MGS 3100
Business Analysis
Decision Analysis
Mar 24, 2016
Georgia State University - Confidential
MGS3100_06.ppt/Mar 24, 2016/Page 1
Agenda
Decision
Analysis
Georgia State University - Confidential
Problems
MGS3100_06.ppt/Mar 24, 2016/Page 2
Decision Analysis
Open MGS3100_06Decision_Making.xls
Decision Alternatives
•
Your options - factors that you have control over
•
A set of alternative actions - We may chose whichever we please
States of Nature
•
Possible outcomes – not affected by decision.
•
Probabilities are assigned to each state of nature
Certainty
•
Only one possible state of nature
•
Decision Maker (DM) knows with certainty what the state of nature will be
Ignorance
•
Several possible states of nature
•
DM Knows all possible states of nature, but does not know probability of
occurrence
Risk
•
Several possible states of nature with an estimate of the probability of each
•
DM Knows all possible states of nature, and can assign probability of occurrence
for each state
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MGS3100_06.ppt/Mar 24, 2016/Page 3
Decision Making Under Ignorance
•
LaPlace-Bayes
– All states of nature are equally likely to occur.
– Select alternative with best average payoff
•
Maximax
– Evaluates each decision by the maximum possible return associated
with that decision
– The decision that yields the maximum of these maximum returns
(maximax) is then selected
•
Maximin
– Evaluates each decision by the minimum possible return associated with
the decision
– The decision that yields the maximum value of the minimum returns
(maximin) is selected
•
Minmax Regret
– The decision is made on the least regret for making that choice
– Select alternative that will minimize the maximum regret
Georgia State University - Confidential
MGS3100_06.ppt/Mar 24, 2016/Page 4
LaPlace-Bayes
State of Nature
Alternative
Actions
Demand
LaPlace-Bayes
Criterion
Low (50 units) Medium (100 units) High (150 units)
Mean
Build 50
400,000
400,000
400,000
400,000
Build 100
100,000
800,000
800,000
566,667
Build 150
(200,000)
500,000
1,200,000
500,000
Georgia State University - Confidential
MGS3100_06.ppt/Mar 24, 2016/Page 5
Maximax
State of Nature
Alternative
Actions
Demand
Maximax
Criterion
Low (50 units) Medium (100 units) High (150 units)
Max
Build 50
400,000
400,000
400,000
400,000
Build 100
100,000
800,000
800,000
800,000
Build 150
(200,000)
500,000
1,200,000
1,200,000
Georgia State University - Confidential
MGS3100_06.ppt/Mar 24, 2016/Page 6
Maximin
State of Nature
Alternative
Actions
Demand
Maximin
Criterion
Low (50 units) Medium (100 units) High (150 units)
Min
Build 50
400,000
400,000
400,000
400,000
Build 100
100,000
800,000
800,000
100,000
Build 150
(200,000)
500,000
1,200,000
(200,000)
Georgia State University - Confidential
MGS3100_06.ppt/Mar 24, 2016/Page 7
MinMax Regret Table
Regret Table: Highest payoff for state of nature
– payoff for this decision
Demand
Minmax
Regret
Criterion
Low (50 units) Medium (100 units) High (150 units)
Max
State of Nature
Decision
Build 50
-
Build 100
300,000
Build 150
600,000
Georgia State University - Confidential
400,000
300,000
800,000
800,000
400,000
400,000
-
600,000
MGS3100_06.ppt/Mar 24, 2016/Page 8
Decision Making Under Risk
•
Expected Return (ER) or Expected Value (EV) or Expected Monetary Value
(EMV)
– SjThe jth state of nature
–
–
–
–
Di
The ith decision
P(Sj)
The probability that Sj will occur
Rij
The return if Di and Sj occur
ERj
The long-term average return
• ERi = S Rij  P(Sj)
• Variance = S (ERi - Rij)2  P(Sj)
•
The EMV criterion chooses the decision alternative which has the highest EMV.
We'll call this EMV the Expected Value Under Initial Information (EVUII) to
distinguish it from what the EMV might become if we later get more information.
Do not make the common student error of believing that the EMV is the payoff
that the decision maker will get. The actual payoff will be the for that alternative
(j) Vi,j and for the State of Nature (i) that actually occurs.
Georgia State University - Confidential
MGS3100_06.ppt/Mar 24, 2016/Page 9
Decision Making Under Risk
•
One way to evaluate the risk associated with an Alternative Action by calculating
the variance of the payoffs. Depending on your willingness to accept risk, an
Alternative Action with only a moderate EMV and a small variance may be
superior to a choice that has a large EMV and also a large variance. The
variance of the payoffs for an Alternative Action is defined as
• Variance = S (ERi - Rij)2  P(Sj)
•
Most of the time, we want to make EMV as large as possible and variance as
small as possible. Unfortunately, the maximum-EMV alternative and the
minimum-variance alternative are usually not the same, so that in the end it boils
down to an educated judgment call.
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MGS3100_06.ppt/Mar 24, 2016/Page 10
Expected Return
State of Nature
Alternative
Actions
Demand
Expected
Return
Low (50 units) Medium (100 units) High (150 units)
ER
Build 50
400,000
400,000
400,000
400,000
Build 100
100,000
800,000
800,000
660,000
Build 150
(200,000)
500,000
1,200,000
570,000
0.5
0.3
1.0
Probability
0.2
Georgia State University - Confidential
MGS3100_06.ppt/Mar 24, 2016/Page 11
Expected Value of Perfect Information
•
EVPI measures how much better you could do on this decision if you could
always know what state of nature would occur.
•
The Expected Value of Perfect Information (EVPI) provides an absolute upper
limit on the value of additional information (ignoring the value of reduced risk). It
measures the amount by which you could improve on your best EMV if you had
perfect information. It is the difference between the Expected Value Under
Perfect Information (EVUPI) and the EMV of the best action (EVUII).
•
The Expected Value of Perfect Information measures how much better you
could do on this decision, averaging over repeating the decision situation many
times, if you could always know what State of Nature would occur, just in time to
make the best decision for that State of Nature. Remember that it does not
imply control of the States of Nature, just perfect prediction. Remember also that
it is a long run average. It places an upper limit on the value of additional
information.
Georgia State University - Confidential
MGS3100_06.ppt/Mar 24, 2016/Page 12
Expected Value of Perfect Information
– EVUPI - Expected Value under perfect information
S P(Si)  max(Vij)
– EVUII – EMV of the best action
max(EMVj)
– EVPI = EVUPI - EVUII
Georgia State University - Confidential
MGS3100_06.ppt/Mar 24, 2016/Page 13
Expected Value of Perfect Information
State of Nature
Alternative
Actions
Demand
Expected
Return
Low (50 units) Medium (100 units) High (150 units)
ER
Build 50
400,000
400,000
400,000
400,000
Build 100
100,000
800,000
800,000
660,000
Build 150
(200,000)
500,000
1,200,000
570,000
0.2
0.5
0.3
1.0
400,000
800,000
1,200,000
840,000
EVPI
180,000
Probability
Best Decision
Georgia State University - Confidential
MGS3100_06.ppt/Mar 24, 2016/Page 14
Expected Value of Sample Information
•
•
•
EVSI = expected value of sample information
EVwSI = expected value with sample information
EVwoSI = expected value without sample information
•
•
EVSI = EVwSI – EVwoSI
Efficiency Index = [EVSI/EVPI]100
Georgia State University - Confidential
MGS3100_06.ppt/Mar 24, 2016/Page 15
Agenda
Decision
Analysis
Georgia State University - Confidential
Problems
MGS3100_06.ppt/Mar 24, 2016/Page 16
What kinds of problems?
•
Alternatives known
•
States of Nature and their probabilities are known.
•
Payoffs computable under different possible scenarios
Georgia State University - Confidential
MGS3100_06.ppt/Mar 24, 2016/Page 17
Basic Terms
•
Decision Alternatives
•
States of Nature (eg. Condition of economy)
•
Payoffs ($ outcome of a choice assuming a state of nature)
•
Criteria (eg. Expected Value)
Z
Georgia State University - Confidential
MGS3100_06.ppt/Mar 24, 2016/Page 18
Example Problem 1
- Expected Value & Decision Tree
Decision
Alternatives
Probablilties
States of Nature
S1
S2
Poor Average
A
300
350
B
-100
600
C
-1000
-200
0.3
0.6
Georgia State University - Confidential
S3
Good
400
700
1200
0.1
MGS3100_06.ppt/Mar 24, 2016/Page 19
Expected Value
Decision
Alternatives
States of Nature
S1
S2
Poor Average
A
300
350
B
-100
600
C
-1000
-200
Georgia State University - Confidential
S3
Good
400
700
1200
EV
340
400
-300
(300 x 0.3) + (350 x 0.6) + (400 x 0.1)
(-100 x 0.3) + (600 x 0.6) + (700 x 0.1)
(-1000 x 0.3) + (-200 x 0.6) + (1200 x 0.1)
MGS3100_06.ppt/Mar 24, 2016/Page 20
Decision Tree
0.3
0.6
340
0.1
A1
0.3
0.6
A2
A2
400
400
A3
0.1
0.3
0.6
-300
0.1
Georgia State University - Confidential
300
350
400
-100
600
700
-1000
-200
1200
MGS3100_06.ppt/Mar 24, 2016/Page 21
Example Problem 2
- Sequential Decisions
•
Would you hire a consultant (or a psychic) to get more info about states of
nature?
•
How would additional info cause you to revise your probabilities of states of
nature occurring?
•
Draw a new tree depicting the complete problem.
•
Consultant’s Track Record
S1-Low
Economy
Favorable
Unfavorable
20
80
100
S1-Low
Economy
A
B
C
Probabilities
S2-Medium
Economy
60
40
100
S2-Medium
Economy
300
-100
-1000
0.3
Georgia State University - Confidential
S3-High
Economy
S3-High
Economy
350
600
-200
0.6
70
30
100
Z
EV : Expected Values
400
340
700
400
1200
-300
0.1
MGS3100_06.ppt/Mar 24, 2016/Page 22
Example Problem 2
- Sequential Decisions (Ans)
Open MGS3100_06Joint_Probabilities_Table.xls
1.
First thing you want to do is get the information (Track Record) from the Consultant in
order to make a decision.
S1-Low
Economy
S2-Medium
Economy
Favorable
Unfavorable
2.
20
80
100
60
40
100
70
30
100
This track record can be converted to look like this:
P(F/S1) = 0.2
P(F/S2) = 0.6
P(F/S3) = 0.7
P(U/S1) = 0.8
P(U/S2) = 0.4
P(U/S3) = 0.3
F= Favorable
3.
S3-High
Economy
U=Unfavorable
Next, you take this information and apply the prior probabilities to get the Joint
Probability Table/Bayles Theorum
S1-Low
Economy
S2-Medium
Economy
S3-High
Economy
Z
FAVorable
UNFAVorable
Prior Probabilities
0.06
0.24
0.3
0.36
0.24
0.6
0.07
0.03
0.1
Total
0.49
0.51
1.00
FAVorable
UNFAVorable
Prior Probabilities
= 0.2 x 0.3
= 0.8 x 0.3
Given
= 0.6 x 0.6
= 0.4 x 0.6
Given
= 0.7 x 0.1
= 0.3 x 0.1
Given
= 0.06 + 0.36 + 0.07
= 0.24 + 0.24 + 0.03
= 0.3 + 0.6 + 0.1
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MGS3100_06.ppt/Mar 24, 2016/Page 23
Example Problem 2
- Sequential Decisions (Ans)
Open MGS3100_06Joint_Probabilities_Table.xls
4.
Next step is to create the Posterior Probabilities (You will need this information to
compute your Expected Values)
P(S1/F) = 0.06/0.49 = 0.122
P(S2/F) = 0.36/0.49 = 0.735
P(S3/F) = 0.07/0.49 = 0.143
P(S1/U) = 0.24/0.51 = 0.47
P(S2/U) = 0.24/0.51 = 0.47
P(S3/U) = 0.03/0.51 = 0.06
5.
Solve the decision tree using the posterior probabilities just computed.
Z
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MGS3100_06.ppt/Mar 24, 2016/Page 24