Step-by-Step Exercises on Decision Making under Risk
- Minimum EOL Approach BSNS2120, J. Wang
Name __J. Wang_______
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
Col. Max
120
100
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
0
200
30
2
30
0
20
3
40
0
10
4
170
20
0
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) = 0*0.7 + 200*0.1 + 30*0.2 = 26;
EOL(Alt. 2) = 30*0.7 + 0*0.1 + 20*0.2 = 25;
EOL(Alt. 3) = 40*0.7 + 0*0.1 + 10*0.2 = 30;
EOL(Alt. 4) = 170*0.7 + 20*0.1 + 0*0.2 = 121.
Step 3.
Pick up the alternative with Minimum EOL, which is Alt. 2 , with EOL= 25.
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
0
200
30
30
0
20
2
3
40
0
10
4
170
20
0
Expected Opportunity
Loss
(EOL)
0*0.7 + 200*0.1 + 30*0.2 = 26
30*0.7 + 0*0.1 + 20*0.2 = 25
40*0.7 + 0*0.1 + 10*0.2 = 30
170*0.7 + 20*0.1 +0*0.2 = 121
(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