decision analysis part iii
TRANSCRIPT
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Core Purpose: To Enable Organisations Become Happier
Decision Analysis- Part III
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Data Analytics | Execution | Deployment | Training | QinT7-Jan-15 2
What is Decision Analysis?
• A quantitative framework for making decisions
• Selection of a decision from a set of possible decision alternativeswhen uncertainties regarding the future exist
• Goal is to optimize the resulting payoff in terms of a decisioncriterion
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Decision Models
• Deterministic models
• Probabilistic models
• Decision-making under pure uncertainty
• Maxmin
• Maxmax
• Minmax
• Decision-making under risk
• Expected value returns
• Expected value of perfect information
• Expected value of additional information- Bayesian analysis
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Case Study
States of nature
>1000 points
300-1000 +/-300-300 to -
1000<-1000 points
Large rise Small rise No change Small fall Large fall
Alt
ern
ativ
es
Bonds 9% 7% 6% 0% -1%
Stocks 17% 9% 5% -3% -10%
Fixed deposit
7% 7% 7% 7% 7%
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MaxMin
Pessimistic approach based on worst case scenario
1. Write min for each row
2. Choose max of the above
States of nature
>1000 points
300-1000
+/-300-300 to -
1000<-1000 points
Large rise
Small rise
No change
Small fallLarge
fallMin
Alt
ern
ativ
es Bonds 9% 7% 6% 0% -1% -1%
Stocks 17% 9% 5% -3% -10% -10%
Fixed deposit
7% 7% 7% 7% 7% 7%
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MaxMax
Optimistic approach based on best case scenario
1. Write max for each row
2. Choose max of the above
States of nature
>1000 points
300-1000
+/-300-300 to -
1000<-1000 points
Large rise
Small rise
No change
Small fallLarge
fallMax
Alt
ern
ativ
es Bonds 9% 7% 6% 0% -1% 9%
Stocks 17% 9% 5% -3% -10% 17%
Fixed deposit
7% 7% 7% 7% 7% 7%
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MinMax
Pessimistic approach to minimize regret or opportunity loss
1. Take the largest number in each coloumn
2. Subtract all the numbers in the coloumn from it
3. Choose maximum number for each option
4. Choose minimum number from step 3
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Case Study
States of nature
>1000 points
300-1000 +/-300-300 to -
1000<-1000 points
Large rise Small rise No change Small fall Large fall
Alt
ern
ativ
es
Bonds 9% 7% 6% 0% -1%
Stocks 17% 9% 5% -3% -10%
Fixed deposit
7% 7% 7% 7% 7%
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Regret Matrix
States of nature
>1000 points
300-1000 +/-300-300 to -
1000<-1000 points
Large rise Small rise No change Small fall Large fall
Alt
ern
ativ
es
Bonds (17%-9%) (9%-7%) (7%-6%) (7%-0%) (7%+1%)
Stocks (17%-17%) (9%-9%) (7%-5%) (7%+3%) (7%+10%)
Fixed deposit
(17%-7%) (9%-7%) (7%-7%) (7%-7%) (7%-7%)
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Regret Matrix
States of nature
>1000 points
300-1000 +/-300-300 to -
1000<-1000 points
Large rise Small riseNo
changeSmall fall Large fall Max
Alt
ern
ativ
es Bonds 8% 2% 1% 7% 8% 8%
Stocks 0% 0% 2% 10% 17% 17%
Fixed deposit
10% 2% 0% 0% 0% 10%
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Decision making under risk
• Probabilistic models
• Decision-making under risk
• Expected value returns
• Expected value of perfect information
• Expected value of additional information- Bayesian analysis
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Expected Value Approach
• Neutral approach to find optimal decision
• The probability estimate for the occurrence ofeach state of nature can be incorporated to arrive at the optimaldecision
1. For each decision add all the payoffs
2. Select the decision with the best expected payoff
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Case Study
States of nature
>1000 points
300-1000 +/-300-300 to -
1000<-1000 points
Large rise Small rise No change Small fall Large fall
Alt
ern
ativ
es Bonds 9% 7% 6% 0% -1%
Stocks 17% 9% 5% -3% -10%
Fixed deposit 7% 7% 7% 7% 7%
Probability 25% 20% 40% 10% 5%
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Expected Value Calculation
States of nature
>1000 points
300-1000
+/-300-300 to -
1000<-1000 points
EV
Large rise
Small rise
No change
Small fall Large fall
Alt
ern
ativ
es Bonds 9% 7% 6% 0% -1% 6%
Stocks 17% 9% 5% -3% -10% 7.25%
Fixed deposit
7% 7% 7% 7% 7% 7%
Probability 25% 20% 40% 10% 5%
EV(Bonds)= 25%x9% + 20%x7% + 40%x6% + 10%x0% + 5%x(-1%)
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States of nature
>1000 points
300-1000 +/-300-300 to -
1000<-1000 points
Large rise Small riseNo
changeSmall fall Large fall
Alt
ern
ativ
es Bonds 9% 7% 6% 0% -1%
Stocks 17% 9% 5% -3% -10%
Fixed deposit 7% 7% 7% 7% 7%
Probability 25% 20% 40% 10% 5%
• ER(PI)= 25%x17% +20%x9% + 40%x7% + 10%x7% + 5%x7% = 9.9%
• Expected value of perfect information: 9.9%-7.25% =2.65%
Expected Value of Perfect Information
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• Uses Bayes’ theorem to calculate refined probabilities
Expected Value of Additional Information
Large rise Small rise No change Small fall Large fall
Positive 80% 70% 50% 40% 0%
Negative 20% 30% 50% 60% 100%
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Probability- Positive Growth
State of naturePrior
probabilityProbability
(State|Positive)Joint
probabilityPosterior
probability
Large rise 25% 80% 20% 34.5%
Small rise 20% 70% 14% 24.1%
No change 40% 50% 20% 34.5%
Small fall 10% 40% 4% 6.9%
Large fall 5% 0% 0% 0%
Probability (Forecast=Positive) = 58%
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Probability- Negative Growth
State of naturePrior
probabilityProbability
(State|Negative)Joint
probabilityPosterior
probability
Large rise 25% 20% 5% 11.9%
Small rise 20% 30% 6% 14.3%
No change 40% 50% 20% 47.6%
Small fall 10% 60% 6% 14.3%
Large fall 5% 100% 5% 11.9%
Probability (Forecast=Negative) = 42%
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States of nature
>1000 points
300-1000 +/-300-300 to -
1000<-1000 points
Large rise Small riseNo
changeSmall fall Large fall
Alt
ern
ativ
es Bonds 9% 7% 6% 0% -1%
Stocks 17% 9% 5% -3% -10%
Fixed deposit 7% 7% 7% 7% 7%
P (Positive) 34.5% 24.1% 34.5% 6.9% 0%
P (Negative) 11.9% 14.3% 47.6% 14.3% 11.9%
• EV(Bonds|Positive)= 9%x34.5% +7%x24.1+ 6%x34.5% + 0%x6.9% + (-1%) x 0%= 6.86%
• EV(Bonds|Negative)= 9%x11.9% +7%x14.3+ 6%x47.6% + 0%x14.3% + (-1%) x 11.9%= 4.81%
Conditional Expected Values
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Positive Forecast
Negative Forecast
Alt
ern
ativ
es
Bonds 6.86% 4.81%
Stocks 9.55% 4.07%
Fixed deposit 7% 7%
• Expected Return from Additional Information: 58%*9.55%+42%*7% = 8.48%
• Expected Value of Additional Information: 8.48%-7.25% = 1.23%
Conditional Expected Values Contd…
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Summary
States of nature
>1000 points
300-1000 +/-300-300 to -
1000<-1000 points
Large rise Small rise No change Small fall Large fall
Alt
ern
ativ
es Bonds 9% 7% 6% 0% -1%
Stocks 17% 9% 5% -3% -10%
Fixed deposit 7% 7% 7% 7% 7%
Probability 25% 20% 40% 10% 5%
• Expected Value Returns: = 7.25%
• Expected value of perfect information: 9.9%-7.25% = 2.65%
• Expected Value of Additional Information: 8.48%-7.25% = 1.23%
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Decision Analysis Models
Personality type
States of nature
Decision models
Complete certainty
RiskyComplete
uncertainty
Optimist Pessimist Neutral
Linear programming
EVR Maxmax MinmaxMaxmin
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Criteria Based Matrix
Criteria Based Matrix is a decision-making tool used tonarrow down from given options to implementablesolutions. The key steps involved in criteria-basedmatrix are:
• Record a final list of solutions
• Create a list of evaluation criteria
• Weight the list of evaluation criteria
• Compare the list of solutions to the weighted criteria andassign rating
• Prioritize based on total weighted score
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CBM Example- Recruitment
Criteria for Recruiting throughVarious sources
1. Cost
2. Turn around time
3. Candidate quality
4. No. of openings
Weight
9
7
10
7
Total
81
49
60
253
63
36
90
238
Job portals Consultants
Likely Solutions
9
7
6
9
4
9
9
763 49
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Decision Analysis- Part III
Decision Analysis Criteria Based Matrix
ObjectiveMaximize/Minimize payoff
Solution selection
Criteria QuantitativeQuantitative as well qualitative
States of natureMutually exclusive and exhaustive
Single
Criteria values Varying Fixed
Application examplesFinancial planning, business expansion, make or buy etc.
Project solution selection, make or buy etc.
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References
• University of Baltimore: http://home.ubalt.edu/ntsbarsh/opre640a/partIX.htm
• John Wiley & Sons
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Thanks!!!
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