$An$ industrial engineering team $atC$&$H$ selects the most suitable supplier for a critical component.

Three suppliers have been shortlisted: Suppliers $S,J,$ and $M.$ The final selection $is$ based $on$ three

evaluation criteria: cost efficiency $(C),$ delivery reliability $(D),$ and quality assurance $(Q).$

The team uses the following pairwise comparison matrix $to$ establish the relative importance $of$

the evaluation criteria:

$A=\left[\begin{array}{ccc}1& 2& \frac{1}{4}\\ \frac{1}{2}& 1& \frac{1}{5}\\ 4& 5& 1\end{array}\right]$

The performance matrices for each supplier based $on$ the three criteria are given $as$:

Supplier performance $incost$ efficiency:

$A_C=\left[\begin{array}{ccc}1& 3& 4\\ \frac{1}{3}& 1& \frac{1}{5}\\ \frac{1}{4}& 5& 1\end{array}\right]$

Supplier performance $in$ delivery reliability:

$A_D=\left[\begin{array}{ccc}1& \frac{1}{3}& 2\\ 3& 1& \frac{1}{2}\\ \frac{1}{2}& 2& 1\end{array}\right]$

Supplier performance $in$ quality assurance:

$A_Q=\left[\begin{array}{ccc}1& \frac{1}{2}& 1\\ 2& 1& \frac{1}{2}\\ 1& 2& 1\end{array}\right]$

Problem Statement

Determine the supplier who should $be$ selected based $on$ the performance matrices and criteria

preferences.

Assess the consistency $of$ the pairwise comparison matrix A and the supplier performance

matrices $A_C,A_D,$ and $A_Q.$