Green supplier appraisement in fuzzy environment

Green supplier appraisementin fuzzy environment

Nitin Kumar Sahu, Saurav Datta and Siba Sankar MahapatraMechanical Engineering Department,

National Institute of Technology Rourkela, Rourkela, India

Abstract

Purpose – In recent years, stimulated environmental awareness (green consciousness) has favoredthe emergence of the green supply chain paradigm. Therefore, apart from traditional supplier selectioncriterions, green criteria are necessarily to be incorporated in the supplier selection problem. In thiscontext, the present study aims to highlight an efficient supplier appraisement platform byconsidering green performance criteria, in fuzzy environment.

Design/methodology/approach – The present work exhibits an efficient fuzzy-based supplierperformance assessment system using generalized trapezoidal fuzzy numbers set. A fuzzy overallevaluation index has been estimated towards assessing suppliers’ green performance extent, thusfacilitating supplier appraisement cum selection decision-making.

Findings – The proposed method has been found efficient for solving the group decision-makingproblem under uncertain environment due to vagueness, ambiguity associated with decision-makers’subjective judgment. The proposed appraisement platform has been explored by an Indian automobilepart manufacturing company at eastern part of India. Suppliers have been evaluated individually tocheck their performance level with respect to green attributes. Apart from estimating overallperformance metric, the model presented here can identify ill-performing areas that necessitate futureattention.

Originality/value – The major contributions of this work have been summarized as follows:Development and implementation of an efficient decision-making procedural hierarchy to supportsuppliers’ green performance extent evaluation. An overall performance metric has been introduced.Concept of generalized trapezoidal fuzzy numbers has been efficiently explored to facilitate such anappraisement cum selection decision-making. The appraisement index system has been extended withthe capability to search ill-performing areas that require future progress.

Keywords Supply chain management, Supplier evaluation

Paper type Research paper

1. Introduction and prior sate of artIn the recent era of globalization, industries are focusing more and more in satisfyingtheir customer needs via increasing their efficiencies, quality and consequently byreducing cost.

Organizations increasingly find that they must rely on effective supply chains, ornetworks, to compete in the global market and networked economy (source: http://en.wikipedia.org/wiki/Supply_chain_management).

Various factors in today’s global marketplace have forced the companies towardstaking competitive advantage, thereby focusing attention to the entire supply chainbecause of existing lesser profit margins, high customer expectations for quality

The current issue and full text archive of this journal is available at

www.emeraldinsight.com/1463-5771.htm

The authors gratefully acknowledge the support provided by Professor Gunasekaran,Editor-in-Chief, Benchmarking: An International Journal and the anonymous reviewer(s) toimprove quality of presentation of this reporting.

Received 18 June 2012Revised 23 August 2012Accepted 23 August 2012

Benchmarking: An InternationalJournalVol. 21 No. 3, 2014pp. 412-429q Emerald Group Publishing Limited1463-5771DOI 10.1108/BIJ-06-2012-0042

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products, increased corporate competitiveness and quick delivery. During recent years,how to determine suitable suppliers in the supply chain has become a key strategicconsideration; because an effective and efficient supplier selection method plays a vitalrole to the success of an organization. There are huge number of potential supplierselection criteria in traditional supply chain management such as reliability, financialstability, quality, competitive pricing, on-time delivery, etc. All are of prime importancefor an organization’s ability to produce a quality product with lesser cost and in atimely manner is heavily influenced by its suppliers’ capabilities. Of the variousactivities involved in supply chain management, environmental aspect is one of theimportant strategic issues as great environmental challenges, such as global warming,have demanded greater concern by organizations regarding their environmentalmanagement. Also, pressures from various sources such as customers and suppliers,financial institutions, regulatory authorities and public bodies (i.e. local, national,regional and global authorities and various other organizations) have also demanded toincorporate environmental aspects in supplier selection criteria process, as it plays amajor role in improving organizational environmental performance againstenvironmental challenges. Hence, involvement of environmental awareness hasencouraged the emergence and results in incorporation of the green criteria also calledgreen supplier selection criteria (GSSC) in supplier selection process.

Emphasis on GSSC is forcing the suppliers towards pollution prevention and itsreduction. It investigates possibilities for reuse, recovery, and recycling of salvage, asmuch as possible of the wastes generated. Its motto is environmental protection andresidues reduction with productivity improvement along with designing a frameworkfor toxic or hazardous substances substitution with the ultimate aim of ensuring highquality of life of product, for environmental excellence in product development, processdesign, operations, logistics, marketing, regulatory compliance, increasing efficiencyand flexibility and waste management via reflecting their great ethical image andreputation against environment consequence.

Noci (1997) designed a conceptual approach that first identified measures forassessing a supplier’s environmental performance and, second, suggested effectivetechniques for developing the supplier selection procedure according to anenvironmental viewpoint.

Angell and Klassen (1999) presented a report on the research that was done in thefield of environmental operations management. The authors developed an integratedand extended perspective of environmental operations management that could be aguidepost for future research. This perspective was structured along two dimensions:process of environmental improvement and level of analysis. Manufacturing strategy,supply chain management, technology management and quality were found areaswhere strong opportunities for gaining better understanding of environmental issuesand enhancing practice could be seen.

Jabbour and Jabbour (2009) attempted to verify if Brazilian companies wereadopting environmental requirements in the supplier selection process. Further, thispaper intended to analyze whether there was a relation between the level ofenvironmental management maturity and the inclusion of environmental criteria in thecompanies’ selection of suppliers.

Wen and Chi (2010) considered a criteria set including green, traditional, andpartnership issues for the green supplier selection problem. The criteria set took carbon

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footprint into account, because the international regulations had paid much attentionon the carbon footprint exposure in recent years. This study introduced dataenvelopment analysis (DEA) into assessment, and combined with analytical hierarchyprocess (AHP) to establish an integrated model.

Kumar and Jain (2010) proposed a comprehensive approach for suppliers’ selection,which aimed to cut across a huge variety of supplier base, cater to almost allbusinesses, was environment-friendly and robust. The approach encouraged suppliersto go green and cut down their carbon footprints in order to survive the competition.

Thongchattu and Siripokapirom (2010) contributed a green supply chain supplierselection model by using an AHP which allowed the decision maker to structure complexproblems. The framework involved a number of difference criteria based on companyreliability, material quality, material price, environmental project and standard forenvironmental management systems (ISO14000). This paper proposed the consensusfinal decision by neural network technique by minimizing a limitation error set.

Peng (2012) applied AHP and grey relational analysis (GRA) to model supplierevaluation index system in green supply chain management. Based on the complexityof the evaluation index for supplier selection in green supply chain, Li et al. (2012)attempted to develop an evaluation index system in green supply chain using BPneural network to select potential supplier with evaluation indexes as BP neuralnetwork’s input and the outcome of DEA/AHP model as BP neural networks expectedoutput. Lee et al. (2009) proposed a model for evaluating green suppliers. The Delphimethod was applied first to differentiate the criteria for evaluating traditional suppliersand green suppliers. A hierarchy was then constructed using fuzzy extended analytichierarchy process to help evaluate the importance of the selected criteria and theperformance of green suppliers. Wang et al. (2011) proposed a supplier selection systemof pharmaceutical green supplier by combining fuzzy set theory and TOPSIS methods.The validity and practicality of the research were demonstrated through a case.

The supplier selection problem involves analyzing and measuring the performanceof a set of candidate suppliers towards ranking and selecting the appropriate one forimproving the competitiveness of the whole supply system. As many conflictingfactors should be taken into account in the analysis, this problem is usually tackledusing multi-criteria group decision making (MCGDM) models. In recent years, anincreasing environmental awareness has favored the emergence of the green supplychain paradigm; therefore, in the supplier selection problem, green criteria have to beincorporated (Genovese et al., 2010).

In practice, GSSC can be considered as a model hierarchy consisting of multiplelevels of green capabilities (Level 1), green attributes (Level 2) as well as green criteria(Level 3). These are correlated in a hierarchical order and the performance of one levelinfluences the other. This necessitates estimation of a unique performance evaluationmetric towards assessment of suppliers’ overall green performance practices.

Most of the supplier selection criteria being subjective in nature, it is difficult toassign numeric score against criteria performance. Moreover, priority weights of thecriterions may vary according to the individual perception of the decision-makers (DMs).Due to uncertainty in subjective judgment of the DMs, ambiguity and fuzziness arises inthe decision-making problem. Literature depicts that such kind of inconsistency,imprecision can be overcome by representing appropriateness rating as well as weightagainst each criterion by fuzzy numbers (Ordoobadi, 2009). In this context, the present

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study highlights application of fuzzy logic towards estimating an equivalent singleperformance index of candidate suppliers in relation to suppliers’ green practices; thus,facilitating selection of the appropriate alternative amongst a set of candidate suppliers.Green supplier evaluation cum selection has been carried out by an Indian automobilesector, presented here as a case study. Apart from assessing suppliers’ overallperformance index, the proposed appraisement model has been extended to identifyill-performing areas that require future attention towards enhancement.

2. Concept of generalized trapezoidal fuzzy numbersBy the definition given by Chen (1985), a generalized trapezoidal fuzzy number can bedefined as ~A ¼ ða1; a2; a3; a4;w ~AÞ, as shown in Figure 1.

And the membership function (MF) m ~AðxÞ : R! ½0; 1� is defined as follows:

m ~AðxÞ ¼

x2 a1

a2 2 a1£ w ~A; x [ ða1; a2Þ

w ~A; x [ ða2; a3Þ

x2 a4

a3 2 a4£ w ~A; x [ ða3; a4Þ

0; x [ ð21; a1Þ< ða4;1Þ

8>>>>>>>><>>>>>>>>:

ð1Þ

Here, a1 # a2 # a3 # a4 and w ~A [ ½0; 1�.The elements of the generalized trapezoidal fuzzy numbers x [ R are real numbers,

and its MF m ~AðxÞ is the regularly and continuous convex function, it shows that the

membership degree to the fuzzy sets. If 21 # a1 # a2 # a3 # a4 # 1, then ~A is called

the normalized trapezoidal fuzzy number. Especially, if w ~A ¼ 1, then ~A is calledtrapezoidal fuzzy number (a1, a2, a3, a4); if a1 , a2 ¼ a3 , a4, then ~A is reduced to atriangular fuzzy number. If a1 ¼ a2 ¼ a3 ¼ a4, then ~A is reduced to a real number.

Suppose that ~a ¼ ða1; a2; a3; a4;w~aÞ and ~b ¼ ðb1; b2; b3; b4;w~bÞ are two generalizedtrapezoidal fuzzy numbers, then the operational rules of the generalized trapezoidalfuzzy numbers ~a and ~b are shown as follows (Chen and Chen, 2009):

Figure 1.Trapezoidal fuzzy

number ~Aa1 a2 a3 a40

x

Aw~

Am~ (x)


415

~a%~b ¼ ða1; a2; a3; a4;w~aÞ%ðb1; b2; b3; b4;w~bÞ

¼ ða1 þ b1; a2 þ b2; a3 þ b3; a4 þ b4; minðw~a;w~bÞÞð2Þ

~a2 ~b ¼ ða1; a2; a3; a4;w~aÞ2 ðb1; b2; b3; b4;w~bÞ

¼ ða1 2 b4; a2 2 b3; a3 2 b2; a4 2 b1; minðw~a;w~bÞÞð3Þ

~a^~b ¼ ða1; a2; a3; a4;w~aÞ^ðb1; b2; b3; b4;w~bÞ ¼ ða; b; c; d; minðw~a;w~bÞÞ ð4Þ

Here:

a ¼ minða1 £ b1; a1 £ b4; a4 £ b1; a4 £ b4Þ

b ¼ minða2 £ b2; a2 £ b3; a3 £ b2; a3 £ b3Þ

c ¼ maxða2 £ b2; a2 £ b3; a3 £ b2; a3 £ b3Þ

d ¼ maxða1 £ b1; a1 £ b4; a4 £ b1; a4 £ b4Þ

If a1, a2, a3, a4, b1, b2, b3, b4 are real numbers, then:

~a^~b ¼ ða1 £ b1; a2 £ b2; a3 £ b3; a4 £ b4; minðw~a;w~bÞÞ

~a=~b ¼ða1; a2; a3; a4;w~aÞ

ðb1; b2; b3; b4;w~bÞ¼ ða1=b4; a2=b3; a3=b2; a4=b1; minðw~a;w~bÞÞ ð5Þ

Chen and Chen (2003) proposed the concept of COG point of generalized trapezoidalfuzzy numbers, and suppose that the COG point of the generalized trapezoidal fuzzynumber ~a ¼ ða1; a2; a3; a4;w~aÞ is ðx~a; y~aÞ, then:

y~a ¼

w~a £ ððða3 2 a2Þ=ða4 2 a1ÞÞ þ 2Þ

6; if a1 – a4

w~a

2; if a1 ¼ a4

8>><>>:

ð6Þ

x~a ¼y~a £ ða2 þ a3Þ þ ða1 þ a4Þ £ ðw~a 2 y~aÞ

2 £ w~að7Þ

3. Revised ranking method of generalized trapezoidal fuzzy numbersThe ranking methodology adapted here has been described as follows (Chou et al.,2011). Considering n normal fuzzy numbers Ai, (i ¼ 1, 2, . . . , n), each with a trapezoidalMF fAi

(x). The revised method performs pair-wise comparisons on the n fuzzynumbers. For each pair of fuzzy numbers, say A1 and A2, the pair-wise comparison ispreceded as follows.

The maximizing set M and minimizing set G with MF fM is given as:

f M ðxÞ ¼

ðx2 xminÞ

ðxmax 2 xminÞ

� �k; xmin # x # xmax

0; Otherwise:

8>><>>:

ð8Þ

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The minimizing set G is a fuzzy subset with MF fG is given as:

f GðxÞ ¼

ðxmax 2 xÞ

ðxmax 2 xminÞ

� �k; xmin # x # xmax

0; Otherwise:

8>><>>:

ð9Þ

Here:

xmin ¼ Inf S; xmax ¼ Sup S; S ¼ Uni¼1Si; Si ¼ {x=f Ai

ðxÞ s 0};

and k is set to be 1. The revised ranking method defines the right utility values of eachalternative Ai as:

uMi1ði Þ ¼ supx f M ðxÞ ^ f

ARiðxÞ

� �; i ¼ 1; 2; ð10Þ

uGi2ði Þ ¼ supx f GðxÞ ^ f

ARiðxÞ

� �; i ¼ 1; 2: ð11Þ

The let utility values of each alternative Ai as:

uGi1ði Þ ¼ supx f GðxÞ ^ f

ALiðxÞ

� �; i ¼ 1; 2; ð12Þ

uMi2ði Þ ¼ supx f M ðxÞ ^ f

ALiðxÞ

� �; i ¼ 1; 2: ð13Þ

The revised ranking method defines the total utility value of each fuzzy number Ai

with index of optimism a as:

UaTði Þ ¼

1

2½a{uMi1

ði Þ þ 1 2 uGi2ði Þ} þ ð1 2 aÞ{uMi2

ði Þ þ 1 2 uGi1ði Þ}�; i ¼ 1; 2:

ð14Þ

The index of optimism (a) represents the degree of optimism of a DM (Kim and Park,1990; Liou and Wang, 1992; Wang and Luo, 2009). A larger a indicates a higher degreeof optimism. More specifically, when a ¼ 0, the total utility value u0

TðAiÞ representinga pessimistic DM’s viewpoint is equal to the total left utility value of Ai. Conversely, foran optimistic DM, i.e. a ¼ 1, the total utility value u1

TðAiÞ is equal to the total rightutility value of Ai. For a moderate (neutral) DM, with a ¼ 0.5, the total utility value ofeach fuzzy number Ai become:

U1=2T ði Þ ¼

1

2

1

2{uMi1

ði Þ þ 1 2 uGi2ði Þ} þ

1

2{uMi2

ði Þ þ 1 2 uGi1ði Þ}

� �; i ¼ 1; 2: ð15Þ

The greater the uaTðAiÞ, the bigger the fuzzy number Ai and the higher it is rankingorder.

As described by Chou et al. (2011), if Ai is a normal trapezoidal fuzzy number,i.e. Ai ¼ (ai, bi, ci, di; 1), the total utility value of each fuzzy number Ai can be written as:


417

uaT ði Þ ¼1

2a

di 2 xmin

di 2 ci þ xmax 2 xminþ

ci 2 xmin

ci 2 di þ xmax 2 xmin

� ��

þð1 2 aÞai 2 xmin

ai 2 bi þ xmax 2 xminþ

bi 2 xmin

bi 2 ai þ xmax 2 xmin

� �� ð16Þ

4. Proposed supplier appraisement platform: procedural hierarchy andcase studyThe green suppler evaluation index platform adapted in this paper has been shown inTable I. The two-level hierarchical model consists of various green enablers followed byseveral green attributes. Enterprise ability, service level, cooperation degree andenvironmental factors have been considered as green capabilities at the first layerfollowed by second layer which encompasses a number of attributes. An approach basedon generalized trapezoidal fuzzy numbers set has been used to evaluate an overallperformance index of candidate suppliers. This method has been found fruitful forsolving the group decision-making problem under uncertain environment due tovagueness, inconsistency and incompleteness associated with DM’s subjectiveevaluation. The proposed evaluation index platform has been explored by an Indianautomobile part manufacturing company at eastern part of India. Suppliers have beenevaluated individually to check their performance level with respect to green attributes.The analysis has been carried out using numerical illustrations on a case study.

In the primary stage, after extensive literature review and periodic discussions withthe industries top management, an integrated hierarchy model towards suppliers’assessment has been constructed and made for ready to implement. The modelencompasses of various green capabilities/attributes as well as criterions. An evaluationteam consisting of five experts (DMs) has been deployed to assign priority weights(importance extent) as well as performance ratings against different greencapabilities/attributes as well as criterions considered in the proposed appraisementmodel. A questionnaire has been formed and circulated among the DMs (experts) toprovide the required detail. During data gathering it has been assured that the datawould be strictly used for academic purpose only. Therefore, experts were requested toprovide personal opinion (without any biasness) based on their experience. The outcome

Target layer (C)Rule layer (Ci)(green capabler)

Project hierarchy (Cij)(green attributes)

Evaluation of green supplier Enterprise ability (C1) Volume flexibility (C11)Scale of production (C12)Information level (C13)

Service level (C2) Price rate (C21)Delivery time (C22)Delivery-check qualified rate (C23)

Cooperation degree (C3) On-time delivery rate (C31)Average order completion ratio (C32)

Environmental factors (C4) Content of hazardous substances (C41)Energy consumption (C42)Harmless rate (C43)

Table I.Green supplier evaluationindex system

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of this survey might be of enormous help to industries for improving productivity andprofitability of companies though effective supplier selection.

In this paper, the attribute weights and corresponding appropriateness ratings(performance estimates) of individual candidate supplier have been considered aslinguistic variables which have been further transformed into fuzzy numbers. Here, theselinguistic variables corresponding to weight assignment has been expressed in fuzzynumbers by 1-9 scale as shown in Table II. The fuzzy performance ratings of individualattributes have also been expressed in fuzzy numbers by 1-9 scale shown in Table II. Theselection of linguistic variables (which have been further converted into fuzzy numbers) isalso a managerial decision. The concept is to divide the domain [0, 1] into some fuzzyintervals represented by corresponding MFs. Better result can be expected if the domain isdivided into large intervals. In this case it has been divided into nine.

Decision science aims to determine a compromise solution while analyzing multipleevaluation criteria. Based on the information gathered, the decision-making basis andcorresponding tools are to be selected by the decision-making group. It can be set by thetop management of the organization. Different tools and techniques are available tofacilitate such decision-making; however, these tools/techniques are not free fromlimitations. The tools which are capable of analyzing quantitative measurable criteriacannot perform well with incomplete-fuzzy information data. In this context, fuzzyrepresentation of such incomplete-vague information can be fruitful in managerialdecision-making. Now, a fuzzy number is represented by its MF. MF may be triangular,trapezoidal, Gaussian type and many others. Selection of MF also depends on thediscretion of the decision-making group. Therefore, in this study trapezoidal fuzzynumber has been explored. Apart from trapezoidal fuzzy number, fuzzy numbers withother MFs can also be applied.

The procedural steps and its implementation results of the proposed model havebeen summarized as follows.

Step 1: measurement of performance ratings and importance weights of greenattributes using linguistic termsFor evaluating importance weights of green capabilities as well as attributes, acommittee of five DMs, DM1, DM2, DM3, DM4, DM5 has been formed to express theirsubjective preferences (priority importance) in linguistic terms (Table II) which havebeen further transformed into fuzzy numbers.

Linguistic terms(attribute/criteria ratings)

Linguistic terms(priority weights)

Generalized trapezoidal fuzzynumbers

Absolutely poor (AP) Absolutely low (AL) (0, 0, 0, 0; 1.0)Very poor (VP) Very low (VL) (0, 0, 0.02, 0.07; 1.0)Poor (P) Low (L) (0.04, 0.1, 0.18, 0.23; 1.0)Medium poor (MP) Medium low (ML) (0.17, 0.22, 0.36, 0.42; 1.0)Medium (M) Medium (M) (0.32, 0.41, 0.58, 0.65; 1.0)Medium good (MG) Medium high (MH) (0.58, 0.63, 0.80, 0.86; 1.0)Good (G) High (H) (0.72, 0.78, 0.92, 0.97; 1.0)Very good (VG) Very high (VH) (0.93, 0.98, 1.0, 1.0; 1.0)Absolutely good (AG) Absolutely high (AH) (1.0, 1.0, 1.0, 1.0; 1.0)

Table II.Definitions of linguistic

variables for criteriaratings (A-9 member

linguistic term set)


419

After the linguistic variables for assessing the performance ratings and importanceweights of green attributes has been accepted by the DMs, the DMs have been asked touse aforesaid linguistic scales to assess the performance rating against each of the greenattributes of candidate suppliers A, B, C and D (Tables III-VI). Similarly, fuzzy priority

Appropriateness rating expressed by linguistic variablesGreen attributes Ci Rating Ui DM1 DM2 DM3 DM4 DM5

C11 U11 VG G MG MG VGC12 U12 G G G MG MGC13 U13 M M MG M MC21 U21 MP M MG MG MGC22 U22 M MG M M MC23 U23 G G VG VG VGC31 U31 G G G G GC32 U32 MG MG M MG MGC41 U41 MP M MP MP MPC42 U42 G VG G VG GC43 U43 MG M G G G

Table III.Appropriateness ratingon green attributes givenby DMs (supplier A)


C11 U11 G G G G GC12 U12 G VG G G GC13 U13 MG G G G MGC21 U21 M MG MG MG MGC22 U22 G VG VG G VGC23 U23 MG G VG G GC31 U31 MP M M M MC32 U32 G G G MG GC41 U41 G G G G VGC42 U42 VG VG MG G GC43 U43 G G VG G G

Table IV.Appropriateness ratingon green attributes givenby DMs (supplier B)


C11 U11 MG G G G MGC12 U12 M MG MG M MC13 U13 G G G VG VGC21 U21 MG G MG G MGC22 U22 VG VG VG G GC23 U23 MG G G G GC31 U31 VG G G G GC32 U32 VG G VG G VGC41 U41 MP M M M MC42 U42 M M M M MC43 U43 MG MG MG G MG

Table V.Appropriateness ratingon green attributes givenby DMs (supplier C)

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weight of green capabilities as well as attributes has been assessed by the DMs andfurnished in Tables VII and VIII.

Step 2: approximation of the linguistic terms by generalized trapezoidal fuzzy numbersUsing the concept of generalized trapezoidal fuzzy numbers in fuzzy set theory (Chenand Chen, 2003, 2009), the linguistic variables have been be approximated by trapezoidalfuzzy numbers (Table II). Next, the aggregated decision-making cum evaluation matrixhas been constructed. The aggregated fuzzy appropriateness rating against individualgreen attributes with corresponding importance weight have been computed and shownin Tables IX-XII for suppliers A, B, C and D, respectively. Aggregated fuzzy priority


C11 U11 G G G G GC12 U12 VG VG VG G GC13 U13 G VG G VG GC21 U21 MG MG MG G VGC22 U22 VG VG VG G VGC23 U23 G G G VG GC31 U31 MG MG MG MG MGC32 U32 M MG MG MG MGC41 U41 VG VG VG VG GC42 U42 G G G G GC43 U43 VG G G VG G

Table VI.Appropriateness rating

on green attributes givenby DMs (supplier D)

Priority weight expressed in linguistic variablesGreen capablers Ci Weight wi DM1 DM2 DM3 DM4 DM5

C1 w1 VH H VH VH VHC2 w2 H VH VH H HC3 w3 H H MH H HC4 w4 VH VH H H H

Table VIII.Priority weight of greencapablers given by DMs

Priority weight expressed in linguistic variablesGreen attributes Cij Weight wij DM1 DM2 DM3 DM4 DM5

C11 w11 VH H H H VHC12 w12 MH MH H H HC13 w13 VH VH VH H VHC21 w21 M MH MH MH MHC22 w22 H MH VH VH VHC23 w23 H H H H HC31 w31 VH VH H VH VHC32 w32 H H H H HC41 w41 H VH H VH HC42 w42 MH H VH MH HC43 w43 VH VH VH H H

Table VII.Priority weight of greenattributes given by DMs


421

Greenattributes Cij

RatingUij

Aggregated rating expressed infuzzy numbers

Weightwij

Aggregated weight expressed infuzzy numbers

C11 U11 (0.72, 0.78, 0.92, 0.97, 1.00) w11 (0.80, 0.86, 0.95, 0.98, 1.00)C12 U12 (0.76, 0.82, 0.94, 0.98, 1.00) w12 (0.66, 0.72, 0.87, 0.93, 1.00)C13 U13 (0.66, 0.72, 0.87, 0.93, 1.00) w13 (0.89, 0.94, 0.98, 0.99, 1.00)C21 U21 (0.53, 0.59, 0.76, 0.82, 1.00) w21 (0.53, 0.59, 0.76, 0.82, 1.00)C22 U22 (0.85, 0.90, 0.97, 0.99, 1.00) w22 (0.82, 0.87, 0.94, 0.97, 1.00)C23 U23 (0.73, 0.79, 0.91, 0.95, 1.00) w23 (0.72, 0.78, 0.92, 0.97, 1.00)C31 U31 (0.29, 0.37, 0.54, 0.60, 1.00) w31 (0.89, 0.94, 0.98, 0.99, 1.00)C32 U32 (0.69, 0.75, 0.90, 0.95, 1.00) w32 (0.72, 0.78, 0.92, 0.97, 1.00)C41 U41 (0.76, 0.82, 0.94, 0.98, 1.00) w41 (0.80, 0.86, 0.95, 0.98, 1.00)C42 U42 (0.78, 0.83, 0.93, 0.96, 1.00) w42 (0.71, 0.76, 0.89, 0.93, 1.00)C43 U43 (0.76, 0.82, 0.94, 0.98, 1.00) w43 (0.85, 0.90, 0.97, 0.99, 1.00)

Table X.Aggregated fuzzy ratingand priority weight ofgreen attributes given byDMs (supplier B)

Greenattributes Cij

RatingUij


Weightwij



Table XI.Aggregated fuzzy ratingand priority weight ofgreen attributes given byDMs (supplier C)

Greenattributes Cij

RatingUij


Weightwij



Table IX.Aggregated fuzzy ratingand priority weight ofgreen attributes given byDMs (supplier A)

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weight of green enablers/capabilities given by DMs has also been furnished inTables XIII-XVI for suppliers A, B, C and D, respectively.

Step 3: estimation of appraisement indexFPI represents the fuzzy performance index. The FPI has been calculated at theattribute level and then extended to enabler (capabler) level. Fuzzy index system atfirst level encompasses several green enablers/capablers.

Greenattributes Cij

RatingUij


Weightwij



Table XII.Aggregated fuzzy rating

and priority weight ofgreen attributes given by

DMs (supplier D)

Greencapablers Ci

RatingUi

Computed rating expressed infuzzy numbers

Weightwi


C1 U1 (0.53, 0.64, 0.93, 1.09, 1.00) w1 (0.89, 0.94, 0.98, 0.99, 1.00)C2 U2 (0.55, 0.68, 1.06, 1.26, 1.00) w2 (0.80, 0.86, 0.95, 0.98, 1.00)C3 U3 (0.65, 0.77, 1.05, 1.20, 1.00) w3 (0.69, 0.75, 0.90, 0.95, 1.00)C4 U4 (0.34, 0.44, 0.72, 0.88, 1.00) w4 (0.80, 0.86, 0.95, 0.98, 1.00)

Table XV.Computed fuzzy rating

and aggregated fuzzypriority weight of greencapabilities (supplier C)

Greencapablers Ci

RatingUi


Weightwi


C1 U1 (0.58, 0.69, 1.01, 1.18, 1.00) w1 (0.89, 0.94, 0.98, 0.99, 1.00)C2 U2 (0.54, 0.67, 1.04, 1.23, 1.00) w2 (0.80, 0.86, 0.95, 0.98, 1.00)C3 U3 (0.38, 0.49, 0.79, 0.95, 1.00) w3 (0.69, 0.75, 0.90, 0.95, 1.00)C4 U4 (0.62, 0.74, 1.04, 1.20, 1.00) w4 (0.80, 0.86, 0.95, 0.98, 1.00)

Table XIV.Computed fuzzy rating

and aggregated fuzzypriority weight of greencapabilities (supplier B)

Greencapablers Ci

RatingUi


Weightwi

Aggregated weight expressedin fuzzy numbers

C1 U1 (0.47, 0.58, 0.89, 1.05, 1.00) w1 (0.89, 0.94, 0.98, 0.99, 1.00)C2 U2 (0.42, 0.53, 0.89, 1.08, 1.00) w2 (0.80, 0.86, 0.95, 0.98, 1.00)C3 U3 (0.52, 0.63, 0.93, 1.09, 1.00) w3 (0.69, 0.75, 0.90, 0.95, 1.00)C4 U4 (0.43, 0.53, 0.81, 0.95, 1.00) w4 (0.80, 0.86, 0.95, 0.98, 1.00)

Table XIII.Computed fuzzy rating

and aggregated fuzzypriority weight of greencapabilities (supplier A)


423

The FPI of first level green capability can be calculated as follows:

Ui ¼

Pnj¼1ðwijÛijÞPn

j¼1wij

ð17Þ

Here Uij represent aggregated performance measure (rating) and wij representaggregated fuzzy weight for priority importance corresponding to green attributes Cij

which is under ith green capability.Thus, overall FPI U(FPI) can be obtained as follows:

U ðFPI Þ ¼

Pni¼1ðwiÛiÞPn

i¼1wi

ð18Þ

Here Ui – rating of ith green capability Ci; wi – weight of ith green capability, andi ¼ 1, 2, 3, . . . , n.

The FPI thus becomes (0.374, 0.509, 0.973, 1.277, 1.000), (0.439, 0.588, 1.079, 1.397,1.000), (0.419, 0.564, 1.045, 1.356, 1.000) and (0.483, 0.637, 1.132, 1.449, 1.000) for suppliersA, B, C and D, respectively. FPI can be compared with predefined green estimate fuzzyscale set by the management to check the existing green performance level for the saidsupplier and to seek for weak performing areas which need future improvement.FPIjA, B, C, D of the candidate suppliers have been utilized to perform supplier ranking(Table XVII) and selection of the best alternative. The revised ranking method of fuzzynumbers (using maximizing and minimizing set) proposed by Chou et al. (2011) has beenutilized here to obtain total utility value of FPIjA, B, C, D. High utility value of FPIcorresponds to higher degree of performance. Based on total utility value FPIjA, B, C, D

have been ranked accordingly.

Step 4: identification of weak areas which need future improvementAfter evaluating FPI, simultaneously it is also felt indeed necessary to identify andanalyze the weak areas towards green performance improvement. fuzzy performanceimportance index (FPII) may be used to identify these ill-performing areas. FPIIcombines the performance rating and importance weight of various green attributes.

Supplier FOPI Total utility value Supplier ranking order

A (0.374, 0.509, 0.973, 1.277, 1.000) a ¼ 0 a ¼ 0.5 a ¼ 1 a ¼ 0 a ¼ 0.5 a ¼ 1B (0.439, 0.588, 1.079, 1.397, 1.000) 0.0560 0.3859 0.7159 4 4 4C (0.419, 0.564, 1.045, 1.356, 1.000) 0.1229 0.4779 0.8329 2 2 2D (0.483, 0.637, 1.132, 1.449, 1.000) 0.1023 0.4480 0.7937 3 3 3

Table XVII.Supplier rankingbased on FOPI

Greencapablers Ci Rating Ui


Weightwi


C1 U1 (0.64, 0.76, 1.05, 1.21, 1.00) w1 (0.89, 0.94, 0.98, 0.99, 1.00)C2 U2 (0.59, 0.72, 1.09, 1.28, 1.00) w2 (0.80, 0.86, 0.95, 0.98, 1.00)C3 U3 (0.46, 0.55, 0.86, 1.03, 1.00) w3 (0.69, 0.75, 0.90, 0.95, 1.00)C4 U4 (0.66, 0.77, 1.06, 1.21, 1.00) w4 (0.80, 0.86, 0.95, 0.98, 1.00)

Table XVI.Computed fuzzy ratingand aggregated fuzzypriority weight of greencapabilities (supplier D)

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The higher the FPII of a factor, the higher is the contribution. The FPII can becalculated as follows in equations (19) and (20). The concept of FPII was introduced byLin et al. (2006) for agility extent measurement in supply chain:

FPII ij ¼ w 0ijÛij ð19Þ

Here:w 0

ij ¼ ½ð1; 1; 1; 1; 1Þ2 wijk� ð20Þ

wij is the grey importance weight of jth green attribute under ith green capability.If used directly to calculate the FPII, the importance weights wij will neutralize the

performance ratings in computing FPII; in this case it will become impossible to identifythe actual weak areas (low performance rating and high importance). If wij is high, thenthe transformation [(1, 1, 1, 1; 1) 2 wij] is low. Consequently, to elicit a factor with lowperformance rating and high importance, for each green-enable-attribute Cij

( jth attribute under ith green capability), the fuzzy performance importance indexFPIIij, indicating the effect of each green-enable-attribute that contributes to FPI, hasbeen defined as:

FPII ij ¼ ½ð1; 1; 1; 1; 1Þ2 wij�Ûij ð21Þ

FPII need to be ranked to identify individual attribute’s performance level. Revisedranking method of fuzzy numbers as proposed by Chou et al. (2011) has been utilized tocompute total utility score against each of the FPII of corresponding green attributes.Based on that green attributes have been ranked accordingly and ill-performingattributes have been sorted out. In future, the particular supplier should pay attentiontowards improving those attribute aspects in order to boost up overall greenperformance extent.

FPII has been computed against each of the green attribute (for suppliers A, B, C andD, respectively) and furnished in Tables XVIII-XXV. By this way, green attributes havebeen ranked accordingly and thus, improvement opportunities have been verified.

5. Managerial implications and conclusionsIn this paper, green supplier selection has been viewed as a complex multi-attributedecision-making problem. With wave of worldwide consciousness of environmental-friendly purchasing; criterions related to green purchasing, green practices as well as green

Attributes Cij W 0ij ¼ [(1, 1, 1, 1; 1) 2 Wij] FPII (W 0

ijÛij)

C11 (0.02, 0.05, 0.14, 0.20, 1.00) (0.0135, 0.0384, 0.1266, 0.1838, 1.0000)C12 (0.07, 0.13, 0.28, 0.34, 1.00) (0.0491, 0.0922, 0.2442, 0.3111, 1.0000)C13 (0.01, 0.02, 0.06, 0.11, 1.00) (0.0022, 0.0073, 0.0374, 0.0775, 1.0000)C21 (0.18, 0.24, 0.41, 0.47, 1.00) (0.0812, 0.1230, 0.2766, 0.3446, 1.0000)C22 (0.03, 0.06, 0.13, 0.18, 1.00) (0.0126, 0.0254, 0.0811, 0.1259, 1.0000)C23 (0.03, 0.08, 0.22, 0.28, 1.00) (0.0254, 0.0720, 0.2130, 0.2766, 1.0000)C31 (0.01, 0.02, 0.06, 0.11, 1.00) (0.0043, 0.0125, 0.0552, 0.1086, 1.0000)C32 (0.03, 0.08, 0.22, 0.28, 1.00) (0.0158, 0.0469, 0.1663, 0.2290, 1.0000)C41 (0.02, 0.05, 0.14, 0.20, 1.00) (0.0036, 0.0124, 0.0566, 0.0913, 1.0000)C42 (0.07, 0.11, 0.24, 0.29, 1.00) (0.0547, 0.0963, 0.2285, 0.2887, 1.0000)C43 (0.01, 0.03, 0.10, 0.15, 1.00) (0.0073, 0.0216, 0.0828, 0.1361, 1.0000)

Table XVIII.Computation of FPII

of green attributes(supplier A)


425

cooperation must be considered and analyzed along with traditional supplier evaluationcriteria. Available decision-making tools are mostly capable of dealing with quantitative(measurable) evaluation criteria. But supplier selection problems are practically associatedwith a number of subjective criteria. Moreover, the integrated hierarchical order ofcapabilities-criterions and attributes cannot be tackled by traditional decision-making tools

Cij

Total utility valuea ¼ 0 Ranking

Total utility valuea ¼ 0.5 Ranking


C11 0.0670 6 0.2562 6 0.4453 6C12 0.1951 3 0.5058 2 0.8166 2C13 0.0073 11 0.0820 11 0.1567 11C21 0.2885 1 0.6028 1 0.9170 1C22 0.0485 7 0.1705 8 0.2924 8C23 0.1289 4 0.4224 4 0.7160 4C31 0.0178 9 0.1220 9 0.2262 9C32 0.0817 5 0.3275 5 0.5734 5C41 0.0166 10 0.1116 10 0.2065 10C42 0.2098 2 0.4833 3 0.7568 3C43 0.0351 8 0.1719 7 0.3086 7

Table XIX.Attribute ranking basedon FPIIs (supplier A)


ijÛij)

C11 (0.02, 0.05, 0.14, 0.20, 1.00) (0.0130, 0.0374, 0.1288, 0.1901, 1.0000)C12 (0.07, 0.13, 0.28, 0.34, 1.00) (0.0564, 0.1050, 0.2621, 0.3279, 1.0000)C13 (0.01, 0.02, 0.06, 0.11, 1.00) (0.0040, 0.0115, 0.0523, 0.1037, 1.0000)C21 (0.18, 0.24, 0.41, 0.47, 1.00) (0.0961, 0.1430, 0.3130, 0.3861, 1.0000)C22 (0.03, 0.06, 0.13, 0.18, 1.00) (0.0288, 0.0504, 0.1258, 0.1798, 1.0000)C23 (0.03, 0.08, 0.22, 0.28, 1.00) (0.0220, 0.0632, 0.2006, 0.2671, 1.0000)C31 (0.01, 0.02, 0.06, 0.11, 1.00) (0.0017, 0.0060, 0.0322, 0.0676, 1.0000)C32 (0.03, 0.08, 0.22, 0.28, 1.00) (0.0208, 0.0600, 0.1971, 0.2654, 1.0000)C41 (0.02, 0.05, 0.14, 0.20, 1.00) (0.0137, 0.0394, 0.1310, 0.1913, 1.0000)C42 (0.07, 0.11, 0.24, 0.29, 1.00) (0.0528, 0.0930, 0.2227, 0.2822, 1.0000)C43 (0.01, 0.03, 0.10, 0.15, 1.00) (0.0091, 0.0262, 0.0936, 0.1503, 1.0000)

Table XX.Computation of FPII ofgreen attributes(supplier B)

Cij




C11 0.0539 8 0.2293 8 0.4047 7C12 0.1960 2 0.4829 2 0.7699 2C13 0.0099 10 0.0991 10 0.1883 10C21 0.2996 1 0.6098 1 0.9200 1C22 0.0921 5 0.2398 6 0.3875 8C23 0.0966 4 0.3508 4 0.6051 4C31 20.0002 , 0 11 0.0584 11 0.1171 11C32 0.0912 6 0.3447 5 0.5982 5C41 0.0573 7 0.2333 7 0.4093 6C42 0.1769 3 0.4156 3 0.6543 3C43 0.0352 9 0.1699 9 0.3047 9

Table XXI.Attribute ranking basedon FPIIs (supplier B)

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and techniques. In practice, selection of attributes cannot be considered straightforward asthey are interconnected and correlated with capabilities as well as criterions. Therefore, anintegrated hierarchical structure followed by an efficient evaluation cum appraisementplatform is indeed essential towards estimating overall performance level of candidatesuppliers. In this study, the concept of fuzzy numbers set has been adapted to capture DMs


ijÛij)

C11 (0.02, 0.05, 0.14, 0.20, 1.00) (0.0120, 0.0346, 0.1221, 0.1815, 1.0000)C12 (0.07, 0.13, 0.28, 0.34, 1.00) (0.0314, 0.0637, 0.1870, 0.2466, 1.0000)C13 (0.01, 0.02, 0.06, 0.11, 1.00) (0.0048, 0.0138, 0.0571, 0.1100, 1.0000)C21 (0.18, 0.24, 0.41, 0.47, 1.00) (0.1158, 0.1684, 0.3511, 0.4267, 1.0000)C22 (0.03, 0.06, 0.13, 0.18, 1.00) (0.0288, 0.0504, 0.1258, 0.1798, 1.0000)C23 (0.03, 0.08, 0.22, 0.28, 1.00) (0.0208, 0.0600, 0.1971, 0.2654, 1.0000)C31 (0.01, 0.02, 0.06, 0.11, 1.00) (0.0046, 0.0131, 0.0562, 0.1093, 1.0000)C32 (0.03, 0.08, 0.22, 0.28, 1.00) (0.0254, 0.0720, 0.2130, 0.2766, 1.0000)C41 (0.02, 0.05, 0.14, 0.20, 1.00) (0.0052, 0.0179, 0.0750, 0.1184, 1.0000)C42 (0.07, 0.11, 0.24, 0.29, 1.00) (0.0218, 0.0459, 0.1392, 0.1911, 1.0000)C43 (0.01, 0.03, 0.10, 0.15, 1.00) (0.0073, 0.0211, 0.0824, 0.1358, 1.0000)

Table XXII.Computation of FPII

of green attributes(supplier C)

Cij




C11 0.0429 7 0.1943 7 0.3456 7C12 0.0994 3 0.3011 4 0.5029 4C13 0.0109 10 0.0965 10 0.1821 10C21 0.3229 1 0.6235 1 0.9240 1C22 0.0818 4 0.2152 6 0.3487 6C23 0.0811 5 0.3096 3 0.5380 3C31 0.0099 11 0.0949 11 0.1800 11C32 0.0996 2 0.3351 2 0.5707 2C41 0.0160 9 0.1156 9 0.2152 9C42 0.0679 6 0.2232 5 0.3785 5C43 0.0222 8 0.1329 8 0.2435 8

Table XXIII.Attribute ranking based

on FPIIs (supplier C)


ijÛij)

C11 (0.02, 0.05, 0.14, 0.20, 1.00) (0.0130, 0.0374, 0.1288, 0.1901, 1.0000)C12 (0.07, 0.13, 0.28, 0.34, 1.00) (0.0626, 0.1152, 0.2710, 0.3320, 1.0000)C13 (0.01, 0.02, 0.06, 0.11, 1.00) (0.0048, 0.0138, 0.0571, 0.1100, 1.0000)C21 (0.18, 0.24, 0.41, 0.47, 1.00) (0.1234, 0.1781, 0.3577, 0.4295, 1.0000)C22 (0.03, 0.06, 0.13, 0.18, 1.00) (0.0302, 0.0526, 0.1279, 0.1809, 1.0000)C23 (0.03, 0.08, 0.22, 0.28, 1.00) (0.0229, 0.0656, 0.2059, 0.2733, 1.0000)C31 (0.01, 0.02, 0.06, 0.11, 1.00) (0.0035, 0.0101, 0.0480, 0.0963, 1.0000)C32 (0.03, 0.08, 0.22, 0.28, 1.00) (0.0158, 0.0469, 0.1663, 0.2290, 1.0000)C41 (0.02, 0.05, 0.14, 0.20, 1.00) (0.0160, 0.0451, 0.1378, 0.1948, 1.0000)C42 (0.07, 0.11, 0.24, 0.29, 1.00) (0.0490, 0.0874, 0.2208, 0.2852, 1.0000)C43 (0.01, 0.03, 0.10, 0.15, 1.00) (0.0096, 0.0275, 0.0952, 0.1512, 1.0000)

Table XXIV.Computation of FPII

of green attributes(supplier D)


427

subjective judgment against qualitative performance attributes. A FPI has been defined torepresent suppliers’ existing performance extent in the context of “green cooperation”.Apart from estimating FPI, the study has been extended towards supplier ranking followedby selection of appropriate supplier from a set of alternative suppliers, in fuzzy environment.In the proposed model, performance rating as well as priority weights of individual greenattributes has been utilized to compute performance level of various green capabilities. Bythis way, large attribute set has been reduced and transformed into lesser number of greencapabilities to facilitate the decision-making process. Performance estimate of variouscapabilities have been aggregated finally to compute an overall assessment index.Aforesaid study may help the industries to judge their suppliers current environmentalperformance practices, to compare among enlisted suppliers and select the best one from thepoint of view green performance. The proposed appraisement platform may help individualsuppliers to identify ill-performing areas which require future improvement to enhanceoverall green performance extent.

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C11 0.0495 8 0.2064 8 0.3633 7C12 0.1958 2 0.4498 2 0.7037 2C13 0.0134 10 0.0982 10 0.1830 10C21 0.3431 1 0.6355 1 0.9279 1C22 0.0879 5 0.2199 7 0.3520 8C23 0.0915 4 0.3236 4 0.5556 4C31 0.0076 11 0.0822 11 0.1568 11C32 0.0631 6 0.2590 5 0.4548 5C41 0.0615 7 0.2207 6 0.3800 6C42 0.1489 3 0.3683 3 0.5877 3C43 0.0346 9 0.1559 9 0.2772 9

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Corresponding authorSaurav Datta can be contacted at: [email protected]


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Green supplier appraisement in fuzzy environment