F o i s i e S c h o o l o f B u s i n e s s | 1 0 0 I n s t i t u t e R d . | W o r c e s t e r , M A 0 1 6 0 9 5 0 8 - 8 3 1 - 5 2 1 8 | w w w . w p i . e d u / + C S B

2014

Green Government Procurement: Decision Making with Rough Set, TOPSIS, and

VIKOR Methodologies Working Paper WP4-2014

Chunguang Bai and Joseph Sarkis

Green Government Procurement: Decision Making with Rough Set,

TOPSIS, and VIKOR Methodologies

Chunguang April Bai School of Management Science and Engineering

Dongbei University of Finance & Economics Jianshan Street 217 | Dalian, 116025, P.R. China

Tel: 86-13664228458 | Fax: (86411) 87403733 E-mail: chunguang.bai@dufe.edu.cn

Joseph Sarkis Foisie School of Business

Worcester Polytechnic Institute 100 Institute Road | Worcester, MA 01609-2280

Tel: (508) 831-4831 E-mail: jsarkis@WPI.edu

OCTOBER 2014

FOR INQUIRY PLEASE REFERENCE THIS WORKING PAPER AS WP4-2014

1

INTRODUCTION

Public and private organizations have started to respond to various stakeholder and market

pressures to improve their environmental and social sustainability performance.

Government agencies represent one of the most pertinent stakeholders. . Government

stakeholder pressures to encourage greater organizational sustainability include coercive

measures such as penalties, fines, and removal of license to operate if organizations are

unable to meet specific regulatory requirements. Yet, non-coercive approaches are also

available to government agencies and regulators for encouraging the greening of

organizations and markets.

The pollution prevention act encouraged government agencies to help develop

non-coercive measures such as benchmarking and information sharing as tools to help private

and public organizations become greener. For example the U.S. government’s 33/50

program was a voluntary, non-coercive, program to help organizations improve their

pollution prevention practices and go beyond compliance to government regulations (Arora

and Cason, 1995). Another voluntary approach was through an information-based

regulatory requirement such as the toxics release inventory (TRI) program. This program

required organizations to gather and publicly release information from a listing of hazardous

materials. The only requirement was the release of this information by organizations. But,

releasing this information to the public had the potential outcome of hurting the image and

reputation of many organizations, especially those that released the largest quantities of

hazardous materials (Norberg-Bohm, 1999; Deltas et al., 2014). Many organizations then

responded by reducing their emissions.

2

One other popular method by governmental bodies to help green industry and

product/service markets, is through market mechanisms such as green (sustainable)

procurement programs (Marron, 1997). Green government procurement (GGP) is a

program designed to purchase and contract with green firms and vendors and focuses more

on the ‘carrot’ rather than ‘stick’ approach to greening organizations. There is a significant

international effort for GGP (e.g. Ho et al., 2010; Michelsen and de Boer, 2009; Preuss, 2009;

Zhu et al., 2013), and may occur at local, national, or international government agency levels.

Investigating and understanding GGP’s processes, practices, and approaches can be helpful at

a global level and is not just a localized concern.

A critical aspect to GGP is the identification and selection of appropriate vendors based

on greening and/or social metrics and not just business criteria. The research in general

green supplier selection has recognized the complexity of supplier selection when

environmental and social sustainability metrics are to be included in the decision process (Bai

and Sarkis, 2010a; Govindan et al., 2013). Government agencies may have to deal with

thousands, if not millions, of potential suppliers of a broad variety of products and services.

These additional complexities and magnitudes for GGP make the supplier selection process a

major undertaking, depending on the size of the contracts. Usually, these contracts and

decisions are not completed by individuals but may require a group decision. Thus, tools to

help aid in this complex and multi-decision maker environment can be helpful to

governmental agencies.

In addition governmental agencies may require and acquire substantial supplier

performance data comprised of many fields and dimensions. This big data set will need to

3

be filtered and evaluated, similar to data mining, to determine the most pertinent and

informative attributes. This filtration and evaluation will be critical for effective and

efficient application of the multiple decision maker, multiple criteria decision approaches.

To help meet these practical requirements, we introduce a series of tools within a broader

methodology. The tools in this chapter are meant filter out decision factors and aggregate

decision maker inputs. Using illustrative data, the focus will be on the methodological

application contributions in this chapter. Practical implications for the implementation of

these tools and methodology, especially given the GGP environment, are also discussed.

The techniques and methodology are extensible to other environments, public and private

organizations.

Contrasting GGP and corporate green supplier selection

The majority of green procurement initiatives studies have focused on private organizations

(McMurray et al, 2014). Green supply chain management in the private setting has been

synonymous with gaining competitive advantage through improving profitability of

organizations (Zhu et al, 2012). Public, governmental agencies, in response to their social

welfare mission, have implemented environmental procurement projects to further support

the greening of various industries and communities (Zhu et al, 2013; Dou et al, 2014).

Although there are similarities, it is sometimes difficult to translate private organization

procurement strategies and modes into the government procurement activities, where certain

rules and regulations bound their decision processes and approaches (Mosgaard et al, 2013).

The analysis of both GGP and corporate green supplier selection differences indicate

what might be critical factors in establishing successful GGP initiatives. First is the difference

4

of the role: GGP is important to provide leadership through internal changes to procurement

policies, procedures, and contract award criteria for supply and services contracts

(CECNA/FWI, 2003; Day, 2005). GGP plays a crucial role because the government as the

single most important customer has a significant influence over the supply base (New et al,

2002). In this regard, there is a prevalent view that “public authorities must act as ‘leaders’

in the process of changes in consumption towards greener products” (Kunzlik, 2003). The

second difference is the size of purchases: The state is usually a large-scale consumer, and

government procurements are often relatively much larger in terms of revenue. GGP of goods

and services expenditures range from 8-25 % of Gross Domestic Product (GDP) for

Organization for Economic Co-Operation and Development (OECD) member countries

(OECD, 2006). This number falls in the middle, estimated at 16 percent, for the European

Union (EU) (EC, 2004). Third is a difference in the procurement goal. GGP is utilized in

order to meet the needs of public service and public service activities while reducing damage

to the environment. The main purpose of private procurement is for profit.

Overall, two key differences have emerged between public and private sector responses

to environmental challenges: a) the effect of regulation on procurement practice and b) the

use of green supply approaches for other than immediate commercial purposes (New et al.,

2002). Another difference is that private organizational green criteria are permitted to be

more flexible, where the organizations can define their own greenness definition. The

government, on the other hand, must incorporate regulation into procurement criteria (New et

al, 2002).

5

To facilitate the GGP process, the central government should be prepared to develop

GGP indicators, criteria, and guidance. Once such tools have been developed, additional

government agencies are likely to seek official certification as a new promotion method

(Geng and Doberstein, 2008). The fourth difference is the process of green procurement:

private organizations use what control procedures they deem appropriate which is open to

considerable flexibility. The public sector, as custodians of public money, must perform

traceability and structured procedures in GGP so that all potential suppliers are treated fairly.

Although differences exist, there are also many similarities. The expressed purpose is

to green products and materials in the operations and practices of organizations, public or

private, as the most critical aspects of GGP and green procurement in general. Also, in most

GGP contexts the most obvious similarity with corporate green supplier selection is the

reliance on multiple decision criteria, formal procedures and mechanisms such as bid

tendering, competitive negotiation and group decision making.

The tools available to aid green procurement in both environments may be

interchangeable. Given the many constraints and considerations, flexible decision support

tools with multiple dimensions for consideration, and ease of use, can prove valuable. In

this chapter, one such group of tools is introduced with a focus on GGP. The tools will now

be introduced, and their illustrative applications and directions for further research and

development are summarized. We begin with a background the three major tools of rough set

theory, TOPSIS, and VIKOR.

6

ROUGH SET AND TOPSIS AND VIKOR BACKGROUND AND NOTATION

A variety of tools and techniques have been developed for green supplier and product

selection and purchase (see Govindan et al., 2013; Brandenburg et al., 2014 for overview

surveys of green supplier selection and analytical modeling). The number of tools, and their

variety, is relatively sparse for green procurement and supply chain management, especially

when compared to the number of tools and applications for basic supplier selection and

supply chain management decisions (Seuring, 2013).

Thus, in this portion of the chapter we introduce tools that have been rarely used together

for any purpose, much less green procurement. The rough set tool helps with reducing the

number of factors for consideration in this relatively complex decision environment, while

the other two tools are aggregation and decision support tools to help rank and evaluate

performance of suppliers and products. We begin with introducing Rough Set methodology

(theory) and then introduce the TOPSIS and Vikor multiple criteria decision making tools

respectively.

Rough Set Theory

Rough set theory (Pawlak, 1982) has been applied as a data-mining technique to help

evaluate large sets of data. It is a valuable tool for policy informatics, especially in the

domain of sustainability. It is a non-parametric method that can classify objects into

similarity classes containing objects that are indiscernible with respect to previous

occurrences and knowledge. It has been utilized for such diverse applications as

investigating marketing data (Shyng et al. 2007), justification for green information

7

technology (Bai & Sarkis, 2013) and more recently for sustainable supply chain and

operations management concerns Error! Reference source not found..

Rough set can integrate both tangible and intangible information, and can select

useful factors from a given information system. In the methodology presented here we

utilize rough set to reduce factors to be integrated into a multi-attribute decision making

(MADM) or multiple criteria decision making (MCDM) set of models, with specific

emphasis on GPP. Attribute reduction through rough set techniques attempts to retain

discernibility of original object factors from a larger universe of factors (Liang et al., 2012).

Heuristic attribute reduction algorithms have been developed in rough set theory to overcome

the difficulty of being computationally very expensive as with other available methods (such

as entropy and regression), especially in cases with large-scale data sets of high dimensions

(Liang et al., 2006). Thus an advantage is its capability to more efficiently utilize data for

decision making. In practical research such as use of empirical surveys makes data

collection easier since it can be used with incomplete and smaller data sets. Rough set

approaches can effectively evaluate incomplete and intangible information (Bai and Sarkis,

2011). Not only can it be used on its own as a tool, but can be integrated with other tools to

arrive at solutions in an efficient manner. Unlike tools such as regression, its

non-parametric characteristics allow for greater flexibility.

Some definitions that help to explain rough set are now introduced.

Definition 1: Let U be the universe and let R be an equivalence relation on U. For any

subset X U∈ , the pair ( , )T U R= is called an approximation space. The two subsets,

regions of a set are:

8

{ |[ ] }RRX x U x X= ∈ ⊆ (1)

{ |[ ] }RRX x U x X φ= ∈ ≠ (2)

R-lower (1) and R-upper (2) are approximations of X, respectively. Lower approximations

describe the domain objects which definitely belong to the subset of interest. Upper

approximations describe objects which may possibly belong to the subset of interest.

Approximation vagueness is usually defined by precise values of lower and upper

approximations.

The difference between the upper and the lower approximations constitutes a boundary

region for the vague set. Hence, rough set theory expresses vagueness by employing a

boundary region of a set. The R-boundary region of X is represented by expression (3).

( )RBN X RX RX= − (3)

If the boundary region of a set is empty ( ( )RBN X = 0), it means that the set is crisp,

otherwise the set is rough (inexact). In many real world applications, the boundary regions

are not always so crisp. ( )RBN X > 0 provides a rough set for evaluation.

( )RPOS X RX= is used to denote the R-positive region of X (represented by the

blackened cells in Figure 1). ( )RNEG X U RX= − is used to denote the R-negative region

of X (which is represented by the white cells in Figure 1). The cells in Figure 1 represent

objects to be evaluated, white cells are considered to be outside the rough set, black cells are

definitely within the rough set. Grey cells in Figure 1 may or may not fit within our set.

The process for the rough set approach to identify various sets is defined within the detailed

9

steps of the illustrative example. The MCDA techniques, TOPSIS and VIKOR, are now

initially introduced.

Figure 1 about here

The TOPSIS Method

The TOPSIS method, a ranking technique for order preference by similarity to an ideal

solution, takes into consideration how an object performs on the basis of multiple criteria.

TOPSIS seeks to rank units based on a shorter distance from the ideal solution and a larger

distance from the negative-ideal solution, the nadir point Error! Reference source not

found.. This method has been widely applied in the literature (Chen and Tzeng, 2004;

Opricovica and Tzeng, 2004; Krohling and Campanharo, 2011; Bai, et al., 2014).

The ideal solution is a solution that maximizes beneficial criteria, criteria which improve

as they increase in value, and minimizes unfavorable criteria, criteria which improve as they

decrease in value. The negative ideal solution maximizes the unfavorable criteria and

minimizes the beneficial criteria. Additional definitions for this methodology are now

present to further set the foundation.

Definition 2: Let S = (U, C, V, f ) be an “information system” where U is the universe, and C

is decision factor sets for U; aa A

V V∈

= indicates the factor range of factor a; :f U C V× →

is an information function, that is for x U∀ ∈ if a A∈ then ( , ) af x a V∈ .

The TOPSIS method can be expressed using the following steps:

(1) Normalize the decision matrix ( )ij n mU x ×= using expression (4):

2

1

, 1, , ; 1, ,ijij n

kjk

xv i n j m

x=

= = =

∑

(4)

10

(2) Determine the ideal (S+) and nadir (negative-ideal) (S-) solutions.

1{ , , }

{(max ), (min )},m

ij ijii

S v vv j I v j J

+ + +=

= ∈ ∈

(5)

1{ , , }

{(min ), (max )},m

ij iji i

S v vv j I v j J

− − −=

= ∈ ∈

(6)

where I is associated with benefit criteria, and J is associated with negative criteria.

(3) Calculate the separation measures using the n-dimensional Euclidian space distance.

The separation of each alternative from the ideal solution is defined by:

2

1( ) , 1, , .

m

i ij jj

v v i nµ+ +

=

= − =∑ (7)

Similarly, the separation from the nadir solution is defined by:

2

1( ) , 1, , .

m

i ij jj

v v i nµ− −

=

= − =∑ (8)

(4) Calculate the relative closeness to the ideal solution. The relative closeness of the

alternative iS with respect to S + is defined as

ii

i i

T µµ µ

−

+ −=+

(9)

(5) Rank the preference order. The larger the value of iT , the better the alternative iS .

The best alternative is the one with the greatest relative closeness to the ideal solution.

Alternatives can be ranked in decreasing order using this index Error! Reference source not

found..

VIKOR Method

The VlseKriterijumska Optimizacija I Kompromisno Resenje (VIKOR) method was

developed for multi-criteria optimization and compromise solutions of complex systems

(Opricovic and Tzeng, 2002; Opricovic & Tzeng, 2004). It is a discrete alternative multiple

11

criteria ranking and selection approach, and determines compromise solutions for a problem

with conflicting criteria. Compromise solutions can aid decision makers reach improved

final decisions. Here, the compromise ranking is a feasible solution which is the “closest”

to the ideal alternative, and a compromise means an agreement established by mutual

concessions (Opricovic & Tzeng, 2007).

The multi-criteria measure for compromise ranking is developed from the Lp-metric used

as an aggregating function in a compromise programming method (Yu, 1973). Development

of the VIKOR method starts with the following form of the Lp-metric:

1/,

1{ [ ( ) / ( )] } ,1 ; 1, , .

mp p

p i j j ij j jj

L w f f f f p i n+ + −

=

= − − ≤ ≤ ∞ =∑ (10)

where i is an alternative, for alternative i, the rating of the jth criteria is denoted by ijf ; m is

the number of criteria. Within the VIKOR method 1,iL (as iS in Eq. (11)) and ,iL∞ (as

iR in Eq. (12)) are used to formulate ranking measure.

1,1

{ [ ( ) / ( )]}, 1, , . m

i p i j j ij j jj

S L w f f f f i n+ + −=

=

= = − − =∑

(11)

, max [ ( ) / ( )], 1, , ; 1, , . i p i j j j ij j jR L w f f f f j m i n+ + −=∞= = − − = =

(12)

Both the VIKOR method and the TOPSIS method are based on an aggregating function

representing “closeness to the ideal” which originates in the compromise programming

method. These two methods introduce different forms of aggregating function for ranking

and different kinds of normalization to eliminate the units of criterion function (Opricovic

and Tzeng, 2004). The VIKOR method uses linear normalization and the TOPSIS method

uses vector normalization. For aggregating functions, the VIKOR method introduces an

aggregating function representing the distance from the ideal solution, considering the

12

relative importance of all criteria, and a balance between total and individual satisfaction. The

TOPSIS method introduces an aggregating function including the distances from the ideal

point and from the nadir point without considering their relative importance. However, the

reference point could be a major concern in decision-making, and to be as close as possible to

the ideal is the rationale of human choice (Opricovic and Tzeng, 2004).

In the proposed methodology in this chapter, TOPSIS will be used initially for single

decision maker evaluation, and later VIKOR will be used for group decision maker ranking,

which are determined from TOPSIS. TOPSIS provides an intuitive reaction foe each decision

maker evaluation for every supplier, and does not consider conflicting attributes. Later, for all

decision makers ranking values by TOPSIS, we use VIKOR to rank green suppliers and

consider conflicting decision maker evaluation and identify compromise solutions.

Triangular Fuzzy Numbers

To capture the real world uncertainties associated with managing green procurement

(governmental or otherwise), the use of fuzzy numbers will be introduced. A fuzzy number

is a convex fuzzy set characterized by a given interval of real numbers, each with a grade of

membership between 0 and 1. The most commonly used fuzzy numbers are triangular fuzzy

numbers. We now briefly introduce some basic definitions of the triangular fuzzy number

function.

Definition 3: A triangular fuzzy number x can be defined by a triplet ( , , )l m ux x x . The

membership function is defined as Error! Reference source not found., depicted as in

Figure 2.

13

( ) / ( ),1,

( )( ) / ( ),0,

l m l l m

mx

u u m m u

x x x x x x xx x

xx x x x x x x

otherwise

µ

− − ≤ < == − − < ≤

(13)

where l m ux x x≤ ≤ , and lx and ux are the lower and upper bounds of x , respectively.

mx is the mean of x .

Figure 2 about here

Obviously, if lx = mx = ux then the triangular fuzzy number x is reduced to a real

number. Conversely, real numbers may be easily rewritten as triangular fuzzy numbers.

The triangular fuzzy number can be flexible and represent various semantics of uncertainty

Error! Reference source not found.. The triangular fuzzy number is based on a

three-value judgment: the minimum possible value lx , the most possible value mx and

the maximum possible value ux .

Definition 4: Let the distance measure of two triangular fuzzy numbers ( 1 1 1 1( , , )l m ux x x x=

and 2 2 2 2( , , )l m ux x x x= ) be the Minkowski space distance represented by expression (14)

(Chen, 2000):

11 2 1 2 1 2 1 2( , ) [1 3(( ) ( ) ( ) )]p p p p

l l m m u uL x x x x x x x x= − + − + − (14)

where p is some exponential power, in our illustrative example p = 2 (quadratic power).

An illustrative example application is now introduced that brings together the various

techniques and characteristics of the green procurement decision environment.

14

AN ILLUSTRATIVE APPLICATION

The fuzzy decision table for green government procurement is introduced in this

section. Assume that a database of suppliers exists (a fuzzy table) by some government

agency. This fuzzy decision table is defined by ( , , , )T U A V f= , where 1{ , , }nU GS GS=

is a set of n alternative green suppliers called the universe. 1{ , , }mA a a= is a set of m

attributes for the suppliers. Where the f is a grey description function used to define the

values V.

For this illustrative case { , 1, ,30}iU GS i= = (i.e. thirty government suppliers)

with nine attributes { , 1, ,9}jA a i= = each. The attributes represent the three

triple-bottom-line factors for sustainability. An example set of attributes for GGP are shown

in Table 1.

Table 1 about here

For the case illustration it assumed that four decision makers { , 1, , 4}kD d k= = ,.

exist.

The multi-stage and multi-step procedure within the context of a green government

procurement is illustrative application is now introduced. There are 3 stages and 12 steps in

the methodology to arrive at our final selection and/or ranking of green suppliers. Further

details of the illustrative application are defined below.

Stage 1: Reducing attributes and determining core attribute weights.

15

In this stage we focus on the use of rough set theory to deduce the reduced set of attributes

and determining core attribute weights. This set reduction will help managers more easily

comprehend the most information bearing factors and lessen effort with the use of the other

stages of the process.

Step 1: Determine performance levels of suppliers on various sustainability factors.

From the team of decision-makers attribute values of suppliers need to be determine for each

of the sustainability attributes. The team members assign textual perceptual scores ranging

from very poor to very good for each supplier and their attributes. The seven level scale

used in this study is shown in Table 2. A fuzzy scale score v that will be assigned to each

supplier (i) by each decision maker (k) for each attribute (j) for each respective scale level is

also defined.

Table 2 about here

The textual assignments for the case example are shown in Table 3. In this step, the

decision makers evaluate the 30 suppliers on each of the nine sustainability attributes.

Table 3 about here

Step 2: Determine information content for each attribute

This step determines how the level of information content across each attribute ( ja )

using the expression (15) Error! Reference source not found.:

21 1

1( )=1 | |K n

kj i

k iI Atr a X

U = =

− ∑∑ (15)

16

In expression (15) ( )jI Atr a is the information content1 of conditional attribute

ja Atr∉ . Atr is the previous reduct set and changes in every cycle of the methodology. In

the initialization step the core conditional attribute set in the reduct set is Atr =∅ . |U| is the

cardinality of the universe (120 in the example: 30 suppliers × 4 decision makers). | |kiX

is the number of suppliers for any decision maker evaluation with the same attribute levels

across conditional attribute(s) jAtr a for a supplier i and decision maker k.

As an example, supplier 01 is ‘VG’ for decision maker 1. There are 21 suppliers with the

same value for different decision makers, thus 101| |X = 22. Thus, using expression (15) for

the original set of conditional attribute 1a is

1 22666( ) 1 0.815120

I a = − =

Step 3: Determine the information significance of a conditional attribute

For this step the information content on the null core conditional attribute set (initially for the

core conditional attribute set Atr has no attributes assigned to it) is defined. That is:

( ) 0I ∅ = .

To calculate the information significance of a conditional attribute j ( ja ) expression (16)

is used.

( ) ( ) ( )j jSig a I Atr a I Atr= − (16)

For example, the significance for the Ev1 conditional attribute can be calculated as:

1 This term has also been defined as information entropy of a system (Liang and Shi, 2004).

17

(Ev1) ( Ev1) ( )0.815 00.815

Sig I I= ∅ − ∅= −=

.Step 4: Select and update core conditional attribute set and reduct

This step requires selecting the conditional attribute ja that satisfies (17):

max ( ( ))jjSig a (17)

To update the core conditional attribute set Atr, the following rule is applied:

If max ( ( ))jjSig a ε> , whereε is a positive infinitesimal real number used to control the

convergence, then jAtr a Atr⇒ . We then return to step 2 with a new core conditional

attribute set Atr. Otherwise if max ( ( ))jjSig a ε≤ we stop and the final reduct set and core

conditional attribute set is Atr.

For the illustrative example ε = 0.001. For So1, (So1) 0.831 0.001Sig = > ， so

So1 {So1}.Atr Atr= = We then return to Step 2.

After a number of iterations the final set Atr is {So1, Ec1, So2, Ev3, Ec2}. The

reduced decision table show in Table 4.

Table 4 about here

Step 5：Determine the core attribute importance weight jw .

The importance weight for each core attribute j ( jw ) is now determined using

expression (18).

( )

( )

jj

jj Atr

I aw

I a∈

=

∑ (18)

18

The aggregated weight value meets the condition:

1jj Atr

w∈

=∑ (19)

The final adjusted attribute importance weight values are shown in Table 5.

Table 5 about here

Stage 2: Evaluating suppliers utilizing TOPSIS for each decision maker.

Step 6： Determine the core final attribute value by adjusting with the importance weight.

Considering the weights of each attribute, the weighted normalized decision matrix can

be computed by multiplying the importance weights of the evaluation attribute and the fuzzy

values in the normalized decision matrix. This step is completed with expression (20):

( , , ) , ,k k kij kij kij

ij j ij j l j m j uwv w v w v w v w v k K j Atr i n= × = × × × ∀ ∈ ∈ ∈ (20)

For the green supplier 01, attribute 3 (Ev3) for the decision maker 1 the adjusted

fuzzy value is: 1 113 3 13wv w v= × = (0.1×0.203, 0.3×0.203, 0.5×0.203) = (0.0203, 0.0609,

0.1015).

The overall adjusted aggregate attribute scores results with the decision maker 01 for

each supplier is presented in Table 6.

Table 6 about here

Step 7：Determine the ideal and nadir solution

First, the most ‘ideal’ reference solution ( )kS wv+ for decision maker k is determined by

selecting the maximum value from amongst each of the attributes using expression (21).

19

( )kS wv+ = { 1max( )kiwv ， 2max( )k

iwv ，……，max( )kimwv } (21)

Second, the most ‘nadir’ reference solution ( )kS wv− for decision maker k is determined

by selecting the minimum value from amongst each of the attributes using expression (22).

( )kS wv− = { 1min( )kiwv ， 2min( )k

iwv ，……，min( )kimwv } (22)

Using expressions (21) and (22) for this illustrative problem, two sub-steps will be

completed. First, the most ‘ideal’ reference green suppliers 1S + for the decision maker 1 is

determined to be:

1S +={(0.1827,0.203,0.203), (0.1845,0.205,0.205), (0.1295,0.1665,0.185),

(0.1854,0.206,0.206), (0.1809,0.201,0.201)}

Second, the most ‘nadir’ reference green supplier alternative 1S − for the decision

maker 1 is determined as:

1S −={ (0,0,0.0203), (0,0,0.0205), (0,0.0185,0.0555), (0,0,0.0206), (0,0,0.0201)}

Step 8：Calculate the n-dimensional distance for separation distance.

Based on the fuzzy numbers distance expression (14) and the TOPSIS separation

measure expressions (7) and (8), new separation measures are defined for an alternative

object and ‘ideal’ (expression 23) and nadir (expression 24) alternative.

( ( ), ( ))k ki k i

j AtrL S j S jµ + +

∈

= ∑ (23)

( ( ), ( ))k ki k i

j AtrL S j S jµ − −

∈

= ∑ (24)

20

For the illustrative example, an example calculation for 101µ + is shown using

expression (23).

1 101 1 1 01( ( ), ( )) 1.1398j

j AtrL S j S jµ + + +

∈

= =∑

The solutions for the alternatives’ separation distances from the ideal point are presented in

Table 7.

Step 9：Calculate the relative closeness to the ideal solution.

The relative closeness of the alternative kiS with respect to kS + is calculated using

expression (9). The relative closeness coefficient helps for rank ordering of all alternatives,

allowing the decision-makers to select the most feasible alternative. A larger for iT value

represents a more superior alternative.

Table 7 about here

Using expression (9), the final comparative distances kiT are shown in Table 7. An

example calculation for the first supplier and the decision maker 1 is presented here:

11 01

01 1 101 01

0.7186 0.5380.6164 0.7186

T µµ µ

−

+ −= = =+ +

After calculating the kiT for each decision maker k we can form the relative-closeness

matrix and the result are shown in the Table 8.

Table 8 about here

Stage 3: Ranking suppliers utilizing VIKOR for all decision makers.

Step 10: Evaluate and assign the importance level for each decision maker.

21

The importance of each decision maker and their input into the decision is defined by

kd . For the four decision makers with ( k K∈ and K=4), we have the following importance

levels respectively: 1 0.4d = , 2 0.3d = , 3d = 0.2, 4d = 0.1.

Step 11: Identify group positive ideal and group nadir solutions

First, the group positive ideal solution ( )f T+ is determined by selecting the maximum

value from amongst each of the decision makers using expression (23):

( )f T+ = { 1max( )iT ，…，max( )kiT } (23)

Second, the nadir reference solution ( )f T− is determined by selecting the minimum

value from amongst each of the decision makers using expression (24):

( )f T− = { 1min( )iT ，…，min( )kiT } (24)

Using expressions (23) and (24) for this illustrative problem, the group positive ideal

solution and nadir reference solutions are:

( )f T+={0.691, 0.694, 0.747, 0.679}

( )f T− = {0.355, 0.367, 0.345, 0.369}

Step 12: Compute the group utility iS and the maximal regret iR using expressions (23)

and (24)

1( ) / ( )

K

i k k ik k kk

S d f f f f+ + −

=

= − −∑ (25)

max( ( ) / ( ))i k k ij k kR d f f f f+ + −= − − (26)

22

where iS and iR show the mean of group utility and maximal regret, respectively. The

group utility is emphasised in the case of p = 1. The importance of maximal regret rises as the

value of parameter p increases when p = ∞.

Step 13: Compute the index values iQ using expression (27)

( ) / ( ) (1 )( ) / ( )i i iQ v S S S S v R R R R+ − + + − += − − + − − − (27)

where min iiS S+ = , max ii

S S− = , min iiR R+ = , max ii

R R− = and v is introduced as a weight

for maximum group utility, whereas 1-v is the weight of the individual regret.

The values of iS , iR and iQ are calculated for all suppliers, are shown in Table 9.

Supplier ranks, sorting by the values iS , iR and iQ , are also shown in Table 9.

Step 14: Propose a compromise solution

We propose as a compromise solution the supplier (A(1)), which is the best ranked by the

measure Q (minimum) when the following two conditions are satisfied:

C1. Acceptable advantage:

( (2)) ( (1)) ,Q A Q A DQ− ≥ (26)

where (2)A is the alternative positioned second in the ranking list by Q;

DQ=1/(U-1).

C2. Acceptable stability in decision making:

The alternative (1)A must also be the best ranked by S and/or R.

This compromise solution is stable within a decision making process, which could be the

strategy of maximum group utility (when v >0.5 is needed), or “by consensus” v ≈0.5, or

23

“with veto” (v <0.5). Here, v is the weight of the decision making strategy that provides

maximum group utility for the majority of criteria.

If one of the conditions is not satisfied, then a set of compromise solutions is proposed,

which consists of:

•Alternatives A(1) and A(2) if only the condition C2 is not satisfied, or

•Alternatives A(1), A(2), …, A(M) if the condition C1 is not satisfied; A(M) is determined by

the relation ( ( )) ( (1))Q A M Q A DQ− < for maximum M (the positions of these alternatives

are “in closeness”).

Ranking the suppliers by the VIKOR method gives, as a compromise solution for the

value v = 0.5, supplier 12. In addition, conditions C1 and C2 are satisfied as this alternative is

also the best ranked by S and R, and Q(A(27))−Q(A(12))≥DQ.

Discussion and Conclusion

The concern of green vendor selection is an important aspect to green procurement.

Although the methodology presented here can have broader application, the use of it for GPP

is clearly evident. The factors

Tools such as these can be used beyond just the selection of specific suppliers, but also

products and product families. For example in California, their green procurement system

focused on developing and ranking product characteristics and their green characteristics

when seeking to develop contracts for procurement (Swanson et al., 2005). For example,

previous government purchasing data can be used to produce a ranked list of product classes

which then can be used for prioritization and selection purposes. Part of this ranking

24

approach may utilize measures such as likelihood or probability of making an environmental

improvement impact.

More recent work on GPP has defined various processes that agencies will go through to

meet specific regulations and policies (Amman et al., 2014). These processes include

investigating whether certain GPP performance metrics, that are typically regulated, are to be

met. For example, whether policy goals are met at the tendering phase, inclusion in offers,

and general goals after delivery are met. There are various international, national, and local

regulatory policies and goals that would need to be met. Incorporating some of these

metrics into tools presented here can prove beneficial for decision makers.

Many rules and regulations also exist, where aggregation from multiple governmental

agencies would need to be involved in GGP to help manage these dispersed rules and

regulations. The use of the multiple decision maker format allows for different agencies to

effectively evaluate and aggregate the best green suppliers. Thus, application across

agencies can be practical in this situation where differing agency importance valuations can

be integrated to find the best overall suppliers.

The tools, as presented in this paper, need to be further evaluated in a practical setting.

The acquisition of data for particular attributes is not a trivial matter and may require the

development of systems to acquire such data. Many times, managers and decision makers

would like to know how the approaches work. Alternatively, very large amounts of data

may exist with government agencies. The technique is valuable in that the rough set

technique is valuable for data mining and identifying the most important and information

attributes before application of the multiple criteria decision approaches.

25

The decision methodology in this chapter uses TOPSIS in evaluating suppliers for each

decision maker and VIKOR in ranking suppliers utilizing all decision makers. In the second

stage, each decision maker evaluates suppliers based on their own unified understanding of

GGP strategy and objectives. The main goal at this stage is to rank the supplier base on the

principle that the optimal point should have the shortest distance from the positive ideal

solution (more profit) and the farthest from the negative ideal solution (avoids the most risk).

In the third stage, all decision makers evaluate suppliers based on their different

understanding of GGP strategy and objectives. The main goal in the third stage is to consider

and integrate different understanding of decision makers or managers and provide a balance

between total and individual satisfaction. VIKOR is good at determining a compromise

solution, which could be accepted by the decision makers because it provides a maximum

“group utility” of the “majority” and a minimum of the individual regret of the “opponent”

(Tzeng et al., 2005).

Both the TOPSIS and VIKOR methods are suitable for evaluating similar problems,

provide excellent results close to reality, and support superior analysis (Chu et al., 2007).

Inverting the use of these two methods or just using VIKOR or TOPSIS in both stages could

be another viable decision making methods. Our selection of TOPSIS first and VIKOR

second is a preference based on our initial thoughts on individual and group relationships, but

joint and mixed order may also be acceptable and left for future investigation.Although

TOPSIS and VIKOR are intuitive, the rough set approach may require significant explanation

to help managers understand the process. Thus, acceptance of the approach by decision

26

makers may take some convincing. Overall, the development of a decision support tool to

help in the process will make it easier for acceptance.

Thus, there is significant direction for future research and application. This chapter

only seeks to introduce this multi-stage, multi-method approach. Its application to GGP,

and general green procurement, is made evident.

27

REFERENCES

Amann, M., Roehrich, J., Eßig, M., & Harland, C. (2014). Driving Sustainable Supply Chain Management in the Public Sector: The Importance of Public Procurement in the European Union. Supply Chain Management: An International Journal, 19(3), 10-10.

Arora, S., & Cason, T. N. (1995). An Experiment in Voluntary Environmental Regulation: Participation in EPA′ s 33/50 Program. Journal of environmental economics and management, 28(3), 271-286.

Bai, C., & Sarkis, J. (2010a). Integrating sustainability into supplier selection with grey system and rough set methodologies. International Journal of Production Economics, 124(1), 252-264.

Bai, C., & Sarkis, J. (2010b). Green supplier development: analytical evaluation using rough set theory. Journal of Cleaner Production, 18(12), 1200-1210.

Bai, C., & Sarkis, J. (2011). Evaluating supplier development programs with a grey based rough set methodology. Expert Systems with Applications, 38(11), 13505-13517.

Bai, C., & Sarkis, J. (2013). Green information technology strategic justification and evaluation. Information Systems Frontiers, 15(5), 831-847.

Bai, C., Dhavale, D., & Sarkis, J. (2014). Integrating Fuzzy C-Means and TOPSIS for performance evaluation: An application and comparative analysis. Expert Systems with Applications, 41(9), 4186-4196.

Brandenburg, M., Govindan, K., Sarkis, J., & Seuring, S. (2014). Quantitative models for sustainable supply chain management: Developments and directions. European Journal of Operational Research, 233(2), 299-312.

CECNA/FWI , 2003. Green procurement: good environmental stories for North Americans. Commission for Environmental Cooperation of North American/Five Winds InternationalAccessed online on October 10, 2006 at 〈http://www.resourcesaver.org/file/toolmanager/CustomO16C45F42803.pdf〉.

Chen, M. F., & Tzeng, G. H. (2004). Combining grey relation and TOPSIS concepts for selecting an expatriate host country. Mathematical and Computer Modelling, 40(13), 1473-1490.

Chen, S. J. J., Hwang, C. L., Beckmann, M. J., & Krelle, W. (1992). Fuzzy multiple attribute decision making: methods and applications. Springer-Verlag New York, Inc..

Chu, M. T., Shyu, J., Tzeng, G. H., & Khosla, R. (2007). Comparison among three analytical methods for knowledge communities group-decision analysis. Expert systems with applications, 33(4), 1011-1024.

28

C. Day (2005). Buying green: the crucial role of public authorities Local Environment, 10 (2) (2005), pp. 201–209

Deltas, G., Harrington, D. R., & Khanna, M. (2014). Green management and the nature of pollution prevention innovation. Applied Economics, 46(5), 465-482.

Dou, Y., Sarkis, J., & Bai, C. (2014). Government Green Procurement: A Fuzzy-DEMATEL Analysis of Barriers. In Supply Chain Management Under Fuzziness (pp. 567-589). Springer Berlin Heidelberg.

European Commission (EC). (2004). Buying Green! – A Handbook on environmental public procurement. Luxembourg: Office for Official Publications of the European Communities http://ec.europa.eu/environment/gpp/buying_handbook_en.htm.

Geng, Y., & Doberstein, B. (2008). Developing the circular economy in China: Challenges and opportunities for achieving' leapfrog development'. The International Journal of Sustainable Development & World Ecology, 15(3), 231-239.

Govindan, K., Rajendran, S., Sarkis, J., & Murugesan, P. (2013). Multi criteria decision making approaches for green supplier evaluation and selection: a literature review. Journal of Cleaner Production.

New, S., Green, K., & Morton, B. (2002). An analysis of private versus public sector responses to the environmental challenges of the supply chain.Journal of Public Procurement, 2(1), 93-105.

Ho, L. W., Dickinson, N. M., & Chan, G. (2010, February). Green procurement in the Asian public sector and the Hong Kong private sector. In Natural resources forum (Vol. 34, No. 1, pp. 24-38). Blackwell Publishing Ltd.

Hwang, C. L., & Yoon, K. Multiple Attribute Decision Making: Methods and Applications, A State of the Art Survey. 1981. Sprinnger-Verlag, New York, NY.

Krohling, R. A., & Campanharo, V. C. (2011). Fuzzy TOPSIS for group decision making: A case study for accidents with oil spill in the sea. Expert Systems with Applications, 38(4), 4190-4197.

Li, D. F. (2012). A fast approach to compute fuzzy values of matrix games with payoffs of triangular fuzzy numbers. European Journal of Operational Research, 223(2), 421-429.

Liang, J., Wang, F., Dang, C., and Qian, Y. An efficient rough feature selection algorithm with a multi-granulation view. International Journal of Approximate Reasoning, 2012. 53(6), 912-926.

29

Liang, J., Z. Shi, and D. Li, Information entropy, rough entropy and knowledge granulation in incomplete information systems. International Journal of General Systems, 2006. 35(6): p. 641-654.

Marron, D. B. (1997). Buying green: Government procurement as an instrument of environmental policy. Public Finance Review, 25(3), 285-305.

McMurray, A. J., Islam, M. M., Siwar, C., & Fien, J. (2014). Sustainable procurement in Malaysian organizations: Practices, barriers and opportunities. Journal of Purchasing and Supply Management.

Michelsen, O., & de Boer, L. (2009). Green procurement in Norway; a survey of practices at the municipal and county level. Journal of Environmental Management, 91(1), 160-167.

Mosgaard, M., Riisgaard, H., & Huulgaard, R. D. (2013). Greening non-product-related procurement–when policy meets reality. Journal of Cleaner Production, 39, 137-145.

Nissinen, A., Parikka-Alhola, K., & Rita, H. (2009). Environmental criteria in the public purchases above the EU threshold values by three Nordic countries: 2003 and 2005. Ecological Economics, 68(6), 1838-1849.

Norberg-Bohm, V. (1999). Stimulating ‘green’technological innovation: an analysis of alternative policy mechanisms. Policy sciences, 32(1), 13-38.

OECD. (2006). OECD Factbook, Paris: OECD.

Ong, C. S., Huang, J. J., & Tzeng, G. H. (2005). Building credit scoring models using genetic programming. Expert Systems with Applications, 29(1), 41-47.

Opricovic, S., & Tzeng, G. H. (2002). Multicriteria planning of post‐earthquake sustainable reconstruction. Computer‐Aided Civil and Infrastructure Engineering, 17(3), 211-220.

Opricovic, S., & Tzeng, G. H. (2004). Compromise solution by MCDM methods: A comparative analysis of VIKOR and TOPSIS. European Journal of Operational Research, 156(2), 445-455.

Opricovic, S., & Tzeng, G. H. (2004). Compromise solution by MCDM methods: A comparative analysis of VIKOR and TOPSIS. European Journal of Operational Research, 156(2), 445-455.

Opricovic, S., & Tzeng, G. H. (2007). Extended VIKOR method in comparison with outranking methods. European Journal of Operational Research, 178(2), 514-529.

30

Parikka-Alhola, K. (2008). Promoting environmentally sound furniture by green public procurement. Ecological Economics, 68(1), 472-485.

Pawlak, Z. (1982). Rough sets. International Journal of Computer & Information Sciences, 11(5), 341-356.

Preuss, L. (2009). Addressing sustainable development through public procurement: the case of local government. Supply Chain Management: An International Journal, 14(3), 213-223.

Sayadi, M. K., Heydari, M., & Shahanaghi, K. (2009). Extension of VIKOR method for decision making problem with interval numbers. Applied Mathematical Modelling, 33(5), 2257-2262.

Seuring, S. (2013). A review of modeling approaches for sustainable supply chain management. Decision Support Systems, 54(4), 1513-1520.

Shyng, J. Y., Wang, F. K., Tzeng, G. H., & Wu, K. S. (2007). Rough set theory in analyzing the attributes of combination values for the insurance market. Expert Systems with Applications, 32(1), 56-64.

Swanson, M., Weissman, A., Davis, G., Socolof, M. L., & Davis, K. (2005). Developing priorities for greener state government purchasing: a California case study. Journal of Cleaner Production, 13(7), 669-677.

Tzeng, G. H., Lin, C. W., & Opricovic, S. (2005). Multi-criteria analysis of alternative-fuel buses for public transportation. Energy Policy, 33(11), 1373-1383.

Walker, H., & Brammer, S. (2009). Sustainable procurement in the United Kingdom public sector. Supply Chain Management: An International Journal,14(2), 128-137.

Yu, P. L. (1973). A class of solutions for group decision problems. Management Science, 19(8), 936-946.

Zhu, Q., Geng, Y., & Sarkis, J. (2013). Motivating green public procurement in China: An individual level perspective. Journal of environmental management, 126, 85-95.

Zhu, Q., Sarkis, J., & Lai, K. H. (2012). Green supply chain management innovation diffusion and its relationship to organizational improvement: An ecological modernization perspective. Journal of Engineering and Technology Management, 29(1), 168-185.

31

Figure 1: A graphical representation of a rough set environment.

Figure 2 A triangular fuzzy number x

RX

( )RBN X

RX The rough set X

0

1

lx ux

( )x xµ

mx x

32

Table 1: Listing of Potential Attributes for Green Government Procurement Decisions

Environmental Attributes Economic Attributes Social Attributes

Energy sources save in providing products The price of green products Customer satisfaction

Waste production in providing product Availability of spare parts and repair services Working conditions: labor standard, health and safety

Reuse and Recoverable of products Durability, adaptability, compatibility of products Operation in a safe manner

Toxic-free and Low chemical content of products Quality management Comply with labor laws

Advanced of Environmental Management System Delivery time Donates to philanthropic organizations

Comply with various environmental regulations Technical capabilities Volunteers at/for local charities

Compulsory use of environmental labels Innovativeness capabilities Organization's/Council's/ public image

Bad environmental records or reports of suppliers Contribute to the modernization and international

competitiveness of local industry

Sources: Bai and Sarkis, (2010a); McMurray et al., (2014); Michelsen & de Boer (2009); Nissinen, (2009); Parikka-Alhola, (2008); Walker & Brammer, (2009); Zhu et al., (2013)

33

Table 2.The scale of attribute ratings v Scale v Very poor (VP) (0,0,0.1) Poor (P) (0,0.1,0.3) Somewhat Fair (SF) (0.1,0.3,0.5) Fair (F) (0.3,0.5,0.7) Somewhat Good (SG) (0.5,0.7,0.9) Good (G) (0.7,0.9,1) Very Good (VG) (0.9,1,1)

34

Table 3: Evaluation of Suppliers on Sustainability Attributes by Decision Makers. Decision Maker 1 Decision Maker 2 Decision Maker 3 Decision Maker 4 Ev1 Ev2 Ev3 Ec1 Ec2 Ec3 So1 So2 So3 Ev1 Ev2 Ev3 Ec1 Ec2 Ec3 So1 So2 So3 Ev1 Ev2 Ev3 Ec1 Ec2 Ec3 So1 So2 So3 Ev1 Ev2 Ev3 Ec1 Ec2 Ec3 So1 So2 So3 Supplier 1 VG SG SF SG G SF F F F VG G F SG SG F F F F G SG SF SG SG P SF SF SF VG G SF SG SG SF SF F SF

Supplier 2 SF P G P SF VG SG G P F VP G VP F VG SG G VP SF VP G VP SF VG SG SG VP SF VP G VP F VG SG SG P

Supplier 3 VG VG SF G G G F SG P VG VG F G G G F SG P G VG SF G G G SF SG P G VG SF G G G SF SG P

Supplier 4 VG G P G F G G F VG VG G P G F G G F VG VG G P G SG G G F G VG G P G F G G F VG

Supplier 5 G VG G P G VG SF SF SF G VG G P G G F F F G VG G P G G P P P G VG G P G G SF P P

Supplier 6 P F F F P P P VP VP P F F F P P P VP VP P F SG SG P P P VP VP P F F SG P P P VP VP

Supplier 7 G SG SF SG SG P SF SF SF VG G SF SG G SF SF F F VG SG SF SG SG SF F F SF VG G F SG SG F F F F

Supplier 8 G F SF P G P VG SG SG G SG SF SF G P G F G G F F P G SF G F SG G F F F G F G F SG

Supplier 9 F G SG G SF VP SF VG G F VG F G SF VP P VG G F G F SG P VP P VG G F G F G F VP F VG G

Supplier 10 G SG SF SG SG P SF SF SF VG G SF SG G SF F F F VG SG SF SG SG SF SF F SF VG G F SG SG F F F F

Supplier 11 VP G G SF SG VP VP SF G VP G G F G VP VP F G VP G G SF G VP VP P G VP G G F G VP P SF SG

Supplier 12 G G G G F G G G VG G G G G F G G G VG G G G G SG G G G VG G G SG G F G G G VG

Supplier 13 P G VP P G SF P F VP P G VP VP G F P F VP P G VP P G P VP SG VP P G P P G P P F VP

Supplier 14 P P G G SF G F P P P P G SG F G F VP F P P G SG SF G F VP P P P G SG SF VG SG VP SF

Supplier 15 F SG P P P VG P G G F SG P P VP VG F G G F SG P P P VG P G G F SG P P P VG SF G SG

Supplier 16 VG SG VP G SG SG VG G G VG SG VP G SG SG VG G G VG SG VP G SG SG VG G G VG SG P G G SG VG G G

Supplier 17 SG F F VP P G G P VP SG F F VP VP G G VP VP SG F F VP VP G G P VP F F SF VP VP G G P P

Supplier 18 SF G SG P P G VG G VP F G SG F P G VG G VP P G F P P G VG G VP P SG SG SF VP G VG G VP

Supplier 19 P VP VP P P G P G G P VP VP VP P G F G G P VP VP VP P G P G G P VP P P P G SF G G

Supplier 20 G P VP VP G G P SF G G P VP VP G G P F G G P VP VP G G P P G G P VP VP G G P SF G

Supplier 21 VP G VG VP G SF P G F VP G VG P G F VP SG F VP G G P G P VP SG F VP G G P G SF VP F F

Supplier 22 F VP P VP G G SG VG SF SG VP P VP G G SG VG F SG VP P VP G G SG VG SF G VP SF P G G SG VG P

Supplier 23 G SG F P G SF G F SG G F SF F G P VG SG SG G F SF P G P G F SG G F F SF G F G F G

Supplier 24 VP F P VG F VP G SG SF VP F P VG F VP G SG F VP F P VG SG P G SG F P F P VG F VP G SG SF

Supplier 25 G SF SG F G G P F F VG F F SG G SG P F F VG SF F SG SG SG P F F VG SF F SG SG G P F SF

Supplier 26 P P SF VG F SG G SF G P P F VG F G G F G P P P G F G G SF G P P SF VG SG G G SF G

Supplier 27 VP P G P G G VG G G P P G F G G G G G P P G P G G G G G P P G SF G G G G G

Supplier 28 G SG F P G SF G F SG G F F F G F G F SG G F SF P G P G SG SG G F SF SF G P VG F G

Supplier 29 G P VG P SG SF VP SF SF SG P G P F F VP F F SG P G P F P VP P SF SG P G VP F P VP P SF

Supplier 30 P G P SF P F SG P F F G P F P SG SG F F SF G P SF P SG SG P F F G P SF SF SG SG SF F

35

Table 4: Evaluation of Suppliers on Reduced Attributes by Decision Makers. Decision Maker 1 Decision Maker 2 Decision Maker 3 Decision Maker 4 Ev3 Ec1 Ec2 So1 So2 Ev3 Ec1 Ec2 So1 So2 Ev3 Ec1 Ec2 So1 So2 Ev3 Ec1 Ec2 So1 So2 Supplier 1 SF SG G F F F SG SG F F SF SG SG SF SF SF SG SG SF F Supplier 2 G P SF SG G G VP F SG G G VP SF SG SG G VP F SG SG Supplier 3 SF G G F SG F G G F SG SF G G SF SG SF G G SF SG Supplier 4 P G F G F P G F G F P G SG G F P G F G F Supplier 5 G P G SF SF G P G F F G P G P P G P G SF P Supplier 6 F F P P VP F F P P VP SG SG P P VP F SG P P VP Supplier 7 SF SG SG SF SF SF SG G SF F SF SG SG F F F SG SG F F Supplier 8 SF P G VG SG SF SF G G F F P G G F F F G G F Supplier 9 SG G SF SF VG F G SF P VG F SG P P VG F G F F VG Supplier 10 SF SG SG SF SF SF SG G F F SF SG SG SF F F SG SG F F Supplier 11 G SF SG VP SF G F G VP F G SF G VP P G F G P SF Supplier 12 G G F G G G G F G G G G SG G G SG G F G G Supplier 13 VP P G P F VP VP G P F VP P G VP SG P P G P F Supplier 14 G G SF F P G SG F F VP G SG SF F VP G SG SF SG VP Supplier 15 P P P P G P P VP F G P P P P G P P P SF G Supplier 16 VP G SG VG G VP G SG VG G VP G SG VG G P G G VG G Supplier 17 F VP P G P F VP VP G VP F VP VP G P SF VP VP G P Supplier 18 SG P P VG G SG F P VG G F P P VG G SG SF VP VG G Supplier 19 VP P P P G VP VP P F G VP VP P P G P P P SF G Supplier 20 VP VP G P SF VP VP G P F VP VP G P P VP VP G P SF Supplier 21 VG VP G P G VG P G VP SG G P G VP SG G P G VP F Supplier 22 P VP G SG VG P VP G SG VG P VP G SG VG SF P G SG VG Supplier 23 F P G G F SF F G VG SG SF P G G F F SF G G F Supplier 24 P VG F G SG P VG F G SG P VG SG G SG P VG F G SG Supplier 25 SG F G P F F SG G P F F SG SG P F F SG SG P F Supplier 26 SF VG F G SF F VG F G F P G F G SF SF VG SG G SF Supplier 27 G P G VG G G F G G G G P G G G G SF G G G Supplier 28 F P G G F F F G G F SF P G G SG SF SF G VG F Supplier 29 VG P SG VP SF G P F VP F G P F VP P G VP F VP P Supplier 30 P SF P SG P P F P SG F P SF P SG P P SF SF SG SF

36

Table 5.The weight of core attributes Core Attributes

Information Content

Weight

Ev3 0.819 0.203

Ec1 0.828 0.205

Ec2 0.749 0.185

So1 0.831 0.206

So2 0.811 0.201

37

Table 6: Combined Weight Scores of Green Suppliers for Decision Maker 01 Decision Maker 1 Ev3 Ec1 Ec2 So1 So2 Supplier 1 (0.0203,0.0609,0.1015) (0.1025,0.1435,0.1845) (0.1295,0.1665,0.185) (0.0618,0.103,0.1442) (0.0603,0.1005,0.1407) Supplier 2 (0.1421,0.1827,0.203) (0,0.0205,0.0615) (0.0185,0.0555,0.0925) (0.103,0.1442,0.1854) (0.1407,0.1809,0.201) Supplier 3 (0.0203,0.0609,0.1015) (0.1435,0.1845,0.205) (0.1295,0.1665,0.185) (0.0618,0.103,0.1442) (0.1005,0.1407,0.1809) Supplier 4 (0,0.0203,0.0609) (0.1435,0.1845,0.205) (0.0555,0.0925,0.1295) (0.1442,0.1854,0.206) (0.0603,0.1005,0.1407) Supplier 5 (0.1421,0.1827,0.203) (0,0.0205,0.0615) (0.1295,0.1665,0.185) (0.0206,0.0618,0.103) (0.0201,0.0603,0.1005) Supplier 6 (0.0609,0.1015,0.1421) (0.0615,0.1025,0.1435) (0,0.0185,0.0555) (0,0.0206,0.0618) (0,0,0.0201) Supplier 7 (0.0203,0.0609,0.1015) (0.1025,0.1435,0.1845) (0.0925,0.1295,0.1665) (0.0206,0.0618,0.103) (0.0201,0.0603,0.1005) Supplier 8 (0.0203,0.0609,0.1015) (0,0.0205,0.0615) (0.1295,0.1665,0.185) (0.1854,0.206,0.206) (0.1005,0.1407,0.1809) Supplier 9 (0.1015,0.1421,0.1827) (0.1435,0.1845,0.205) (0.0185,0.0555,0.0925) (0.0206,0.0618,0.103) (0.1809,0.201,0.201) Supplier 10 (0.0203,0.0609,0.1015) (0.1025,0.1435,0.1845) (0.0925,0.1295,0.1665) (0.0206,0.0618,0.103) (0.0201,0.0603,0.1005) Supplier 11 (0.1421,0.1827,0.203) (0.0205,0.0615,0.1025) (0.0925,0.1295,0.1665) (0,0,0.0206) (0.0201,0.0603,0.1005) Supplier 12 (0.1421,0.1827,0.203) (0.1435,0.1845,0.205) (0.0555,0.0925,0.1295) (0.1442,0.1854,0.206) (0.1407,0.1809,0.201) Supplier 13 (0,0,0.0203) (0,0.0205,0.0615) (0.1295,0.1665,0.185) (0,0.0206,0.0618) (0.0603,0.1005,0.1407) Supplier 14 (0.1421,0.1827,0.203) (0.1435,0.1845,0.205) (0.0185,0.0555,0.0925) (0.0618,0.103,0.1442) (0,0.0201,0.0603) Supplier 15 (0,0.0203,0.0609) (0,0.0205,0.0615) (0,0.0185,0.0555) (0,0.0206,0.0618) (0.1407,0.1809,0.201) Supplier 16 (0,0,0.0203) (0.1435,0.1845,0.205) (0.0925,0.1295,0.1665) (0.1854,0.206,0.206) (0.1407,0.1809,0.201) Supplier 17 (0.0609,0.1015,0.1421) (0,0,0.0205) (0,0.0185,0.0555) (0.1442,0.1854,0.206) (0,0.0201,0.0603) Supplier 18 (0.1015,0.1421,0.1827) (0,0.0205,0.0615) (0,0.0185,0.0555) (0.1854,0.206,0.206) (0.1407,0.1809,0.201) Supplier 19 (0,0,0.0203) (0,0.0205,0.0615) (0,0.0185,0.0555) (0,0.0206,0.0618) (0.1407,0.1809,0.201) Supplier 20 (0,0,0.0203) (0,0,0.0205) (0.1295,0.1665,0.185) (0,0.0206,0.0618) (0.0201,0.0603,0.1005) Supplier 21 (0.1827,0.203,0.203) (0,0,0.0205) (0.1295,0.1665,0.185) (0,0.0206,0.0618) (0.1407,0.1809,0.201) Supplier 22 (0,0.0203,0.0609) (0,0,0.0205) (0.1295,0.1665,0.185) (0.103,0.1442,0.1854) (0.1809,0.201,0.201) Supplier 23 (0.0609,0.1015,0.1421) (0,0.0205,0.0615) (0.1295,0.1665,0.185) (0.1442,0.1854,0.206) (0.0603,0.1005,0.1407) Supplier 24 (0,0.0203,0.0609) (0.1845,0.205,0.205) (0.0555,0.0925,0.1295) (0.1442,0.1854,0.206) (0.1005,0.1407,0.1809) Supplier 25 (0.1015,0.1421,0.1827) (0.0615,0.1025,0.1435) (0.1295,0.1665,0.185) (0,0.0206,0.0618) (0.0603,0.1005,0.1407) Supplier 26 (0.0203,0.0609,0.1015) (0.1845,0.205,0.205) (0.0555,0.0925,0.1295) (0.1442,0.1854,0.206) (0.0201,0.0603,0.1005) Supplier 27 (0.1421,0.1827,0.203) (0,0.0205,0.0615) (0.1295,0.1665,0.185) (0.1854,0.206,0.206) (0.1407,0.1809,0.201) Supplier 28 (0.0609,0.1015,0.1421) (0,0.0205,0.0615) (0.1295,0.1665,0.185) (0.1442,0.1854,0.206) (0.0603,0.1005,0.1407) Supplier 29 (0.1827,0.203,0.203) (0,0.0205,0.0615) (0.0925,0.1295,0.1665) (0,0,0.0206) (0.0201,0.0603,0.1005) Supplier 30 (0,0.0203,0.0609) (0.0205,0.0615,0.1025) (0,0.0185,0.0555) (0.103,0.1442,0.1854) (0,0.0201,0.0603)

38

Table 7: The Relative Closeness of Green Suppliers for Decision Maker 01

1iµ+

1iµ−

1iT

Supplier 1 1.140 1.549 0.576 Supplier 2 1.113 1.576 0.586 Supplier 3 0.917 1.772 0.659 Supplier 4 1.116 1.573 0.585 Supplier 5 1.387 1.302 0.484 Supplier 6 2.056 0.633 0.235 Supplier 7 1.477 1.213 0.451 Supplier 8 1.079 1.610 0.599 Supplier 9 0.950 1.739 0.647 Supplier 10 1.477 1.213 0.451 Supplier 11 1.542 1.147 0.426 Supplier 12 0.448 2.241 0.833 Supplier 13 1.877 0.812 0.302 Supplier 14 1.228 1.461 0.543 Supplier 15 2.002 0.687 0.255 Supplier 16 0.783 1.906 0.709 Supplier 17 1.830 0.860 0.320 Supplier 18 1.142 1.547 0.575 Supplier 19 2.063 0.626 0.233 Supplier 20 2.059 0.630 0.234 Supplier 21 1.149 1.540 0.573 Supplier 22 1.246 1.443 0.537 Supplier 23 1.140 1.549 0.576 Supplier 24 0.934 1.755 0.653 Supplier 25 1.246 1.443 0.537 Supplier 26 1.073 1.616 0.601 Supplier 27 0.634 2.055 0.764 Supplier 28 1.140 1.549 0.576 Supplier 29 1.584 1.105 0.411 Supplier 30 1.992 0.697 0.259

39

Table 8:

Decision

Maker 1

Decision

Maker 2

Decision

Maker 3

Decision

Maker 4

Supplier 1 0.538 0.548 0.486 0.509

Supplier 2 0.543 0.557 0.524 0.545

Supplier 3 0.582 0.61 0.569 0.569

Supplier 4 0.543 0.547 0.576 0.554

Supplier 5 0.492 0.542 0.465 0.484

Supplier 6 0.357 0.367 0.422 0.397

Supplier 7 0.475 0.52 0.532 0.555

Supplier 8 0.55 0.539 0.549 0.594

Supplier 9 0.575 0.536 0.506 0.61

Supplier 10 0.475 0.543 0.509 0.555

Supplier 11 0.463 0.53 0.472 0.526

Supplier 12 0.691 0.694 0.747 0.679

Supplier 13 0.397 0.392 0.421 0.421

Supplier 14 0.522 0.517 0.502 0.525

Supplier 15 0.369 0.414 0.382 0.404

Supplier 16 0.609 0.613 0.622 0.659

Supplier 17 0.407 0.391 0.407 0.381

Supplier 18 0.538 0.585 0.526 0.558

Supplier 19 0.355 0.4 0.354 0.404

Supplier 20 0.356 0.392 0.345 0.369

Supplier 21 0.536 0.522 0.517 0.495

Supplier 22 0.518 0.523 0.529 0.56

Supplier 23 0.538 0.598 0.526 0.569

Supplier 24 0.578 0.582 0.614 0.59

Supplier 25 0.518 0.523 0.512 0.512

Supplier 26 0.551 0.603 0.531 0.584

Supplier 27 0.643 0.687 0.642 0.668

Supplier 28 0.538 0.586 0.549 0.558

Supplier 29 0.455 0.452 0.413 0.4

Supplier 30 0.372 0.449 0.384 0.425

40

Table 9:

S Ranking

R Ranking

Q Ranking

Supplier 01 0.429 14 0.455 11 0.442 14 Supplier 02 0.391 13 0.44 9 0.415 13 Supplier 03 0.284 4 0.326 4 0.305 4 Supplier 04 0.374 12 0.441 10 0.408 11 Supplier 05 0.497 21 0.592 19 0.545 19 Supplier 06 0.815 28 0.995 28 0.905 28 Supplier 07 0.483 20 0.642 21 0.562 21 Supplier 08 0.374 11 0.42 8 0.397 8 Supplier 09 0.364 9 0.361 6 0.363 6 Supplier 10 0.475 19 0.642 20 0.558 20 Supplier 11 0.521 22 0.679 22 0.6 22 Supplier 12 0 1 0 1 0 1 Supplier 13 0.748 25 0.876 25 0.812 25 Supplier 14 0.459 18 0.504 16 0.481 17 Supplier 15 0.78 27 0.958 27 0.869 27 Supplier 16 0.206 3 0.243 3 0.224 3 Supplier 17 0.756 26 0.847 24 0.801 24 Supplier 18 0.369 10 0.456 14 0.413 12 Supplier 19 0.817 29 1 30 0.909 29 Supplier 20 0.836 30 0.997 29 0.917 30 Supplier 21 0.442 16 0.46 15 0.451 15 Supplier 22 0.436 15 0.514 18 0.475 16 Supplier 23 0.356 7 0.455 12 0.405 9 Supplier 24 0.284 5 0.336 5 0.31 5 Supplier 25 0.457 17 0.514 17 0.485 18 Supplier 26 0.333 6 0.417 7 0.375 7 Supplier 27 0.102 2 0.143 2 0.122 2 Supplier 28 0.359 8 0.455 13 0.407 10 Supplier 29 0.651 23 0.702 23 0.676 23 Supplier 30 0.743 24 0.951 26 0.847 26