Step-by-Step Exercises on Decision Making under Risk
- EMV and EVPI BSNS2120, J. Wang
Name _________________________
A payoff table is given as below.
States of Nature
A
B
C
Alternatives P(A)=0.7 P(B)=0.1 P(C)=0.2
1
120
-100
60
2
90
100
70
3
80
100
80
4
-50
80
90
Show your calculations in Part 1 and Part 2.
Part 1. What is the best decision? – Do the two steps below.
Step 1. Calculate EMV (expected payoff) of each alternative:
EMV(Alt. 1) = ______________________________
EMV(Alt. 2) = ______________________________
EMV(Alt. 3) = ______________________________
EMV(Alt. 4) = ______________________________
Step 2. Pick up the alternative with highest EMV, which is ____________________ .
Your answer to Part 1 question:
The best decision is selecting Alternative ___ whose expected payoff is
___________.
Part 2. What is EVPI (expected value of perfect information) ? – Do the three steps below.
Note: EVPI = (EV with PI)  (EV without PI)
Step 1.
EV without PI = Expected payoff of your decision without using additional PI
In Part 1, you made decision without using additional PI:
Your decision:
Alternative _____ ,
EMV of the decision: ___________ .
Therefore,
EV without PI = ____________________.
Step 2.
Calculate (EV with PI).
If PI says ‘A will occur’, then you would select Alternative _______ with payoff _____ .
If PI says ‘B will occur’, then you would select Alternative _______ with payoff _____ .
If PI says ‘C will occur’, then you would select Alternative _______ with payoff _____ .
The probability for PI to say ‘A will occur’ is ______ .
The probability for PI to say ‘B will occur’ is ______ .
The probability for PI to say ‘C will occur’ is ______ .
The expected payoff with PI
= sum of all possible payoffs weighted by their probabilities
= _____________________________________________________
= _______________________
Step 3.
EVPI = (EV with PI)  (EV without PI)
= ______________________________
= ____________
This is your answer to Part 2 question.
Part 3.
Part 1 and Part 2 can be put in the extended Payoff table.
(1) Put your results in Part 1 and Part 2 into the extended payoff table below.
Alternatives
1
2
3
4
States of Nature
A
B
C
P(A)=0.7 P(B)=0.1 P(C)=0.2
120
-100
60
90
100
70
80
100
80
-50
80
90
(2) Circle and label your decision and its EMV you calculated in Part 1 in the table.
(3) Circle and label (EV without PI) and (EV with PI) in the table.
(4) Calculate EVPI.
Step-by-Step Exercises on Decision Making under Risk
- Minimum EOL Approach BSNS2120, J. Wang
Name _________________________
A payoff table is given as below.
States of Nature
A
B
C
Alternatives P(A)=0.7 P(B)=0.1 P(C)=0.2
1
120
-100
60
2
90
100
70
3
80
100
80
4
-50
80
90
Part 1. Select the best decision by using the Minimum EOL Approach.
(EOL = Expected Opportunity Loss)
Do the three steps below (Show your calculations):
Step 1.
Construct the opportunity loss table.
(a) Calculate the maximum payoff of each column (each state of nature); Put you result
into the table above.
(b) Calculate the opportunity loss of each cell below.
Example: Opportunity loss for cell ‘A2’
= maximum payoff in column A – payoff in cell ‘A2’.
Opportunity loss for cell ‘C3’
= maximum payoff in column C – payoff in cell ‘C3’.
The opportunity loss table (Regret table).
States of Nature
A
B
C
Alternatives P(A)=0.7 P(B)=0.1 P(C)=0.2
1
2
3
4
Is the following statement true or false?
Opportunity losses can never be negative.
a. True
b. False
Step 2.
Calculate the expected opportunity loss for each alternative.
EOL(Alt. 1) = __________________________________________ = __________;
EOL(Alt. 2) = __________________________________________ = __________;
EOL(Alt. 3) = __________________________________________ = __________;
EOL(Alt. 4) = __________________________________________ = __________.
Step 3.
Pick up the alternative with Minimum EOL, which is Alt. _______ , with
EOL=______________.
Part 2.
Calculations in Part 1 can be put in the extended opportunity loss table.
(1) Put your results in Part 1 into the extended opportunity loss table below.
Extended opportunity losses (regrets) table:
States of Nature
A
B
C
Alternatives P(A)=0.7 P(B)=0.1 P(C)=0.2
1
2
3
4
Expected Opportunity
Loss
(EOL)
(2) Circle and label the best decision and its EOL in the table.
Part 3.
Compare the result we have here to those we had in Exercise on EMV and EVPI.
1. The decision from the Minimum EOL Approach is the same as the decision from
the Maximum EMV Approach is.
a. True
b. False
2. Minimum EOL = EVPI.
a. True
b. False