The following table shows cost payoffs for four decision variables and four states of nature.
$\begin{array} { c | c c c c } & \mathbf { S } _ { 1 } & \mathbf { S } _ { \mathbf { z } } & \mathbf { S } _ { \mathbf { 3 } } & \mathbf { S } _ { \mathbf { 4 } } \\\hline \mathrm { d } _ { 1 } & 16 & \mathbf { 8 } & 15 & 4 \\\mathbf { d } _ { 2 } & 12 & 12 & 10 & 6 \\d _ { 3 } & 10 & 12 & 16 & 10 \\d _ { 4 } & 9 & 14 & 20 & 12\end{array}$
a. Which decision variable would be selected using minimin criteria?
b. Remembering that the data represents cost, which decision variable would be selected using minimax?
c. Remembering that the data represents cost, which decision variable would be selected using minimax-regrets criteria.
d. Suppose the decision-maker assigns the probability for S₁ = 0.10; S₂ = 0.25; S₃ = 0.45; and S₄ = 0.20, which decision variable would be picked using the expected value criterion?

Question

The following table shows cost payoffs for four decision variables and four states of nature.

\begin{array} { c | c c c c } & \mathbf { S } _ { 1 } & \mathbf { S } _ { \mathbf { z } } & \mathbf { S } _ { \mathbf { 3 } } & \mathbf { S } _ { \mathbf { 4 } } \\\hline \mathrm { d } _ { 1 } & 16 & \mathbf { 8 } & 15 & 4 \\\mathbf { d } _ { 2 } & 12 & 12 & 10 & 6 \\d _ { 3 } & 10 & 12 & 16 & 10 \\d _ { 4 } & 9 & 14 & 20 & 12\end{array}

a. Which decision variable would be selected using minimin criteria?
b. Remembering that the data represents cost, which decision variable would be selected using minimax?
c. Remembering that the data represents cost, which decision variable would be selected using minimax-regrets criteria.
d. Suppose the decision-maker assigns the probability for S₁ = 0.10; S₂ = 0.25; S₃ = 0.45; and S₄ = 0.20, which decision variable would be picked using the expected value criterion?

Quizplus · Accepted Answer

The Answer of The following table shows cost payoffs for four decision variables and four states of nature. $$\begin{array} { c | c c c c } & \mathbf { S } _ { 1 } & \mathbf { S } _ { \mathbf { z } } & \mathbf { S } _ { \mathbf { 3 } } & \mathbf { S } _ { \mathbf { 4 } } \ \hline \mathrm { d } _ { 1 } & 16 & \mathbf { 8 } & 15 & 4 \ \mathbf { d } _ { 2 } & 12 & 12 & 10 & 6 \ d _ { 3 } & 10 & 12 & 16 & 10 \ d _ { 4 } & 9 & 14 & 20 & 12 \end{array}$$ a. Which decision variable would be selected using minimin criteria? b. Remembering that the data represents cost, which decision variable would be selected using minimax? c. Remembering that the data represents cost, which decision variable would be selected using minimax-regrets criteria. d. Suppose the decision-maker assigns the probability for S₁ = 0.10; S₂ = 0.25; S₃ = 0.45; and S₄ = 0.20, which decision variable would be picked using the expected value criterion?

The Following Table Shows Cost Payoffs for Four Decision Variables