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Events alternative A2 A3 Probabilities following table: S, S; and Sa. The monetary payoffs of cach combination of A, and S, are given n the Si 27 45 be affected by the occurrence of any one of the four possible evexits Si 52 1S2 12 17 36 Ai, A2 and As. where the oulcone of 0.3 Answer following based on the information is given above 0.4 c) By using minmax regrct identify lowest regrets (3pts) S3 14 D compute amount of expected monetary value (3pis) 35 g) What is value ofexpected opportunity losses (3pts?) 29 h) what is expected value of perfect infomation(3pts) 0.2 S4 26 A) ldentuly the best alternatives that maximize profit and minimize the costs by using maxmin approaches (2pts) 20 b) ldentify the best alternatives that maximize profit and minimize the costs by using maximas approaches (2pts) 15 0.10 d) ldentify the best alternatives that maximize profit and ninimize the costs by using Lapla approaches(2pts) e) ldentily the best alternatives that maximize profit and minimize the costs by using Hu criteria at u-0.60(3pts)

1 answer

Based on the information given, it appears you're dealing with a decision-making problem incorporating various decision-making criteria and approaches. Let's break this down step-by-step.

Given Probabilities

  • P(A1): 0.3
  • P(A2): 0.4
  • P(A3): 0.2

Payoff Matrix

The monetary payoffs for different alternatives \( A1, A2, A3 \) across states \( S1, S2, S3, S4 \) seem to be as follows (assuming a typical structure):

  • \( A1 \): [27, 45, 12, 26]
  • \( A2 \): [52, 1, 17, 20]
  • \( A3 \): [14, 35, 29, 15]

a) Identify Best Alternatives for Maximin Approach

To use the maximin approach, find the worst outcome for each alternative and then choose the alternative with the highest worst outcome.

  • A1: Min(27, 45, 12, 26) = 12
  • A2: Min(52, 1, 17, 20) = 1
  • A3: Min(14, 35, 29, 15) = 14

Best alternative (Maximin): \( A3 \) with a minimum of 14.

b) Identify Best Alternatives for Maximax Approach

For the maximax approach, take the best outcome for each alternative and choose the one with the highest maximum.

  • A1: Max(27, 45, 12, 26) = 45
  • A2: Max(52, 1, 17, 20) = 52
  • A3: Max(14, 35, 29, 15) = 35

Best alternative (Maximax): \( A2 \) with a maximum of 52.

c) Minimax Regret Approach

To find the minimax regret, first calculate the regrets for each strategy.

  1. Determine Best Payoff for each state:

    • S1: 52 (A2)
    • S2: 45 (A1)
    • S3: 29 (A3)
    • S4: 26 (A1)

  2. Calculate Regrets:

    • A1: [52-27, 45-45, 29-12, 26-26] = [25, 0, 17, 0] → Max Regret = 25
    • A2: [52-52, 45-1, 29-17, 26-20] = [0, 44, 12, 6] → Max Regret = 44
    • A3: [52-14, 45-35, 29-29, 26-15] = [38, 10, 0, 11] → Max Regret = 38

Lowest regrets: A1 with a max regret of 25.

d) Expected Monetary Value (EMV)

To calculate the expected monetary value, multiply the payoffs by their probabilities and sum them up.

  • EMV(A1): \( 0.3 * 27 + 0.4 * 45 + 0.2 * 12 + 0 * 26 \)
  • EMV(A2): \( 0.3 * 52 + 0.4 * 1 + 0.2 * 17 + 0 * 20 \)
  • EMV(A3): \( 0.3 * 14 + 0.4 * 35 + 0.2 * 29 + 0 * 15 \)

Calculate accordingly.

e) Expected Opportunity Loss

Calculate the expected opportunity loss (EOL) by taking the regrets from the previous section and calculating the expected loss.

f) Expected Value of Perfect Information (EVPI)

EVPI is calculated as the difference between the expected value with perfect information and the expected value under uncertainty.

EVPI: (Maximum Payoff of each state - Best EMV) across all states.

g) Hurwicz Criterion

The Hurwicz criterion is a compromise between the maximax and maximin approaches. Using a coefficient of optimism \( \alpha = 0.6 \): \[ Hurwicz(A) = \alpha * Max(A) + (1 - \alpha) * Min(A) \]

Conclusion

Calculating specific numerical values for EMV, EOL, and EVPI needs data completion and careful arithmetic. Make sure you perform all calculations accurately to arrive at definitive answers!