Decision analysis part iii

Core Purpose: To Enable Organisations Become Happier

Decision Analysis- Part III

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


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


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%


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%


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%


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


Case Study

States of nature

>1000 points

300-1000 +/-300-300 to -

1000<-1000 points


Alt

ern

ativ

es

Bonds 9% 7% 6% 0% -1%

Stocks 17% 9% 5% -3% -10%

Fixed deposit

7% 7% 7% 7% 7%


Regret Matrix

States of nature

>1000 points

300-1000 +/-300-300 to -

1000<-1000 points


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%)


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%


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


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


Case Study

States of nature

>1000 points

300-1000 +/-300-300 to -

1000<-1000 points


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 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%)


States of nature

>1000 points

300-1000 +/-300-300 to -

1000<-1000 points


changeSmall fall Large fall

Alt

ern

ativ

es Bonds 9% 7% 6% 0% -1%

Stocks 17% 9% 5% -3% -10%


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


• Uses Bayes’ theorem to calculate refined probabilities

Expected Value of Additional Information


Positive 80% 70% 50% 40% 0%

Negative 20% 30% 50% 60% 100%


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%


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%


States of nature

>1000 points

300-1000 +/-300-300 to -

1000<-1000 points


changeSmall fall Large fall

Alt

ern

ativ

es Bonds 9% 7% 6% 0% -1%

Stocks 17% 9% 5% -3% -10%


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


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…


Summary

States of nature

>1000 points

300-1000 +/-300-300 to -

1000<-1000 points


Alt

ern

ativ

es Bonds 9% 7% 6% 0% -1%

Stocks 17% 9% 5% -3% -10%


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%


Decision Analysis Models

Personality type

States of nature

Decision models

Complete certainty

RiskyComplete

uncertainty

Optimist Pessimist Neutral

Linear programming

EVR Maxmax MinmaxMaxmin


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


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


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.


References

• University of Baltimore: http://home.ubalt.edu/ntsbarsh/opre640a/partIX.htm

• John Wiley & Sons

http://home.ubalt.edu/ntsbarsh/opre640a/partIX.htm

Data Analytics | Execution | Deployment | Training | QinT

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7-Jan-15 27

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Decision analysis part iii