The Following Table Shows Cost Payoffs for Four Decision Variables

Essay

The following table shows cost payoffs for four decision variables and four states of nature. $\begin{array}{c|cccc}& \mathrm{S}_{1} & \mathrm{~S}_{2} & \mathrm{~S}_{3} & \mathrm{~S}_{4} \\\hline\mathrm{d}_{1} & 16 & 8 & 15 & 4 \\\mathrm{~d}_{2} & 12 & 12 & 10 & 6 \\\mathrm{~d}_{3} & 10 & 12 & 16 & 10 \\\mathrm{~d}_{4} & 9 & 14 & 20 & 12\end{array}$
a. Which decision variable would be selected using minimin criteria?
b. Which decision variable would be selected using minimax?
c. Which decision variable would be selected using minimax-regret 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 selected using the expected value criterion?