Decision Analysis
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Transcript of Decision Analysis
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Chapter 3
Decision Analysis
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Learning Objectives
1. List the steps of the decision-making process
2. Describe the types of decision-making environments
3. Make decisions under uncertainty4. Use probability values to make decisions
under risk
After completing this chapter, students will be able to:After completing this chapter, students will be able to:
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Learning Objectives
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 making
After completing this chapter, students will be able to:After completing this chapter, students will be able to:
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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 the quantitative approach described here
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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 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
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Thompson Lumber Company
Step 1 –Step 1 – Define the problem Expand by manufacturing and
marketing a new product, backyard storage sheds
Step 2 –Step 2 – List alternatives Construct a large new plant A small plant No plant at all
Step 3 –Step 3 – Identify possible outcomes The market could be favorable or
unfavorable
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Thompson Lumber Company
Step 4 –Step 4 – List the payoffs Identify conditional valuesconditional values for the
profits for large, small, and no plants for the two possible market conditions
Step 5 –Step 5 – Select the decision model Depends on the environment and
amount of risk and uncertaintyStep 6 –Step 6 – Apply the model to the data
Solution and analysis used to help the decision making
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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
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Types of Decision-Making Environments
Type 1:Type 1: Decision making under certainty Decision maker knows with certaintyknows with certainty the
consequences of every alternative or decision choice
Type 2:Type 2: Decision making under uncertainty The decision maker does not knowdoes not know the
probabilities of the various outcomesType 3:Type 3: Decision making under risk
The decision maker knows the knows the probabilitiesprobabilities of the various outcomes
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Decision Making Under Uncertainty
1. Maximax (optimistic)2. Maximin (pessimistic)3. Criterion of realism (Hurwicz)4. Equally likely (Laplace) 5. Minimax regret
There are several criteria for making decisions under uncertainty
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MaximaxUsed to find the alternative that maximizes the maximum payoff
Locate the maximum payoff for each alternative Select the alternative with the maximum
numberSTATE OF NATURE
ALTERNATIVEFAVORABLE MARKET ($)
UNFAVORABLE MARKET ($)
MAXIMUM IN A ROW ($)
Construct a large plant 200,000 –180,000 200,000
Construct a small plant 100,000 –20,000 100,000
Do nothing 0 0 0
Table 3.2
MaximaxMaximax
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MaximinUsed to find the alternative that maximizes the minimum payoff
Locate the minimum payoff for each alternative Select the alternative with the maximum
numberSTATE OF NATURE
ALTERNATIVEFAVORABLE MARKET ($)
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 MaximinMaximin
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Criterion of Realism (Hurwicz)A weighted averageweighted average compromise between optimistic and pessimistic
Select a coefficient of realism Coefficient is between 0 and 1 A value of 1 is 100% optimistic Compute the weighted averages for each
alternative Select the alternative with the highest value
Weighted average = (maximum in row) + (1 – )(minimum in row)
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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
STATE OF NATURE
ALTERNATIVEFAVORABLE MARKET ($)
UNFAVORABLE MARKET ($)
CRITERION OF REALISM
( = 0.8)$Construct a large plant 200,000 –180,000 124,000
Construct a small plant 100,000 –20,000 76,000
Do nothing 0 0 0
Table 3.4
RealismRealism
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Equally Likely (Laplace)Considers all the payoffs for each alternative
Find the average payoff for each alternative Select the alternative with the highest average
STATE OF NATURE
ALTERNATIVEFAVORABLE MARKET ($)
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
Equally likelyEqually likely
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Minimax Regret
Based on opportunity lossopportunity loss or regretregret, the difference between the optimal profit and actual payoff for a decision
Create an opportunity loss table by determining the opportunity loss for not choosing the best alternative
Opportunity loss is calculated by subtracting each payoff in the column from the best payoff in the column
Find the maximum opportunity loss for each alternative and pick the alternative with the minimum number
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Minimax RegretSTATE OF NATURE
FAVORABLE MARKET ($)
UNFAVORABLE MARKET ($)
200,000 – 200,000 0 – (–180,000)
200,000 – 100,000 0 – (–20,000)
200,000 – 0 0 – 0Table 3.6
Table 3.7
STATE OF NATURE
ALTERNATIVEFAVORABLE MARKET ($)
UNFAVORABLE MARKET ($)
Construct a large plant 0 180,000Construct a small plant 100,000 20,000Do nothing 200,000 0
Opportunity Loss Tables
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Minimax Regret
Table 3.8
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 0 200,000MinimaxMinimax
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Decision Making Under Risk
Decision making when there are several possible states of nature and we know the probabilities associated with each possible state
Most popular method is to choose the alternative with the highest expected monetary value (expected monetary value (EMVEMV))
EMV(alternative i) = (payoff of 1st state of nature) x (prob. of 1st state of nature) + (payoff of 2nd state of nature) x (prob. of 2nd state of nature)
+ … + (payoff of last state of nature) x (prob. of last state of nature)
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EMV for Thompson Lumber
Each market has a probability of 0.50 Which alternative would give the highest EMV? The calculations are
EMV (large plant) = (0.50)($200,000) + (0.50)(–$180,000)= $10,000
EMV (small plant) = (0.50)($100,000) + (0.50)(–$20,000)= $40,000
EMV (do nothing) = (0.50)($0) + (0.50)($0)= $0
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EMV for Thompson LumberSTATE OF NATURE
ALTERNATIVEFAVORABLE MARKET ($)
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 0.50Table 3.9
Largest Largest EMVEMV
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Expected Value of Perfect Information (EVPI)
EVwPI (Expected Value with Perfect Information) is the long run average return if we have perfect information before a decision is made
EVwPI = (best payoff for 1st SoN)x P1st SoN
+ (best payoff for 2nd SoN)x P2nd SoN
+ … + (best payoff for nth SoN)x Pnth
SoN
EVPI (Expected Value of Perfect Information) places an upper bound on what you should pay for additional information
EVPI = EVwPI – Maximum EMV
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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 Is it worth purchasing the information?
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Expected Value of Perfect Information (EVPI)
1. Best alternative for favorable state of nature is build a large plant with a payoff of $200,000Best alternative for unfavorable state of nature is to do nothing with a payoff of $0EVwPI = ($200,000)(0.50) + ($0)(0.50) = $100,000
2. The maximum EMV without additional information is $40,000EVPI = EVwPI – Maximum EMV = $100,000 - $40,000 = $60,000
ALTERNATIVES STATE OF NATUREEMV
($)FAVORABLE MARKET ($)
UNFAVORABLE MARKET ($)
Construct a large plant
200,000 -180,000 10,000
Construct a small plant
100,000 -20,000 40,000 Largest EMV
Do nothing 0 0 0Probabilities 0.5 0.5
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Expected Value of Perfect Information (EVPI)
1. Best alternative for favorable state of nature is build a large plant with a payoff of $200,000Best alternative for unfavorable state of nature is to do nothing with a payoff of $0EVwPI = ($200,000)(0.50) + ($0)(0.50) = $100,000
2. The maximum EMV without additional information is $40,000
EVPI = EVwPI – Maximum EMV= $100,000 - $40,000= $60,000
So the maximum Thompson should pay for the additional information is $60,000
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Expected Opportunity Loss
Expected opportunity lossExpected opportunity loss (EOL) is the cost of not picking the best solution
First construct an opportunity loss table For each alternative, multiply the opportunity
loss by the probability of that loss for each possible outcome and add these together
Minimum EOL will always result in the same decision as maximum EMV
Minimum EOL will always equal EVPI
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Opportunity Loss TableSTATE OF NATURE
ALTERNATIVEFAVORABLE MARKET ($)
UNFAVORABLE MARKET ($)
Construct a large plant 200,000 –180,000Construct a small plant 100,000 –20,000Do nothing 0 0
STATE OF NATURE
ALTERNATIVEFAVORABLE MARKET
($)UNFAVORABLE MARKET
($)Construct a large plant Max - 200,000 = 0 Max – (-180,000) = 180,000Construct a small plant Max - 100,000 = 100,000 Max – (-20,000) = 20,000Do nothing Max - 0 = 200,000 Max – 0 = 0
Opportunity loss table
Best
Best
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Expected Opportunity Loss
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)= $100,000
Table 3.10
STATE OF NATURE
ALTERNATIVEFAVORABLE MARKET ($)
UNFAVORABLE MARKET ($) EOL
Construct a large plant 0 180,000 90,000Construct a small plant 100,000 20,000 60,000Do nothing 200,000 0 100,000Probabilities 0.50 0.50
Minimum Minimum EOLEOL
Opportunity loss table
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Summary Risk (1)
ALTERNATIVES STATE OF NATURE EMV= payoff 1 * P1st SoN + … +
payoff n * Pnth SoN
EVwPI= (best payoff for 1st SoN)x P1st
SoN
+… + (best payoff for nth SoN)x Pnth SoN
EVPI
=EVwPI – Maximum EMVFAVORABLEMARKET ($)
UNFAVORABLE MARKET
($)
Construct a large plant
200,000Best payoff
for 1st SoN
-180,000 10,000
100,000
(=200,000x0.5+ 0x0.5)
60,000
(=100,000-40,000)
Construct a small plant 100,000 -20,000 40,000
Largest EMV
Do nothing 0 0best payoff
for 2nd SoN
0
Probabilities
0.5 0.5
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ALTERNATIVES STATE OF NATURE ALTERNATIVES STATE OF NATURE EOL
FAVORABLE MARKET ($)
UNFAVORABLE MARKET ($)
FAVORABLE MARKET ($)
UNFAVORABLE MARKET
($)
Construct a large plant
200,000best payoff for 1st SoN
-180,000 Construct a large plant
0
=200,000-200,000
180,000
=0-(-180,000)
90,000
=0x0.5+180,000x0.5
Construct a small plant
100,000 -20,000 Construct a small plant
100,000
=200,000-100,000
20,000
=0-(-20,000)
60,000 Minimium EOL
=100,000x0.5+20,000x0.5
Do nothing 0 0best payoff for 2nd SoN
Do nothing 200,000
=200,000-0
0
=0-0
100,000
=200,000x0.5+0x0.5
Probabilities 0.5 0.5 Probabilities 0.5 0.5
Original Table Opportunity Loss Table
Summary Risk (2)
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Sensitivity Analysis Sensitivity analysis examines how our decision
might change with different input data For the Thompson Lumber example
P = probability of a favorable market
(1 – P) = probability of an unfavorable market
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Sensitivity AnalysisALTERNATIVES STATE OF NATURE EMV
= Payoff 1 * P1st SoN + Payoff 2 * P2nd SoN + … + Payoff n * Pnth SoN
FAVORABLE MARKET
($)
UNFAVORABLE MARKET
($)
Construct a large plant
200,000 -180,000 = $200,000P – $180,000(1 – P)
= $380,000P – $180,000
Construct a small plant
100,000 -20,000 = $100,000P – $20,000(1 – P)
= $120,000P – $20,000
Do nothing 0 0 = $0P – $0(1 – P)
= $0
Probabilities p (1-p)
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Sensitivity Analysis
$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 1Values of P
Figure 3.1
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Sensitivity Analysis
Figure 3.1
$300,000
$200,000
$100,000
0
–$100,000
–$200,000
EMV Values
EMV (large plant)
EMV (small plant)
EMV (do nothing)
Point 1
Point 2
.167 .615 1Values of P
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Sensitivity Analysis
Point 1:Point 1:EMV(do nothing) = EMV(small plant)
000200001200 ,$,$ P 167000012000020 .,
,P
00018000038000020000120 ,$,$,$,$ PP
6150000260000160 .,,
P
Point 2:Point 2:EMV(small plant) = EMV(large plant)
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Sensitivity AnalysisBEST ALTERNATIVE
RANGE 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
Figure 3.1
$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 1Values of P
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Using Excel QM to Solve Decision Theory Problems
Program 3.1A
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Using Excel QM to Solve Decision Theory Problems
Program 3.1B
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Homework 03
Prob. 3.16, 3.18, 3.19, 3.22, 3.26, 3.27