The Following Table Shows Cost Payoffs for Four Decision Variables

question 8

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?

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Definitions:

Utter Defeat

A term describing a situation where one party is completely overpowered or overwhelmed in a contest or competition.

Owning Responsibility

The act of acknowledging and accepting responsibility for one's actions or decisions.

Step 6

Refers to a specific step in various step-based recovery programs, generally involving preparation for self-improvement and rectification of wrongs.

Honesty

The quality of being truthful, transparent, and free from deceit or fraud in one's actions and statements.