Decision Matrices

An industrial engineering team at $C$&$H$ 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 in cost 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:

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

roblem 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 $A_Q.$