The operations manager for a well-drilling company must recommend whether to build a new facility, expand his existing one, or do nothing. He estimates that long-run profits (in $000) will vary with the amount of precipitation (rainfall) as follows: $$\begin{array} { | l | l | l | l | }
\hline { \text { ALTERNATIVE } } & { \text { PRECIPITATION } } \
\hline& \text { LOW } & \text { NORMAL } & \text { HIGH } \
\hline \text { Do Nothing } & - 100 & 100 & 300 \
\hline \text { Expand } & 350 & 500 & 200 \
\hline \text { Build New } & 750 & 300 & 0 \
\hline
\end{array}$$ If he uses the minimax regret criterion, which alternative will he decide to select?
A) do nothing
B) expand
C) build new
D) either do nothing or expand
E) either expand or build new

Question

The operations manager for a well-drilling company must recommend whether to build a new facility, expand his existing one, or do nothing. He estimates that long-run profits (in $000) will vary with the amount of precipitation (rainfall) as follows: $$\begin{array} { | l | l | l | l | } 
\hline   { \text { ALTERNATIVE } } & { \text { PRECIPITATION } } \
\hline& \text { LOW } & \text { NORMAL } & \text { HIGH } \
\hline  \text { Do Nothing } & - 100 & 100 & 300 \
\hline \text { Expand } & 350 & 500 & 200 \
\hline \text { Build New } & 750 & 300 & 0 \
\hline
\end{array}$$ If he uses the minimax regret criterion, which alternative will he decide to select?
A) do nothing
B) expand
C) build new
D) either do nothing or expand
E) either expand or build new

Quizplus · Accepted Answer

To use the minimax regret criterion, we must first calculate the regret table by finding the maximum profit for each precipitation level and subtracting the profit of each alternative from it. The regret table is shown below:

$$\begin{array} { | l | l | l | l | | l | } 
\hline   { \text { ALTERNATIVE } } & { \text { PRECIPITATION } } & {\text { MAX PROFIT}} & {\text { REGRET}}\
\hline& \text { LOW } & \text { NORMAL } & \text { HIGH } & \
\hline  \text { Do Nothing } & - 100 & 100 & 300 & 400 \
\hline \text { Expand } & 350 & 500 & 200 & 150 \
\hline \text { Build New } & 750 & 300 & 0 & 450 \
\hline
\text { MAX REGRET} & 450 & 450 & 450 & \
\hline
\end{array}$$

We can see that the maximum regret for each precipitation level is 450. The minimax regret criterion tells us to choose the alternative that minimizes the maximum regret. Looking at the regret table, we see that the minimum of the maximum regrets is 150, which is achieved by choosing to Build New. Therefore, the operations manager should recommend building a new facility.

The Operations Manager for a Well-Drilling Company Must Recommend Whether