# Step-by-Step Exercises on Decision Making under Risk Minimum eol approach bsns2120, J. Wang

 Дата канвертавання 19.04.2016 Памер 29.1 Kb.
Step-by-Step Exercises on Decision Making under Risk

BSNS2120, J. Wang
Name __J. Wang_______
A payoff table is given as below.
 Alternatives States of Nature A B C 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).

 Alternatives States of Nature A B C 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:

 Alternatives States of Nature Expected Opportunity Loss (EOL) A B C P(A)=0.7 P(B)=0.1 P(C)=0.2 1 0 200 30 0*0.7 + 200*0.1 + 30*0.2 = 26 2 30 0 20 30*0.7 + 0*0.1 + 20*0.2 = 25 3 40 0 10 40*0.7 + 0*0.1 + 10*0.2 = 30 4 170 20 0 170*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

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