Question

D1

D2

D3

D4

S1

2500

3700

4900

7500

S2

5000

3500

5200

8000

S3

5400

4200

5000

7600

Note that the PAYOFFS represent COST, determine the best alternative under the following:

1- The optimistic criterion.

2- The conservative/pessimistic criterion.

3- The regret criterion.

4- Draw a decision tree for this problem

5- If P(Sj) = 0.2, 0.35 for S1 and S2 respectively, find the best Expected Monetary Value.

Answer 1

The image below shows some of the calculations and the decision tree. Based on these, we can answer the questions

1

Optimistic criteria is to choose the best among the best options. That is D1 with the cost of 2500 only

2.

The pessimistic criteria is to choose the best among the worst options. That is D2 with the cost of 4200 only

3.

The regret criteria chooses the best among the regrets. That is D2 with the regret of 1200

4.

The decision tree is shown below. The circle nodes are D1, D2, D3, and D4 respectively.

5.

The expected monetary value is calculated by multiplying the probabilities with their payoff for each decision. The probabilities are 0.2, 0.35 and 0.45 for S1, S2, and S3. The EMVs are shown. The best EMV is alternative D2 with the least cost of 3855