Assume that a plant manager has to decide where to locate its warehouse The decision has been narrowed down to choices among the following three cities: Detroit, Cleveland, and St. Louis. The following pairwise comparison matrix summarizes the preferences of the plant manager.
$$\begin{array} { | c | c | c | c | }
\hline & \text { Detroit } & \text { Cleveland } & \text { St. Louis } \
\hline \text { Detroit } & 1 & 1 / 3 & 1 / 4 \
\hline \text { Cleveland } & 3 & 1 & 1 / 2 \
\hline \text { St. Louis } & 4 & 2 & 1 \
\hline
\end{array}$$
Which choice does the decision maker prefer?
A) Detroit
B) Cleveland
C) St. Louis
D) Cleveland and St. Louis are equally preferred.

Question

Assume that a plant manager has to decide where to locate its warehouse The decision has been narrowed down to choices among the following three cities: Detroit, Cleveland, and St. Louis. The following pairwise comparison matrix summarizes the preferences of the plant manager.
$$\begin{array} { | c | c | c | c | } 
\hline & \text { Detroit } & \text { Cleveland } & \text { St. Louis } \
\hline \text { Detroit } & 1 & 1 / 3 & 1 / 4 \
\hline \text { Cleveland } & 3 & 1 & 1 / 2 \
\hline \text { St. Louis } & 4 & 2 & 1 \
\hline
\end{array}$$
Which choice does the decision maker prefer?
A) Detroit
B) Cleveland
C) St. Louis
D) Cleveland and St. Louis are equally preferred.

Quizplus · Accepted Answer

The preference for each city can be determined by calculating the geometric mean of each row and then normalizing these means. The city with the highest normalized value is the most preferred. In this matrix, St. Louis has the highest values when comparing directly with the other cities, indicating it is the most preferred choice.

Assume That a Plant Manager Has to Decide Where to Locate