Upper Saddle River, NJ 07458
In-Class Example 1:In-Class Example 1:MaximinMaximin
Alternative
State of Nature
MaximinGood
Market
($)
Average
Market
($)
Poor
Market
($)
Construct a large plant
75,000 25,000 -40,000 -40,000
Construct a small plant
100,000 35,000 -60,000 -60,000
Do nothing 0 0 0 0
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3-24 © 2006 by Prentice Hall, Inc. Upper Saddle River, NJ 07458
In-Class Example 1:In-Class Example 1:Minimax Regret Minimax Regret
Opportunity Loss TableOpportunity Loss Table
Alternative
State of Nature
Maximum Opp. Loss
Good
Market
($)
Average
Market
($)
Poor
Market
($)
Construct a large plant
25,000 75,000 40,000 40,000
Construct a small plant
0 0 60,000 60,000
Do nothing 100,000 35,000 0 100,000
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Decision Making under Decision Making under RiskRisk
Expected Monetary Value:
In other words:
EMVAlternative n = Payoff 1 * PAlt. 1 + Payoff 2 * PAlt. 2 + … + Payoff n * PAlt.
n
nature. of stagesof numbern where
SP SPayoffative)EMV(Altern j
n
jj
)(*1
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Thompson Lumber:Thompson Lumber:EMVEMV
Alternative
State of Nature
EMVFavorable Market ($)
Unfavorable Market ($)
Construct a large plant
200,000 -180,000200,000*0.5 +
(-180,000)*0.5 = 10,000
Construct a small plant
100,000 -20,000100,000*0.5 +
(-20,000)*0.5 = 40,000
Do nothing 0 0 0*0.5 + 0*0.5 = 0
Probabilities 0.50 0.50
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Thompson Lumber:Thompson Lumber: EV|PI and EMV EV|PI and EMV
SolutionSolution
Alternative
State of Nature
EMVFavorable Market
($)
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
EV׀PI200,000*
0.5 = 100,000
0*0.5 = 0
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Expected Value of Expected Value of Perfect Information Perfect Information
((EVPIEVPI)) 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.
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Expected Value with Expected Value with Perfect Information (Perfect Information (EV|EV|
PIPI))
In other words
EV׀PI = Best Outcome of Alt 1 * PAlt. 1 + Best Outcome of Alt 2 * PAlt. 2 +… + Best Outcome of Alt n * PAlt. n
nature. of states ofnumber n
)P(S*nature) of statefor outcome(Best PI|EVn
1jj
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Expected Value of Expected Value of Perfect InformationPerfect Information
EVPI = EV|PI - maximum EMV
Expected value with perfect information
Expected value with no additional
information
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3-31 © 2006 by Prentice Hall, Inc. Upper Saddle River, NJ 07458
Thompson Lumber:Thompson Lumber:EVPI SolutionEVPI Solution
EVPIEVPI = expected value with perfect
information - max(EMVEMV)
= $200,000*0.50 + 0*0.50 - $40,000
= $60,000 From previous slide
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In-Class Example 2In-Class Example 2
Let’s practice what we’ve learned. Using the table below compute EMV, EV׀PI, and EVPI.
Alternative
State of Nature
Good
Market
($)
Average
Market
($)
Poor
Market
($)
Construct a large plant
75,000 25,000 -40,000
Construct a small plant
100,000 35,000 -60,000
Do nothing 0 0 0
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3-33 © 2006 by Prentice Hall, Inc. Upper Saddle River, NJ 07458
In-Class Example 2:In-Class Example 2: EMV and EV EMV and EV׀׀PIPI
SolutionSolution
Alternative
State of Nature
EMVGood
Market
($)
Average
Market
($)
Poor
Market
($)
Construct a large plant
75,000 25,000 -40,000 21,250
Construct a small plant
100,000 35,000 -60,000 27,500
Do nothing 0 0 0 0
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3-34 © 2006 by Prentice Hall, Inc. Upper Saddle River, NJ 07458
In-Class Example 2:In-Class Example 2:EVPI SolutionEVPI Solution
EVPIEVPI = expected value with perfect
information - max(EMVEMV)
= $100,000*0.25 + 35,000*0.50 +0*0.25
= $ 42,500 - 27,500
= $ 15,000
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Expected Opportunity Expected Opportunity LossLoss
EOL is the cost of not picking the best solution.EOL = Expected Regret
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Thompson Lumber: EOLThompson Lumber: EOLThe Opportunity Loss TableThe Opportunity Loss Table
Alternative
State of Nature
Favorable Market ($)
Unfavorable Market ($)
Construct a large plant
200,000 – 200,000
0- (-180,000)
Construct a small plant
200,000 - 100,000
0 – (-20,000)
Do nothing 200,000 - 0 0-0
Probabilities 0.50 0.50
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3-37 © 2006 by Prentice Hall, Inc. Upper Saddle River, NJ 07458
Thompson Lumber: Thompson Lumber: EOL TableEOL Table
Alternative
State of Nature
Favorable Market ($)
Unfavorable Market ($)
Construct a large plant
200,000 -180,000
Construct a small plant
100,000 -20,000
Do nothing 0 0
Probabilities 0.50 0.50
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3-38 © 2006 by Prentice Hall, Inc. Upper Saddle River, NJ 07458
Thompson Lumber: Thompson Lumber: EOL SolutionEOL Solution
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
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Thompson Lumber:Thompson Lumber:Sensitivity AnalysisSensitivity 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)
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Thompson Lumber:Thompson Lumber:Sensitivity AnalysisSensitivity Analysis (continued)(continued)
-200000
-150000
-100000
-50000
0
50000
100000
150000
200000
250000
0 0.2 0.4 0.6 0.8 1
Values of P
EM
V V
alue
s
Point 1 Point 2Small Plant
Large Plant EMV
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Marginal AnalysisMarginal Analysis
P = probability that demand > a given supply.
1-P = probability that demand < supply. MP = marginal profit. ML = marginal loss. Optimal decision rule is: P*MP (1-P)*ML
or
MLMPML
P
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Marginal Analysis -Marginal Analysis -Discrete DistributionsDiscrete Distributions
Steps using Discrete Distributions: Determine the value for P.P. 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.P.
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Café du Donut:Café du Donut:Marginal AnalysisMarginal Analysis
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
Café du Donut sells a dozen donuts for $6. It costs $4 to make each dozen. The following table shows the discrete distribution for Café du Donut sales.
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Café du Donut: Café du Donut: Marginal Analysis SolutionMarginal Analysis Solution
Marginal profit = selling price - cost
= $6 - $4 = $2Marginal loss = cost
Therefore:
667.06
4
24
4
MPML
MLP
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Café du Donut: Café du Donut: Marginal Analysis SolutionMarginal Analysis Solution
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
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In-Class Example 3In-Class Example 3
Let’s practice what we’ve learned. You sell cases of goods for $15/case, the raw materials cost you $4/case, and you pay $1/case commission.
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In-Class Example 3:In-Class Example 3:SolutionSolution
Daily Sales Cases
Probability of Sales at this Level
Probability that Sales Will Be at this
Level or Greater 4 0.1 1.0 > .286 5 0.1 .9 > .286 6 0.4 .8 > .286 7 0.3 .4 > .286 8 0.1 .1 1.00
MP = $15-$4-$1 = $10 per case ML = $4P>= $4 / $10+$4 = .286
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Marginal AnalysisMarginal AnalysisNormal DistributionNormal Distribution
= average or mean sales = standard deviation of sales MPMP = marginal profit MLML = Marginal loss
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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:
*XZ
MPML
MLP
X*
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Marginal Analysis:Marginal Analysis:Normal Curve ReviewNormal Curve Review
*
00.1
xZ
Pcumulative
ZoZo
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Marginal Analysis -Marginal Analysis -Normal Curve ReviewNormal Curve Review
*X
area = .30
Use table to find Z
area = .70
MPML
ML.3
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Joe’s Newsstand Joe’s Newsstand ExampleExample
Joe sells newspapers for $1.00 each.
Papers cost him $.40 each. His average
daily demand is 50 papers with a standard
deviation of 10 papers. Assuming sales
follow a normal distribution, how many
papers should Joe stock?
MLML = $0.40 MPMP = $0.60 = Average demand = 50 papers per
day = Standard deviation of demand =
10
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Joe’s Newsstand ExampleJoe’s Newsstand Example (continued)(continued)
Step 1:
..
MPMPMLML
MLMLPP
.
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Joe’s Newsstand ExampleJoe’s Newsstand Example (continued)(continued)
Step 2: Look on the Normal table for
PP = 0.6 (i.e., 1 - .4) ZZ = 0.25,
and
or:
**XX
XX** = 10 * 0.25 + 50 = 52.5 or 53 newspapers = 10 * 0.25 + 50 = 52.5 or 53 newspapers
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Joe’s Newsstand Joe’s Newsstand Example BExample B
Joe also offers his clients the “Times” for $1.00. This paper is flown in from out of state, which greatly increases its costs. Joe pays $.80 for the “Times.” The “Times” has average daily sales of 100 papers with a standard deviation of 10. Assuming sales follow a normal distribution, how many “Times” papers should Joe stock?
MLML = $0.80 MPMP = $0.20 = Average demand = 100 papers per day = Standard deviation of demand = 10
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Joe’s Newsstand Joe’s Newsstand Example BExample B (continued)(continued)
Step 1:
..
MPMPMLML
MLMLPP
.
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Step 2:
Z = 0.80
= -0.84 for an area of 0.80
And
or: X=-8.4+100 or 92 newspapers
**XX
Joe’s Newsstand Joe’s Newsstand Example BExample B (continued)(continued)
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Decision Making with Decision Making with Uncertainty: Using the Uncertainty: Using the
Decision TreesDecision Trees
Decision treesDecision trees enable one to look at
decisions:
With many alternativesalternatives and states states
of nature,of nature,
which must be made in sequence.
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Five Steps toFive Steps toDecision Tree AnalysisDecision Tree Analysis
1. Define the problem.
2. Structure or draw the decision tree.
3. Assign probabilities to the states of nature.
4. Estimate payoffs for each possible combination of alternatives and states of nature.
5. Solve the problem by computing expected monetary values (EMVs) for each state of nature node.
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Structure of Decision Structure of Decision TreesTrees
A graphical representation where:
A decision node from which one of several alternatives may be chosen.
A state-of-nature node out of which one state of nature will occur.
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Thompson’s Decision Thompson’s Decision TreeTree
1
2
A A Decision Decision
NodeNode
A State of A State of Nature Nature NodeNode
Favorable Market
Unfavorable Market
Favorable Market
Unfavorable Market
Construct
Large Plant
Construct Small Plant
Do Nothing
Step 1: Define the problem
Lets re-look at John Thompson’s decision regarding storage sheds. This simple problem can be depicted using a decision tree.
Step 2: Draw the tree
To accompany Quantitative Analysis for Management, 9e by Render/Stair/Hanna
3-62 © 2006 by Prentice Hall, Inc. Upper Saddle River, NJ 07458
Thompson’s Decision Thompson’s Decision TreeTree
1
2
A A Decision Decision
NodeNode
A State of A State of Nature NodeNature Node Favorable (0.5)
Market
Unfavorable (0.5) Market
Favorable (0.5) Market
Unfavorable (0.5) Market
Construct
Large Plant
Construct Small Plant
Do Nothing
$200,000$200,000
-$180,000-$180,000
$100,000$100,000
-$20,000-$20,000
00
Step 3: Assign probabilities to the states of nature.
Step 4: Estimate payoffs.
To accompany Quantitative Analysis for Management, 9e by Render/Stair/Hanna
3-63 © 2006 by Prentice Hall, Inc. Upper Saddle River, NJ 07458
Thompson’s Decision Thompson’s Decision TreeTree
1
2
A Decision A Decision NodeNode
A State A State of Nature of Nature NodeNode
Favorable (0.5) Market
Unfavorable (0.5) Market
Favorable (0.5) Market
Unfavorable (0.5) Market
Construct
Large Plant
Construct Small Plant
Do Nothing
$200,000$200,000
-$180,000-$180,000
$100,000$100,000
-$20,000-$20,000
00
EMV EMV =$40,000=$40,000
EMVEMV=$10,000=$10,000
Step 5: Compute EMVs and make decision.
To accompany Quantitative Analysis for Management, 9e by Render/Stair/Hanna
3-64 © 2006 by Prentice Hall, Inc. Upper Saddle River, NJ 07458
Thompson’s Decision:Thompson’s Decision:A More Complex A More Complex
ProblemProblem John Thompson has the opportunity of
obtaining a market survey that will give additional information on the probable state of nature. Results of the market survey will likely indicate there is a percent change of a favorable market. Historical data show market surveys accurately predict favorable markets 78 % of the time. Thus P(Fav. Mkt / Fav. Survey Results) = .78
Likewise, if the market survey predicts an unfavorable market, there is a 13 % chance of its occurring. P(Unfav. Mkt / Unfav. Survey Results) = .13
Now that we have redefined the problem (Step 1), let’s use this additional data and redraw Thompson’s decision tree (Step 2).
To accompany Quantitative Analysis for Management, 9e by Render/Stair/Hanna
3-65 © 2006 by Prentice Hall, Inc. Upper Saddle River, NJ 07458
Thompson’s Decision Thompson’s Decision TreeTree
To accompany Quantitative Analysis for Management, 9e by Render/Stair/Hanna
3-66 © 2006 by Prentice Hall, Inc. Upper Saddle River, NJ 07458
Thompson’s Decision Thompson’s Decision TreeTree
Step 3: Assign the new probabilities to the states of nature.
Step 4: Estimate the payoffs.
To accompany Quantitative Analysis for Management, 9e by Render/Stair/Hanna
3-67 © 2006 by Prentice Hall, Inc. Upper Saddle River, NJ 07458
Thompson’s Decision Thompson’s Decision TreeTree
Step 5: Compute the EMVs and make decision.
To accompany Quantitative Analysis for Management, 9e by Render/Stair/Hanna
3-68 © 2006 by Prentice Hall, Inc. Upper Saddle River, NJ 07458
John Thompson DilemmaJohn Thompson Dilemma
John Thompson is not sure how much value to place on market survey. He wants to determine the monetary worth of the survey. John Thompson is also interested in how sensitive his decision is to changes in the market survey results. What should he do?
Expected Value of Sample Information
Sensitivity Analysis
To accompany Quantitative Analysis for Management, 9e by Render/Stair/Hanna
3-69 © 2006 by Prentice Hall, Inc. Upper Saddle River, NJ 07458
Expected Value of Expected Value of Sample InformationSample Information
Expected value of best decision withwith sample information, assuming no cost to gather it
Expected value of best decision withoutwithout sample information
EVSIEVSI =
EVSI for Thompson Lumber = $59,200 - $40,000 = $19,200Thompson could pay up to $19,200 and come out ahead.
To accompany Quantitative Analysis for Management, 9e by Render/Stair/Hanna
3-70 © 2006 by Prentice Hall, Inc. Upper Saddle River, NJ 07458
Calculations for Thompson Calculations for Thompson Lumber Sensitivity Lumber Sensitivity
AnalysisAnalysis
2,400$104,000
($2,400)($106,400)1) EMV(node
p
)p(p
Equating the EMVEMV(node 1) to the EMV of not conducting the survey, we have
0.36$104,000
$37,600
or
$37,600$104,000
$40,000$2,400$104,000
p
p
p
To accompany Quantitative Analysis for Management, 9e by Render/Stair/Hanna
3-71 © 2006 by Prentice Hall, Inc. Upper Saddle River, NJ 07458
In-Class Problem 3In-Class Problem 3
Let’s practice what we’ve learned
Leo can purchase a historic home for $200,000 or land in a growing area for $50,000. There is a 60% chance the economy will grow and a 40% change it will not. If it grows, the historic home will appreciate in value by 15% yielding a $30,00 profit. If it does not grow, the profit is only $10,000. If Leo purchases the land he will hold it for 1 year to assess the economic growth. If the economy grew during the first year, there is an 80% chance it will continue to grow. If it did not grow during the first year, there is a 30% chance it will grow in the next 4 years. After a year, if the economy grew, Leo will decide either to build and sell a house or simply sell the land. It will cost Leo $75,000 to build a house that will sell for a profit of $55,000 if the economy grows, or $15,000 if it does not grow. Leo can sell the land for a profit of $15,000. If, after a year, the economy does not grow, Leo will either develop the land, which will cost $75,000, or sell the land for a profit of $5,000. If he develops the land and the economy begins to grow, he will make $45,000. If he develops the land and the economy does not grow, he will make $5,000.
To accompany Quantitative Analysis for Management, 9e by Render/Stair/Hanna
3-72 © 2006 by Prentice Hall, Inc. Upper Saddle River, NJ 07458
In-Class Problem 3: In-Class Problem 3: SolutionSolution
1
2
3
4
5
6
7
Purchase historic home
Purchase land
Economy grows (.6)
No growth (.4)
Economy grows (.6)
No growth (.4)
Build house
Economy grows (.8)
No growth (.2)
Sell land
Develop land
Sell land
Economy grows (.3)
No growth (.7)
To accompany Quantitative Analysis for Management, 9e by Render/Stair/Hanna
3-73 © 2006 by Prentice Hall, Inc. Upper Saddle River, NJ 07458
In-Class Problem 3: In-Class Problem 3: SolutionSolution
1
2
3
4
5
6
7
Purchase historic home
Purchase land
$35,000
$22,000 Economy grows (.6) $30,000
No growth (.4)
$10,000
Economy grows (.6)
No growth (.4)
$35,000
$47,000
Build house
$47,000
Economy grows (.8) $55,000
$15,000No growth (.2)
Sell land
$15,000
$17,000
Develop land
Sell land
$5,000
Economy grows (.3)
No growth (.7)
$45,000
$5,000
$17,000
To accompany Quantitative Analysis for Management, 9e by Render/Stair/Hanna
3-74 © 2006 by Prentice Hall, Inc. Upper Saddle River, NJ 07458
Estimating Probability Estimating Probability Values with BayesianValues with Bayesian
Management experience or intuition History Existing data Need to be able to revise
probabilities based upon new data
Posteriorprobabilities
Priorprobabilities New data
Baye’s Theorem
To accompany Quantitative Analysis for Management, 9e by Render/Stair/Hanna
3-75 © 2006 by Prentice Hall, Inc. Upper Saddle River, NJ 07458
Bayesian AnalysisBayesian Analysis
Market Survey Reliability in Predicting Actual States of Nature
Actual States of Nature
Result of Survey Favorable
Market (FM)
Unfavorable
Market (UM)
Positive (predicts
favorable market
for product)
P(survey positive|FM)
= 0.70
P(survey positive|UM)
= 0.20
Negative (predicts
unfavorable
market for
product)
P(survey
negative|FM) = 0.30
P(survey negative|UM)
= 0.80
The probabilities of a favorable / unfavorable state of nature can be obtained by analyzing the Market Survey Reliability in Predicting Actual States of Nature.
To accompany Quantitative Analysis for Management, 9e by Render/Stair/Hanna
3-76 © 2006 by Prentice Hall, Inc. Upper Saddle River, NJ 07458
Bayesian Analysis Bayesian Analysis (continued):(continued): Favorable SurveyFavorable Survey
Probability Revisions Given a Favorable Survey
Conditional
Probability
Posterior
Probability
State
of
Nature
P(Survey positive|State of Nature
Prior ProbabilityJoint Probability
FM 0.70 * 0.50 0.350.45
0.35 = 0.78
UM 0.20 * 0.500.45
0.10 0.10 = 0.22
0.45 1.00
To accompany Quantitative Analysis for Management, 9e by Render/Stair/Hanna
3-77 © 2006 by Prentice Hall, Inc. Upper Saddle River, NJ 07458
Bayesian Analysis Bayesian Analysis (continued):(continued): Unfavorable SurveyUnfavorable Survey
Probability Revisions Given an Unfavorable Survey
Conditional
Probability
Posterior
Probability
State
of
Nature
P(Survey
negative|State
of Nature)
Prior Probability
Joint Probability
FM 0.30 * 0.50 0.150.55
0.15 = 0.27
UM 0.80 * 0.50 0.400.55
0.40 = 0.73
0.55 1.00
To accompany Quantitative Analysis for Management, 9e by Render/Stair/Hanna
3-78 © 2006 by Prentice Hall, Inc. Upper Saddle River, NJ 07458
Decision Making Using Decision Making Using Utility TheoryUtility Theory
Utility assessment assigns the worst outcome a utility of 0, and the best outcome, a utility of 1.
A standard gamble is used to determine utility values.
When you are indifferent, the utility values are equal.
To accompany Quantitative Analysis for Management, 9e by Render/Stair/Hanna
3-79 © 2006 by Prentice Hall, Inc. Upper Saddle River, NJ 07458
Standard Gamble for Standard Gamble for Utility AssessmentUtility Assessment
Best outcomeUtility = 1
Worst outcomeUtility = 0
Other outcomeUtility = ??
(p)
(1-p)Alternative 1
Alternative 2
To accompany Quantitative Analysis for Management, 9e by Render/Stair/Hanna
3-80 © 2006 by Prentice Hall, Inc. Upper Saddle River, NJ 07458
Simple Example: Utility Simple Example: Utility TheoryTheory
$5,000,000
$0
$2,000,000
Accept Offer
Reject Offer
Heads(0.5)
Tails(0.5)
Let’s say you were offered $2,000,000 right now on a chance to win $5,000,000. The $5,000,000 is won only if you flip a coin and get tails. If you get heads you lose and get $0. What should you do?
To accompany Quantitative Analysis for Management, 9e by Render/Stair/Hanna
3-81 © 2006 by Prentice Hall, Inc. Upper Saddle River, NJ 07458
Real Estate Example: Real Estate Example: Utility TheoryUtility Theory
Jane Dickson is considering a 3-year real estate investment. There is an 80 % chance the real estate market will soar and a 20 % chance it will bust. In a good market the real estate investment will pay $10,000, in an unfavorable market it is $0. Of course, she could leave her money in the bank and earn a $5,000 return. What should she do?
To accompany Quantitative Analysis for Management, 9e by Render/Stair/Hanna
3-82 © 2006 by Prentice Hall, Inc. Upper Saddle River, NJ 07458
Real Estate Example: Real Estate Example: SolutionSolution
$10,000U($10,000) = 1.0
0U(0)=0
$5,000U($5,000)=p=0.80
p= 0.80
(1-p)= 0.20
Invest in
Real Estate
Invest in Bank
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3-83 © 2006 by Prentice Hall, Inc. Upper Saddle River, NJ 07458
Utility Curve for Jane Utility Curve for Jane DicksonDickson
00.10.20.30.40.50.60.70.80.9
1
$- $2,000 $4,000 $6,000 $8,000 $10,000
Monetary Value
Utility
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3-84 © 2006 by Prentice Hall, Inc. Upper Saddle River, NJ 07458
Preferences for RiskPreferences for Risk
Monetary Outcome
Risk
Avoider
Risk
Seeker
Risk In
differe
nce
Uti
lity
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3-85 © 2006 by Prentice Hall, Inc. Upper Saddle River, NJ 07458
Decision Facing Mark Decision Facing Mark SimkinSimkin
Tack landspoint up (0.45)
Tack lands point down (0.55)
$10,000
-$10,000
0
Alternative 1
Mark plays
the game
Alternative 2
Mark does not play the game
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3-86 © 2006 by Prentice Hall, Inc. Upper Saddle River, NJ 07458
Utility Curve for Mark Utility Curve for Mark SimkinSimkin
0
0.1
0.20.3
0.4
0.5
0.6
0.70.8
0.9
1
-$20,000 -$10,000 $0 $10,000 $20,000 $30,000
To accompany Quantitative Analysis for Management, 9e by Render/Stair/Hanna
3-87 © 2006 by Prentice Hall, Inc. Upper Saddle River, NJ 07458
Thompson Decision Tree Thompson Decision Tree Problem Using QM for Problem Using QM for
WindowsWindows
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Thompson Decision Tree Thompson Decision Tree Problem Using ExcelProblem Using Excel