A Methodology for Green Supplier Selection in Food Industries - Technology Management for Sustainable Production and Logistics - page 15

As stated previously, in TOPSIS technique, best alternatives have shortest distance
from the positive ideal solution and the longest distance from the negative ideal
solution calculated by closeness index (CI). The positive ideal solution ( A + ) is
determined by selecting the largest normalized and weighted score for each crite-
rion. Similarly, the negative ideal solution ( A − ) is determined by selecting the least
normalized and weighted score of each criterion (Roy 2004 ). So based on defini-
tion, the positive ideal solution and the negative ideal solution are:

A + = [0.037, 0.182, 0.059, 0.113]

(8)

A

− =[ 0.016, 0.121, 0.039, 0.050 ]

(9)

The distances of each alternative to the positive ideal solution R + and negative
ideal solution R − calculated.

n
j =

+
i

+
j

) 2

R (ϑ ij − ϑ for the alternative i , i = 1, 2, ... , m

=

(10)

1

n
j =

−
i

−
j

) 2

R (ϑ ij − ϑ for the alternative i , i = 1, 2, ... , m

=

(11)

1

where ϑ

i is the negative ideal for the evaluation factor j.
Using these calculated values closeness index (CI) for each alternative is com-
puted using Eq. ( 12 ):

+
i

is the positive ideal, ϑ

−

−
( R ) + + ( R ) − FOR THE ALTERNATIVE I

( R )

CLOSENESS INDEX ( CI ) =

(12)

The closeness index (CI) can get values between 0 and 1 and the alternative which
has the highest CI is selected as the best alternative (Oztaysi 2014 ).
The distances of each alternative to the positive ideal solution ( R + ) and nega-
tive ideal solution ( R − ) and closeness index (CI) are calculated preference order
ranked as shown in Table 5 . Also the ranking in Table 6 shows that qualitative,
service, EMS and financial criteria are the high ranked and most important criteria
for this case study.

4.4 Part D

Company decided to use four high ranked criteria (service, qualitative, EMS and
financial criteria) for supplier selection, because more than four criteria make
the process too complicated and less may decrease certainty of the decision.
Description of high ranked criteria is in Table 7 .