Decision Analysis
3
To accompanyQuantitative Analysis for Management, Twelfth Edition, by Render, Stair, Hanna and HalePower Point slides created by Jeff Heyl Copyright ©2015 Pearson Education, Inc.
After completing this chapter, students will be able to:
LEARNING OBJECTIVES
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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. Understand the importance and use of utility theory in
decision making.
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3.1 Introduction
3.2 The Six Steps in Decision Making
3.3 Types of Decision-Making Environments
3.4 Decision Making Under Uncertainty
3.5 Decision Making Under Risk
3.6 A Minimization Example
3.8 Decision Trees
3.10 Utility Theory
CHAPTER OUTLINE
Introduction
• What is involved in making a good decision?• Decision theory is an analytic and systematic
approach to the study of decision making• A good decision is one that is based on logic,
considers all available data and possible alternatives, and applies a quantitative approach
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The Six Steps in Decision Making
1. Clearly define the problem at hand2. List the possible alternatives3. Identify the possible outcomes or states of
nature4. List the payoff (typically profit) of each
combination of alternatives and outcomes5. Select one of the mathematical decision
theory models6. Apply the model and make your decision
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Thompson Lumber Company
Step 1 – Define the problem• Consider expanding by manufacturing
and marketing a new product – backyard storage sheds
Step 2 – List alternatives• Construct a large new plant• Construct a small new plant• Do not develop the new product line
Step 3 – Identify possible outcomes, states of nature• The market could be favorable or
unfavorable
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Thompson Lumber Company
Step 4 – List the payoffs• Identify conditional values for the profits
for large plant, small plant, and no development for the two possible market conditions
Step 5 – Select the decision model• Depends on the environment and
amount of risk and uncertaintyStep 6 – Apply the model to the data
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Thompson Lumber Company
STATE OF NATURE
ALTERNATIVEFAVORABLE MARKET ($)
UNFAVORABLE MARKET ($)
Construct a large plant 200,000 –180,000
Construct a small plant 100,000 –20,000
Do nothing 0 0
TABLE 3.1 – Conditional Values
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Types of Decision-Making Environments
• Decision making under certainty– The decision maker knows with certainty the
consequences of every alternative or decision choice
• Decision making under uncertainty– The decision maker does not know the
probabilities of the various outcomes
• Decision making under risk– The decision maker knows the probabilities of the
various outcomes
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Decision Making Under Uncertainty
• Criteria for making decisions under uncertainty
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1. Maximax (optimistic)2. Maximin (pessimistic) (Wald)3. Criterion of realism (Hurwicz)4. Equally likely (Laplace) 5. Minimax regret (Savage)
Optimistic• Used to find the alternative that maximizes
the maximum payoff – maximax criterion– Locate the maximum payoff for each alternative– Select the alternative with the maximum number
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STATE OF NATURE
ALTERNATIVEFAVORABLE MARKET ($)
UNFAVORABLE MARKET ($)
MAXIMUM IN A ROW ($)
Construct a large plant 200,000–
180,000 200,000
Construct a small plant 100,000 –20,000 100,000
Do nothing 0 0 0
TABLE 3.2 – Thompson’s Maximax Decision
Maximax
Pessimistic• Used to find the alternative that maximizes
the minimum payoff – maximin criterion– Locate the minimum payoff for each alternative– Select the alternative with the maximum number
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STATE OF NATURE
ALTERNATIVEFAVORABLE MARKET ($)
UNFAVORABLE MARKET ($)
MINIMUM IN A ROW ($)
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
TABLE 3.3 – Thompson’s Maximin Decision
Maximin
Criterion of Realism (Hurwicz)
• Often called weighted average – Compromise between optimism and pessimism– Select a coefficient of realism , with 0 ≤ a ≤ 1
a = 1 is perfectly optimistica = 0 is perfectly pessimistic
– Compute the weighted averages for each alternative
– Select the alternative with the highest value
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Weighted average = (best in row) + (1 – )(worst in row)
Criterion of Realism (Hurwicz)For the large plant alternative using = 0.8
(0.8)(200,000) + (1 – 0.8)(–180,000) = 124,000
For the small plant alternative using = 0.8
(0.8)(100,000) + (1 – 0.8)(–20,000) = 76,000
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STATE OF NATURE
ALTERNATIVEFAVORABLE MARKET ($)
UNFAVORABLE MARKET ($)
CRITERION OF REALISM
( = 0.8) $
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
TABLE 3.4 – Thompson’s Criterion of Realism Decision
Realism
Equally Likely (Laplace)• Considers all the payoffs for each alternative
– Find the average payoff for each alternative– Select the alternative with the highest average
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STATE OF NATURE
ALTERNATIVEFAVORABLE MARKET ($)
UNFAVORABLE MARKET ($)
ROW AVERAGE ($)
Construct a large plant 200,000–
180,000 10,000
Construct a small plant 100,000 –20,000 40,000
Do nothing 0 0 0
TABLE 3.5 – Thompson’s Equally Likely Decision
Equally likely
Minimax Regret
• Based on opportunity loss or regret– The difference between the optimal profit and
actual payoff for a decision1. Create an opportunity loss table by determining
the opportunity loss from not choosing the best alternative
2. Calculate opportunity loss by subtracting each payoff in the column from the best payoff in the column
3. Find the maximum opportunity loss for each alternative and pick the alternative with the minimum number
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Minimax Regret
3 – 17
STATE OF NATURE
FAVORABLEMARKET
($)
UNFAVORABLEMARKET
($)
200,000 – 200,000 0 – (–180,000)
200,000 – 100,000 0 – (–20,000)
200,000 – 0 0 – 0
TABLE 3.6 – Determining Opportunity Losses for Thompson Lumber
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Minimax Regret
3 – 18
TABLE 3.7 – Opportunity Loss Table for Thompson Lumber
STATE OF NATURE
ALTERNATIVEFAVORABLE MARKET ($)
UNFAVORABLE MARKET ($)
Construct a large plant 0 180,000
Construct a small plant 100,000 20,000
Do nothing 200,000 0
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Minimax Regret
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TABLE 3.8 – Thompson’s Minimax Decision Using Opportunity Loss
STATE OF NATURE
ALTERNATIVEFAVORABLE MARKET ($)
UNFAVORABLE MARKET ($)
MAXIMUM IN A ROW ($)
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
Minimax
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Decision Making Under Risk• When there are several possible states of
nature and the probabilities associated with each possible state are known– Most popular method – choose the alternative with
the highest expected monetary value (EMV)
3 – 20Copyright ©2015 Pearson Education, Inc.
whereXi = payoff for the alternative in state of nature i
P(Xi) = probability of achieving payoff Xi (i.e., probability of state of nature i)∑ = summation symbol
Decision Making Under Risk
• Expanding the equation
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EMV (alternative i) = (payoff of first state of nature)x (probability of first state of nature)+ (payoff of second state of nature)x (probability of second state of nature)+ … + (payoff of last state of nature)x (probability of last state of nature)
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EMV for Thompson Lumber
• Each market outcome has a probability of occurrence of 0.50
• Which alternative would give the highest EMV?
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EMV (large plant) = ($200,000)(0.5) + (–$180,000)(0.5)= $10,000
EMV (small plant) = ($100,000)(0.5) + (–$20,000)(0.5)= $40,000
EMV (do nothing) = ($0)(0.5) + ($0)(0.5)= $0
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EMV for Thompson Lumber
STATE OF NATURE
ALTERNATIVEFAVORABLE MARKET ($)
UNFAVORABLE MARKET ($) EMV ($)
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
Probabilities 0.50 0.50
TABLE 3.9 – Decision Table with Probabilities and EMVs
Best EMV
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Expected Value of Perfect Information (EVPI)
• EVPI places an upper bound on what you should pay for additional information
• EVwPI is the long run average return if we have perfect information before a decision is made
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EVwPI = ∑(best payoff in state of nature i)(probability of state of nature i)
Expected Value of Perfect Information (EVPI)
• Expanded EVwPI becomes
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EVwPI = (best payoff for first state of nature)x (probability of first state of nature)+ (best payoff for second state of nature)x (probability of second state of nature)+ … + (best payoff for last state of nature)x (probability of last state of nature)
• And
EVPI = EVwPI – Best EMV
Expected Value of Perfect Information (EVPI)
• Scientific Marketing, Inc. offers analysis that will provide certainty about market conditions (favorable)
• Additional information will cost $65,000• Should Thompson Lumber purchase the
information?
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Expected Value of Perfect Information (EVPI)
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STATE OF NATURE
ALTERNATIVEFAVORABLE MARKET ($)
UNFAVORABLE MARKET ($) EMV ($)
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
With perfect information 200,000 0 100,000
Probabilities 0.5 0.5
TABLE 3.10 – Decision Table with Perfect Information
EVwPI
Expected Value of Perfect Information (EVPI)
• The maximum EMV without additional information is $40,000– Therefore
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EVPI = EVwPI – Maximum EMV= $100,000 - $40,000= $60,000
So the maximum Thompson should pay for the additional information is $60,000
• The maximum EMV without additional information is $40,000– Therefore
Expected Value of Perfect Information (EVPI)
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EVPI = EVwPI – Maximum EMV= $100,000 - $40,000= $60,000
So the maximum Thompson should pay for the additional information is $60,000
Thompson should not pay $65,000 for this information
Expected Opportunity Loss
• Expected opportunity loss (EOL) is the cost of not picking the best solution– Construct an opportunity loss table– For each alternative, multiply the opportunity loss
by the probability of that loss for each possible outcome and add these together
– Minimum EOL will always result in the same decision as maximum EMV
– Minimum EOL will always equal EVPI
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Expected Opportunity Loss
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STATE OF NATURE
ALTERNATIVEFAVORABLE MARKET ($)
UNFAVORABLE MARKET ($) EOL
Construct a large plant 0 180,000 90,000
Construct a small plant 100,000 20,000 60,000
Do nothing 200,000 0 100,000
Probabilities 0.5 0.5
TABLE 3.11 – EOL Table for Thompson Lumber
Best EOL
EOL (large plant) = (0.50)($0) + (0.50)($180,000) = $90,000
EOL (small plant) = (0.50)($100,000) + (0.50)($20,000) = $60,000
EOL (do nothing) = (0.50)($200,000) + (0.50)($0) = $100,000
Sensitivity Analysis
EMV(large plant) = $200,000P – $180,000)(1 – P)= $200,000P – $180,000 + $180,000P= $380,000P – $180,000
EMV(small plant) = $100,000P – $20,000)(1 – P)= $100,000P – $20,000 + $20,000P= $120,000P – $20,000
EMV(do nothing) = $0P + 0(1 – P)= $0
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Sensitivity Analysis
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$300,000
$200,000
$100,000
0
–$100,000
–$200,000
EMV Values
EMV (large plant)
EMV (small plant)
EMV (do nothing)
Point 1
Point 2
.167 .615 1
Values of P
FIGURE 3.1
Sensitivity Analysis
Point 1: EMV(do nothing) = EMV(small plant)
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Point 2: EMV(small plant) = EMV(large plant)
Sensitivity Analysis
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BEST ALTERNATIVERANGE OF P VALUES
Do nothing Less than 0.167
Construct a small plant 0.167 – 0.615
Construct a large plant Greater than 0.615
$300,000
$200,000
$100,000
0
–$100,000
–$200,000
EMV Values
EMV (large plant)
EMV (small plant)
EMV (do nothing)
Point 1
Point 2
.167 .615 1
Values of P
FIGURE 3.1
A Minimization Example
• Three year lease for a copy machine– Which machine should be selected?
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10,000 COPIES PER MONTH
20,000 COPIES PER MONTH
30,000 COPIES PER MONTH
Machine A 950 1,050 1,150
Machine B 850 1,100 1,350
Machine C 700 1,000 1,300
TABLE 3.12 – Payoff Table
• Three year lease for a copy machine– Which machine should be selected?
A Minimization Example
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10,000 COPIES
PER MONTH
20,000 COPIES
PER MONTH
30,000 COPIES
PER MONTH
BEST PAYOFF
(MINIMUM)
WORST PAYOFF
(MAXIMUM)
Machine A 950 1,050 1,150 950 1,150
Machine B 850 1,100 1,350 850 1,350
Machine C 700 1,000 1,300 700 1,300
TABLE 3.13 – Best and Worst Payoffs
A Minimization Example
• Using Hurwicz criteria with 70% coefficient
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Weighted average = 0.7(best payoff) + (1 – 0.7)(worst payoff)
For each machine
Machine A: 0.7(950) + 0.3(1,150) = 1,010
Machine B: 0.7(850) + 0.3(1,350) = 1,000
Machine C: 0.7(700) + 0.3(1,300) = 880
A Minimization Example
• For equally likely criteria
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For each machine
Machine A: (950 + 1,050 + 1,150)/3 = 1,050
Machine B: (850 + 1,100 + 1,350)/3 = 1,100
Machine C: (700 + 1,000 + 1,300)/3 = 1,000
A Minimization Example• For EMV criteria
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USAGE PROBABILITY10,000 0.40
20,000 0.30
30,000 0.30
• For EMV criteria
A Minimization Example
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10,000 COPIES
PER MONTH
20,000 COPIES
PER MONTH
30,000 COPIES
PER MONTH
EMV
Machine A 950 1,050 1,150 1,040
Machine B 850 1,100 1,350 1,075
Machine C 700 1,000 1,300 970
With perfect information 700 1,000 1,150 925
Probability 0.4 0.3 0.3
TABLE 3.14 – Expected Monetary Values and Expected Value with Perfect Information
• For EVPI
A Minimization Example• For EVPI
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10,000 COPIES
PER MONTH
20,000 COPIES
PER MONTH
30,000 COPIES
PER MONTH
EMV
Machine A 950 1,050 1,150 1,040
Machine B 850 1,100 1,350 1,075
Machine C 700 1,000 1,300 970
With perfect information 700 1,000 1,150 925
Probability 0.4 0.3 0.3
TABLE 3.15 – Expected Monetary Values and Expected Value with Perfect Information EVwPI = $925
Best EMV without perfect information = $970
EVPI = 970 – 925 = $45
• Opportunity loss criteria
A Minimization Example
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10,000 COPIES
PER MONTH
20,000 COPIES
PER MONTH
30,000 COPIES
PER MONTH MAXIMUM EOL
Machine A 250 50 0 250 115
Machine B 150 100 200 200 150
Machine C 0 0 150 150 45
Probability 0.4 0.3 0.3
TABLE 3.15 – Opportunity Loss Table
Decision Trees
• Any problem that can be presented in a decision table can be graphically represented in a decision tree– Most beneficial when a sequence of decisions
must be made– All decision trees contain decision points/nodes
and state-of-nature points/nodes– At decision nodes one of several alternatives may
be chosen– At state-of-nature nodes one state of nature will
occur
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Five Steps ofDecision Tree Analysis
1. Define the problem2. Structure or draw the decision tree3. Assign probabilities to the states of nature4. 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 Trees• Trees start from left to right• Trees represent decisions and outcomes in sequential
order• Squares represent decision nodes• Circles represent states of nature nodes• Lines or branches connect the decisions nodes and
the states of nature
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Thompson’s Decision Tree
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Favorable Market
Unfavorable Market
Favorable Market
Unfavorable MarketDo Nothing
Construct
Large Plant
1
Construct
Small Plant2
FIGURE 3.2
A Decision Node
A State-of-Nature Node
Thompson’s Decision Tree
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Favorable Market
Unfavorable Market
Favorable Market
Unfavorable MarketDo Nothing
Construct
Large Plant
1
Construct
Small Plant2
Alternative with best EMV is selected
FIGURE 3.3EMV for Node 1
= $10,000= (0.5)($200,000) + (0.5)(–$180,000)
EMV for Node 2 = $40,000
= (0.5)($100,000) + (0.5)(–$20,000)
Payoffs
$200,000
–$180,000
$100,000
–$20,000
$0
(0.5)
(0.5)
(0.5)
(0.5)
Thompson’s Complex Decision Tree
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First Decision Point
Second Decision Point
Favorable Market (0.78)
Unfavorable Market (0.22)
Favorable Market (0.78)
Unfavorable Market (0.22)
Favorable Market (0.27)
Unfavorable Market (0.73)
Favorable Market (0.27)
Unfavorable Market (0.73)
Favorable Market (0.50)
Unfavorable Market (0.50)
Favorable Market (0.50)
Unfavorable Market (0.50)Large Plant
Small Plant
No Plant
6
7
Condu
ct M
arke
t Sur
vey
Do Not Conduct Survey
Large Plant
Small Plant
No Plant
2
3
Large Plant
Small Plant
No Plant
4
5
1Resu
lts
Favora
ble
ResultsNegative
Survey (
0.45)
Survey (0.55)
Payoffs
–$190,000
$190,000
$90,000
–$30,000
–$10,000
–$180,000
$200,000
$100,000
–$20,000
$0
–$190,000
$190,000
$90,000
–$30,000
–$10,000
FIGURE 3.4
Thompson’s Complex Decision Tree
1. Given favorable survey results
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EMV(node 2) = EMV(large plant | positive survey)
= (0.78)($190,000) + (0.22)(– $190,000) = $106,400
EMV(node 3) = EMV(small plant | positive survey)
= (0.78)($90,000) + (0.22)(– $30,000) = $63,600
EMV for no plant = – $10,000
Thompson’s Complex Decision Tree
2. Given negative survey results
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EMV(node 4) = EMV(large plant | negative survey)
= (0.27)($190,000) + (0.73)(– $190,000) = – $87,400
EMV(node 5) = EMV(small plant | negative survey)
= (0.27)($90,000) + (0.73)(– $30,000) = $2,400
EMV for no plant = – $10,000
Thompson’s Complex Decision Tree
3. Expected value of the market survey
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EMV(node 1) = EMV(conduct survey)
= (0.45)($106,400) + (0.55)($2,400)
= $47,880 + $1,320 = $49,200
4. Expected value no market survey
EMV(node 6) = EMV(large plant)
= (0.50)($200,000) + (0.50)(– $180,000) = $10,000
EMV(node 7) = EMV(small plant)
= (0.50)($100,000) + (0.50)(– $20,000) = $40,000
EMV for no plant = $0
The best choice is to seek marketing information
Thompson’s Complex Decision Tree
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FIGURE 3.5
First Decision Point
Second Decision Point
Favorable Market (0.78)
Unfavorable Market (0.22)
Favorable Market (0.78)
Unfavorable Market (0.22)
Favorable Market (0.27)
Unfavorable Market (0.73)
Favorable Market (0.27)
Unfavorable Market (0.73)
Favorable Market (0.50)
Unfavorable Market (0.50)
Favorable Market (0.50)
Unfavorable Market (0.50)Large Plant
Small Plant
No Plant
6
7
Condu
ct M
arke
t Sur
vey
Do Not Conduct Survey
Large Plant
Small Plant
No Plant
2
3
Large Plant
Small Plant
No Plant
4
5
1Resu
lts
Favora
ble
ResultsNegative
Survey (
0.45)
Survey (0.55)
Payoffs
–$190,000
$190,000
$90,000
–$30,000
–$10,000
–$180,000
$200,000
$100,000
–$20,000
$0
–$190,000
$190,000
$90,000
–$30,000
–$10,000
$40
,00
0$2
,400
$10
6,4
00
$49
,20
0
$106,400
$63,600
–$87,400
$2,400
$10,000
$40,000
Expected Value of Sample Information
• Thompson wants to know the actual value of doing the survey
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= (EV with SI + cost) – (EV without SI)
EVSI = ($49,200 + $10,000) – $40,000 = $19,200
EVSI = –Expected value
with sampleinformation
Expected value of best decision without sample
information
Efficiency of Sample Information
• Possibly many types of sample information available
• Different sources can be evaluated
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• For Thompson
Market survey is only 32% as efficient as perfect information
Sensitivity Analysis
• How sensitive are the decisions to changes in the probabilities?
• How sensitive is our decision to the probability of a favorable survey result?
• If the probability of a favorable result (p = .45) where to change, would we make the same decision?
• How much could it change before we would make a different decision?
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Sensitivity Analysisp = probability of a favorable survey result
(1 – p) = probability of a negative survey result
EMV(node 1) = ($106,400)p +($2,400)(1 – p)= $104,000p + $2,400
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We are indifferent when the EMV of node 1 is the same as the EMV of not conducting the survey
$104,000p + $2,400 = $40,000$104,000p = $37,600
p = $37,600/$104,000 = 0.36
If p < 0.36, do not conduct the surveyIf p > 0.36, conduct the survey
Utility Theory
• Monetary value is not always a true indicator of the overall value of the result of a decision
• The overall value of a decision is called utility• Economists assume that rational people make
decisions to maximize their utility
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Heads (0.5)
Tails (0.5)
$5,000,000
$0
Utility Theory
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Accept Offer
Reject Offer
$2,000,000
EMV = $2,500,000
FIGURE 3.6 – Decision Tree for the Lottery Ticket
Utility 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, your utility values are equal
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Utility Theory
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Best OutcomeUtility = 1
Worst OutcomeUtility = 0
Other OutcomeUtility = ?
(p)
(1 – p)
Alternative 1
Alternative 2
FIGURE 3.7 – Standard Gamble for Utility Assessment
Utility Theory
Expected utility of alternative 2 = Expected utility of alternative 1
Utility of other outcome = (p)(utility of best outcome, which is 1)
+ (1 – p)(utility of the worst outcome,
which is 0)Utility of other outcome
= (p)(1) + (1 – p)(0) = p
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Investment Example• Construct a utility curve revealing preference
for money between $0 and $10,000• A utility curve plots the utility value versus
the monetary value– An investment in a bank will result in $5,000– An investment in real estate will result in $0 or
$10,000– Unless there is an 80% chance of getting $10,000
from the real estate deal, prefer to have her money in the bank
– If p = 0.80, Jane is indifferent between the bank or the real estate investment
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Investment Example
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Figure 3.8 – Utility of $5,000p = 0.80
(1 – p) = 0.20
Invest in
Real Estate
Invest in Bank
$10,000U($10,000) = 1.0
$0U($0.00) = 0.0
$5,000U($5,000) = p = 0.80
Utility for $5,000 = U($5,000) = pU($10,000) + (1 – p)U($0)= (0.8)(1) + (0.2)(0) = 0.8
• Use the three different dollar amounts and assess utilities
Investment Example
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• Assess other utility values
Utility for $7,000 = 0.90Utility for $3,000 = 0.50
Utility Curve
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U ($7,000) = 0.90
U ($5,000) = 0.80
U ($3,000) = 0.50
U ($0) = 0
FIGURE 3.9 – Utility Curve
1.0 –
0.9 –
0.8 –
0.7 –
0.6 –
0.5 –
0.4 –
0.3 –
0.2 –
0.1 –
| | | | | | | | | | |
$0 $1,000 $3,000 $5,000 $7,000 $10,000
Monetary Value
Util
ity
U ($10,000) = 1.0
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Utility Curve
• Typical of a risk avoider– Less utility from greater risk– Avoids situations where high losses might occur– As monetary value increases, utility curve
increases at a slower rate
• A risk seeker gets more utility from greater risk– As monetary value increases, the utility curve
increases at a faster rate
• Risk indifferent gives a linear utility curve
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Preferences for Risk
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FIGURE 3.10
Monetary Outcome
Util
ity
Risk Avoider
Risk In
diffe
renc
e
Risk Seeker
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Utility as a Decision-Making Criteria
• Once a utility curve has been developed it can be used in making decisions
• Replaces monetary outcomes with utility values
• Expected utility is computed instead of the EMV
3 – 69Copyright ©2015 Pearson Education, Inc.
Utility as a Decision-Making Criteria
• Mark Simkin loves to gamble– A game tossing thumbtacks in the air– If the thumbtack lands point up, Mark wins $10,000– If the thumbtack lands point down, Mark loses
$10,000– Mark believes that there is a 45% chance the
thumbtack will land point up
• Should Mark play the game (alternative 1)?
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Utility as a Decision-Making Criteria
3 – 71
FIGURE 3.11 – Decision Facing Mark Simkin
Tack Lands Point Up (0.45)
Alternative 1
Mark Plays the Game
Alternative 2
$10,000
–$10,000
$0
Tack Lands Point Down (0.55)
Mark Does Not Play the Game
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Utility as a Decision-Making Criteria
Step 1– Define Mark’s utilities
3 – 72
U(–$10,000) = 0.05U($0) = 0.15
U($10,000) = 0.30
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FIGURE 3.12
1.00 –
0.75 –
0.50 –
0.30 –0.25 –
0.15 –
0.05 –0 –| | | | |
–$20,000 –$10,000 $0 $10,000 $20,000
Monetary Outcome
Util
ity
Utility as a Decision-Making Criteria
Step 2 – Replace monetary values with utility values
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E(alternative 1: play the game) = (0.45)(0.30) + (0.55)(0.05)= 0.135 + 0.027 = 0.162
E(alternative 2: don’t play the game) = 0.15
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Utility as a Decision-Making Criteria
3 – 74
FIGURE 3.13 – Using Expected Utilities
Tack Lands Point Up (0.45)
Alternative 1
Mark Plays the Game
Alternative 2
0.30
0.05
0.15
Tack Lands Point Down (0.55)
Don’t Play
UtilityE = 0.162
Copyright ©2015 Pearson Education, Inc.