A Methodology for Green Supplier Selection in Food Industries - Technology Management for Sustainable Production and Logistics - page 12

4.2 Part B

Weights of four evaluation factors are calculated based on pairwise comparisons
(by means of a nine points Likert scale) which represent the importance of eval-
uation factors. A questionnaire according to the format proposed by Humphreys
et al. ( 2003 ), ought to be carried out to determine the weight of evaluation factors.
According to Saaty ( 1990 ) pairwise comparisons are classically carried out by
asking the decision maker about the value of a criterion (C1) when compared to
another criterion (C2) with respect to overall goal, then verbal judgments of the
decision maker are transformed into numerical values (Oztaysi 2014 ). The ver-
bal judgments of the decision makers are then transformed into numerical values
using the scale presented in Table 2 .
The pairwise comparisons of evaluation factors can be summarized in a square
evaluation matrix A = ( a ij ) where every element ( i, j = 1, 2, …, n ) is the quotient
of weights of the evaluation factors. After construction of square and reciprocal
matrix (Eq. 1 ), the procedure of developing weights in AHP which is described in
Saaty ( 1990 ) has been done.

1 A 12 ··· A 1 N
A 21 1 ··· A 2 N
. . . . . .
A N 1 A N 2 ··· 1

; A =

1
3
5132
2

1
5

1
2

1

A = ( A IJ ) =

(1)

1
3

1
2

1

1

3

2 21

In the next point, matrix is normalized and the relative weights are calculated. The
relative weights are given by the right eigenvector ( w ) corresponding to the largest
eigenvalue ( MAX ), as:

(2)

A w = MAX . w

If the pairwise comparisons are completely consistent, the matrix A has rank 1 and
MAX = n . In this case, weights can be obtained by normalizing any of the rows or

columns of A (Saaty 1990 ). It should be noted that the quality of the output of the
AHP is related to the consistency of the pairwise comparison. Consistency index
(CI) are calculated (Eq. 3 ) for pairwise comparison matrix and checked for con-
sistency ratio (Eq. 4 ) using a random index (RI) presented in Table 3 (Saaty 1990 ).

Table 2 Verbal judgments and numerical rate
Verbal judgment of preference Numerical rate

Equal importance 1

3

Weal importance of one over another

Essential or strong importance 5

Demonstrated importance 7

9

Absolute importance

Intermediate values between the two adjacent judgments 2, 4, 6, 8