A Methodology for Green Supplier Selection in Food Industries - Technology Management for Sustainable Production and Logistics - page 19

Table 11 Decision
matrices (The distance δ ij
for suppliers)

Suppliers Criteria

C1 C2 C3 C4

0.16 0.21 0.22 0.34

(a) Steel sheet

δ a 1 j

0.58 0.65 0.73 0.53

δ a 2 j

0.39 0.34 0.24 0.38

δ a 3 j

(b) PET granule 0.12 0.15 0.10 0.19 δ b 1 j

0.47 0.57 0.41 0.44

δ b 2 j

0.62 0.55 0.59 0.51

δ b 3 j

By comparing δ ij and obtaining the biggest value δ MAX and the smallest value
δ MIN , the grey relational coefficient ( ξ ij ) can be calculated by formula (Zhang and
Liu 2011 ):

ξ ij = δ MIN

+ ρδ MAX

i ∈ M , j ∈ N

(21)

δ ij + ρδ MAX

Grey relation coefficient matrix ( A ) for steel sheet suppliers is:

1 0.91 0.88 0.74

A = 0.55 0.51 0.47 0.57

0.68 0.73 0.86 0.69

(22)

Grey relational grades are calculated by substituting grey relational coefficients
and weights of high ranked criteria into Eq. ( 23 ) (Zhang and Liu 2011 ); shown in
Table 12 .

n

γ i = w j ξ ij i ∈ M

(23)

j = 1

w j is calculated using AHP in section D (Table 8 ).
The greater the value of grey relational grade (γ ) , the better the alternative is.
Alternatives are ranked according to descending order of grey relational grade:

γ a 1 >γ a 3 >γ a 2 potential supplier for steel sheet

(24)

γ b 1 >γ b 2 >γ b 3 potential supplier for PET granule

(25)

Thus the most appropriate PMS candidates are a 1 for steel sheet and b 1 for PET
granule.

Table 12 Grey relational
grade for suppliers

Suppliers ʳ 1 ʳ 2 ʳ 3

0.88 0.50 0.79

Steel sheet (a)

PET granule (b) 0.94 0.47 0.40