8-1 CHAPTER 8 Decision Analysis
Dec 23, 2015
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CHAPTER 8Decision Analysis
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LEARNING OBJECTIVES
1. List the steps of the decision-making process and describe the different types of decision-making environments.
2. Make decisions under uncertainty and under risk.
3. Use Excel to set up and solve problems involving decision tables.
4. Develop accurate and useful decision trees.
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LEARNING OBJECTIVES
5. Use TreePlan to set up and analyze decision tree problems with Excel.
6. Understand the importance and use of utility theory in decision making.
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Decision Analysis
• An analytic and systematic approach to the study of decision making• Based on logic
• Considers all possible alternatives
• Examines all available information about the future
• Applies the decision modeling approach
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Five Steps
1. Clearly define the problem2. List all possible alternatives3. Identify all possible outcomes for
each alternative4. Identify the payoff for each alternative
and outcome combination5. Use a decision modeling technique to
choose an alternative
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Thompson Lumber1. Decision: Should he make and sell
storage sheds2. Alternatives:
1. Build a large plant2. Build a small plant3. Do nothing
3. Outcomes: Demand for sheds will be 1. High2. Moderate3. Low
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Thompson Lumber
4. Payoff table
OUTCOMES
HIGH MODERATE LOWALTERNATIVES DEMAND DEMAND DEMAND
Build large plant $200,000 $100,000 –$120,000Build small plant $ 90,000 $ 50,000 –$ 20,000No plant $ 0 $ 0 $ 0
Table 8.1
5. Select and apply decision analysis model
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Decision-Making Environments
Type 1: Decision making under certainty
Type 2: Decision making under uncertainty
Type 3: Decision making under risk
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Certainty
• Consequence of every alternative is known
• Usually only one outcome for each alternative
• Seldom occurs in reality
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Uncertainty
• Probabilities of possible outcomes not known
• Decision making methods:1. Maximax
2. Maximin
3. Criterion of realism
4. Equally likely
5. Minimax regret
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Thompson Lumber
• Maximax Criterion• Maximizes the maximum payoff
OUTCOMES
HIGH MODERATE LOWALTERNATIVES DEMAND DEMAND DEMAND
Build large plant $200,000 $100,000 –$120,000Build small plant $ 90,000 $ 50,000 –$ 20,000No plant $ 0 $ 0 $ 0
Table 8.2Maximax
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Thompson Lumber
• Maximin Criterion• Maximizes the minimum payoff
OUTCOMES
HIGH MODERATE LOWALTERNATIVES DEMAND DEMAND DEMAND
Build large plant $200,000 $100,000 –$120,000Build small plant $ 90,000 $ 50,000 –$ 20,000No plant $ 0 $ 0 $ 0
Table 8.3
Maximin
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Thompson Lumber
• Criterion of Realism (Hurwicz)
Table 8.4
Thompson’s coefficient of realism a = 0.45
Realism payoff for alternative
= a x (Maximum payoff for alternative)+ (1 – a) x (Minimum payoff for alternative)
OUTCOMES
HIGH MODERATE LOW WT. AVG. FORALTERNATIVES DEMAND DEMAND DEMAND ALTERNATIVE
Build large plant $200,000 $100,000 –$120,000 $24,000Build small plant $ 90,000 $ 50,000 –$ 20,000 $29,500No plant $ 0 $ 0 $ 0 $ 0
Realism
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Thompson Lumber
• Equally Likely (Laplace) Criterion• Highest average payoff
Table 8.5
OUTCOMES
HIGH MODERATE LOW AVERAGE FORALTERNATIVES DEMAND DEMAND DEMAND ALTERNATIVE
Build large plant $200,000 $100,000 –$120,000 $60,000Build small plant $ 90,000 $ 50,000 –$ 20,000 $40,000No plant $ 0 $ 0 $ 0 $ 0
Equallylikely
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Thompson Lumber• Minimax Regret Criterion
Table 8.6
OUTCOMES
ALTERNATIVES HIGH DEMAND
Build large plant $200,000 – $200,000 = $ 0Build small plant $200,000 – $ 90,000 = $110,000No plant $200,000 – $ 0 = $200,000
MODERATE DEMAND
Build large plant $100,000 – $100,000 = $ 0Build small plant $100,000 – $ 50,000 = $ 50,000No plant $100,000 – $ 0 = $100,000
LOW DEMAND
Build large plant $0 – (–$120,000) = $120,000Build small plant $0 – (–$ 20,000) = $ 20,000No plant $0 – $ 0 = $ 0
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• Minimax Regret Criterion
Thompson Lumber
Table 8.7
Minimax
OUTCOMES
HIGH MODERATE LOW MAXIMUM FORALTERNATIVES DEMAND DEMAND DEMAND ALTERNATIVE
Build large plant $ 0 $ 0 $120,000 $120,000Build small plant $110,000 $ 50,000 $ 20,000 $110,000No plant $200,000 $100,000 $ 0 $200,000
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Using Excel
Screenshot 8-1A
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Using ExcelScreenshot 8-1B
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Under Risk
• Expected Monetary Value (EMV)
EMV (Alternative i) = (Payoff of first outcome)x (Probability of first outcome)+ (Payoff of second outcome)x (Probability of second outcome)+ … + (Payoff of last outcome)x (Probability of last outcome)
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Thompson LumberOUTCOMES
HIGH MODERATE LOW EMV FORALTERNATIVES DEMAND DEMAND DEMAND ALTERNATIVE
Build large plant $200,000 $100,000 –$120,000 $200,000 x 0.3+ $100,000 x 0.5
+ (–$120,000) x 0.2= $86,000
Build small plant $ 90,000 $ 50,000 –$ 20,000 $90,000 x 0.3+ $50,000 x 0.5
+ (–$20,000) x 0.2= $48,000
No plant $ 0 $ 0 $ 0 $0 x 0.3 + $0 x 0.5+ $0 x 0.2 = $ 0
Probabilities 0.3 0.5 0.2
Table 8.8
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Under Risk
• Expected Opportunity Loss (EOL)
EOL (Alternative i) = (Regret of first outcome)x (Probability of first outcome)+ (Regret of second outcome)x (Probability of second outcome)+ … + (Regret of last outcome)x (Probability of last outcome)
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Thompson Lumber
Table 8.9
OUTCOMESHIGH MODERATE LOW EOL FOR
ALTERNATIVES DEMAND DEMAND DEMAND ALTERNATIVE
Build large plant $ 0 $ 0 $120,000 $0 x 0.3 + $0 x 0.5+ $120,000 x 0.2
= $24,000
Build small plant $110,000 $ 50,000 $ 20,000 $110,000 x 0.3+ $50,000 x 0.5+ $20,000 x 0.2
= $62,000
No plant $200,000 $100,000 $ 0 $200,000 x 0.3+ $100,000 x 0.5
+ $0 x 0.2 = $110,000
Probabilities 0.3 0.5 0.2
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Decision Trees
• Presents decision alternatives and outcomes in a sequential manner
Decision node
Outcome node
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High Demand
Moderate Demand
Low Demand
High Demand
Moderate Demand
Low Demand
All Demands
$200,000
$100,000
–$120,000
Payoffs
$90,000
$50,000
–$20,000
$0
Decision Trees
• Thompson Lumber
1
2
3
Large Plant
Small Plant
No Plant
Decision Node
Outcome Node
Figure 8.1
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Decision Trees
• Thompson Lumber
High Demand (0.30)
Moderate Demand (0.50)
Low Demand (0.20)
High Demand (0.30)
Moderate Demand (0.50)
Low Demand (0.20)
All Demands
$200,000
$100,000
–$120,000
Payoffs
$90,000
$50,000
–$20,000
$0
1
2
3
Large Plant
Small Plant
No Plant
Decision Node
Outcome Node
Figure 8.2
Probability
$86,000
$48,000
$0
1EMV = $200,000 x 0.3 + $100,000 x 0.05 + (–$120,000) x 0.2 = $86,000
2EMV = $90,000 x 0.3 + $50,000 x 0.05 + (–$20,000) x 0.2 = $48,000
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Decision Trees
• Thompson Lumber
Figure 8.3
1
2
3
Large Plant
Small Plant
No Plant
Decision Node
EMV = $86,000
EMV = $48,000
$0
EMV = $0
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Using TreePlan With Excel
Screenshot 8-3A
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Using TreePlan With Excel
Screenshot 8-3B
(a)
(b)
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Using TreePlan With Excel
Screenshot 8-3B
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Using TreePlan With Excel
Screenshot 8-3C
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Using TreePlan With Excel
Screenshot 8-3D
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Utility Theory
• An alternative to EMV
• Incorporates a person’s attitude toward risk
• A utility function converts a person’s attitude toward money and risk into a number between 0 and 1
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Utility Theory
= $100,000 x 0.5 + $0 x 0.5
Figure 8.6
$35,000
$50,000Tails (0.5)
Heads (0.5)
$35,000
Payoffs
$100,000
$0
$50,000
Accept Offer
Reject Offer
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Jane’s Utility Function
Figure 8.7
Certainty Equivalent
EMV = $25,000
$50,000
Outcome 2 (0.5)
Outcome 1 (0.5)
$50,000
?
$0
Alternative
Alternative 2
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Jane’s Utility Function
• Worst payoff utility = 0
• Best payoff utility = 1
• Certainty equivalent – the minimum guaranteed amount you are willing to accept to avoid the risk associated with a gamble
U($15,000) = U($0) x 0.5 + U($50,000) x 0.5 = 0 x 0.5 + 1 x 0.5 = 0.5
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Jane’s Utility Function
• Repeat for multiple amountsUtility Value
1.00 –
0.80 –
0.60 –
0.40 –
0.20 –
0.00 –| | | | | |
$0 $10,000 $20,000 $30,000 $40,000 $50,000 Monetary Value
U ($27,000) = 0.75
U ($50,000) = 1.00
U ($6,000) = 0.25
U ($15,000) = 0.50
U ($50) = 0.00
Figure 8.8
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Jane’s Utility Function
• Risk premium• The EMV a person is willing to give up to
avoid the risk associated with a gamble
Risk premium = (EMV of gamble) – (Certainty equivalent)
• Risk avoider/risk adverse: Risk premium > 0
• Risk indifferent/risk-neutral: Risk premium = 0
• Risk seeker/risk-prone: Risk premium < 0
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Exponential Utility Function
• Risk avoider
U(X) = 1 – e–X/R
Risk In
diffe
rent
Risk Seeker
Risk Avoider
Monetary Outcome
Util
ity
Figure 8.9
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Utility as a Criteria
• Utility replaces monetary values in decision tree
Best Choice
Figure 8.10
EMV = –$4,000
$0
| |$0
Invest
Do Not Invest$0
Big Success (0.2)$40,000
Payoffs
$10,000
–$30,000Failure (0.5)
Moderate Success (0.3)1
2
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Utility as a CriteriaFigure 8.11
U ($40,000) = 1.00
U ($0) = 0.15
U ($10,000) = 0.30
U ($30,000) = 0.00
| | | | | | | |–$30,000 $–20,000 –$10,000 $0 $10,000 $20,000 $30,000 $40,000
Utility Value
1.00 –
0.80 –
0.60 –
0.40 –
0.20 –
0.00 –Monetary Value
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Utility as a Criteria
• Utility replaces monetary values in decision tree
Best Choice
Figure 8.10
0.29
0.15
0.29
| |Invest
Do Not Invest0.15
Big Success (0.2)1.00
Utilities
0.30
0.00Failure (0.5)
Moderate Success (0.3)1
2
Expected Utility