Research ArticleA Fuzzy MCDM Approach for Green Supplier Selection fromthe Economic and Environmental Aspects

Hsiu Mei Wang Chen1 Shuo-Yan Chou1 Quoc Dat Luu2 and Tiffany Hui-Kuang Yu3

1Department of Industrial Management National Taiwan University of Science and Technology No 43 Section 4Keelung Road Darsquoan District Taipei 10607 Taiwan2University of Economics and Business Vietnam National University 144 XuanThuy Hanoi Vietnam3Department of Public Finance Feng Chia University Taichung Taiwan

Correspondence should be addressed to Hsiu Mei Wang Chen gracesmc1gmailcom

Received 22 October 2015 Revised 26 January 2016 Accepted 31 January 2016

Academic Editor Young Hae Lee

Copyright copy 2016 Hsiu Mei Wang Chen et al This is an open access article distributed under the Creative Commons AttributionLicense which permits unrestricted use distribution and reproduction in any medium provided the original work is properlycited

Due to the challenge of rising public awareness of environmental issues and governmental regulations green supply chainmanagement (SCM) has become an important issue for companies to gain environmental sustainability Supplier selection isone of the key operational tasks necessary to construct a green SCM To select the most suitable suppliers many economic andenvironmental criteria must be considered in the decision process Although numerous studies have used economic criteria suchas cost quality and lead time in the supplier selection process only some studies have taken into account the environmental issuesThis study proposes a comprehensive fuzzy multicriteria decision making (MCDM) approach for green supplier selection andevaluation using both economic and environmental criteria In the proposed approach a fuzzy analytic hierarchy process (AHP)is employed to determine the important weights of criteria under vague environment In addition a fuzzy technique for orderperformance by similarity to ideal solution (TOPSIS) is used to evaluate and rank the potential suppliers Finally a case study inLuminance Enhancement Film (LEF) industry is presented to illustrate the applicability and efficiency of the proposed method

1 Introduction

The change of climate and the escalation in global warm-ing have driven increasing worldwide concern about theenvironmental protection To gain and retain competitiveadvantages in the global market firms have started to focuson the development of green products to satisfy customerenvironmental needs and requirements [1] Consequentlygreen supply chain management (SCM) development withenvironmental thinking and strategies has become an impor-tant task for firms [2]

Green supplier selection is a critical activity because theenvironmental performance of the supply chain is affectedsignificantly by its constituent supplier [3 4] Environmentaland economic dimensions must be considered simultane-ously when firms select a suitable supplier [5] The greensuppliers are chosen and must fit a firmrsquos expectations andobjectives so as to minimize negative environmental impact

and maximize economic performance Thus the green sup-plier selection process integrates environmental concernsinto the interorganizational practices of SCM includingreverse logistics [6]

Despite the growing work of green SCM however exis-tent researches generally concentrate mainly on decisionmaking techniqueswith complicatedmathematical computa-tionalmodels in supplier selection problem In addition con-sider environmental aspects in isolated way [7] The imple-mentation of green supply management is not well under-stood and understanding the environmental sustainabilitypractices involving SCM activities is still limited [8] There-fore more researches are needed to answer how companiesactually carry out green supplier selection [9] consideringenvironmental and economic aspects simultaneously

In recent years TOPSIS (technique for order perfor-mance by similarity to ideal solution) proposed by Shih et al[10] has been a popular technique to solveMCDMproblems

Hindawi Publishing CorporationMathematical Problems in EngineeringVolume 2016 Article ID 8097386 10 pageshttpdxdoiorg10115520168097386

2 Mathematical Problems in Engineering

The fundamental idea of TOPSIS is that the chosen alternativeshould have the shortest Euclidian distance from the positive-ideal solution and the farthest distance from the negative-ideal solution The positive-ideal solution is a solution thatmaximizes the benefit criteria andminimizes the cost criteriawhereas the negative ideal solution maximizes the costcriteria and minimizes the benefit criteria In the classicalTOPSIS method the weights of the criteria and the ratingsof alternatives are known precisely and crisp values are usedin the evaluation process Under many circumstances how-ever crisp data are inadequate to simulate real-life decisionproblems Consequently a fuzzy TOPSISmethod is proposedto deal with the deficiency in the traditional TOPSIS Themethodbased on theweights of criteria and ratings of alterna-tives are evaluated by linguistic variables represented by fuzzynumbers Some advantages of the TOPSIS [11] and fuzzyTOPSIS method include the following (i) a sound logic thatembodies rational human choice (ii) a simple computationprocess that can be used and programmed easily (iii) thenumber of steps that remains the same regardless of thenumber of attributes (iv) a scalar value that accounts for boththe best and worst alternatives at the same time As a resultfuzzy TOPSIS approach has been broadly applied to decision-making applications over the past few decades

Several studies in the literature have mentioned thedifficulty of weighting the criteria and keeping consistency ofjudgment when using fuzzy TOPSIS Thus the combinationof the fuzzy TOPSIS with another method such as fuzzyanalytic hierarchy process (AHP) might be able to determineproper objective weightings under a vague environmentTheAHP a powerful tool in applying MCDA was introducedand developed by Buyukozkan and Cifci [12]The AHP helpsidentify theweights or priority vector of the alternatives or thecriteria using a hierarchical model that includes target maincriteria subcriteria and alternatives Nevertheless a majordisadvantage of AHP is that it is unable to handle adequatelythe inherent uncertainty and imprecision of human thinkingFuzzy AHP has been developed to solve this problem [13] InFAHP method the application of the fuzzy comparison ratiotolerates vagueness in themodel Decisionmakers use naturallinguistic emphasis as well as certain numbers to evaluatecriteria and alternatives Fuzzy AHP impressively resembleshuman thought and perception In the literature manystudies have used either fuzzy TOPSIS or fuzzyAHPmethodsto select and evaluate the suppliers [14ndash19] However fewstudies have proposed an integrated fuzzy MCDM approachfor suppliers selection and evaluation especially in the caseof green suppliers

This paper proposes an integrated fuzzy multicriteriadecision making (MCDM) approach to solve problemsof green supplier selection and supply chain constructionsimultaneously effectively and efficiently To address theresearch need we leverage a small and medium sized hightech company to draw a case study of an actual greensupplier selection and green SCM experience of a Taiwaneseoptical prism manufacturing entity (hereinafter referred toas TOP a pseudonym) in the Luminance EnhancementFilm (LEF) industry The company was selected because therapidly changing environment of the optical prism industry

forces firm to develop ongoing sustainable capabilities and torespond to the uncertain environment

The remainder of this paper is organized as follows InSection 2 green supplier selection criteria and method liter-ature is reviewed The basic concepts of fuzzy numbers areshown in Section 3 The integrated fuzzy MCDM approachis proposed in Section 4 Section 5 applies the proposedapproach to a real case Concluding remarks are presented inSection 6

2 Literature Review on Green SupplierSelection Criteria and Methods

As a result of escalated global warming and increasing envi-ronmental protection awareness EU environmental orderssuch as RoHS WEEE ErP and REACH have been enforcedThe supply chains of firm and the products are requiredto become more ecofriendly especially in the electronicsindustryThe circumstance has driven supply chains not onlyto comply with environmental policies but also to enforcefirms govern their own corporate environmental policies tosustain in the global market

Green SCM has become a strategy to improve a firmrsquosenvironmental and economic performance [25 38] Procure-ment constitutes one of the key strategic functions in SCMSelecting the right supplier gives the firm a competitive edgeto either reduce costs enhance the quality [39] or minimizenegative environmental impact avoiding violating relevantlegislation [20]

In practice when a firm is purchasing the professionalpurchaser chooses the favorite suppliers on the basis ofspecifications and conditions A firm primarily prioritizeseconomic criteria such as cost quality delivery and flexibil-ityThe environmental certificate of ISO 14000 as one of envi-ronmental criteria is usually applied for purchaser referenceonly Efficient evaluation criteria can help the firm to reducethe risks associated with suppliers [21] Current literaturesaddress themost popular economic criteria considered by thedecision makers for supplier selection and evaluation whichare quality [4 12 22 23 25] cost [20ndash24] delivery [21 23 2627] flexibility [22 28 29] and relationship [23 28 29] Envi-ronmental criteria are environmental management system[2 19 28 32ndash34 36 37] green competencies [2 33 34 36 37]and ecodesign [28 32 34 35] Few studies simultaneouslyconsidered economic and environmental aspects for greensupplier selection

Currently environmental factors play a vital role for thelong term success of a supply chain and the purchasingprocess has become more complicated with environmentalconsideration [3] Several studies have examined the criteriaof supplier selection and focused on different approaches orcriteria Table 1 presents the most commonly used criteriain the literature to evaluate the environmental and economicperformance of green supplier selection

In the literature numerous techniques have been devel-oped to select the most suitable suppliers or green suppliersbased on specific methods including fuzzy AHP [3 40ndash43]analytic network process (ANP) [6 29] data envelopmentanalysis (DEA) [6] MCDM approach [13 21 31 33 44ndash47]

Mathematical Problems in Engineering 3

Table 1 Green supplier selection and evaluation criteria

Criteria Subcriteria Sub-subcriteriadefinition References

Economic criteria

Cost Product price logistics cost and payment terms [20ndash24]

Quality ISO quality system installed quality award product performancewarranties and claim policies and repair and return rate [4 12 22 23 25]

Delivery Lead time on-time delivery safety and security of components andappropriateness of the packaging [21 23 26 27]

Technology Communication and e-commerce systems capability of researchdevelopment and innovation and production facilities and capacity [22 23 26]

Flexibility

Product volume changes short setup time conflict resolution usingflexible machines the demand that can be profitably sustained andtime or cost required to add new products to the existing productionoperation

[22 28 29]

Financialcapability Financial position economical stability and price strategy [12 23 30]

Culture Communication openness vendorrsquos image and mutual trust [20 23 27]Innovativeness New launch of products and new launch of technologies [31]

Relationship Long term relationship relationship closeness communicationopenness and reputation for integrity [23 28 29]

Environmental criteria

Pollutionproduction

Average volume of air pollutants waste water solid waste andharmful materials released [19 22 32]

Pollutioncontrol Remediation and end-of-pipe controls [2 19 33]

Resourceconsumption Consumption of resources in terms of raw material energy and water [19 32]

EcodesignDesign for resource efficiency design of products for reuse recycleand recovery of material design for reduction or elimination ofhazardous materials

[28 32 34 35]

Environmentalmanagementsystem

Environmental certificates such as ISO 14000 continuous monitoringand regulatory compliance environmental policies green processplanning and internal control process

[2 19 28 32ndash34 36 37]

Green image Ratio of green customers to total customers and social responsibility [2 33 35]

Greencompetencies

Materials used in the supplied components that reduce the impact onnatural resources and ability to alter process and product for reducingthe impact on natural resources

[2 33 34 36 37]

Green product Use of recycled and nontoxic materials green packaging and excesspackaging reduction [6 34 36]

Staffenvironmentaltraining

Staff training on environmental issues [36]

Managementcommitment

Commitment of senior managers to support and improve greensupply chain management initiatives [34 36]

GreenTechnology

The application of the environmental science to conserve the naturalenvironment and resources and to curb the negative impact of humaninvolvement

[6 34]

structural equation modeling and fuzzy logic [23] optimummathematical planning model [35] linguistic preferences[28] fuzzy linguistic computing approach [27] Fuzzy Adap-tive ResonanceTheory algorithm [30] and genetic algorithm(GA) [48]

Although a number of methods have been studiedmost of the studies have only used either economic orenvironmental criteria for evaluating the suppliers Thereare few studies considering economic and environmentalcriteria simultaneously in the supplier selection process

And each of those methods has its own advantages anddisadvantages this study proposes the integrated approachby combining the two most popular techniques for solvinggreen supplier problems that is fuzzy TOPSIS and fuzzyAHP In the proposed approach the fuzzy AHP is employedto determine the important weights of criteria under vagueenvironmentThen the fuzzy TOPSIS is used to evaluate andrank the potential suppliers In addition both economic andenvironmental criteria are considered in proposed MCDMapproach

4 Mathematical Problems in Engineering

3 Fuzzy Numbers

There are various ways to define fuzzy numbers This paperdefines the concept of fuzzy numbers as follows [49 50]

Definition 1 A real fuzzy number119860 is described as any fuzzysubset of the real line 119877with membership function119891

119860 which

has the following properties

(a) 119891119860is a continuous mapping from 119877 to the closed

interval [0 1](b) 119891119860(119909) = 0 for all 119909 isin (minusinfin 119886]

(c) 119891119860is strictly increasing on [119886 119887]

(d) 119891119860(119909) = 1 for all 119909 isin [119887 119888]

(e) 119891119860is strictly decreasing on [119888 119889]

(f) 119891119860(119909) = 0 for all 119909 isin (119889infin]

where 119886 119887 119888 and 119889 are real numbers Unless elsewherespecified this research assumes that119860 is convex and bounded(ie minusinfin lt 119886 119889 lt infin)

Definition 2 The fuzzy number 119860 = [119886 119887 119888 119889] is a trape-zoidal fuzzy number if its membership function is given by

119891119860 (119909) =

119891119871

119860(119909) 119886 le 119909 le 119887

1 119887 le 119909 le 119888

119891119877

119860(119909) 119888 le 119909 le 119889

0 otherwise

(1)

where 119891119871119860(119909) and 119891

119877

119860(119909) are the left and right membership

functions of 119860 respectively [50]When 119887 = 119888 the trapezoidal fuzzy number is reduced

to a triangular fuzzy number and can be denoted by 119860 =

(119886 119887 119889) Thus triangular fuzzy numbers are special cases oftrapezoidal fuzzy numbers

Definition 3 (the distance between fuzzy triangular numbers)Let119860 = (119886

1 1198871 1198891) and119861 = (119886

2 1198872 1198892) be two triangular fuzzy

numbersThedistance between them is given using the vertexmethod by

119889 (119860 119861) = radic1

3[(1198861minus 1198862)2+ (1198871minus 1198872)2+ (1198891minus 1198892)2] (2)

Definition 4 (120572-cuts) The 120572-cuts of fuzzy number 119860 can bedefined as 119860120572 = 119909 | 119891

119860(119909) ge 120572 120572 isin [0 1] where 119860120572

is a nonempty bounded closed interval contained in 119877 andcan be denoted by 119860120572 = [119860

120572

119897 119860120572

119906] where 119860120572

119897and 119860120572

119906are its

lower and upper bounds respectively [50] For example if atriangular fuzzy number 119860 = (119886 119887 119889) then the 120572-cuts of 119860can be expressed as follows

119860120572= [119860120572

119897 119860120572

119906] = [(119887 minus 119886) 120572 + 119886 (119887 minus 119889) 120572 + 119889] (3)

Definition 5 (arithmetic operations on fuzzy numbers)Given fuzzy numbers 119860 and 119861 where 119860 119861 isin 119877

+ the 120572-cutsof119860 and 119861 are119860120572 = [119860

120572

119897 119860120572

119906] and 119861120572 = [119861

120572

119897 119861120572

119906] respectively

By the interval arithmetic some main operations of 119860 and 119861can be expressed as follows [50]

(119860 oplus 119861)120572= [119860120572

119897+ 119861120572

119897 119860120572

119906+ 119861120572

119906]

(119860 ⊖ 119861)120572= [119860120572

119897minus 119861120572

119906 119860120572

119906minus 119861120572

119897]

(119860 otimes 119861)120572= [119860120572

119897sdot 119861120572

119897 119860120572

119906sdot 119861120572

119906]

(119860 ⊘ 119861)120572= [

119860120572

119897

119861120572119906

119860120572

119906

119861120572

119897

]

(119860 otimes 119903)120572= [119860120572

119897sdot 119903 119860120572

119906sdot 119903] 119903 isin 119877

+

(4)

4 Proposed Approach forGreen Suppliers Selection

In this section an approach for green supplier selection bycombining fuzzy TOPSIS and fuzzy AHP method is pre-sented The proposed approach offers a new way to solve thegreen supplier selection problem effectively and efficientlysince it enables decision makers to minimize the negativeenvironmental impact of the supply chain while simultane-ously maximizing business performance The procedure ofthe proposed approach is stated as follows

Step 1 Identify a number of economic and environmentalcriteria

Step 2 Aggregate the important weights of the criteria

Step 3 Aggregate the ratings of suppliers versus the criteria

Step 4 Normalize the fuzzy decision matrix

Step 5 Construct the weighted normalized fuzzy decisionmatrix

Step 6 Calculate normalized weighted rating

Step 7 Calculate 119860+ 119860minus 119889+119894 and 119889minus

119894

Step 8 Obtain the closeness coefficient

Assume that a committee of 119897decisionmakers (119863119905 119905 = 1 sim

119897) is responsible for evaluating 119898 suppliers (119860119894 119894 = 1 sim 119898)

under 119899 selected criteria (119862119895 119895 = 1 sim 119899) where the suitability

ratings of alternatives under each of the criteria as well as theweights of the criteria are assessed in linguistic terms [51 52]represented by triangular fuzzy numbers

41 Identify a Number of Economic and EnvironmentalCriteria In this study the criteria are classified into twocategories that is economic criteria (119862

119895 119895 = 1 119897) and

environmental criteria (119862119895 119895 = 119897 + 1 119899) The number of

economic and environmental criteria is selected from Table 1through screening by the decision makers

42 Aggregate the Important Weights of the Criteria In thissection a fuzzy AHP is applied to obtain more decisivejudgments by prioritizing the economic and environmental

Mathematical Problems in Engineering 5

criteria Several fuzzy AHP methods have been proposed inliterature to solve the MCDM problems This study adoptsthe extent analysis method proposed by Chang [53] dueto its popularity and computational simplicity Changrsquos [53]method is briefly discussed as follows

Let 119883 = 1199091 1199092 119909

119899 be an object set and let 119880 =

1199061 1199062 119906

119898 be a goal set According to Chang [53] each

object is taken and an extent analysis for each goal (119892119894)

is performed respectively Therefore the 119898 extent analysisvalues for each object are obtained as1198721

1198921198941198722

119892119894 119872

119899

119892119894 119894 =

1 2 119899 where 119872119895119892119894(119895 = 1 2 119898) are triangular fuzzy

numbers (TFNs)Assume that 119872119895

119892119894are the values of extent analysis of the

119894th object for119898 goalsThe value of fuzzy synthetic extent 119878119894is

defined as follows

119878119894=

119898

sum

119895=1

119872119895

119892119894otimes [

[

119899

sum

119894=1

119898

sum

119895=1

119872119895

119892119894

]

]

minus1

(5)

where sum119898

119895=1119872119895

119892119894= (sum

119898

119895=1119897119895 sum119898

119895=1119898119895 sum119898

119895=1119906119895) 119895 = 1 2

119898 119894 = 1 2 119899

Let1198721= (1198971 1198981 1199061) and119872

2= (1198972 1198982 1199062) be two TFNs

whereby the degree of possibility of 1198721ge 1198722is defined as

follows119881 (1198721ge 1198722) = sup119909ge119910

[min (1205831198721

(119909) 1205831198722(119909))] (6)

Themembership degree of possibility is expressed as follows

119881 (1198721ge 1198722) = hgt (119872

1cap1198722) = 1205831198722

(119889)

=

1 if 1198981ge 1198982

0 if 1198972ge 1199061

1198972minus 1199061

(1198972minus 1199061) + (119898

1minus 1198982)

otherwise

(7)

where 119889 is the ordinate of the highest intersection point oftwo membership functions 120583

1198721(119909) and 120583

1198722(119909)

The degree of possibility for a convex fuzzy number to begreater than 119896 convex fuzzy numbers is defined as follows

119881 (119872 ge 11987211198722 119872

119896) = min119881 (119872 ge 119872

119894)

119894 = 1 2 119896

(8)

The weight vector is given by

1198821015840= (1198891015840(1198601) 1198891015840(1198602) 119889

1015840(119860119899))119879

(9)

where1198891015840(119860119894) = min119881 (119878

119894ge 119878119896)

(119894 = 1 2 119899) 119896 = 1 2 119899 119896 = 119894

(10)

Via normalization we obtain the weight vectors as follows

119882 = (119889 (1198601) 119889 (119860

2) 119889 (119860

119899))119879 (11)

where119882 is a nonfuzzy numberThis study adopts a ldquoLikert Scalerdquo of fuzzy numbers

starting from 1 to 9 to transform the linguistic values intotriangular fuzzy numbers as shown in Table 2

43 Aggregate the Ratings of Suppliers versus the Criteria Let119909119894119895119905= (119890119894119895119905 119891119894119895119905 119892119894119895119905) 119894 = 1 sim 119898 119895 = 1 sim 119899 119905 = 1 sim 119897 be the

suitability rating assigned to green supplier 119860119894 by decision

maker 119863119905 for criterion 119862

119895 The averaged suitability rating

119909119894119895= (119890119894119895 119891119894119895 119892119894119895) can be evaluated as follows

119909119894119895=1

119897otimes (1199091198941198951oplus 1199091198941198952oplus sdot sdot sdot oplus 119909

119894119895119905oplus sdot sdot sdot oplus 119909

119894119895119897) (12)

where 119890119894119895= (1119897) sum

119897

119905=1119890119894119895119905 119891119894119895= (1119897) sum

119897

119905=1119891119894119895119905 and 119892

119894119895=

(1119897) sum119897

119905=1119892119894119895119905

44 Normalize Performance of Suppliers versus Criteria Toensure compatibility between average ratings and averageweights the average ratings are normalized into comparablescales Suppose that 119903

119894119895= (119886119894119895 119887119894119895 119888119894119895) is the performance of

green supplier 119894 on criteria 119895 The normalized value 119909119894119895can

then be denoted as follows

119909119894119895= (

119886119894119895

119888lowast

119895

119887119894119895

119888lowast

119895

119888119894119895

119888lowast

119895

) 119895 isin 119861

119909119894119895= (

119886minus

119895

119888119894119895

119886minus

119895

119887119894119895

119886minus

119895

119886119894119895

) 119895 isin 119862

(13)

where 119886minus119895= min

119894119886119894119895 119888lowast119895= max

119894119888119894119895 119894 = 1 119898 and 119895 =

1 119899

45 Calculate Normalized Weighted Rating The normalizedweighted ratings 119866

119894are calculated by multiplying the nor-

malized average rating 119909119894119895with its associated weights 119908

119895119905as

follows

119866119894= 119909119894119895otimes 119908119895 119894 = 1 119898 119895 = 1 ℎ (14)

46 Calculate 119860+ 119860minus 119889+

119894 and 119889

minus

119894 The fuzzy positive-

ideal solution (FPIS 119860+) and fuzzy negative-ideal solution(FNIS 119860minus) are obtained as follows

119860+= (10 10 10)

119860minus= (00 00 00)

(15)

The distance of each green supplier119860119894 119894 = 1 119898 from119860

+

and 119860minus is calculated as follows

119889+

119894= radic

119899

sum

119894=1

(119866119894minus 119860+)

2

119889minus

119894= radic

119899

sum

119894=1

(119866119894minus 119860minus)

2

(16)

where 119889+119894represents the shortest distance of alternative 119860

119894

and 119889minus119894represents the farthest distance of green supplier 119860

119894

6 Mathematical Problems in Engineering

Table 2 Linguistic variables describing weights of the ldquoHOWsrdquo criteria

Linguistic scale for importance Triangular fuzzy scale119872 = (119897119898 119906)Just equal (10 10 10)Equal importance (10 10 30)Weak importance (10 30 50)Strong importance (30 50 70)Very strong importance (50 70 90)Extremely importance (70 90 90)If factor 119894 has one of the above numbers assigned to it when compared tofactor 119895 then 119895 has the reciprocal value when compared with 119894

Reciprocals of above119872minus1

1asymp (1119906

1 11198981 11198971)

47 Obtain the Closeness Coefficient Thecloseness coefficientof each green supplier which is usually defined to determinethe ranking order of all green suppliers is calculated asfollows

CC119894=

119889minus

119894

119889+

119894+ 119889minus

119894

(17)

A higher value of the closeness coefficient indicates thatan alternative is simultaneously closer to PIS and furtherfromNISThe closeness coefficient of each alternative is usedto determine the ranking order of all green suppliers andindicates the best one among a set of given feasible greensuppliers

5 Case Study

In this paper a comprehensive green supplier selectionmodel is proposed by considering the important criteria ineconomic and environmental aspects for evaluating greensuppliers The proposed method is applied on the case ofthe Taiwanese optical prism (TOP) manufacturing entity inLuminance Enhancement Film (LEF) industry to solve greensuppliers selection

TOP founded in late 2003 is the leading optical prismmanufacturer in Taiwan TOP focuses on advanced productdevelopment and quality improvement However TOP isnow dealing with the increase in competition Moreover theLCD product life cycle is very short qualified suppliers asTOP frequently have to provide innovative products withina limited lead time for customers verification to meet time-to-market as well Consequently with the purpose of main-taining the existing customers satisfaction and attractingnew international customers to improve market share theselection of quality constant green suppliers for long termcooperation is extremely essential for survival of TOP

When TOP confirmed its role and strategy as a greensupplier TOP needs to evaluate its core competences andidentify the gap between customer needs and consultantsuggestions TOP then restructures the ecological environ-ment of the industry TOP has employed the green SCMsimultaneously considering environmental and economicaspects to either comply with regulation or meet customerneeds Furthermore TOP has proactively invested both qual-ity and environmental management system such as quality

system of economic criteria ISO9001 and QC080000 andenvironmental criteria ISO14001 and OHSAS18001 TOP hasimplemented a continuous quality improvement programand constituted an international standard as a platform totraining staffs as well as suppliers Those activities eithersave the costs of customers involved with their supplierdevelopment program or strengthen TOPrsquos green brandimage

TOP has learned and accumulated plenty of green SCMdomain knowledge and capabilities as a main supplier ofLCD supply chain through the two-stage process of the rawmaterial quality verification and integration all of material inone product for each customerThus TOP reversely requeststhe suppliers to comply with its customer environmental andeconomic requirement Under the consensus of a multidisci-plinary group of decision makers with various points of viewand representing the different services of the company TOPrsquosmanagers and heads of departments have decided that prod-uct price ISO quality system and lead time are economiccriteria Green technology and environmental certificate areenvironmental criteria The managers of the departmentssuch as Employee Health and Safety Production QualityControl and Assessment and Purchasing were required tomake their evaluation respectively

In reality TOP must work with suppliers for green prod-uct development Quality control and supply ability of eco-nomic criteria are the most important customer requirementfactors which related to green products TOPrsquos managementteam continuously integrates resources to investigate greenproducts such as light lean production and energy savingto satisfy stakeholders TOP is keeping good relationshipwiththe suppliers that will benefit from the purchasingmaterials ifneeded Additionally TOP also maintains good relationshipwith customers who will provide TOP opportunities ininnovative product developing and meeting the needs ofcustomers easier

The case revealed that the green criteria such as environ-ment and sustainability do not yet play a crucial role withingreen supplier selection procedures in enterprise practiceDue to the environmental regulations suppliers must meetsome minimum requirements in order to be eligible to workwith focal firms on the supply chain After that most of thecompanies do not apply environmental criteria to discrimi-nate qualified suppliers instead customers require suppliersto provide information such as Certificate of Nonuse of

Mathematical Problems in Engineering 7

Table 3 Fuzzy pairwise comparison of economic and environmental criteria

Criteria 1198621

1198622

1198623

1198624

1198625

1198621

(10 10 10) (10 30 50) (50 70 90) (10 30 50) (10 10 30)1198622

(15 13 11) (10 10 10) (19 17 15) (15 13 11) (50 70 90)1198623

(19 17 15) (50 70 90) (10 10 10) (17 15 13) (17 15 13)1198624

(15 13 11) (10 30 50) (30 50 70) (10 10 10) (13 11 11)1198625

(13 11 11) (19 17 15) (30 50 70) (10 10 30) (10 10 10)

Table 4 Fuzzy weights of the economic and environmental criteria

Criteria Fuzzy weight1198621

(0123 0295 0699)1198622

(0089 0173 0371)1198623

(0087 0168 0330)1198624

(0076 0203 0456)1198625

(0074 0160 0371)

Controlled Substances Certificate of Nonuse of Other Con-trolled Substances Material Safety Data Sheet and TestReport of customer assigned items issued by SGS annuallyThose certificates concern quality of economic criterion andpollution control of environmental criterion

According to institutional theory implementation ofgreen SCM is due to mimetic and normative (competitiveand benchmarking)mechanisms Facing environmental pro-tection pressure and legitimacy isomorphism pressure enter-prises must comply with social expectation and maintainconsistency with external environment to survive Thus theenvironmental and economic dimensionsmust be consideredsimultaneously [5] Consequently the proposed method isapplied on the case of TOP following the steps below

Step 1 (identify a number of economic and environmental cri-teria) In this study the data used as input to implement theproposed green supplier selection and evaluate the methodwere collected by means of semistructured interviews withthe top managers and head of departments Four companymanagers were required to make their evaluation respec-tively according to their preferences for important weightsof selection criteria and ratings of green suppliers

Using Table 1 and discussions with a companyrsquos top man-agers and heads of departments five criteria of economicsand environment for green supplier selection were selectedEconomic criteria include product price (119862

1) ISO quality

system (1198622) and lead time (119862

3) Green technology (119862

4) and

environmental certificate (1198625) are environmental criteria

Step 2 (aggregate the important weights of the criteria)After the determination of the green supplier criteria eachof four company managers is asked to conduct a pairwisecomparison with regard to the different criteria using thefuzzy linguistic assessment variables (see Table 2 for thesevariables) The completed matrices for the required cell areshown in Table 3 Applying (5)ndash(8) the final weights of theeconomic and environmental criteria are obtained as shownin Table 4

Step 3 (aggregate the ratings of suppliers versus the criteria)After the determination of the suppliers assessment criteriafour company managers rate each supplier according to eachcriterion A linguistic rating set of S was used to express theopinions of the managers where S = (VP P F G VG) VP(Very Poor) = (00 01 02) P (Poor) = (01 03 05) F (Fair) =(03 05 07) G (Good) = (05 07 09) and VG (Very Good)= (08 09 10) Table 5 gives the aggregated suitability ratingsof four green suppliers (119860

1 1198602 1198603 and 119860

4) using (12)

Step 4 (normalized performance of suppliers versus criteria)For simplicity and practicality all of the fuzzy numbers in thispaper are defined in the closed interval [0 1] Consequentlythe normalization procedure is no longer needed

Step 5 (calculate normalized weighted rating) Using (14) thenormalized weighted ratings 119866

119894can be obtained as shown in

Table 6

Step 6 (calculate 119860+ 119860minus 119889+119894 and 119889minus

119894) As shown in Table 7

the distance of each green supplier from 119860+ and 119860minus can be

calculated by (15)sim(16)

Step 7 (obtain the closeness coefficient) The closeness coef-ficients of green suppliers can be calculated by (17) as shownin Table 8 Therefore the ranking order of the four greensuppliers is 119860

3gt 1198604gt 1198601gt 1198602 Consequently the best

green supplier is 1198603

6 Conclusion

While the types of industry vary the key strategies ofgreen supplier selection also are changed Nevertheless allindustries should concern suppliers from both economicand environmental aspects because suppliers could influencefirmsrsquo performance and stakeholders

Green supplier selection is an important and complicatedMCDM problem requiring evaluation of multiple economicand environmental criteria incorporating vagueness andimprecision with the involvement of a group of expertsAlthough numerous studies have used economic criteria inthe supplier selection process limited studies have consid-ered the economic and environmental criteria simultane-ously The implementation of green supply management wasnot well understood This paper has proposed an integratedfuzzy MCDM approach to support the green suppliers selec-tion and the evaluation process In the proposed approachboth economic and environmental criteria were consideredIn order to overcome the shortcomings of the existing fuzzy

8 Mathematical Problems in Engineering

Table 5 Aggregate of the green supplier ratings versus criteria

Criteria Green suppliers Company managers119903119894119895

1198631

1198632

1198633

1198634

1198621

1198601

VG G G VG (0650 0800 0950)1198602

F G G F (0400 0600 0800)1198603

G G G G (0500 0700 0900)1198604

G F G G (0450 0650 0850)

1198622

1198601

G G G G (0500 0700 0900)1198602

F F G F (0350 0550 0750)1198603

G G VG G (0575 0750 0925)1198604

VG G VG G (0650 0800 0950)

1198623

1198601

G F G F (0400 0600 0800)1198602

F F F G (0350 0550 0750)1198603

VG G VG G (0650 0800 0950)1198604

F G F F (0350 0550 0750)

1198624

1198601

F G G F (0400 0600 0800)1198602

G VG G G (0575 0750 0925)1198603

G VG VG G (0650 0800 0950)1198604

VG G VG G (0650 0800 0950)

1198625

1198601

G G G G (0500 0700 0900)1198602

VG G G VG (0650 0800 0950)1198603

G G G VG (0575 0750 0925)1198604

VG G G VG (0650 0800 0950)

Table 6 Normalized weighted ratings of each market segment

Green suppliers 119866119894

1198601

(0045 0138 0392)1198602

(0041 0129 0372)1198603

(0052 0151 0413)1198604

(0048 0143 0396)

Table 7 The distance of each green supplier from 119860+ and 119860minus

Green suppliers 119889+

119889minus

1198601

1422 04181198602

1440 03961198603

1402 04421198604

1416 0424

Table 8 Closeness coefficients of alternatives

Alternatives Closeness coefficient Ranking1198601

0227 31198602

0216 41198603

0240 11198604

0230 2

TOPSIS technique this study has integrated the fuzzy TOP-SIS technique with the fuzzy AHP method to determine theimportant weights of economic and environmental criteriaFinally the proposed approach was employed to solve a realproblem in the LEF industry The results showed that the

proposed approach is effective in supplier selection for thecompany The application also indicated that the computa-tional procedure is efficient and easy to use in practice Futureresearch should focus on developing an extension of fuzzyMCDM approach to segment the green suppliers based onthe economic and environmental aspects Different methodsmay be applied to select green suppliers and the results shouldbe compared with the proposed approach The proposedapproach can also be applied to other management problemswith similar settings

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

References

[1] Y-S Chen and C-H Chang ldquoThe determinants of green prod-uct development performance Green dynamic capabilitiesgreen transformational leadership and green creativityrdquo Journalof Business Ethics vol 116 no 1 pp 107ndash119 2013

[2] A H I Lee H-Y Kang C-F Hsu and H-C Hung ldquoA greensupplier selectionmodel for high-tech industryrdquo Expert Systemswith Applications vol 36 no 4 pp 7917ndash7927 2009

[3] K Govindan S Rajendran J Sarkis and P Murugesan ldquoMulticriteria decision making approaches for green supplier evalua-tion and selection a literature reviewrdquo Journal of Cleaner Pro-duction vol 98 pp 66ndash83 2015

Mathematical Problems in Engineering 9

[4] R J Kuo Y C Wang and F C Tien ldquoIntegration of artificialneural network and MADA methods for green supplier selec-tionrdquo Journal of Cleaner Production vol 18 no 12 pp 1161ndash11702010

[5] A Gunasekaran and D Gallear ldquoSpecial Issue on Sustainabledevelopment of manufacturing and servicesrdquo InternationalJournal of Production Economics vol 140 no 1 pp 1ndash6 2012

[6] J Sarkis Q Zhu and K-H Lai ldquoAn organizational theoreticreview of green supply chain management literaturerdquo Interna-tional Journal of Production Economics vol 130 no 1 pp 1ndash152011

[7] A Appolloni H Sun F Jia and X Li ldquoGreen Procurement inthe private sector a state of the art review between 1996 and2013rdquo Journal of Cleaner Production vol 85 pp 122ndash133 2014

[8] H C Pimenta and P D Ball ldquoAnalysis of environmentalsustainability practices across upstream supply chain manage-mentrdquo Procedia CIRP vol 26 pp 677ndash682 2015

[9] C-L Hwang andK YoonMultiple Attribute DecisionMakingmdashMethods and Applications A State of the Art Survey SpringerNew York NY USA 1981

[10] H-S Shih H-J Shyur and E S Lee ldquoAn extension of TOPSISfor group decision makingrdquoMathematical and Computer Mod-elling vol 45 no 7-8 pp 801ndash813 2007

[11] T L SaatyTheAnalytical Hierarchy Process McGraw-Hill NewYork NY USA 1980

[12] G Buyukozkan and G Cifci ldquoEvaluation of the green supplychain management practices a fuzzy ANP approachrdquo Produc-tion Planning and Control vol 23 no 6 pp 405ndash418 2012

[13] C-C Sun ldquoA performance evaluation model by integratingfuzzy AHP and fuzzy TOPSIS methodsrdquo Expert Systems withApplications vol 37 no 12 pp 7745ndash7754 2010

[14] W Xia and Z Wu ldquoSupplier selection with multiple criteria involume discount environmentsrdquoOmega vol 35 no 5 pp 494ndash504 2007

[15] I Chamodrakas D Batis and D Martakos ldquoSupplier selectionin electronic marketplaces using satisficing and fuzzy AHPrdquoExpert Systems with Applications vol 37 no 1 pp 490ndash4982010

[16] K Shaw R Shankar S S Yadav and L S Thakur ldquoSupplierselection using fuzzy AHP and fuzzy multi-objective linearprogramming for developing low carbon supply chainrdquo ExpertSystems with Applications vol 39 no 9 pp 8182ndash8192 2012

[17] O Kilincci and S A Onal ldquoFuzzy AHP approach for supplierselection in a washing machine companyrdquo Expert Systems withApplications vol 38 no 8 pp 9656ndash9664 2011

[18] A H I Lee ldquoA fuzzy supplier selection model with the consid-eration of benefits opportunities costs and risksrdquo Expert Sys-tems with Applications vol 36 no 2 pp 2879ndash2893 2009

[19] C Bai and J Sarkis ldquoGreen supplier development analyticalevaluation using rough set theoryrdquo Journal of Cleaner Produc-tion vol 18 no 12 pp 1200ndash1210 2010

[20] M Abdollahi M Arvan and J Razmi ldquoAn integrated approachfor supplier portfolio selection lean or agilerdquo Expert Systemswith Applications vol 42 no 1 pp 679ndash690 2015

[21] M S Memon Y H Lee and S I Mari ldquoGroup multi-criteriasupplier selection using combined grey systems theory anduncertainty theoryrdquo Expert Systems with Applications vol 42no 21 pp 7951ndash7959 2015

[22] S H Hashemi A Karimi and M Tavana ldquoAn integratedgreen supplier selection approachwith analytic network processand improved Grey relational analysisrdquo International Journal ofProduction Economics vol 159 pp 178ndash191 2015

[23] M Punniyamoorthy P Mathiyalagan and P Parthiban ldquoAstrategic model using structural equation modeling and fuzzylogic in supplier selectionrdquo Expert Systems with Applicationsvol 38 no 1 pp 458ndash474 2011

[24] R M Grisi L Guerra and G Naviglio ldquoSupplier performanceevaluation for green supply chainmanagementrdquo inBusiness Per-formanceMeasurement andManagement pp 149ndash163 SpringerBerlin Germany 2010

[25] F Mafakheri M Breton and A Ghoniem ldquoSupplier selection-order allocation a two-stage multiple criteria dynamic pro-gramming approachrdquo International Journal of Production Eco-nomics vol 132 no 1 pp 52ndash57 2011

[26] Y-J Chen ldquoStructured methodology for supplier selection andevaluation in a supply chainrdquo Information Sciences vol 181 no9 pp 1651ndash1670 2011

[27] W-PWang ldquoA fuzzy linguistic computing approach to supplierevaluationrdquo Applied Mathematical Modelling vol 34 no 10 pp3130ndash3141 2010

[28] M-L Tseng and A S F Chiu ldquoEvaluating firmrsquos green supplychain management in linguistic preferencesrdquo Journal of CleanerProduction vol 40 pp 22ndash31 2013

[29] Q Zhu Y Dou and J Sarkis ldquoA portfolio-based analysisfor green supplier management using the analytical networkprocessrdquo Supply Chain Management vol 15 no 4 pp 306ndash3192010

[30] G A Keskin S Ilhan and C Ozkan ldquoThe Fuzzy ARTalgorithm a categorization method for supplier evaluation andselectionrdquo Expert Systems with Applications vol 37 no 2 pp1235ndash1240 2010

[31] C-Y Shen and K-T Yu ldquoEnhancing the efficacy of supplierselection decision-making on the initial stage of new productdevelopment a hybrid fuzzy approach considering the strategicand operational factors simultaneouslyrdquo Expert Systems withApplications vol 36 no 8 pp 11271ndash11281 2009

[32] K Govindan R Khodaverdi and A Jafarian ldquoA fuzzy multicriteria approach for measuring sustainability performance ofa supplier based on triple bottom line approachrdquo Journal ofCleaner Production vol 47 pp 345ndash354 2013

[33] G Tuzkaya A Ozgen D Ozgen and U R Tuzkaya ldquoEnvi-ronmental performance evaluation of suppliers a hybrid fuzzymulti-criteria decision approachrdquo International Journal of Envi-ronmental ScienceampTechnology vol 6 no 3 pp 477ndash490 2009

[34] Q Zhu J Sarkis and K-H Lai ldquoInitiatives and outcomes ofgreen supply chain management implementation by Chinesemanufacturersrdquo Journal of Environmental Management vol 85no 1 pp 179ndash189 2007

[35] W-C Yeh and M-C Chuang ldquoUsing multi-objective geneticalgorithm for partner selection in green supply chain problemsrdquoExpert Systems with Applications vol 38 no 4 pp 4244ndash42532011

[36] A Awasthi S S Chauhan and S K Goyal ldquoA fuzzy multi-criteria approach for evaluating environmental performance ofsuppliersrdquo International Journal of Production Economics vol126 no 2 pp 370ndash378 2010

[37] J Sarkis ldquoManufacturingrsquos role in corporate environmentalsustainability-Concerns for the new millenniumrdquo InternationalJournal of Operations amp Production Management vol 21 no 5-6 pp 666ndash686 2001

[38] S MMirhedayatian M Azadi and R Farzipoor Saen ldquoA novelnetwork data envelopment analysis model for evaluating greensupply chain managementrdquo International Journal of ProductionEconomics vol 147 pp 544ndash554 2014

10 Mathematical Problems in Engineering

[39] C Wu and D Barnes ldquoAn integrated model for green partnerselection and supply chain constructionrdquo Journal of CleanerProduction vol 112 pp 2114ndash2132 2016

[40] G Bruno E Esposito A Genovese andR Passaro ldquoAHP-basedapproaches for supplier evaluation problems and perspectivesrdquoJournal of Purchasing and Supply Management vol 18 no 3 pp159ndash172 2012

[41] F R L Junior L Osiro and L C R Carpinetti ldquoA comparisonbetween Fuzzy AHP and Fuzzy TOPSIS methods to supplierselectionrdquo Applied Soft Computing vol 21 pp 194ndash209 2014

[42] A Kawa and W W Koczkodaj ldquoSupplier evaluation process bypairwise comparisonsrdquo Mathematical Problems in Engineeringvol 2015 Article ID 976742 9 pages 2015

[43] X Deng Y Hu Y Deng and S Mahadevan ldquoSupplier selectionusing AHP methodology extended by D numbersrdquo ExpertSystems with Applications vol 41 no 1 pp 156ndash167 2014

[44] N Xie and J Xin ldquoInterval grey numbers based multi-attributedecisionmakingmethod for supplier selectionrdquoKybernetes vol43 no 7 pp 1064ndash1078 2014

[45] J Lee H Cho and Y S Kim ldquoAssessing business impacts ofagility criterion and order allocation strategy in multi-criteriasupplier selectionrdquo Expert Systems with Applications vol 42 no3 pp 1136ndash1148 2015

[46] L Shen L Olfat K Govindan R Khodaverdi and A DiabatldquoA fuzzy multi criteria approach for evaluating green supplierrsquosperformance in green supply chain with linguistic preferencesrdquoResources Conservation and Recycling vol 74 pp 170ndash179 2012

[47] B Kanga Y Hu Y Deng and D Zhou ldquoA new methodologyof multicriteria decision-making in supplier selection based onZ-numbersrdquo Mathematical Problems in Engineering vol 2016Article ID 8475987 17 pages 2016

[48] N Asthana and M Gupta ldquoSupplier selection using artificialneural network and genetic algorithmrdquo International Journal ofIndian Culture and Business Management vol 11 no 4 pp 457ndash472 2015

[49] D Dubois and H Prade ldquoOperations on fuzzy numbersrdquo Inter-national Journal of Systems Science vol 9 no 6 pp 613ndash6261978

[50] A Kaufmann and M M Gupta Introduction to Fuzzy Arith-metic Theory and Applications The Arden Shakespeare 1991

[51] L A Zadeh ldquoThe concept of a linguistic variable and its appli-cation to approximate reasoningmdashIrdquo Information Sciences vol8 no 3 pp 199ndash249 1975

[52] L A Zadeh ldquoThe concept of a linguistic variable and its applica-tion to approximate reasoningmdashIIrdquo Information Sciences vol 8no 4 pp 301ndash357 1975

[53] D-Y Chang ldquoApplications of the extent analysis method onfuzzy AHPrdquo European Journal of Operational Research vol 95no 3 pp 649ndash655 1996

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical Problems in Engineering

Hindawi Publishing Corporationhttpwwwhindawicom

Differential EquationsInternational Journal of

Volume 2014

Applied MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical PhysicsAdvances in

Complex AnalysisJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

OptimizationJournal of

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CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

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Operations ResearchAdvances in

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Function Spaces

Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of Mathematics and Mathematical Sciences

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

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Algebra

Discrete Dynamics in Nature and Society

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

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Decision SciencesAdvances in

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Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Stochastic AnalysisInternational Journal of

2 Mathematical Problems in Engineering

The fundamental idea of TOPSIS is that the chosen alternativeshould have the shortest Euclidian distance from the positive-ideal solution and the farthest distance from the negative-ideal solution The positive-ideal solution is a solution thatmaximizes the benefit criteria andminimizes the cost criteriawhereas the negative ideal solution maximizes the costcriteria and minimizes the benefit criteria In the classicalTOPSIS method the weights of the criteria and the ratingsof alternatives are known precisely and crisp values are usedin the evaluation process Under many circumstances how-ever crisp data are inadequate to simulate real-life decisionproblems Consequently a fuzzy TOPSISmethod is proposedto deal with the deficiency in the traditional TOPSIS Themethodbased on theweights of criteria and ratings of alterna-tives are evaluated by linguistic variables represented by fuzzynumbers Some advantages of the TOPSIS [11] and fuzzyTOPSIS method include the following (i) a sound logic thatembodies rational human choice (ii) a simple computationprocess that can be used and programmed easily (iii) thenumber of steps that remains the same regardless of thenumber of attributes (iv) a scalar value that accounts for boththe best and worst alternatives at the same time As a resultfuzzy TOPSIS approach has been broadly applied to decision-making applications over the past few decades

Several studies in the literature have mentioned thedifficulty of weighting the criteria and keeping consistency ofjudgment when using fuzzy TOPSIS Thus the combinationof the fuzzy TOPSIS with another method such as fuzzyanalytic hierarchy process (AHP) might be able to determineproper objective weightings under a vague environmentTheAHP a powerful tool in applying MCDA was introducedand developed by Buyukozkan and Cifci [12]The AHP helpsidentify theweights or priority vector of the alternatives or thecriteria using a hierarchical model that includes target maincriteria subcriteria and alternatives Nevertheless a majordisadvantage of AHP is that it is unable to handle adequatelythe inherent uncertainty and imprecision of human thinkingFuzzy AHP has been developed to solve this problem [13] InFAHP method the application of the fuzzy comparison ratiotolerates vagueness in themodel Decisionmakers use naturallinguistic emphasis as well as certain numbers to evaluatecriteria and alternatives Fuzzy AHP impressively resembleshuman thought and perception In the literature manystudies have used either fuzzy TOPSIS or fuzzyAHPmethodsto select and evaluate the suppliers [14ndash19] However fewstudies have proposed an integrated fuzzy MCDM approachfor suppliers selection and evaluation especially in the caseof green suppliers

This paper proposes an integrated fuzzy multicriteriadecision making (MCDM) approach to solve problemsof green supplier selection and supply chain constructionsimultaneously effectively and efficiently To address theresearch need we leverage a small and medium sized hightech company to draw a case study of an actual greensupplier selection and green SCM experience of a Taiwaneseoptical prism manufacturing entity (hereinafter referred toas TOP a pseudonym) in the Luminance EnhancementFilm (LEF) industry The company was selected because therapidly changing environment of the optical prism industry

forces firm to develop ongoing sustainable capabilities and torespond to the uncertain environment

The remainder of this paper is organized as follows InSection 2 green supplier selection criteria and method liter-ature is reviewed The basic concepts of fuzzy numbers areshown in Section 3 The integrated fuzzy MCDM approachis proposed in Section 4 Section 5 applies the proposedapproach to a real case Concluding remarks are presented inSection 6

2 Literature Review on Green SupplierSelection Criteria and Methods

As a result of escalated global warming and increasing envi-ronmental protection awareness EU environmental orderssuch as RoHS WEEE ErP and REACH have been enforcedThe supply chains of firm and the products are requiredto become more ecofriendly especially in the electronicsindustryThe circumstance has driven supply chains not onlyto comply with environmental policies but also to enforcefirms govern their own corporate environmental policies tosustain in the global market

Green SCM has become a strategy to improve a firmrsquosenvironmental and economic performance [25 38] Procure-ment constitutes one of the key strategic functions in SCMSelecting the right supplier gives the firm a competitive edgeto either reduce costs enhance the quality [39] or minimizenegative environmental impact avoiding violating relevantlegislation [20]

In practice when a firm is purchasing the professionalpurchaser chooses the favorite suppliers on the basis ofspecifications and conditions A firm primarily prioritizeseconomic criteria such as cost quality delivery and flexibil-ityThe environmental certificate of ISO 14000 as one of envi-ronmental criteria is usually applied for purchaser referenceonly Efficient evaluation criteria can help the firm to reducethe risks associated with suppliers [21] Current literaturesaddress themost popular economic criteria considered by thedecision makers for supplier selection and evaluation whichare quality [4 12 22 23 25] cost [20ndash24] delivery [21 23 2627] flexibility [22 28 29] and relationship [23 28 29] Envi-ronmental criteria are environmental management system[2 19 28 32ndash34 36 37] green competencies [2 33 34 36 37]and ecodesign [28 32 34 35] Few studies simultaneouslyconsidered economic and environmental aspects for greensupplier selection

Currently environmental factors play a vital role for thelong term success of a supply chain and the purchasingprocess has become more complicated with environmentalconsideration [3] Several studies have examined the criteriaof supplier selection and focused on different approaches orcriteria Table 1 presents the most commonly used criteriain the literature to evaluate the environmental and economicperformance of green supplier selection

In the literature numerous techniques have been devel-oped to select the most suitable suppliers or green suppliersbased on specific methods including fuzzy AHP [3 40ndash43]analytic network process (ANP) [6 29] data envelopmentanalysis (DEA) [6] MCDM approach [13 21 31 33 44ndash47]

Mathematical Problems in Engineering 3

Table 1 Green supplier selection and evaluation criteria

Criteria Subcriteria Sub-subcriteriadefinition References

Economic criteria

Cost Product price logistics cost and payment terms [20ndash24]

Quality ISO quality system installed quality award product performancewarranties and claim policies and repair and return rate [4 12 22 23 25]

Delivery Lead time on-time delivery safety and security of components andappropriateness of the packaging [21 23 26 27]

Technology Communication and e-commerce systems capability of researchdevelopment and innovation and production facilities and capacity [22 23 26]

Flexibility

Product volume changes short setup time conflict resolution usingflexible machines the demand that can be profitably sustained andtime or cost required to add new products to the existing productionoperation

[22 28 29]

Financialcapability Financial position economical stability and price strategy [12 23 30]

Culture Communication openness vendorrsquos image and mutual trust [20 23 27]Innovativeness New launch of products and new launch of technologies [31]

Relationship Long term relationship relationship closeness communicationopenness and reputation for integrity [23 28 29]

Environmental criteria

Pollutionproduction

Average volume of air pollutants waste water solid waste andharmful materials released [19 22 32]

Pollutioncontrol Remediation and end-of-pipe controls [2 19 33]

Resourceconsumption Consumption of resources in terms of raw material energy and water [19 32]

EcodesignDesign for resource efficiency design of products for reuse recycleand recovery of material design for reduction or elimination ofhazardous materials

[28 32 34 35]

Environmentalmanagementsystem

Environmental certificates such as ISO 14000 continuous monitoringand regulatory compliance environmental policies green processplanning and internal control process

[2 19 28 32ndash34 36 37]

Green image Ratio of green customers to total customers and social responsibility [2 33 35]

Greencompetencies

Materials used in the supplied components that reduce the impact onnatural resources and ability to alter process and product for reducingthe impact on natural resources

[2 33 34 36 37]

Green product Use of recycled and nontoxic materials green packaging and excesspackaging reduction [6 34 36]

Staffenvironmentaltraining

Staff training on environmental issues [36]

Managementcommitment

Commitment of senior managers to support and improve greensupply chain management initiatives [34 36]

GreenTechnology

The application of the environmental science to conserve the naturalenvironment and resources and to curb the negative impact of humaninvolvement

[6 34]

structural equation modeling and fuzzy logic [23] optimummathematical planning model [35] linguistic preferences[28] fuzzy linguistic computing approach [27] Fuzzy Adap-tive ResonanceTheory algorithm [30] and genetic algorithm(GA) [48]

Although a number of methods have been studiedmost of the studies have only used either economic orenvironmental criteria for evaluating the suppliers Thereare few studies considering economic and environmentalcriteria simultaneously in the supplier selection process

And each of those methods has its own advantages anddisadvantages this study proposes the integrated approachby combining the two most popular techniques for solvinggreen supplier problems that is fuzzy TOPSIS and fuzzyAHP In the proposed approach the fuzzy AHP is employedto determine the important weights of criteria under vagueenvironmentThen the fuzzy TOPSIS is used to evaluate andrank the potential suppliers In addition both economic andenvironmental criteria are considered in proposed MCDMapproach

4 Mathematical Problems in Engineering

3 Fuzzy Numbers

There are various ways to define fuzzy numbers This paperdefines the concept of fuzzy numbers as follows [49 50]

Definition 1 A real fuzzy number119860 is described as any fuzzysubset of the real line 119877with membership function119891

119860 which

has the following properties

(a) 119891119860is a continuous mapping from 119877 to the closed

interval [0 1](b) 119891119860(119909) = 0 for all 119909 isin (minusinfin 119886]

(c) 119891119860is strictly increasing on [119886 119887]

(d) 119891119860(119909) = 1 for all 119909 isin [119887 119888]

(e) 119891119860is strictly decreasing on [119888 119889]

(f) 119891119860(119909) = 0 for all 119909 isin (119889infin]

where 119886 119887 119888 and 119889 are real numbers Unless elsewherespecified this research assumes that119860 is convex and bounded(ie minusinfin lt 119886 119889 lt infin)

Definition 2 The fuzzy number 119860 = [119886 119887 119888 119889] is a trape-zoidal fuzzy number if its membership function is given by

119891119860 (119909) =

119891119871

119860(119909) 119886 le 119909 le 119887

1 119887 le 119909 le 119888

119891119877

119860(119909) 119888 le 119909 le 119889

0 otherwise

(1)

where 119891119871119860(119909) and 119891

119877

119860(119909) are the left and right membership

functions of 119860 respectively [50]When 119887 = 119888 the trapezoidal fuzzy number is reduced

to a triangular fuzzy number and can be denoted by 119860 =

(119886 119887 119889) Thus triangular fuzzy numbers are special cases oftrapezoidal fuzzy numbers

Definition 3 (the distance between fuzzy triangular numbers)Let119860 = (119886

1 1198871 1198891) and119861 = (119886

2 1198872 1198892) be two triangular fuzzy

numbersThedistance between them is given using the vertexmethod by

119889 (119860 119861) = radic1

3[(1198861minus 1198862)2+ (1198871minus 1198872)2+ (1198891minus 1198892)2] (2)

Definition 4 (120572-cuts) The 120572-cuts of fuzzy number 119860 can bedefined as 119860120572 = 119909 | 119891

119860(119909) ge 120572 120572 isin [0 1] where 119860120572

is a nonempty bounded closed interval contained in 119877 andcan be denoted by 119860120572 = [119860

120572

119897 119860120572

119906] where 119860120572

119897and 119860120572

119906are its

lower and upper bounds respectively [50] For example if atriangular fuzzy number 119860 = (119886 119887 119889) then the 120572-cuts of 119860can be expressed as follows

119860120572= [119860120572

119897 119860120572

119906] = [(119887 minus 119886) 120572 + 119886 (119887 minus 119889) 120572 + 119889] (3)

Definition 5 (arithmetic operations on fuzzy numbers)Given fuzzy numbers 119860 and 119861 where 119860 119861 isin 119877

+ the 120572-cutsof119860 and 119861 are119860120572 = [119860

120572

119897 119860120572

119906] and 119861120572 = [119861

120572

119897 119861120572

119906] respectively

By the interval arithmetic some main operations of 119860 and 119861can be expressed as follows [50]

(119860 oplus 119861)120572= [119860120572

119897+ 119861120572

119897 119860120572

119906+ 119861120572

119906]

(119860 ⊖ 119861)120572= [119860120572

119897minus 119861120572

119906 119860120572

119906minus 119861120572

119897]

(119860 otimes 119861)120572= [119860120572

119897sdot 119861120572

119897 119860120572

119906sdot 119861120572

119906]

(119860 ⊘ 119861)120572= [

119860120572

119897

119861120572119906

119860120572

119906

119861120572

119897

]

(119860 otimes 119903)120572= [119860120572

119897sdot 119903 119860120572

119906sdot 119903] 119903 isin 119877

+

(4)

4 Proposed Approach forGreen Suppliers Selection

In this section an approach for green supplier selection bycombining fuzzy TOPSIS and fuzzy AHP method is pre-sented The proposed approach offers a new way to solve thegreen supplier selection problem effectively and efficientlysince it enables decision makers to minimize the negativeenvironmental impact of the supply chain while simultane-ously maximizing business performance The procedure ofthe proposed approach is stated as follows

Step 1 Identify a number of economic and environmentalcriteria

Step 2 Aggregate the important weights of the criteria

Step 3 Aggregate the ratings of suppliers versus the criteria

Step 4 Normalize the fuzzy decision matrix

Step 5 Construct the weighted normalized fuzzy decisionmatrix

Step 6 Calculate normalized weighted rating

Step 7 Calculate 119860+ 119860minus 119889+119894 and 119889minus

119894

Step 8 Obtain the closeness coefficient

Assume that a committee of 119897decisionmakers (119863119905 119905 = 1 sim

119897) is responsible for evaluating 119898 suppliers (119860119894 119894 = 1 sim 119898)

under 119899 selected criteria (119862119895 119895 = 1 sim 119899) where the suitability

ratings of alternatives under each of the criteria as well as theweights of the criteria are assessed in linguistic terms [51 52]represented by triangular fuzzy numbers

41 Identify a Number of Economic and EnvironmentalCriteria In this study the criteria are classified into twocategories that is economic criteria (119862

119895 119895 = 1 119897) and

environmental criteria (119862119895 119895 = 119897 + 1 119899) The number of

economic and environmental criteria is selected from Table 1through screening by the decision makers

42 Aggregate the Important Weights of the Criteria In thissection a fuzzy AHP is applied to obtain more decisivejudgments by prioritizing the economic and environmental

Mathematical Problems in Engineering 5

criteria Several fuzzy AHP methods have been proposed inliterature to solve the MCDM problems This study adoptsthe extent analysis method proposed by Chang [53] dueto its popularity and computational simplicity Changrsquos [53]method is briefly discussed as follows

Let 119883 = 1199091 1199092 119909

119899 be an object set and let 119880 =

1199061 1199062 119906

119898 be a goal set According to Chang [53] each

object is taken and an extent analysis for each goal (119892119894)

is performed respectively Therefore the 119898 extent analysisvalues for each object are obtained as1198721

1198921198941198722

119892119894 119872

119899

119892119894 119894 =

1 2 119899 where 119872119895119892119894(119895 = 1 2 119898) are triangular fuzzy

numbers (TFNs)Assume that 119872119895

119892119894are the values of extent analysis of the

119894th object for119898 goalsThe value of fuzzy synthetic extent 119878119894is

defined as follows

119878119894=

119898

sum

119895=1

119872119895

119892119894otimes [

[

119899

sum

119894=1

119898

sum

119895=1

119872119895

119892119894

]

]

minus1

(5)

where sum119898

119895=1119872119895

119892119894= (sum

119898

119895=1119897119895 sum119898

119895=1119898119895 sum119898

119895=1119906119895) 119895 = 1 2

119898 119894 = 1 2 119899

Let1198721= (1198971 1198981 1199061) and119872

2= (1198972 1198982 1199062) be two TFNs

whereby the degree of possibility of 1198721ge 1198722is defined as

follows119881 (1198721ge 1198722) = sup119909ge119910

[min (1205831198721

(119909) 1205831198722(119909))] (6)

Themembership degree of possibility is expressed as follows

119881 (1198721ge 1198722) = hgt (119872

1cap1198722) = 1205831198722

(119889)

=

1 if 1198981ge 1198982

0 if 1198972ge 1199061

1198972minus 1199061

(1198972minus 1199061) + (119898

1minus 1198982)

otherwise

(7)

where 119889 is the ordinate of the highest intersection point oftwo membership functions 120583

1198721(119909) and 120583

1198722(119909)

The degree of possibility for a convex fuzzy number to begreater than 119896 convex fuzzy numbers is defined as follows

119881 (119872 ge 11987211198722 119872

119896) = min119881 (119872 ge 119872

119894)

119894 = 1 2 119896

(8)

The weight vector is given by

1198821015840= (1198891015840(1198601) 1198891015840(1198602) 119889

1015840(119860119899))119879

(9)

where1198891015840(119860119894) = min119881 (119878

119894ge 119878119896)

(119894 = 1 2 119899) 119896 = 1 2 119899 119896 = 119894

(10)

Via normalization we obtain the weight vectors as follows

119882 = (119889 (1198601) 119889 (119860

2) 119889 (119860

119899))119879 (11)

where119882 is a nonfuzzy numberThis study adopts a ldquoLikert Scalerdquo of fuzzy numbers

starting from 1 to 9 to transform the linguistic values intotriangular fuzzy numbers as shown in Table 2

43 Aggregate the Ratings of Suppliers versus the Criteria Let119909119894119895119905= (119890119894119895119905 119891119894119895119905 119892119894119895119905) 119894 = 1 sim 119898 119895 = 1 sim 119899 119905 = 1 sim 119897 be the

suitability rating assigned to green supplier 119860119894 by decision

maker 119863119905 for criterion 119862

119895 The averaged suitability rating

119909119894119895= (119890119894119895 119891119894119895 119892119894119895) can be evaluated as follows

119909119894119895=1

119897otimes (1199091198941198951oplus 1199091198941198952oplus sdot sdot sdot oplus 119909

119894119895119905oplus sdot sdot sdot oplus 119909

119894119895119897) (12)

where 119890119894119895= (1119897) sum

119897

119905=1119890119894119895119905 119891119894119895= (1119897) sum

119897

119905=1119891119894119895119905 and 119892

119894119895=

(1119897) sum119897

119905=1119892119894119895119905

44 Normalize Performance of Suppliers versus Criteria Toensure compatibility between average ratings and averageweights the average ratings are normalized into comparablescales Suppose that 119903

119894119895= (119886119894119895 119887119894119895 119888119894119895) is the performance of

green supplier 119894 on criteria 119895 The normalized value 119909119894119895can

then be denoted as follows

119909119894119895= (

119886119894119895

119888lowast

119895

119887119894119895

119888lowast

119895

119888119894119895

119888lowast

119895

) 119895 isin 119861

119909119894119895= (

119886minus

119895

119888119894119895

119886minus

119895

119887119894119895

119886minus

119895

119886119894119895

) 119895 isin 119862

(13)

where 119886minus119895= min

119894119886119894119895 119888lowast119895= max

119894119888119894119895 119894 = 1 119898 and 119895 =

1 119899

45 Calculate Normalized Weighted Rating The normalizedweighted ratings 119866

119894are calculated by multiplying the nor-

malized average rating 119909119894119895with its associated weights 119908

119895119905as

follows

119866119894= 119909119894119895otimes 119908119895 119894 = 1 119898 119895 = 1 ℎ (14)

46 Calculate 119860+ 119860minus 119889+

119894 and 119889

minus

119894 The fuzzy positive-

ideal solution (FPIS 119860+) and fuzzy negative-ideal solution(FNIS 119860minus) are obtained as follows

119860+= (10 10 10)

119860minus= (00 00 00)

(15)

The distance of each green supplier119860119894 119894 = 1 119898 from119860

+

and 119860minus is calculated as follows

119889+

119894= radic

119899

sum

119894=1

(119866119894minus 119860+)

2

119889minus

119894= radic

119899

sum

119894=1

(119866119894minus 119860minus)

2

(16)

where 119889+119894represents the shortest distance of alternative 119860

119894

and 119889minus119894represents the farthest distance of green supplier 119860

119894

6 Mathematical Problems in Engineering

Table 2 Linguistic variables describing weights of the ldquoHOWsrdquo criteria

Linguistic scale for importance Triangular fuzzy scale119872 = (119897119898 119906)Just equal (10 10 10)Equal importance (10 10 30)Weak importance (10 30 50)Strong importance (30 50 70)Very strong importance (50 70 90)Extremely importance (70 90 90)If factor 119894 has one of the above numbers assigned to it when compared tofactor 119895 then 119895 has the reciprocal value when compared with 119894

Reciprocals of above119872minus1

1asymp (1119906

1 11198981 11198971)

47 Obtain the Closeness Coefficient Thecloseness coefficientof each green supplier which is usually defined to determinethe ranking order of all green suppliers is calculated asfollows

CC119894=

119889minus

119894

119889+

119894+ 119889minus

119894

(17)

A higher value of the closeness coefficient indicates thatan alternative is simultaneously closer to PIS and furtherfromNISThe closeness coefficient of each alternative is usedto determine the ranking order of all green suppliers andindicates the best one among a set of given feasible greensuppliers

5 Case Study

In this paper a comprehensive green supplier selectionmodel is proposed by considering the important criteria ineconomic and environmental aspects for evaluating greensuppliers The proposed method is applied on the case ofthe Taiwanese optical prism (TOP) manufacturing entity inLuminance Enhancement Film (LEF) industry to solve greensuppliers selection

TOP founded in late 2003 is the leading optical prismmanufacturer in Taiwan TOP focuses on advanced productdevelopment and quality improvement However TOP isnow dealing with the increase in competition Moreover theLCD product life cycle is very short qualified suppliers asTOP frequently have to provide innovative products withina limited lead time for customers verification to meet time-to-market as well Consequently with the purpose of main-taining the existing customers satisfaction and attractingnew international customers to improve market share theselection of quality constant green suppliers for long termcooperation is extremely essential for survival of TOP

When TOP confirmed its role and strategy as a greensupplier TOP needs to evaluate its core competences andidentify the gap between customer needs and consultantsuggestions TOP then restructures the ecological environ-ment of the industry TOP has employed the green SCMsimultaneously considering environmental and economicaspects to either comply with regulation or meet customerneeds Furthermore TOP has proactively invested both qual-ity and environmental management system such as quality

system of economic criteria ISO9001 and QC080000 andenvironmental criteria ISO14001 and OHSAS18001 TOP hasimplemented a continuous quality improvement programand constituted an international standard as a platform totraining staffs as well as suppliers Those activities eithersave the costs of customers involved with their supplierdevelopment program or strengthen TOPrsquos green brandimage

TOP has learned and accumulated plenty of green SCMdomain knowledge and capabilities as a main supplier ofLCD supply chain through the two-stage process of the rawmaterial quality verification and integration all of material inone product for each customerThus TOP reversely requeststhe suppliers to comply with its customer environmental andeconomic requirement Under the consensus of a multidisci-plinary group of decision makers with various points of viewand representing the different services of the company TOPrsquosmanagers and heads of departments have decided that prod-uct price ISO quality system and lead time are economiccriteria Green technology and environmental certificate areenvironmental criteria The managers of the departmentssuch as Employee Health and Safety Production QualityControl and Assessment and Purchasing were required tomake their evaluation respectively

In reality TOP must work with suppliers for green prod-uct development Quality control and supply ability of eco-nomic criteria are the most important customer requirementfactors which related to green products TOPrsquos managementteam continuously integrates resources to investigate greenproducts such as light lean production and energy savingto satisfy stakeholders TOP is keeping good relationshipwiththe suppliers that will benefit from the purchasingmaterials ifneeded Additionally TOP also maintains good relationshipwith customers who will provide TOP opportunities ininnovative product developing and meeting the needs ofcustomers easier

The case revealed that the green criteria such as environ-ment and sustainability do not yet play a crucial role withingreen supplier selection procedures in enterprise practiceDue to the environmental regulations suppliers must meetsome minimum requirements in order to be eligible to workwith focal firms on the supply chain After that most of thecompanies do not apply environmental criteria to discrimi-nate qualified suppliers instead customers require suppliersto provide information such as Certificate of Nonuse of

Mathematical Problems in Engineering 7

Table 3 Fuzzy pairwise comparison of economic and environmental criteria

Criteria 1198621

1198622

1198623

1198624

1198625

1198621

(10 10 10) (10 30 50) (50 70 90) (10 30 50) (10 10 30)1198622

(15 13 11) (10 10 10) (19 17 15) (15 13 11) (50 70 90)1198623

(19 17 15) (50 70 90) (10 10 10) (17 15 13) (17 15 13)1198624

(15 13 11) (10 30 50) (30 50 70) (10 10 10) (13 11 11)1198625

(13 11 11) (19 17 15) (30 50 70) (10 10 30) (10 10 10)

Table 4 Fuzzy weights of the economic and environmental criteria

Criteria Fuzzy weight1198621

(0123 0295 0699)1198622

(0089 0173 0371)1198623

(0087 0168 0330)1198624

(0076 0203 0456)1198625

(0074 0160 0371)

Controlled Substances Certificate of Nonuse of Other Con-trolled Substances Material Safety Data Sheet and TestReport of customer assigned items issued by SGS annuallyThose certificates concern quality of economic criterion andpollution control of environmental criterion

According to institutional theory implementation ofgreen SCM is due to mimetic and normative (competitiveand benchmarking)mechanisms Facing environmental pro-tection pressure and legitimacy isomorphism pressure enter-prises must comply with social expectation and maintainconsistency with external environment to survive Thus theenvironmental and economic dimensionsmust be consideredsimultaneously [5] Consequently the proposed method isapplied on the case of TOP following the steps below

Step 1 (identify a number of economic and environmental cri-teria) In this study the data used as input to implement theproposed green supplier selection and evaluate the methodwere collected by means of semistructured interviews withthe top managers and head of departments Four companymanagers were required to make their evaluation respec-tively according to their preferences for important weightsof selection criteria and ratings of green suppliers

Using Table 1 and discussions with a companyrsquos top man-agers and heads of departments five criteria of economicsand environment for green supplier selection were selectedEconomic criteria include product price (119862

1) ISO quality

system (1198622) and lead time (119862

3) Green technology (119862

4) and

environmental certificate (1198625) are environmental criteria

Step 2 (aggregate the important weights of the criteria)After the determination of the green supplier criteria eachof four company managers is asked to conduct a pairwisecomparison with regard to the different criteria using thefuzzy linguistic assessment variables (see Table 2 for thesevariables) The completed matrices for the required cell areshown in Table 3 Applying (5)ndash(8) the final weights of theeconomic and environmental criteria are obtained as shownin Table 4

Step 3 (aggregate the ratings of suppliers versus the criteria)After the determination of the suppliers assessment criteriafour company managers rate each supplier according to eachcriterion A linguistic rating set of S was used to express theopinions of the managers where S = (VP P F G VG) VP(Very Poor) = (00 01 02) P (Poor) = (01 03 05) F (Fair) =(03 05 07) G (Good) = (05 07 09) and VG (Very Good)= (08 09 10) Table 5 gives the aggregated suitability ratingsof four green suppliers (119860

1 1198602 1198603 and 119860

4) using (12)

Step 4 (normalized performance of suppliers versus criteria)For simplicity and practicality all of the fuzzy numbers in thispaper are defined in the closed interval [0 1] Consequentlythe normalization procedure is no longer needed

Step 5 (calculate normalized weighted rating) Using (14) thenormalized weighted ratings 119866

119894can be obtained as shown in

Table 6

Step 6 (calculate 119860+ 119860minus 119889+119894 and 119889minus

119894) As shown in Table 7

the distance of each green supplier from 119860+ and 119860minus can be

calculated by (15)sim(16)

Step 7 (obtain the closeness coefficient) The closeness coef-ficients of green suppliers can be calculated by (17) as shownin Table 8 Therefore the ranking order of the four greensuppliers is 119860

3gt 1198604gt 1198601gt 1198602 Consequently the best

green supplier is 1198603

6 Conclusion

While the types of industry vary the key strategies ofgreen supplier selection also are changed Nevertheless allindustries should concern suppliers from both economicand environmental aspects because suppliers could influencefirmsrsquo performance and stakeholders

Green supplier selection is an important and complicatedMCDM problem requiring evaluation of multiple economicand environmental criteria incorporating vagueness andimprecision with the involvement of a group of expertsAlthough numerous studies have used economic criteria inthe supplier selection process limited studies have consid-ered the economic and environmental criteria simultane-ously The implementation of green supply management wasnot well understood This paper has proposed an integratedfuzzy MCDM approach to support the green suppliers selec-tion and the evaluation process In the proposed approachboth economic and environmental criteria were consideredIn order to overcome the shortcomings of the existing fuzzy

8 Mathematical Problems in Engineering

Table 5 Aggregate of the green supplier ratings versus criteria

Criteria Green suppliers Company managers119903119894119895

1198631

1198632

1198633

1198634

1198621

1198601

VG G G VG (0650 0800 0950)1198602

F G G F (0400 0600 0800)1198603

G G G G (0500 0700 0900)1198604

G F G G (0450 0650 0850)

1198622

1198601

G G G G (0500 0700 0900)1198602

F F G F (0350 0550 0750)1198603

G G VG G (0575 0750 0925)1198604

VG G VG G (0650 0800 0950)

1198623

1198601

G F G F (0400 0600 0800)1198602

F F F G (0350 0550 0750)1198603

VG G VG G (0650 0800 0950)1198604

F G F F (0350 0550 0750)

1198624

1198601

F G G F (0400 0600 0800)1198602

G VG G G (0575 0750 0925)1198603

G VG VG G (0650 0800 0950)1198604

VG G VG G (0650 0800 0950)

1198625

1198601

G G G G (0500 0700 0900)1198602

VG G G VG (0650 0800 0950)1198603

G G G VG (0575 0750 0925)1198604

VG G G VG (0650 0800 0950)

Table 6 Normalized weighted ratings of each market segment

Green suppliers 119866119894

1198601

(0045 0138 0392)1198602

(0041 0129 0372)1198603

(0052 0151 0413)1198604

(0048 0143 0396)

Table 7 The distance of each green supplier from 119860+ and 119860minus

Green suppliers 119889+

119889minus

1198601

1422 04181198602

1440 03961198603

1402 04421198604

1416 0424

Table 8 Closeness coefficients of alternatives

Alternatives Closeness coefficient Ranking1198601

0227 31198602

0216 41198603

0240 11198604

0230 2

TOPSIS technique this study has integrated the fuzzy TOP-SIS technique with the fuzzy AHP method to determine theimportant weights of economic and environmental criteriaFinally the proposed approach was employed to solve a realproblem in the LEF industry The results showed that the

proposed approach is effective in supplier selection for thecompany The application also indicated that the computa-tional procedure is efficient and easy to use in practice Futureresearch should focus on developing an extension of fuzzyMCDM approach to segment the green suppliers based onthe economic and environmental aspects Different methodsmay be applied to select green suppliers and the results shouldbe compared with the proposed approach The proposedapproach can also be applied to other management problemswith similar settings

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

References

[1] Y-S Chen and C-H Chang ldquoThe determinants of green prod-uct development performance Green dynamic capabilitiesgreen transformational leadership and green creativityrdquo Journalof Business Ethics vol 116 no 1 pp 107ndash119 2013

[2] A H I Lee H-Y Kang C-F Hsu and H-C Hung ldquoA greensupplier selectionmodel for high-tech industryrdquo Expert Systemswith Applications vol 36 no 4 pp 7917ndash7927 2009

[3] K Govindan S Rajendran J Sarkis and P Murugesan ldquoMulticriteria decision making approaches for green supplier evalua-tion and selection a literature reviewrdquo Journal of Cleaner Pro-duction vol 98 pp 66ndash83 2015

Mathematical Problems in Engineering 9

[4] R J Kuo Y C Wang and F C Tien ldquoIntegration of artificialneural network and MADA methods for green supplier selec-tionrdquo Journal of Cleaner Production vol 18 no 12 pp 1161ndash11702010

[5] A Gunasekaran and D Gallear ldquoSpecial Issue on Sustainabledevelopment of manufacturing and servicesrdquo InternationalJournal of Production Economics vol 140 no 1 pp 1ndash6 2012

[6] J Sarkis Q Zhu and K-H Lai ldquoAn organizational theoreticreview of green supply chain management literaturerdquo Interna-tional Journal of Production Economics vol 130 no 1 pp 1ndash152011

[7] A Appolloni H Sun F Jia and X Li ldquoGreen Procurement inthe private sector a state of the art review between 1996 and2013rdquo Journal of Cleaner Production vol 85 pp 122ndash133 2014

[8] H C Pimenta and P D Ball ldquoAnalysis of environmentalsustainability practices across upstream supply chain manage-mentrdquo Procedia CIRP vol 26 pp 677ndash682 2015

[9] C-L Hwang andK YoonMultiple Attribute DecisionMakingmdashMethods and Applications A State of the Art Survey SpringerNew York NY USA 1981

[10] H-S Shih H-J Shyur and E S Lee ldquoAn extension of TOPSISfor group decision makingrdquoMathematical and Computer Mod-elling vol 45 no 7-8 pp 801ndash813 2007

[11] T L SaatyTheAnalytical Hierarchy Process McGraw-Hill NewYork NY USA 1980

[12] G Buyukozkan and G Cifci ldquoEvaluation of the green supplychain management practices a fuzzy ANP approachrdquo Produc-tion Planning and Control vol 23 no 6 pp 405ndash418 2012

[13] C-C Sun ldquoA performance evaluation model by integratingfuzzy AHP and fuzzy TOPSIS methodsrdquo Expert Systems withApplications vol 37 no 12 pp 7745ndash7754 2010

[14] W Xia and Z Wu ldquoSupplier selection with multiple criteria involume discount environmentsrdquoOmega vol 35 no 5 pp 494ndash504 2007

[15] I Chamodrakas D Batis and D Martakos ldquoSupplier selectionin electronic marketplaces using satisficing and fuzzy AHPrdquoExpert Systems with Applications vol 37 no 1 pp 490ndash4982010

[16] K Shaw R Shankar S S Yadav and L S Thakur ldquoSupplierselection using fuzzy AHP and fuzzy multi-objective linearprogramming for developing low carbon supply chainrdquo ExpertSystems with Applications vol 39 no 9 pp 8182ndash8192 2012

[17] O Kilincci and S A Onal ldquoFuzzy AHP approach for supplierselection in a washing machine companyrdquo Expert Systems withApplications vol 38 no 8 pp 9656ndash9664 2011

[18] A H I Lee ldquoA fuzzy supplier selection model with the consid-eration of benefits opportunities costs and risksrdquo Expert Sys-tems with Applications vol 36 no 2 pp 2879ndash2893 2009

[19] C Bai and J Sarkis ldquoGreen supplier development analyticalevaluation using rough set theoryrdquo Journal of Cleaner Produc-tion vol 18 no 12 pp 1200ndash1210 2010

[20] M Abdollahi M Arvan and J Razmi ldquoAn integrated approachfor supplier portfolio selection lean or agilerdquo Expert Systemswith Applications vol 42 no 1 pp 679ndash690 2015

[21] M S Memon Y H Lee and S I Mari ldquoGroup multi-criteriasupplier selection using combined grey systems theory anduncertainty theoryrdquo Expert Systems with Applications vol 42no 21 pp 7951ndash7959 2015

[22] S H Hashemi A Karimi and M Tavana ldquoAn integratedgreen supplier selection approachwith analytic network processand improved Grey relational analysisrdquo International Journal ofProduction Economics vol 159 pp 178ndash191 2015

[23] M Punniyamoorthy P Mathiyalagan and P Parthiban ldquoAstrategic model using structural equation modeling and fuzzylogic in supplier selectionrdquo Expert Systems with Applicationsvol 38 no 1 pp 458ndash474 2011

[24] R M Grisi L Guerra and G Naviglio ldquoSupplier performanceevaluation for green supply chainmanagementrdquo inBusiness Per-formanceMeasurement andManagement pp 149ndash163 SpringerBerlin Germany 2010

[25] F Mafakheri M Breton and A Ghoniem ldquoSupplier selection-order allocation a two-stage multiple criteria dynamic pro-gramming approachrdquo International Journal of Production Eco-nomics vol 132 no 1 pp 52ndash57 2011

[26] Y-J Chen ldquoStructured methodology for supplier selection andevaluation in a supply chainrdquo Information Sciences vol 181 no9 pp 1651ndash1670 2011

[27] W-PWang ldquoA fuzzy linguistic computing approach to supplierevaluationrdquo Applied Mathematical Modelling vol 34 no 10 pp3130ndash3141 2010

[28] M-L Tseng and A S F Chiu ldquoEvaluating firmrsquos green supplychain management in linguistic preferencesrdquo Journal of CleanerProduction vol 40 pp 22ndash31 2013

[29] Q Zhu Y Dou and J Sarkis ldquoA portfolio-based analysisfor green supplier management using the analytical networkprocessrdquo Supply Chain Management vol 15 no 4 pp 306ndash3192010

[30] G A Keskin S Ilhan and C Ozkan ldquoThe Fuzzy ARTalgorithm a categorization method for supplier evaluation andselectionrdquo Expert Systems with Applications vol 37 no 2 pp1235ndash1240 2010

[31] C-Y Shen and K-T Yu ldquoEnhancing the efficacy of supplierselection decision-making on the initial stage of new productdevelopment a hybrid fuzzy approach considering the strategicand operational factors simultaneouslyrdquo Expert Systems withApplications vol 36 no 8 pp 11271ndash11281 2009

[32] K Govindan R Khodaverdi and A Jafarian ldquoA fuzzy multicriteria approach for measuring sustainability performance ofa supplier based on triple bottom line approachrdquo Journal ofCleaner Production vol 47 pp 345ndash354 2013

[33] G Tuzkaya A Ozgen D Ozgen and U R Tuzkaya ldquoEnvi-ronmental performance evaluation of suppliers a hybrid fuzzymulti-criteria decision approachrdquo International Journal of Envi-ronmental ScienceampTechnology vol 6 no 3 pp 477ndash490 2009

[34] Q Zhu J Sarkis and K-H Lai ldquoInitiatives and outcomes ofgreen supply chain management implementation by Chinesemanufacturersrdquo Journal of Environmental Management vol 85no 1 pp 179ndash189 2007

[35] W-C Yeh and M-C Chuang ldquoUsing multi-objective geneticalgorithm for partner selection in green supply chain problemsrdquoExpert Systems with Applications vol 38 no 4 pp 4244ndash42532011

[36] A Awasthi S S Chauhan and S K Goyal ldquoA fuzzy multi-criteria approach for evaluating environmental performance ofsuppliersrdquo International Journal of Production Economics vol126 no 2 pp 370ndash378 2010

[37] J Sarkis ldquoManufacturingrsquos role in corporate environmentalsustainability-Concerns for the new millenniumrdquo InternationalJournal of Operations amp Production Management vol 21 no 5-6 pp 666ndash686 2001

[38] S MMirhedayatian M Azadi and R Farzipoor Saen ldquoA novelnetwork data envelopment analysis model for evaluating greensupply chain managementrdquo International Journal of ProductionEconomics vol 147 pp 544ndash554 2014

10 Mathematical Problems in Engineering

[39] C Wu and D Barnes ldquoAn integrated model for green partnerselection and supply chain constructionrdquo Journal of CleanerProduction vol 112 pp 2114ndash2132 2016

[40] G Bruno E Esposito A Genovese andR Passaro ldquoAHP-basedapproaches for supplier evaluation problems and perspectivesrdquoJournal of Purchasing and Supply Management vol 18 no 3 pp159ndash172 2012

[41] F R L Junior L Osiro and L C R Carpinetti ldquoA comparisonbetween Fuzzy AHP and Fuzzy TOPSIS methods to supplierselectionrdquo Applied Soft Computing vol 21 pp 194ndash209 2014

[42] A Kawa and W W Koczkodaj ldquoSupplier evaluation process bypairwise comparisonsrdquo Mathematical Problems in Engineeringvol 2015 Article ID 976742 9 pages 2015

[43] X Deng Y Hu Y Deng and S Mahadevan ldquoSupplier selectionusing AHP methodology extended by D numbersrdquo ExpertSystems with Applications vol 41 no 1 pp 156ndash167 2014

[44] N Xie and J Xin ldquoInterval grey numbers based multi-attributedecisionmakingmethod for supplier selectionrdquoKybernetes vol43 no 7 pp 1064ndash1078 2014

[45] J Lee H Cho and Y S Kim ldquoAssessing business impacts ofagility criterion and order allocation strategy in multi-criteriasupplier selectionrdquo Expert Systems with Applications vol 42 no3 pp 1136ndash1148 2015

[46] L Shen L Olfat K Govindan R Khodaverdi and A DiabatldquoA fuzzy multi criteria approach for evaluating green supplierrsquosperformance in green supply chain with linguistic preferencesrdquoResources Conservation and Recycling vol 74 pp 170ndash179 2012

[47] B Kanga Y Hu Y Deng and D Zhou ldquoA new methodologyof multicriteria decision-making in supplier selection based onZ-numbersrdquo Mathematical Problems in Engineering vol 2016Article ID 8475987 17 pages 2016

[48] N Asthana and M Gupta ldquoSupplier selection using artificialneural network and genetic algorithmrdquo International Journal ofIndian Culture and Business Management vol 11 no 4 pp 457ndash472 2015

[49] D Dubois and H Prade ldquoOperations on fuzzy numbersrdquo Inter-national Journal of Systems Science vol 9 no 6 pp 613ndash6261978

[50] A Kaufmann and M M Gupta Introduction to Fuzzy Arith-metic Theory and Applications The Arden Shakespeare 1991

[51] L A Zadeh ldquoThe concept of a linguistic variable and its appli-cation to approximate reasoningmdashIrdquo Information Sciences vol8 no 3 pp 199ndash249 1975

[52] L A Zadeh ldquoThe concept of a linguistic variable and its applica-tion to approximate reasoningmdashIIrdquo Information Sciences vol 8no 4 pp 301ndash357 1975

[53] D-Y Chang ldquoApplications of the extent analysis method onfuzzy AHPrdquo European Journal of Operational Research vol 95no 3 pp 649ndash655 1996

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MathematicsJournal of

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Mathematical Problems in Engineering

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Differential EquationsInternational Journal of

Volume 2014

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Mathematical PhysicsAdvances in

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CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

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Function Spaces

Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

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Algebra

Discrete Dynamics in Nature and Society

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Decision SciencesAdvances in

Discrete MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom

Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Stochastic AnalysisInternational Journal of

Mathematical Problems in Engineering 3

Table 1 Green supplier selection and evaluation criteria

Criteria Subcriteria Sub-subcriteriadefinition References

Economic criteria

Cost Product price logistics cost and payment terms [20ndash24]

Quality ISO quality system installed quality award product performancewarranties and claim policies and repair and return rate [4 12 22 23 25]

Delivery Lead time on-time delivery safety and security of components andappropriateness of the packaging [21 23 26 27]

Technology Communication and e-commerce systems capability of researchdevelopment and innovation and production facilities and capacity [22 23 26]

Flexibility

Product volume changes short setup time conflict resolution usingflexible machines the demand that can be profitably sustained andtime or cost required to add new products to the existing productionoperation

[22 28 29]

Financialcapability Financial position economical stability and price strategy [12 23 30]

Culture Communication openness vendorrsquos image and mutual trust [20 23 27]Innovativeness New launch of products and new launch of technologies [31]

Relationship Long term relationship relationship closeness communicationopenness and reputation for integrity [23 28 29]

Environmental criteria

Pollutionproduction

Average volume of air pollutants waste water solid waste andharmful materials released [19 22 32]

Pollutioncontrol Remediation and end-of-pipe controls [2 19 33]

Resourceconsumption Consumption of resources in terms of raw material energy and water [19 32]

EcodesignDesign for resource efficiency design of products for reuse recycleand recovery of material design for reduction or elimination ofhazardous materials

[28 32 34 35]

Environmentalmanagementsystem

Environmental certificates such as ISO 14000 continuous monitoringand regulatory compliance environmental policies green processplanning and internal control process

[2 19 28 32ndash34 36 37]

Green image Ratio of green customers to total customers and social responsibility [2 33 35]

Greencompetencies

Materials used in the supplied components that reduce the impact onnatural resources and ability to alter process and product for reducingthe impact on natural resources

[2 33 34 36 37]

Green product Use of recycled and nontoxic materials green packaging and excesspackaging reduction [6 34 36]

Staffenvironmentaltraining

Staff training on environmental issues [36]

Managementcommitment

Commitment of senior managers to support and improve greensupply chain management initiatives [34 36]

GreenTechnology

The application of the environmental science to conserve the naturalenvironment and resources and to curb the negative impact of humaninvolvement

[6 34]

structural equation modeling and fuzzy logic [23] optimummathematical planning model [35] linguistic preferences[28] fuzzy linguistic computing approach [27] Fuzzy Adap-tive ResonanceTheory algorithm [30] and genetic algorithm(GA) [48]

Although a number of methods have been studiedmost of the studies have only used either economic orenvironmental criteria for evaluating the suppliers Thereare few studies considering economic and environmentalcriteria simultaneously in the supplier selection process

And each of those methods has its own advantages anddisadvantages this study proposes the integrated approachby combining the two most popular techniques for solvinggreen supplier problems that is fuzzy TOPSIS and fuzzyAHP In the proposed approach the fuzzy AHP is employedto determine the important weights of criteria under vagueenvironmentThen the fuzzy TOPSIS is used to evaluate andrank the potential suppliers In addition both economic andenvironmental criteria are considered in proposed MCDMapproach

4 Mathematical Problems in Engineering

3 Fuzzy Numbers

There are various ways to define fuzzy numbers This paperdefines the concept of fuzzy numbers as follows [49 50]

Definition 1 A real fuzzy number119860 is described as any fuzzysubset of the real line 119877with membership function119891

119860 which

has the following properties

(a) 119891119860is a continuous mapping from 119877 to the closed

interval [0 1](b) 119891119860(119909) = 0 for all 119909 isin (minusinfin 119886]

(c) 119891119860is strictly increasing on [119886 119887]

(d) 119891119860(119909) = 1 for all 119909 isin [119887 119888]

(e) 119891119860is strictly decreasing on [119888 119889]

(f) 119891119860(119909) = 0 for all 119909 isin (119889infin]

where 119886 119887 119888 and 119889 are real numbers Unless elsewherespecified this research assumes that119860 is convex and bounded(ie minusinfin lt 119886 119889 lt infin)

Definition 2 The fuzzy number 119860 = [119886 119887 119888 119889] is a trape-zoidal fuzzy number if its membership function is given by

119891119860 (119909) =

119891119871

119860(119909) 119886 le 119909 le 119887

1 119887 le 119909 le 119888

119891119877

119860(119909) 119888 le 119909 le 119889

0 otherwise

(1)

where 119891119871119860(119909) and 119891

119877

119860(119909) are the left and right membership

functions of 119860 respectively [50]When 119887 = 119888 the trapezoidal fuzzy number is reduced

to a triangular fuzzy number and can be denoted by 119860 =

(119886 119887 119889) Thus triangular fuzzy numbers are special cases oftrapezoidal fuzzy numbers

Definition 3 (the distance between fuzzy triangular numbers)Let119860 = (119886

1 1198871 1198891) and119861 = (119886

2 1198872 1198892) be two triangular fuzzy

numbersThedistance between them is given using the vertexmethod by

119889 (119860 119861) = radic1

3[(1198861minus 1198862)2+ (1198871minus 1198872)2+ (1198891minus 1198892)2] (2)

Definition 4 (120572-cuts) The 120572-cuts of fuzzy number 119860 can bedefined as 119860120572 = 119909 | 119891

119860(119909) ge 120572 120572 isin [0 1] where 119860120572

is a nonempty bounded closed interval contained in 119877 andcan be denoted by 119860120572 = [119860

120572

119897 119860120572

119906] where 119860120572

119897and 119860120572

119906are its

lower and upper bounds respectively [50] For example if atriangular fuzzy number 119860 = (119886 119887 119889) then the 120572-cuts of 119860can be expressed as follows

119860120572= [119860120572

119897 119860120572

119906] = [(119887 minus 119886) 120572 + 119886 (119887 minus 119889) 120572 + 119889] (3)

Definition 5 (arithmetic operations on fuzzy numbers)Given fuzzy numbers 119860 and 119861 where 119860 119861 isin 119877

+ the 120572-cutsof119860 and 119861 are119860120572 = [119860

120572

119897 119860120572

119906] and 119861120572 = [119861

120572

119897 119861120572

119906] respectively

By the interval arithmetic some main operations of 119860 and 119861can be expressed as follows [50]

(119860 oplus 119861)120572= [119860120572

119897+ 119861120572

119897 119860120572

119906+ 119861120572

119906]

(119860 ⊖ 119861)120572= [119860120572

119897minus 119861120572

119906 119860120572

119906minus 119861120572

119897]

(119860 otimes 119861)120572= [119860120572

119897sdot 119861120572

119897 119860120572

119906sdot 119861120572

119906]

(119860 ⊘ 119861)120572= [

119860120572

119897

119861120572119906

119860120572

119906

119861120572

119897

]

(119860 otimes 119903)120572= [119860120572

119897sdot 119903 119860120572

119906sdot 119903] 119903 isin 119877

+

(4)

4 Proposed Approach forGreen Suppliers Selection

In this section an approach for green supplier selection bycombining fuzzy TOPSIS and fuzzy AHP method is pre-sented The proposed approach offers a new way to solve thegreen supplier selection problem effectively and efficientlysince it enables decision makers to minimize the negativeenvironmental impact of the supply chain while simultane-ously maximizing business performance The procedure ofthe proposed approach is stated as follows

Step 1 Identify a number of economic and environmentalcriteria

Step 2 Aggregate the important weights of the criteria

Step 3 Aggregate the ratings of suppliers versus the criteria

Step 4 Normalize the fuzzy decision matrix

Step 5 Construct the weighted normalized fuzzy decisionmatrix

Step 6 Calculate normalized weighted rating

Step 7 Calculate 119860+ 119860minus 119889+119894 and 119889minus

119894

Step 8 Obtain the closeness coefficient

Assume that a committee of 119897decisionmakers (119863119905 119905 = 1 sim

119897) is responsible for evaluating 119898 suppliers (119860119894 119894 = 1 sim 119898)

under 119899 selected criteria (119862119895 119895 = 1 sim 119899) where the suitability

ratings of alternatives under each of the criteria as well as theweights of the criteria are assessed in linguistic terms [51 52]represented by triangular fuzzy numbers

41 Identify a Number of Economic and EnvironmentalCriteria In this study the criteria are classified into twocategories that is economic criteria (119862

119895 119895 = 1 119897) and

environmental criteria (119862119895 119895 = 119897 + 1 119899) The number of

economic and environmental criteria is selected from Table 1through screening by the decision makers

42 Aggregate the Important Weights of the Criteria In thissection a fuzzy AHP is applied to obtain more decisivejudgments by prioritizing the economic and environmental

Mathematical Problems in Engineering 5

criteria Several fuzzy AHP methods have been proposed inliterature to solve the MCDM problems This study adoptsthe extent analysis method proposed by Chang [53] dueto its popularity and computational simplicity Changrsquos [53]method is briefly discussed as follows

Let 119883 = 1199091 1199092 119909

119899 be an object set and let 119880 =

1199061 1199062 119906

119898 be a goal set According to Chang [53] each

object is taken and an extent analysis for each goal (119892119894)

is performed respectively Therefore the 119898 extent analysisvalues for each object are obtained as1198721

1198921198941198722

119892119894 119872

119899

119892119894 119894 =

1 2 119899 where 119872119895119892119894(119895 = 1 2 119898) are triangular fuzzy

numbers (TFNs)Assume that 119872119895

119892119894are the values of extent analysis of the

119894th object for119898 goalsThe value of fuzzy synthetic extent 119878119894is

defined as follows

119878119894=

119898

sum

119895=1

119872119895

119892119894otimes [

[

119899

sum

119894=1

119898

sum

119895=1

119872119895

119892119894

]

]

minus1

(5)

where sum119898

119895=1119872119895

119892119894= (sum

119898

119895=1119897119895 sum119898

119895=1119898119895 sum119898

119895=1119906119895) 119895 = 1 2

119898 119894 = 1 2 119899

Let1198721= (1198971 1198981 1199061) and119872

2= (1198972 1198982 1199062) be two TFNs

whereby the degree of possibility of 1198721ge 1198722is defined as

follows119881 (1198721ge 1198722) = sup119909ge119910

[min (1205831198721

(119909) 1205831198722(119909))] (6)

Themembership degree of possibility is expressed as follows

119881 (1198721ge 1198722) = hgt (119872

1cap1198722) = 1205831198722

(119889)

=

1 if 1198981ge 1198982

0 if 1198972ge 1199061

1198972minus 1199061

(1198972minus 1199061) + (119898

1minus 1198982)

otherwise

(7)

where 119889 is the ordinate of the highest intersection point oftwo membership functions 120583

1198721(119909) and 120583

1198722(119909)

The degree of possibility for a convex fuzzy number to begreater than 119896 convex fuzzy numbers is defined as follows

119881 (119872 ge 11987211198722 119872

119896) = min119881 (119872 ge 119872

119894)

119894 = 1 2 119896

(8)

The weight vector is given by

1198821015840= (1198891015840(1198601) 1198891015840(1198602) 119889

1015840(119860119899))119879

(9)

where1198891015840(119860119894) = min119881 (119878

119894ge 119878119896)

(119894 = 1 2 119899) 119896 = 1 2 119899 119896 = 119894

(10)

Via normalization we obtain the weight vectors as follows

119882 = (119889 (1198601) 119889 (119860

2) 119889 (119860

119899))119879 (11)

where119882 is a nonfuzzy numberThis study adopts a ldquoLikert Scalerdquo of fuzzy numbers

starting from 1 to 9 to transform the linguistic values intotriangular fuzzy numbers as shown in Table 2

43 Aggregate the Ratings of Suppliers versus the Criteria Let119909119894119895119905= (119890119894119895119905 119891119894119895119905 119892119894119895119905) 119894 = 1 sim 119898 119895 = 1 sim 119899 119905 = 1 sim 119897 be the

suitability rating assigned to green supplier 119860119894 by decision

maker 119863119905 for criterion 119862

119895 The averaged suitability rating

119909119894119895= (119890119894119895 119891119894119895 119892119894119895) can be evaluated as follows

119909119894119895=1

119897otimes (1199091198941198951oplus 1199091198941198952oplus sdot sdot sdot oplus 119909

119894119895119905oplus sdot sdot sdot oplus 119909

119894119895119897) (12)

where 119890119894119895= (1119897) sum

119897

119905=1119890119894119895119905 119891119894119895= (1119897) sum

119897

119905=1119891119894119895119905 and 119892

119894119895=

(1119897) sum119897

119905=1119892119894119895119905

44 Normalize Performance of Suppliers versus Criteria Toensure compatibility between average ratings and averageweights the average ratings are normalized into comparablescales Suppose that 119903

119894119895= (119886119894119895 119887119894119895 119888119894119895) is the performance of

green supplier 119894 on criteria 119895 The normalized value 119909119894119895can

then be denoted as follows

119909119894119895= (

119886119894119895

119888lowast

119895

119887119894119895

119888lowast

119895

119888119894119895

119888lowast

119895

) 119895 isin 119861

119909119894119895= (

119886minus

119895

119888119894119895

119886minus

119895

119887119894119895

119886minus

119895

119886119894119895

) 119895 isin 119862

(13)

where 119886minus119895= min

119894119886119894119895 119888lowast119895= max

119894119888119894119895 119894 = 1 119898 and 119895 =

1 119899

45 Calculate Normalized Weighted Rating The normalizedweighted ratings 119866

119894are calculated by multiplying the nor-

malized average rating 119909119894119895with its associated weights 119908

119895119905as

follows

119866119894= 119909119894119895otimes 119908119895 119894 = 1 119898 119895 = 1 ℎ (14)

46 Calculate 119860+ 119860minus 119889+

119894 and 119889

minus

119894 The fuzzy positive-

ideal solution (FPIS 119860+) and fuzzy negative-ideal solution(FNIS 119860minus) are obtained as follows

119860+= (10 10 10)

119860minus= (00 00 00)

(15)

The distance of each green supplier119860119894 119894 = 1 119898 from119860

+

and 119860minus is calculated as follows

119889+

119894= radic

119899

sum

119894=1

(119866119894minus 119860+)

2

119889minus

119894= radic

119899

sum

119894=1

(119866119894minus 119860minus)

2

(16)

where 119889+119894represents the shortest distance of alternative 119860

119894

and 119889minus119894represents the farthest distance of green supplier 119860

119894

6 Mathematical Problems in Engineering

Table 2 Linguistic variables describing weights of the ldquoHOWsrdquo criteria

Linguistic scale for importance Triangular fuzzy scale119872 = (119897119898 119906)Just equal (10 10 10)Equal importance (10 10 30)Weak importance (10 30 50)Strong importance (30 50 70)Very strong importance (50 70 90)Extremely importance (70 90 90)If factor 119894 has one of the above numbers assigned to it when compared tofactor 119895 then 119895 has the reciprocal value when compared with 119894

Reciprocals of above119872minus1

1asymp (1119906

1 11198981 11198971)

47 Obtain the Closeness Coefficient Thecloseness coefficientof each green supplier which is usually defined to determinethe ranking order of all green suppliers is calculated asfollows

CC119894=

119889minus

119894

119889+

119894+ 119889minus

119894

(17)

A higher value of the closeness coefficient indicates thatan alternative is simultaneously closer to PIS and furtherfromNISThe closeness coefficient of each alternative is usedto determine the ranking order of all green suppliers andindicates the best one among a set of given feasible greensuppliers

5 Case Study

In this paper a comprehensive green supplier selectionmodel is proposed by considering the important criteria ineconomic and environmental aspects for evaluating greensuppliers The proposed method is applied on the case ofthe Taiwanese optical prism (TOP) manufacturing entity inLuminance Enhancement Film (LEF) industry to solve greensuppliers selection

TOP founded in late 2003 is the leading optical prismmanufacturer in Taiwan TOP focuses on advanced productdevelopment and quality improvement However TOP isnow dealing with the increase in competition Moreover theLCD product life cycle is very short qualified suppliers asTOP frequently have to provide innovative products withina limited lead time for customers verification to meet time-to-market as well Consequently with the purpose of main-taining the existing customers satisfaction and attractingnew international customers to improve market share theselection of quality constant green suppliers for long termcooperation is extremely essential for survival of TOP

When TOP confirmed its role and strategy as a greensupplier TOP needs to evaluate its core competences andidentify the gap between customer needs and consultantsuggestions TOP then restructures the ecological environ-ment of the industry TOP has employed the green SCMsimultaneously considering environmental and economicaspects to either comply with regulation or meet customerneeds Furthermore TOP has proactively invested both qual-ity and environmental management system such as quality

system of economic criteria ISO9001 and QC080000 andenvironmental criteria ISO14001 and OHSAS18001 TOP hasimplemented a continuous quality improvement programand constituted an international standard as a platform totraining staffs as well as suppliers Those activities eithersave the costs of customers involved with their supplierdevelopment program or strengthen TOPrsquos green brandimage

TOP has learned and accumulated plenty of green SCMdomain knowledge and capabilities as a main supplier ofLCD supply chain through the two-stage process of the rawmaterial quality verification and integration all of material inone product for each customerThus TOP reversely requeststhe suppliers to comply with its customer environmental andeconomic requirement Under the consensus of a multidisci-plinary group of decision makers with various points of viewand representing the different services of the company TOPrsquosmanagers and heads of departments have decided that prod-uct price ISO quality system and lead time are economiccriteria Green technology and environmental certificate areenvironmental criteria The managers of the departmentssuch as Employee Health and Safety Production QualityControl and Assessment and Purchasing were required tomake their evaluation respectively

In reality TOP must work with suppliers for green prod-uct development Quality control and supply ability of eco-nomic criteria are the most important customer requirementfactors which related to green products TOPrsquos managementteam continuously integrates resources to investigate greenproducts such as light lean production and energy savingto satisfy stakeholders TOP is keeping good relationshipwiththe suppliers that will benefit from the purchasingmaterials ifneeded Additionally TOP also maintains good relationshipwith customers who will provide TOP opportunities ininnovative product developing and meeting the needs ofcustomers easier

The case revealed that the green criteria such as environ-ment and sustainability do not yet play a crucial role withingreen supplier selection procedures in enterprise practiceDue to the environmental regulations suppliers must meetsome minimum requirements in order to be eligible to workwith focal firms on the supply chain After that most of thecompanies do not apply environmental criteria to discrimi-nate qualified suppliers instead customers require suppliersto provide information such as Certificate of Nonuse of

Mathematical Problems in Engineering 7

Table 3 Fuzzy pairwise comparison of economic and environmental criteria

Criteria 1198621

1198622

1198623

1198624

1198625

1198621

(10 10 10) (10 30 50) (50 70 90) (10 30 50) (10 10 30)1198622

(15 13 11) (10 10 10) (19 17 15) (15 13 11) (50 70 90)1198623

(19 17 15) (50 70 90) (10 10 10) (17 15 13) (17 15 13)1198624

(15 13 11) (10 30 50) (30 50 70) (10 10 10) (13 11 11)1198625

(13 11 11) (19 17 15) (30 50 70) (10 10 30) (10 10 10)

Table 4 Fuzzy weights of the economic and environmental criteria

Criteria Fuzzy weight1198621

(0123 0295 0699)1198622

(0089 0173 0371)1198623

(0087 0168 0330)1198624

(0076 0203 0456)1198625

(0074 0160 0371)

Controlled Substances Certificate of Nonuse of Other Con-trolled Substances Material Safety Data Sheet and TestReport of customer assigned items issued by SGS annuallyThose certificates concern quality of economic criterion andpollution control of environmental criterion

According to institutional theory implementation ofgreen SCM is due to mimetic and normative (competitiveand benchmarking)mechanisms Facing environmental pro-tection pressure and legitimacy isomorphism pressure enter-prises must comply with social expectation and maintainconsistency with external environment to survive Thus theenvironmental and economic dimensionsmust be consideredsimultaneously [5] Consequently the proposed method isapplied on the case of TOP following the steps below

Step 1 (identify a number of economic and environmental cri-teria) In this study the data used as input to implement theproposed green supplier selection and evaluate the methodwere collected by means of semistructured interviews withthe top managers and head of departments Four companymanagers were required to make their evaluation respec-tively according to their preferences for important weightsof selection criteria and ratings of green suppliers

Using Table 1 and discussions with a companyrsquos top man-agers and heads of departments five criteria of economicsand environment for green supplier selection were selectedEconomic criteria include product price (119862

1) ISO quality

system (1198622) and lead time (119862

3) Green technology (119862

4) and

environmental certificate (1198625) are environmental criteria

Step 2 (aggregate the important weights of the criteria)After the determination of the green supplier criteria eachof four company managers is asked to conduct a pairwisecomparison with regard to the different criteria using thefuzzy linguistic assessment variables (see Table 2 for thesevariables) The completed matrices for the required cell areshown in Table 3 Applying (5)ndash(8) the final weights of theeconomic and environmental criteria are obtained as shownin Table 4

Step 3 (aggregate the ratings of suppliers versus the criteria)After the determination of the suppliers assessment criteriafour company managers rate each supplier according to eachcriterion A linguistic rating set of S was used to express theopinions of the managers where S = (VP P F G VG) VP(Very Poor) = (00 01 02) P (Poor) = (01 03 05) F (Fair) =(03 05 07) G (Good) = (05 07 09) and VG (Very Good)= (08 09 10) Table 5 gives the aggregated suitability ratingsof four green suppliers (119860

1 1198602 1198603 and 119860

4) using (12)

Step 4 (normalized performance of suppliers versus criteria)For simplicity and practicality all of the fuzzy numbers in thispaper are defined in the closed interval [0 1] Consequentlythe normalization procedure is no longer needed

Step 5 (calculate normalized weighted rating) Using (14) thenormalized weighted ratings 119866

119894can be obtained as shown in

Table 6

Step 6 (calculate 119860+ 119860minus 119889+119894 and 119889minus

119894) As shown in Table 7

the distance of each green supplier from 119860+ and 119860minus can be

calculated by (15)sim(16)

Step 7 (obtain the closeness coefficient) The closeness coef-ficients of green suppliers can be calculated by (17) as shownin Table 8 Therefore the ranking order of the four greensuppliers is 119860

3gt 1198604gt 1198601gt 1198602 Consequently the best

green supplier is 1198603

6 Conclusion

While the types of industry vary the key strategies ofgreen supplier selection also are changed Nevertheless allindustries should concern suppliers from both economicand environmental aspects because suppliers could influencefirmsrsquo performance and stakeholders

Green supplier selection is an important and complicatedMCDM problem requiring evaluation of multiple economicand environmental criteria incorporating vagueness andimprecision with the involvement of a group of expertsAlthough numerous studies have used economic criteria inthe supplier selection process limited studies have consid-ered the economic and environmental criteria simultane-ously The implementation of green supply management wasnot well understood This paper has proposed an integratedfuzzy MCDM approach to support the green suppliers selec-tion and the evaluation process In the proposed approachboth economic and environmental criteria were consideredIn order to overcome the shortcomings of the existing fuzzy

8 Mathematical Problems in Engineering

Table 5 Aggregate of the green supplier ratings versus criteria

Criteria Green suppliers Company managers119903119894119895

1198631

1198632

1198633

1198634

1198621

1198601

VG G G VG (0650 0800 0950)1198602

F G G F (0400 0600 0800)1198603

G G G G (0500 0700 0900)1198604

G F G G (0450 0650 0850)

1198622

1198601

G G G G (0500 0700 0900)1198602

F F G F (0350 0550 0750)1198603

G G VG G (0575 0750 0925)1198604

VG G VG G (0650 0800 0950)

1198623

1198601

G F G F (0400 0600 0800)1198602

F F F G (0350 0550 0750)1198603

VG G VG G (0650 0800 0950)1198604

F G F F (0350 0550 0750)

1198624

1198601

F G G F (0400 0600 0800)1198602

G VG G G (0575 0750 0925)1198603

G VG VG G (0650 0800 0950)1198604

VG G VG G (0650 0800 0950)

1198625

1198601

G G G G (0500 0700 0900)1198602

VG G G VG (0650 0800 0950)1198603

G G G VG (0575 0750 0925)1198604

VG G G VG (0650 0800 0950)

Table 6 Normalized weighted ratings of each market segment

Green suppliers 119866119894

1198601

(0045 0138 0392)1198602

(0041 0129 0372)1198603

(0052 0151 0413)1198604

(0048 0143 0396)

Table 7 The distance of each green supplier from 119860+ and 119860minus

Green suppliers 119889+

119889minus

1198601

1422 04181198602

1440 03961198603

1402 04421198604

1416 0424

Table 8 Closeness coefficients of alternatives

Alternatives Closeness coefficient Ranking1198601

0227 31198602

0216 41198603

0240 11198604

0230 2

TOPSIS technique this study has integrated the fuzzy TOP-SIS technique with the fuzzy AHP method to determine theimportant weights of economic and environmental criteriaFinally the proposed approach was employed to solve a realproblem in the LEF industry The results showed that the

proposed approach is effective in supplier selection for thecompany The application also indicated that the computa-tional procedure is efficient and easy to use in practice Futureresearch should focus on developing an extension of fuzzyMCDM approach to segment the green suppliers based onthe economic and environmental aspects Different methodsmay be applied to select green suppliers and the results shouldbe compared with the proposed approach The proposedapproach can also be applied to other management problemswith similar settings

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

References

[1] Y-S Chen and C-H Chang ldquoThe determinants of green prod-uct development performance Green dynamic capabilitiesgreen transformational leadership and green creativityrdquo Journalof Business Ethics vol 116 no 1 pp 107ndash119 2013

[2] A H I Lee H-Y Kang C-F Hsu and H-C Hung ldquoA greensupplier selectionmodel for high-tech industryrdquo Expert Systemswith Applications vol 36 no 4 pp 7917ndash7927 2009

[3] K Govindan S Rajendran J Sarkis and P Murugesan ldquoMulticriteria decision making approaches for green supplier evalua-tion and selection a literature reviewrdquo Journal of Cleaner Pro-duction vol 98 pp 66ndash83 2015

Mathematical Problems in Engineering 9

[4] R J Kuo Y C Wang and F C Tien ldquoIntegration of artificialneural network and MADA methods for green supplier selec-tionrdquo Journal of Cleaner Production vol 18 no 12 pp 1161ndash11702010

[5] A Gunasekaran and D Gallear ldquoSpecial Issue on Sustainabledevelopment of manufacturing and servicesrdquo InternationalJournal of Production Economics vol 140 no 1 pp 1ndash6 2012

[6] J Sarkis Q Zhu and K-H Lai ldquoAn organizational theoreticreview of green supply chain management literaturerdquo Interna-tional Journal of Production Economics vol 130 no 1 pp 1ndash152011

[7] A Appolloni H Sun F Jia and X Li ldquoGreen Procurement inthe private sector a state of the art review between 1996 and2013rdquo Journal of Cleaner Production vol 85 pp 122ndash133 2014

[8] H C Pimenta and P D Ball ldquoAnalysis of environmentalsustainability practices across upstream supply chain manage-mentrdquo Procedia CIRP vol 26 pp 677ndash682 2015

[9] C-L Hwang andK YoonMultiple Attribute DecisionMakingmdashMethods and Applications A State of the Art Survey SpringerNew York NY USA 1981

[10] H-S Shih H-J Shyur and E S Lee ldquoAn extension of TOPSISfor group decision makingrdquoMathematical and Computer Mod-elling vol 45 no 7-8 pp 801ndash813 2007

[11] T L SaatyTheAnalytical Hierarchy Process McGraw-Hill NewYork NY USA 1980

[12] G Buyukozkan and G Cifci ldquoEvaluation of the green supplychain management practices a fuzzy ANP approachrdquo Produc-tion Planning and Control vol 23 no 6 pp 405ndash418 2012

[13] C-C Sun ldquoA performance evaluation model by integratingfuzzy AHP and fuzzy TOPSIS methodsrdquo Expert Systems withApplications vol 37 no 12 pp 7745ndash7754 2010

[14] W Xia and Z Wu ldquoSupplier selection with multiple criteria involume discount environmentsrdquoOmega vol 35 no 5 pp 494ndash504 2007

[15] I Chamodrakas D Batis and D Martakos ldquoSupplier selectionin electronic marketplaces using satisficing and fuzzy AHPrdquoExpert Systems with Applications vol 37 no 1 pp 490ndash4982010

[16] K Shaw R Shankar S S Yadav and L S Thakur ldquoSupplierselection using fuzzy AHP and fuzzy multi-objective linearprogramming for developing low carbon supply chainrdquo ExpertSystems with Applications vol 39 no 9 pp 8182ndash8192 2012

[17] O Kilincci and S A Onal ldquoFuzzy AHP approach for supplierselection in a washing machine companyrdquo Expert Systems withApplications vol 38 no 8 pp 9656ndash9664 2011

[18] A H I Lee ldquoA fuzzy supplier selection model with the consid-eration of benefits opportunities costs and risksrdquo Expert Sys-tems with Applications vol 36 no 2 pp 2879ndash2893 2009

[19] C Bai and J Sarkis ldquoGreen supplier development analyticalevaluation using rough set theoryrdquo Journal of Cleaner Produc-tion vol 18 no 12 pp 1200ndash1210 2010

[20] M Abdollahi M Arvan and J Razmi ldquoAn integrated approachfor supplier portfolio selection lean or agilerdquo Expert Systemswith Applications vol 42 no 1 pp 679ndash690 2015

[21] M S Memon Y H Lee and S I Mari ldquoGroup multi-criteriasupplier selection using combined grey systems theory anduncertainty theoryrdquo Expert Systems with Applications vol 42no 21 pp 7951ndash7959 2015

[22] S H Hashemi A Karimi and M Tavana ldquoAn integratedgreen supplier selection approachwith analytic network processand improved Grey relational analysisrdquo International Journal ofProduction Economics vol 159 pp 178ndash191 2015

[23] M Punniyamoorthy P Mathiyalagan and P Parthiban ldquoAstrategic model using structural equation modeling and fuzzylogic in supplier selectionrdquo Expert Systems with Applicationsvol 38 no 1 pp 458ndash474 2011

[24] R M Grisi L Guerra and G Naviglio ldquoSupplier performanceevaluation for green supply chainmanagementrdquo inBusiness Per-formanceMeasurement andManagement pp 149ndash163 SpringerBerlin Germany 2010

[25] F Mafakheri M Breton and A Ghoniem ldquoSupplier selection-order allocation a two-stage multiple criteria dynamic pro-gramming approachrdquo International Journal of Production Eco-nomics vol 132 no 1 pp 52ndash57 2011

[26] Y-J Chen ldquoStructured methodology for supplier selection andevaluation in a supply chainrdquo Information Sciences vol 181 no9 pp 1651ndash1670 2011

[27] W-PWang ldquoA fuzzy linguistic computing approach to supplierevaluationrdquo Applied Mathematical Modelling vol 34 no 10 pp3130ndash3141 2010

[28] M-L Tseng and A S F Chiu ldquoEvaluating firmrsquos green supplychain management in linguistic preferencesrdquo Journal of CleanerProduction vol 40 pp 22ndash31 2013

[29] Q Zhu Y Dou and J Sarkis ldquoA portfolio-based analysisfor green supplier management using the analytical networkprocessrdquo Supply Chain Management vol 15 no 4 pp 306ndash3192010

[30] G A Keskin S Ilhan and C Ozkan ldquoThe Fuzzy ARTalgorithm a categorization method for supplier evaluation andselectionrdquo Expert Systems with Applications vol 37 no 2 pp1235ndash1240 2010

[31] C-Y Shen and K-T Yu ldquoEnhancing the efficacy of supplierselection decision-making on the initial stage of new productdevelopment a hybrid fuzzy approach considering the strategicand operational factors simultaneouslyrdquo Expert Systems withApplications vol 36 no 8 pp 11271ndash11281 2009

[32] K Govindan R Khodaverdi and A Jafarian ldquoA fuzzy multicriteria approach for measuring sustainability performance ofa supplier based on triple bottom line approachrdquo Journal ofCleaner Production vol 47 pp 345ndash354 2013

[33] G Tuzkaya A Ozgen D Ozgen and U R Tuzkaya ldquoEnvi-ronmental performance evaluation of suppliers a hybrid fuzzymulti-criteria decision approachrdquo International Journal of Envi-ronmental ScienceampTechnology vol 6 no 3 pp 477ndash490 2009

[34] Q Zhu J Sarkis and K-H Lai ldquoInitiatives and outcomes ofgreen supply chain management implementation by Chinesemanufacturersrdquo Journal of Environmental Management vol 85no 1 pp 179ndash189 2007

[35] W-C Yeh and M-C Chuang ldquoUsing multi-objective geneticalgorithm for partner selection in green supply chain problemsrdquoExpert Systems with Applications vol 38 no 4 pp 4244ndash42532011

[36] A Awasthi S S Chauhan and S K Goyal ldquoA fuzzy multi-criteria approach for evaluating environmental performance ofsuppliersrdquo International Journal of Production Economics vol126 no 2 pp 370ndash378 2010

[37] J Sarkis ldquoManufacturingrsquos role in corporate environmentalsustainability-Concerns for the new millenniumrdquo InternationalJournal of Operations amp Production Management vol 21 no 5-6 pp 666ndash686 2001

[38] S MMirhedayatian M Azadi and R Farzipoor Saen ldquoA novelnetwork data envelopment analysis model for evaluating greensupply chain managementrdquo International Journal of ProductionEconomics vol 147 pp 544ndash554 2014

10 Mathematical Problems in Engineering

[39] C Wu and D Barnes ldquoAn integrated model for green partnerselection and supply chain constructionrdquo Journal of CleanerProduction vol 112 pp 2114ndash2132 2016

[40] G Bruno E Esposito A Genovese andR Passaro ldquoAHP-basedapproaches for supplier evaluation problems and perspectivesrdquoJournal of Purchasing and Supply Management vol 18 no 3 pp159ndash172 2012

[41] F R L Junior L Osiro and L C R Carpinetti ldquoA comparisonbetween Fuzzy AHP and Fuzzy TOPSIS methods to supplierselectionrdquo Applied Soft Computing vol 21 pp 194ndash209 2014

[42] A Kawa and W W Koczkodaj ldquoSupplier evaluation process bypairwise comparisonsrdquo Mathematical Problems in Engineeringvol 2015 Article ID 976742 9 pages 2015

[43] X Deng Y Hu Y Deng and S Mahadevan ldquoSupplier selectionusing AHP methodology extended by D numbersrdquo ExpertSystems with Applications vol 41 no 1 pp 156ndash167 2014

[44] N Xie and J Xin ldquoInterval grey numbers based multi-attributedecisionmakingmethod for supplier selectionrdquoKybernetes vol43 no 7 pp 1064ndash1078 2014

[45] J Lee H Cho and Y S Kim ldquoAssessing business impacts ofagility criterion and order allocation strategy in multi-criteriasupplier selectionrdquo Expert Systems with Applications vol 42 no3 pp 1136ndash1148 2015

[46] L Shen L Olfat K Govindan R Khodaverdi and A DiabatldquoA fuzzy multi criteria approach for evaluating green supplierrsquosperformance in green supply chain with linguistic preferencesrdquoResources Conservation and Recycling vol 74 pp 170ndash179 2012

[47] B Kanga Y Hu Y Deng and D Zhou ldquoA new methodologyof multicriteria decision-making in supplier selection based onZ-numbersrdquo Mathematical Problems in Engineering vol 2016Article ID 8475987 17 pages 2016

[48] N Asthana and M Gupta ldquoSupplier selection using artificialneural network and genetic algorithmrdquo International Journal ofIndian Culture and Business Management vol 11 no 4 pp 457ndash472 2015

[49] D Dubois and H Prade ldquoOperations on fuzzy numbersrdquo Inter-national Journal of Systems Science vol 9 no 6 pp 613ndash6261978

[50] A Kaufmann and M M Gupta Introduction to Fuzzy Arith-metic Theory and Applications The Arden Shakespeare 1991

[51] L A Zadeh ldquoThe concept of a linguistic variable and its appli-cation to approximate reasoningmdashIrdquo Information Sciences vol8 no 3 pp 199ndash249 1975

[52] L A Zadeh ldquoThe concept of a linguistic variable and its applica-tion to approximate reasoningmdashIIrdquo Information Sciences vol 8no 4 pp 301ndash357 1975

[53] D-Y Chang ldquoApplications of the extent analysis method onfuzzy AHPrdquo European Journal of Operational Research vol 95no 3 pp 649ndash655 1996

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical Problems in Engineering

Hindawi Publishing Corporationhttpwwwhindawicom

Differential EquationsInternational Journal of

Volume 2014

Applied MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical PhysicsAdvances in

Complex AnalysisJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

OptimizationJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Operations ResearchAdvances in

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Function Spaces

Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of Mathematics and Mathematical Sciences

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Algebra

Discrete Dynamics in Nature and Society

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

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Decision SciencesAdvances in

Discrete MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom

Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Stochastic AnalysisInternational Journal of

4 Mathematical Problems in Engineering

3 Fuzzy Numbers

There are various ways to define fuzzy numbers This paperdefines the concept of fuzzy numbers as follows [49 50]

Definition 1 A real fuzzy number119860 is described as any fuzzysubset of the real line 119877with membership function119891

119860 which

has the following properties

(a) 119891119860is a continuous mapping from 119877 to the closed

interval [0 1](b) 119891119860(119909) = 0 for all 119909 isin (minusinfin 119886]

(c) 119891119860is strictly increasing on [119886 119887]

(d) 119891119860(119909) = 1 for all 119909 isin [119887 119888]

(e) 119891119860is strictly decreasing on [119888 119889]

(f) 119891119860(119909) = 0 for all 119909 isin (119889infin]

where 119886 119887 119888 and 119889 are real numbers Unless elsewherespecified this research assumes that119860 is convex and bounded(ie minusinfin lt 119886 119889 lt infin)

Definition 2 The fuzzy number 119860 = [119886 119887 119888 119889] is a trape-zoidal fuzzy number if its membership function is given by

119891119860 (119909) =

119891119871

119860(119909) 119886 le 119909 le 119887

1 119887 le 119909 le 119888

119891119877

119860(119909) 119888 le 119909 le 119889

0 otherwise

(1)

where 119891119871119860(119909) and 119891

119877

119860(119909) are the left and right membership

functions of 119860 respectively [50]When 119887 = 119888 the trapezoidal fuzzy number is reduced

to a triangular fuzzy number and can be denoted by 119860 =

(119886 119887 119889) Thus triangular fuzzy numbers are special cases oftrapezoidal fuzzy numbers

Definition 3 (the distance between fuzzy triangular numbers)Let119860 = (119886

1 1198871 1198891) and119861 = (119886

2 1198872 1198892) be two triangular fuzzy

numbersThedistance between them is given using the vertexmethod by

119889 (119860 119861) = radic1

3[(1198861minus 1198862)2+ (1198871minus 1198872)2+ (1198891minus 1198892)2] (2)

Definition 4 (120572-cuts) The 120572-cuts of fuzzy number 119860 can bedefined as 119860120572 = 119909 | 119891

119860(119909) ge 120572 120572 isin [0 1] where 119860120572

is a nonempty bounded closed interval contained in 119877 andcan be denoted by 119860120572 = [119860

120572

119897 119860120572

119906] where 119860120572

119897and 119860120572

119906are its

lower and upper bounds respectively [50] For example if atriangular fuzzy number 119860 = (119886 119887 119889) then the 120572-cuts of 119860can be expressed as follows

119860120572= [119860120572

119897 119860120572

119906] = [(119887 minus 119886) 120572 + 119886 (119887 minus 119889) 120572 + 119889] (3)

Definition 5 (arithmetic operations on fuzzy numbers)Given fuzzy numbers 119860 and 119861 where 119860 119861 isin 119877

+ the 120572-cutsof119860 and 119861 are119860120572 = [119860

120572

119897 119860120572

119906] and 119861120572 = [119861

120572

119897 119861120572

119906] respectively

By the interval arithmetic some main operations of 119860 and 119861can be expressed as follows [50]

(119860 oplus 119861)120572= [119860120572

119897+ 119861120572

119897 119860120572

119906+ 119861120572

119906]

(119860 ⊖ 119861)120572= [119860120572

119897minus 119861120572

119906 119860120572

119906minus 119861120572

119897]

(119860 otimes 119861)120572= [119860120572

119897sdot 119861120572

119897 119860120572

119906sdot 119861120572

119906]

(119860 ⊘ 119861)120572= [

119860120572

119897

119861120572119906

119860120572

119906

119861120572

119897

]

(119860 otimes 119903)120572= [119860120572

119897sdot 119903 119860120572

119906sdot 119903] 119903 isin 119877

+

(4)

4 Proposed Approach forGreen Suppliers Selection

In this section an approach for green supplier selection bycombining fuzzy TOPSIS and fuzzy AHP method is pre-sented The proposed approach offers a new way to solve thegreen supplier selection problem effectively and efficientlysince it enables decision makers to minimize the negativeenvironmental impact of the supply chain while simultane-ously maximizing business performance The procedure ofthe proposed approach is stated as follows

Step 1 Identify a number of economic and environmentalcriteria

Step 2 Aggregate the important weights of the criteria

Step 3 Aggregate the ratings of suppliers versus the criteria

Step 4 Normalize the fuzzy decision matrix

Step 5 Construct the weighted normalized fuzzy decisionmatrix

Step 6 Calculate normalized weighted rating

Step 7 Calculate 119860+ 119860minus 119889+119894 and 119889minus

119894

Step 8 Obtain the closeness coefficient

Assume that a committee of 119897decisionmakers (119863119905 119905 = 1 sim

119897) is responsible for evaluating 119898 suppliers (119860119894 119894 = 1 sim 119898)

under 119899 selected criteria (119862119895 119895 = 1 sim 119899) where the suitability

ratings of alternatives under each of the criteria as well as theweights of the criteria are assessed in linguistic terms [51 52]represented by triangular fuzzy numbers

41 Identify a Number of Economic and EnvironmentalCriteria In this study the criteria are classified into twocategories that is economic criteria (119862

119895 119895 = 1 119897) and

environmental criteria (119862119895 119895 = 119897 + 1 119899) The number of

economic and environmental criteria is selected from Table 1through screening by the decision makers

42 Aggregate the Important Weights of the Criteria In thissection a fuzzy AHP is applied to obtain more decisivejudgments by prioritizing the economic and environmental

Mathematical Problems in Engineering 5

criteria Several fuzzy AHP methods have been proposed inliterature to solve the MCDM problems This study adoptsthe extent analysis method proposed by Chang [53] dueto its popularity and computational simplicity Changrsquos [53]method is briefly discussed as follows

Let 119883 = 1199091 1199092 119909

119899 be an object set and let 119880 =

1199061 1199062 119906

119898 be a goal set According to Chang [53] each

object is taken and an extent analysis for each goal (119892119894)

is performed respectively Therefore the 119898 extent analysisvalues for each object are obtained as1198721

1198921198941198722

119892119894 119872

119899

119892119894 119894 =

1 2 119899 where 119872119895119892119894(119895 = 1 2 119898) are triangular fuzzy

numbers (TFNs)Assume that 119872119895

119892119894are the values of extent analysis of the

119894th object for119898 goalsThe value of fuzzy synthetic extent 119878119894is

defined as follows

119878119894=

119898

sum

119895=1

119872119895

119892119894otimes [

[

119899

sum

119894=1

119898

sum

119895=1

119872119895

119892119894

]

]

minus1

(5)

where sum119898

119895=1119872119895

119892119894= (sum

119898

119895=1119897119895 sum119898

119895=1119898119895 sum119898

119895=1119906119895) 119895 = 1 2

119898 119894 = 1 2 119899

Let1198721= (1198971 1198981 1199061) and119872

2= (1198972 1198982 1199062) be two TFNs

whereby the degree of possibility of 1198721ge 1198722is defined as

follows119881 (1198721ge 1198722) = sup119909ge119910

[min (1205831198721

(119909) 1205831198722(119909))] (6)

Themembership degree of possibility is expressed as follows

119881 (1198721ge 1198722) = hgt (119872

1cap1198722) = 1205831198722

(119889)

=

1 if 1198981ge 1198982

0 if 1198972ge 1199061

1198972minus 1199061

(1198972minus 1199061) + (119898

1minus 1198982)

otherwise

(7)

where 119889 is the ordinate of the highest intersection point oftwo membership functions 120583

1198721(119909) and 120583

1198722(119909)

The degree of possibility for a convex fuzzy number to begreater than 119896 convex fuzzy numbers is defined as follows

119881 (119872 ge 11987211198722 119872

119896) = min119881 (119872 ge 119872

119894)

119894 = 1 2 119896

(8)

The weight vector is given by

1198821015840= (1198891015840(1198601) 1198891015840(1198602) 119889

1015840(119860119899))119879

(9)

where1198891015840(119860119894) = min119881 (119878

119894ge 119878119896)

(119894 = 1 2 119899) 119896 = 1 2 119899 119896 = 119894

(10)

Via normalization we obtain the weight vectors as follows

119882 = (119889 (1198601) 119889 (119860

2) 119889 (119860

119899))119879 (11)

where119882 is a nonfuzzy numberThis study adopts a ldquoLikert Scalerdquo of fuzzy numbers

starting from 1 to 9 to transform the linguistic values intotriangular fuzzy numbers as shown in Table 2

43 Aggregate the Ratings of Suppliers versus the Criteria Let119909119894119895119905= (119890119894119895119905 119891119894119895119905 119892119894119895119905) 119894 = 1 sim 119898 119895 = 1 sim 119899 119905 = 1 sim 119897 be the

suitability rating assigned to green supplier 119860119894 by decision

maker 119863119905 for criterion 119862

119895 The averaged suitability rating

119909119894119895= (119890119894119895 119891119894119895 119892119894119895) can be evaluated as follows

119909119894119895=1

119897otimes (1199091198941198951oplus 1199091198941198952oplus sdot sdot sdot oplus 119909

119894119895119905oplus sdot sdot sdot oplus 119909

119894119895119897) (12)

where 119890119894119895= (1119897) sum

119897

119905=1119890119894119895119905 119891119894119895= (1119897) sum

119897

119905=1119891119894119895119905 and 119892

119894119895=

(1119897) sum119897

119905=1119892119894119895119905

44 Normalize Performance of Suppliers versus Criteria Toensure compatibility between average ratings and averageweights the average ratings are normalized into comparablescales Suppose that 119903

119894119895= (119886119894119895 119887119894119895 119888119894119895) is the performance of

green supplier 119894 on criteria 119895 The normalized value 119909119894119895can

then be denoted as follows

119909119894119895= (

119886119894119895

119888lowast

119895

119887119894119895

119888lowast

119895

119888119894119895

119888lowast

119895

) 119895 isin 119861

119909119894119895= (

119886minus

119895

119888119894119895

119886minus

119895

119887119894119895

119886minus

119895

119886119894119895

) 119895 isin 119862

(13)

where 119886minus119895= min

119894119886119894119895 119888lowast119895= max

119894119888119894119895 119894 = 1 119898 and 119895 =

1 119899

45 Calculate Normalized Weighted Rating The normalizedweighted ratings 119866

119894are calculated by multiplying the nor-

malized average rating 119909119894119895with its associated weights 119908

119895119905as

follows

119866119894= 119909119894119895otimes 119908119895 119894 = 1 119898 119895 = 1 ℎ (14)

46 Calculate 119860+ 119860minus 119889+

119894 and 119889

minus

119894 The fuzzy positive-

ideal solution (FPIS 119860+) and fuzzy negative-ideal solution(FNIS 119860minus) are obtained as follows

119860+= (10 10 10)

119860minus= (00 00 00)

(15)

The distance of each green supplier119860119894 119894 = 1 119898 from119860

+

and 119860minus is calculated as follows

119889+

119894= radic

119899

sum

119894=1

(119866119894minus 119860+)

2

119889minus

119894= radic

119899

sum

119894=1

(119866119894minus 119860minus)

2

(16)

where 119889+119894represents the shortest distance of alternative 119860

119894

and 119889minus119894represents the farthest distance of green supplier 119860

119894

6 Mathematical Problems in Engineering

Table 2 Linguistic variables describing weights of the ldquoHOWsrdquo criteria

Linguistic scale for importance Triangular fuzzy scale119872 = (119897119898 119906)Just equal (10 10 10)Equal importance (10 10 30)Weak importance (10 30 50)Strong importance (30 50 70)Very strong importance (50 70 90)Extremely importance (70 90 90)If factor 119894 has one of the above numbers assigned to it when compared tofactor 119895 then 119895 has the reciprocal value when compared with 119894

Reciprocals of above119872minus1

1asymp (1119906

1 11198981 11198971)

47 Obtain the Closeness Coefficient Thecloseness coefficientof each green supplier which is usually defined to determinethe ranking order of all green suppliers is calculated asfollows

CC119894=

119889minus

119894

119889+

119894+ 119889minus

119894

(17)

A higher value of the closeness coefficient indicates thatan alternative is simultaneously closer to PIS and furtherfromNISThe closeness coefficient of each alternative is usedto determine the ranking order of all green suppliers andindicates the best one among a set of given feasible greensuppliers

5 Case Study

In this paper a comprehensive green supplier selectionmodel is proposed by considering the important criteria ineconomic and environmental aspects for evaluating greensuppliers The proposed method is applied on the case ofthe Taiwanese optical prism (TOP) manufacturing entity inLuminance Enhancement Film (LEF) industry to solve greensuppliers selection

TOP founded in late 2003 is the leading optical prismmanufacturer in Taiwan TOP focuses on advanced productdevelopment and quality improvement However TOP isnow dealing with the increase in competition Moreover theLCD product life cycle is very short qualified suppliers asTOP frequently have to provide innovative products withina limited lead time for customers verification to meet time-to-market as well Consequently with the purpose of main-taining the existing customers satisfaction and attractingnew international customers to improve market share theselection of quality constant green suppliers for long termcooperation is extremely essential for survival of TOP

When TOP confirmed its role and strategy as a greensupplier TOP needs to evaluate its core competences andidentify the gap between customer needs and consultantsuggestions TOP then restructures the ecological environ-ment of the industry TOP has employed the green SCMsimultaneously considering environmental and economicaspects to either comply with regulation or meet customerneeds Furthermore TOP has proactively invested both qual-ity and environmental management system such as quality

system of economic criteria ISO9001 and QC080000 andenvironmental criteria ISO14001 and OHSAS18001 TOP hasimplemented a continuous quality improvement programand constituted an international standard as a platform totraining staffs as well as suppliers Those activities eithersave the costs of customers involved with their supplierdevelopment program or strengthen TOPrsquos green brandimage

TOP has learned and accumulated plenty of green SCMdomain knowledge and capabilities as a main supplier ofLCD supply chain through the two-stage process of the rawmaterial quality verification and integration all of material inone product for each customerThus TOP reversely requeststhe suppliers to comply with its customer environmental andeconomic requirement Under the consensus of a multidisci-plinary group of decision makers with various points of viewand representing the different services of the company TOPrsquosmanagers and heads of departments have decided that prod-uct price ISO quality system and lead time are economiccriteria Green technology and environmental certificate areenvironmental criteria The managers of the departmentssuch as Employee Health and Safety Production QualityControl and Assessment and Purchasing were required tomake their evaluation respectively

In reality TOP must work with suppliers for green prod-uct development Quality control and supply ability of eco-nomic criteria are the most important customer requirementfactors which related to green products TOPrsquos managementteam continuously integrates resources to investigate greenproducts such as light lean production and energy savingto satisfy stakeholders TOP is keeping good relationshipwiththe suppliers that will benefit from the purchasingmaterials ifneeded Additionally TOP also maintains good relationshipwith customers who will provide TOP opportunities ininnovative product developing and meeting the needs ofcustomers easier

The case revealed that the green criteria such as environ-ment and sustainability do not yet play a crucial role withingreen supplier selection procedures in enterprise practiceDue to the environmental regulations suppliers must meetsome minimum requirements in order to be eligible to workwith focal firms on the supply chain After that most of thecompanies do not apply environmental criteria to discrimi-nate qualified suppliers instead customers require suppliersto provide information such as Certificate of Nonuse of

Mathematical Problems in Engineering 7

Table 3 Fuzzy pairwise comparison of economic and environmental criteria

Criteria 1198621

1198622

1198623

1198624

1198625

1198621

(10 10 10) (10 30 50) (50 70 90) (10 30 50) (10 10 30)1198622

(15 13 11) (10 10 10) (19 17 15) (15 13 11) (50 70 90)1198623

(19 17 15) (50 70 90) (10 10 10) (17 15 13) (17 15 13)1198624

(15 13 11) (10 30 50) (30 50 70) (10 10 10) (13 11 11)1198625

(13 11 11) (19 17 15) (30 50 70) (10 10 30) (10 10 10)

Table 4 Fuzzy weights of the economic and environmental criteria

Criteria Fuzzy weight1198621

(0123 0295 0699)1198622

(0089 0173 0371)1198623

(0087 0168 0330)1198624

(0076 0203 0456)1198625

(0074 0160 0371)

Controlled Substances Certificate of Nonuse of Other Con-trolled Substances Material Safety Data Sheet and TestReport of customer assigned items issued by SGS annuallyThose certificates concern quality of economic criterion andpollution control of environmental criterion

According to institutional theory implementation ofgreen SCM is due to mimetic and normative (competitiveand benchmarking)mechanisms Facing environmental pro-tection pressure and legitimacy isomorphism pressure enter-prises must comply with social expectation and maintainconsistency with external environment to survive Thus theenvironmental and economic dimensionsmust be consideredsimultaneously [5] Consequently the proposed method isapplied on the case of TOP following the steps below

Step 1 (identify a number of economic and environmental cri-teria) In this study the data used as input to implement theproposed green supplier selection and evaluate the methodwere collected by means of semistructured interviews withthe top managers and head of departments Four companymanagers were required to make their evaluation respec-tively according to their preferences for important weightsof selection criteria and ratings of green suppliers

Using Table 1 and discussions with a companyrsquos top man-agers and heads of departments five criteria of economicsand environment for green supplier selection were selectedEconomic criteria include product price (119862

1) ISO quality

system (1198622) and lead time (119862

3) Green technology (119862

4) and

environmental certificate (1198625) are environmental criteria

Step 2 (aggregate the important weights of the criteria)After the determination of the green supplier criteria eachof four company managers is asked to conduct a pairwisecomparison with regard to the different criteria using thefuzzy linguistic assessment variables (see Table 2 for thesevariables) The completed matrices for the required cell areshown in Table 3 Applying (5)ndash(8) the final weights of theeconomic and environmental criteria are obtained as shownin Table 4

Step 3 (aggregate the ratings of suppliers versus the criteria)After the determination of the suppliers assessment criteriafour company managers rate each supplier according to eachcriterion A linguistic rating set of S was used to express theopinions of the managers where S = (VP P F G VG) VP(Very Poor) = (00 01 02) P (Poor) = (01 03 05) F (Fair) =(03 05 07) G (Good) = (05 07 09) and VG (Very Good)= (08 09 10) Table 5 gives the aggregated suitability ratingsof four green suppliers (119860

1 1198602 1198603 and 119860

4) using (12)

Step 4 (normalized performance of suppliers versus criteria)For simplicity and practicality all of the fuzzy numbers in thispaper are defined in the closed interval [0 1] Consequentlythe normalization procedure is no longer needed

Step 5 (calculate normalized weighted rating) Using (14) thenormalized weighted ratings 119866

119894can be obtained as shown in

Table 6

Step 6 (calculate 119860+ 119860minus 119889+119894 and 119889minus

119894) As shown in Table 7

the distance of each green supplier from 119860+ and 119860minus can be

calculated by (15)sim(16)

Step 7 (obtain the closeness coefficient) The closeness coef-ficients of green suppliers can be calculated by (17) as shownin Table 8 Therefore the ranking order of the four greensuppliers is 119860

3gt 1198604gt 1198601gt 1198602 Consequently the best

green supplier is 1198603

6 Conclusion

While the types of industry vary the key strategies ofgreen supplier selection also are changed Nevertheless allindustries should concern suppliers from both economicand environmental aspects because suppliers could influencefirmsrsquo performance and stakeholders

Green supplier selection is an important and complicatedMCDM problem requiring evaluation of multiple economicand environmental criteria incorporating vagueness andimprecision with the involvement of a group of expertsAlthough numerous studies have used economic criteria inthe supplier selection process limited studies have consid-ered the economic and environmental criteria simultane-ously The implementation of green supply management wasnot well understood This paper has proposed an integratedfuzzy MCDM approach to support the green suppliers selec-tion and the evaluation process In the proposed approachboth economic and environmental criteria were consideredIn order to overcome the shortcomings of the existing fuzzy

8 Mathematical Problems in Engineering

Table 5 Aggregate of the green supplier ratings versus criteria

Criteria Green suppliers Company managers119903119894119895

1198631

1198632

1198633

1198634

1198621

1198601

VG G G VG (0650 0800 0950)1198602

F G G F (0400 0600 0800)1198603

G G G G (0500 0700 0900)1198604

G F G G (0450 0650 0850)

1198622

1198601

G G G G (0500 0700 0900)1198602

F F G F (0350 0550 0750)1198603

G G VG G (0575 0750 0925)1198604

VG G VG G (0650 0800 0950)

1198623

1198601

G F G F (0400 0600 0800)1198602

F F F G (0350 0550 0750)1198603

VG G VG G (0650 0800 0950)1198604

F G F F (0350 0550 0750)

1198624

1198601

F G G F (0400 0600 0800)1198602

G VG G G (0575 0750 0925)1198603

G VG VG G (0650 0800 0950)1198604

VG G VG G (0650 0800 0950)

1198625

1198601

G G G G (0500 0700 0900)1198602

VG G G VG (0650 0800 0950)1198603

G G G VG (0575 0750 0925)1198604

VG G G VG (0650 0800 0950)

Table 6 Normalized weighted ratings of each market segment

Green suppliers 119866119894

1198601

(0045 0138 0392)1198602

(0041 0129 0372)1198603

(0052 0151 0413)1198604

(0048 0143 0396)

Table 7 The distance of each green supplier from 119860+ and 119860minus

Green suppliers 119889+

119889minus

1198601

1422 04181198602

1440 03961198603

1402 04421198604

1416 0424

Table 8 Closeness coefficients of alternatives

Alternatives Closeness coefficient Ranking1198601

0227 31198602

0216 41198603

0240 11198604

0230 2

TOPSIS technique this study has integrated the fuzzy TOP-SIS technique with the fuzzy AHP method to determine theimportant weights of economic and environmental criteriaFinally the proposed approach was employed to solve a realproblem in the LEF industry The results showed that the

proposed approach is effective in supplier selection for thecompany The application also indicated that the computa-tional procedure is efficient and easy to use in practice Futureresearch should focus on developing an extension of fuzzyMCDM approach to segment the green suppliers based onthe economic and environmental aspects Different methodsmay be applied to select green suppliers and the results shouldbe compared with the proposed approach The proposedapproach can also be applied to other management problemswith similar settings

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

References

[1] Y-S Chen and C-H Chang ldquoThe determinants of green prod-uct development performance Green dynamic capabilitiesgreen transformational leadership and green creativityrdquo Journalof Business Ethics vol 116 no 1 pp 107ndash119 2013

[2] A H I Lee H-Y Kang C-F Hsu and H-C Hung ldquoA greensupplier selectionmodel for high-tech industryrdquo Expert Systemswith Applications vol 36 no 4 pp 7917ndash7927 2009

[3] K Govindan S Rajendran J Sarkis and P Murugesan ldquoMulticriteria decision making approaches for green supplier evalua-tion and selection a literature reviewrdquo Journal of Cleaner Pro-duction vol 98 pp 66ndash83 2015

Mathematical Problems in Engineering 9

[4] R J Kuo Y C Wang and F C Tien ldquoIntegration of artificialneural network and MADA methods for green supplier selec-tionrdquo Journal of Cleaner Production vol 18 no 12 pp 1161ndash11702010

[5] A Gunasekaran and D Gallear ldquoSpecial Issue on Sustainabledevelopment of manufacturing and servicesrdquo InternationalJournal of Production Economics vol 140 no 1 pp 1ndash6 2012

[6] J Sarkis Q Zhu and K-H Lai ldquoAn organizational theoreticreview of green supply chain management literaturerdquo Interna-tional Journal of Production Economics vol 130 no 1 pp 1ndash152011

[7] A Appolloni H Sun F Jia and X Li ldquoGreen Procurement inthe private sector a state of the art review between 1996 and2013rdquo Journal of Cleaner Production vol 85 pp 122ndash133 2014

[8] H C Pimenta and P D Ball ldquoAnalysis of environmentalsustainability practices across upstream supply chain manage-mentrdquo Procedia CIRP vol 26 pp 677ndash682 2015

[9] C-L Hwang andK YoonMultiple Attribute DecisionMakingmdashMethods and Applications A State of the Art Survey SpringerNew York NY USA 1981

[10] H-S Shih H-J Shyur and E S Lee ldquoAn extension of TOPSISfor group decision makingrdquoMathematical and Computer Mod-elling vol 45 no 7-8 pp 801ndash813 2007

[11] T L SaatyTheAnalytical Hierarchy Process McGraw-Hill NewYork NY USA 1980

[12] G Buyukozkan and G Cifci ldquoEvaluation of the green supplychain management practices a fuzzy ANP approachrdquo Produc-tion Planning and Control vol 23 no 6 pp 405ndash418 2012

[13] C-C Sun ldquoA performance evaluation model by integratingfuzzy AHP and fuzzy TOPSIS methodsrdquo Expert Systems withApplications vol 37 no 12 pp 7745ndash7754 2010

[14] W Xia and Z Wu ldquoSupplier selection with multiple criteria involume discount environmentsrdquoOmega vol 35 no 5 pp 494ndash504 2007

[15] I Chamodrakas D Batis and D Martakos ldquoSupplier selectionin electronic marketplaces using satisficing and fuzzy AHPrdquoExpert Systems with Applications vol 37 no 1 pp 490ndash4982010

[16] K Shaw R Shankar S S Yadav and L S Thakur ldquoSupplierselection using fuzzy AHP and fuzzy multi-objective linearprogramming for developing low carbon supply chainrdquo ExpertSystems with Applications vol 39 no 9 pp 8182ndash8192 2012

[17] O Kilincci and S A Onal ldquoFuzzy AHP approach for supplierselection in a washing machine companyrdquo Expert Systems withApplications vol 38 no 8 pp 9656ndash9664 2011

[18] A H I Lee ldquoA fuzzy supplier selection model with the consid-eration of benefits opportunities costs and risksrdquo Expert Sys-tems with Applications vol 36 no 2 pp 2879ndash2893 2009

[19] C Bai and J Sarkis ldquoGreen supplier development analyticalevaluation using rough set theoryrdquo Journal of Cleaner Produc-tion vol 18 no 12 pp 1200ndash1210 2010

[20] M Abdollahi M Arvan and J Razmi ldquoAn integrated approachfor supplier portfolio selection lean or agilerdquo Expert Systemswith Applications vol 42 no 1 pp 679ndash690 2015

[21] M S Memon Y H Lee and S I Mari ldquoGroup multi-criteriasupplier selection using combined grey systems theory anduncertainty theoryrdquo Expert Systems with Applications vol 42no 21 pp 7951ndash7959 2015

[22] S H Hashemi A Karimi and M Tavana ldquoAn integratedgreen supplier selection approachwith analytic network processand improved Grey relational analysisrdquo International Journal ofProduction Economics vol 159 pp 178ndash191 2015

[23] M Punniyamoorthy P Mathiyalagan and P Parthiban ldquoAstrategic model using structural equation modeling and fuzzylogic in supplier selectionrdquo Expert Systems with Applicationsvol 38 no 1 pp 458ndash474 2011

[24] R M Grisi L Guerra and G Naviglio ldquoSupplier performanceevaluation for green supply chainmanagementrdquo inBusiness Per-formanceMeasurement andManagement pp 149ndash163 SpringerBerlin Germany 2010

[25] F Mafakheri M Breton and A Ghoniem ldquoSupplier selection-order allocation a two-stage multiple criteria dynamic pro-gramming approachrdquo International Journal of Production Eco-nomics vol 132 no 1 pp 52ndash57 2011

[26] Y-J Chen ldquoStructured methodology for supplier selection andevaluation in a supply chainrdquo Information Sciences vol 181 no9 pp 1651ndash1670 2011

[27] W-PWang ldquoA fuzzy linguistic computing approach to supplierevaluationrdquo Applied Mathematical Modelling vol 34 no 10 pp3130ndash3141 2010

[28] M-L Tseng and A S F Chiu ldquoEvaluating firmrsquos green supplychain management in linguistic preferencesrdquo Journal of CleanerProduction vol 40 pp 22ndash31 2013

[29] Q Zhu Y Dou and J Sarkis ldquoA portfolio-based analysisfor green supplier management using the analytical networkprocessrdquo Supply Chain Management vol 15 no 4 pp 306ndash3192010

[30] G A Keskin S Ilhan and C Ozkan ldquoThe Fuzzy ARTalgorithm a categorization method for supplier evaluation andselectionrdquo Expert Systems with Applications vol 37 no 2 pp1235ndash1240 2010

[31] C-Y Shen and K-T Yu ldquoEnhancing the efficacy of supplierselection decision-making on the initial stage of new productdevelopment a hybrid fuzzy approach considering the strategicand operational factors simultaneouslyrdquo Expert Systems withApplications vol 36 no 8 pp 11271ndash11281 2009

[32] K Govindan R Khodaverdi and A Jafarian ldquoA fuzzy multicriteria approach for measuring sustainability performance ofa supplier based on triple bottom line approachrdquo Journal ofCleaner Production vol 47 pp 345ndash354 2013

[33] G Tuzkaya A Ozgen D Ozgen and U R Tuzkaya ldquoEnvi-ronmental performance evaluation of suppliers a hybrid fuzzymulti-criteria decision approachrdquo International Journal of Envi-ronmental ScienceampTechnology vol 6 no 3 pp 477ndash490 2009

[34] Q Zhu J Sarkis and K-H Lai ldquoInitiatives and outcomes ofgreen supply chain management implementation by Chinesemanufacturersrdquo Journal of Environmental Management vol 85no 1 pp 179ndash189 2007

[35] W-C Yeh and M-C Chuang ldquoUsing multi-objective geneticalgorithm for partner selection in green supply chain problemsrdquoExpert Systems with Applications vol 38 no 4 pp 4244ndash42532011

[36] A Awasthi S S Chauhan and S K Goyal ldquoA fuzzy multi-criteria approach for evaluating environmental performance ofsuppliersrdquo International Journal of Production Economics vol126 no 2 pp 370ndash378 2010

[37] J Sarkis ldquoManufacturingrsquos role in corporate environmentalsustainability-Concerns for the new millenniumrdquo InternationalJournal of Operations amp Production Management vol 21 no 5-6 pp 666ndash686 2001

[38] S MMirhedayatian M Azadi and R Farzipoor Saen ldquoA novelnetwork data envelopment analysis model for evaluating greensupply chain managementrdquo International Journal of ProductionEconomics vol 147 pp 544ndash554 2014

10 Mathematical Problems in Engineering

[39] C Wu and D Barnes ldquoAn integrated model for green partnerselection and supply chain constructionrdquo Journal of CleanerProduction vol 112 pp 2114ndash2132 2016

[40] G Bruno E Esposito A Genovese andR Passaro ldquoAHP-basedapproaches for supplier evaluation problems and perspectivesrdquoJournal of Purchasing and Supply Management vol 18 no 3 pp159ndash172 2012

[41] F R L Junior L Osiro and L C R Carpinetti ldquoA comparisonbetween Fuzzy AHP and Fuzzy TOPSIS methods to supplierselectionrdquo Applied Soft Computing vol 21 pp 194ndash209 2014

[42] A Kawa and W W Koczkodaj ldquoSupplier evaluation process bypairwise comparisonsrdquo Mathematical Problems in Engineeringvol 2015 Article ID 976742 9 pages 2015

[43] X Deng Y Hu Y Deng and S Mahadevan ldquoSupplier selectionusing AHP methodology extended by D numbersrdquo ExpertSystems with Applications vol 41 no 1 pp 156ndash167 2014

[44] N Xie and J Xin ldquoInterval grey numbers based multi-attributedecisionmakingmethod for supplier selectionrdquoKybernetes vol43 no 7 pp 1064ndash1078 2014

[45] J Lee H Cho and Y S Kim ldquoAssessing business impacts ofagility criterion and order allocation strategy in multi-criteriasupplier selectionrdquo Expert Systems with Applications vol 42 no3 pp 1136ndash1148 2015

[46] L Shen L Olfat K Govindan R Khodaverdi and A DiabatldquoA fuzzy multi criteria approach for evaluating green supplierrsquosperformance in green supply chain with linguistic preferencesrdquoResources Conservation and Recycling vol 74 pp 170ndash179 2012

[47] B Kanga Y Hu Y Deng and D Zhou ldquoA new methodologyof multicriteria decision-making in supplier selection based onZ-numbersrdquo Mathematical Problems in Engineering vol 2016Article ID 8475987 17 pages 2016

[48] N Asthana and M Gupta ldquoSupplier selection using artificialneural network and genetic algorithmrdquo International Journal ofIndian Culture and Business Management vol 11 no 4 pp 457ndash472 2015

[49] D Dubois and H Prade ldquoOperations on fuzzy numbersrdquo Inter-national Journal of Systems Science vol 9 no 6 pp 613ndash6261978

[50] A Kaufmann and M M Gupta Introduction to Fuzzy Arith-metic Theory and Applications The Arden Shakespeare 1991

[51] L A Zadeh ldquoThe concept of a linguistic variable and its appli-cation to approximate reasoningmdashIrdquo Information Sciences vol8 no 3 pp 199ndash249 1975

[52] L A Zadeh ldquoThe concept of a linguistic variable and its applica-tion to approximate reasoningmdashIIrdquo Information Sciences vol 8no 4 pp 301ndash357 1975

[53] D-Y Chang ldquoApplications of the extent analysis method onfuzzy AHPrdquo European Journal of Operational Research vol 95no 3 pp 649ndash655 1996

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical Problems in Engineering

Hindawi Publishing Corporationhttpwwwhindawicom

Differential EquationsInternational Journal of

Volume 2014

Applied MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical PhysicsAdvances in

Complex AnalysisJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

OptimizationJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Operations ResearchAdvances in

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Function Spaces

Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of Mathematics and Mathematical Sciences

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Algebra

Discrete Dynamics in Nature and Society

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Decision SciencesAdvances in

Discrete MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom

Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Stochastic AnalysisInternational Journal of

Mathematical Problems in Engineering 5

criteria Several fuzzy AHP methods have been proposed inliterature to solve the MCDM problems This study adoptsthe extent analysis method proposed by Chang [53] dueto its popularity and computational simplicity Changrsquos [53]method is briefly discussed as follows

Let 119883 = 1199091 1199092 119909

119899 be an object set and let 119880 =

1199061 1199062 119906

119898 be a goal set According to Chang [53] each

object is taken and an extent analysis for each goal (119892119894)

is performed respectively Therefore the 119898 extent analysisvalues for each object are obtained as1198721

1198921198941198722

119892119894 119872

119899

119892119894 119894 =

1 2 119899 where 119872119895119892119894(119895 = 1 2 119898) are triangular fuzzy

numbers (TFNs)Assume that 119872119895

119892119894are the values of extent analysis of the

119894th object for119898 goalsThe value of fuzzy synthetic extent 119878119894is

defined as follows

119878119894=

119898

sum

119895=1

119872119895

119892119894otimes [

[

119899

sum

119894=1

119898

sum

119895=1

119872119895

119892119894

]

]

minus1

(5)

where sum119898

119895=1119872119895

119892119894= (sum

119898

119895=1119897119895 sum119898

119895=1119898119895 sum119898

119895=1119906119895) 119895 = 1 2

119898 119894 = 1 2 119899

Let1198721= (1198971 1198981 1199061) and119872

2= (1198972 1198982 1199062) be two TFNs

whereby the degree of possibility of 1198721ge 1198722is defined as

follows119881 (1198721ge 1198722) = sup119909ge119910

[min (1205831198721

(119909) 1205831198722(119909))] (6)

Themembership degree of possibility is expressed as follows

119881 (1198721ge 1198722) = hgt (119872

1cap1198722) = 1205831198722

(119889)

=

1 if 1198981ge 1198982

0 if 1198972ge 1199061

1198972minus 1199061

(1198972minus 1199061) + (119898

1minus 1198982)

otherwise

(7)

where 119889 is the ordinate of the highest intersection point oftwo membership functions 120583

1198721(119909) and 120583

1198722(119909)

The degree of possibility for a convex fuzzy number to begreater than 119896 convex fuzzy numbers is defined as follows

119881 (119872 ge 11987211198722 119872

119896) = min119881 (119872 ge 119872

119894)

119894 = 1 2 119896

(8)

The weight vector is given by

1198821015840= (1198891015840(1198601) 1198891015840(1198602) 119889

1015840(119860119899))119879

(9)

where1198891015840(119860119894) = min119881 (119878

119894ge 119878119896)

(119894 = 1 2 119899) 119896 = 1 2 119899 119896 = 119894

(10)

Via normalization we obtain the weight vectors as follows

119882 = (119889 (1198601) 119889 (119860

2) 119889 (119860

119899))119879 (11)

where119882 is a nonfuzzy numberThis study adopts a ldquoLikert Scalerdquo of fuzzy numbers

starting from 1 to 9 to transform the linguistic values intotriangular fuzzy numbers as shown in Table 2

43 Aggregate the Ratings of Suppliers versus the Criteria Let119909119894119895119905= (119890119894119895119905 119891119894119895119905 119892119894119895119905) 119894 = 1 sim 119898 119895 = 1 sim 119899 119905 = 1 sim 119897 be the

suitability rating assigned to green supplier 119860119894 by decision

maker 119863119905 for criterion 119862

119895 The averaged suitability rating

119909119894119895= (119890119894119895 119891119894119895 119892119894119895) can be evaluated as follows

119909119894119895=1

119897otimes (1199091198941198951oplus 1199091198941198952oplus sdot sdot sdot oplus 119909

119894119895119905oplus sdot sdot sdot oplus 119909

119894119895119897) (12)

where 119890119894119895= (1119897) sum

119897

119905=1119890119894119895119905 119891119894119895= (1119897) sum

119897

119905=1119891119894119895119905 and 119892

119894119895=

(1119897) sum119897

119905=1119892119894119895119905

44 Normalize Performance of Suppliers versus Criteria Toensure compatibility between average ratings and averageweights the average ratings are normalized into comparablescales Suppose that 119903

119894119895= (119886119894119895 119887119894119895 119888119894119895) is the performance of

green supplier 119894 on criteria 119895 The normalized value 119909119894119895can

then be denoted as follows

119909119894119895= (

119886119894119895

119888lowast

119895

119887119894119895

119888lowast

119895

119888119894119895

119888lowast

119895

) 119895 isin 119861

119909119894119895= (

119886minus

119895

119888119894119895

119886minus

119895

119887119894119895

119886minus

119895

119886119894119895

) 119895 isin 119862

(13)

where 119886minus119895= min

119894119886119894119895 119888lowast119895= max

119894119888119894119895 119894 = 1 119898 and 119895 =

1 119899

45 Calculate Normalized Weighted Rating The normalizedweighted ratings 119866

119894are calculated by multiplying the nor-

malized average rating 119909119894119895with its associated weights 119908

119895119905as

follows

119866119894= 119909119894119895otimes 119908119895 119894 = 1 119898 119895 = 1 ℎ (14)

46 Calculate 119860+ 119860minus 119889+

119894 and 119889

minus

119894 The fuzzy positive-

ideal solution (FPIS 119860+) and fuzzy negative-ideal solution(FNIS 119860minus) are obtained as follows

119860+= (10 10 10)

119860minus= (00 00 00)

(15)

The distance of each green supplier119860119894 119894 = 1 119898 from119860

+

and 119860minus is calculated as follows

119889+

119894= radic

119899

sum

119894=1

(119866119894minus 119860+)

2

119889minus

119894= radic

119899

sum

119894=1

(119866119894minus 119860minus)

2

(16)

where 119889+119894represents the shortest distance of alternative 119860

119894

and 119889minus119894represents the farthest distance of green supplier 119860

119894

6 Mathematical Problems in Engineering

Table 2 Linguistic variables describing weights of the ldquoHOWsrdquo criteria

Linguistic scale for importance Triangular fuzzy scale119872 = (119897119898 119906)Just equal (10 10 10)Equal importance (10 10 30)Weak importance (10 30 50)Strong importance (30 50 70)Very strong importance (50 70 90)Extremely importance (70 90 90)If factor 119894 has one of the above numbers assigned to it when compared tofactor 119895 then 119895 has the reciprocal value when compared with 119894

Reciprocals of above119872minus1

1asymp (1119906

1 11198981 11198971)

47 Obtain the Closeness Coefficient Thecloseness coefficientof each green supplier which is usually defined to determinethe ranking order of all green suppliers is calculated asfollows

CC119894=

119889minus

119894

119889+

119894+ 119889minus

119894

(17)

A higher value of the closeness coefficient indicates thatan alternative is simultaneously closer to PIS and furtherfromNISThe closeness coefficient of each alternative is usedto determine the ranking order of all green suppliers andindicates the best one among a set of given feasible greensuppliers

5 Case Study

In this paper a comprehensive green supplier selectionmodel is proposed by considering the important criteria ineconomic and environmental aspects for evaluating greensuppliers The proposed method is applied on the case ofthe Taiwanese optical prism (TOP) manufacturing entity inLuminance Enhancement Film (LEF) industry to solve greensuppliers selection

TOP founded in late 2003 is the leading optical prismmanufacturer in Taiwan TOP focuses on advanced productdevelopment and quality improvement However TOP isnow dealing with the increase in competition Moreover theLCD product life cycle is very short qualified suppliers asTOP frequently have to provide innovative products withina limited lead time for customers verification to meet time-to-market as well Consequently with the purpose of main-taining the existing customers satisfaction and attractingnew international customers to improve market share theselection of quality constant green suppliers for long termcooperation is extremely essential for survival of TOP

When TOP confirmed its role and strategy as a greensupplier TOP needs to evaluate its core competences andidentify the gap between customer needs and consultantsuggestions TOP then restructures the ecological environ-ment of the industry TOP has employed the green SCMsimultaneously considering environmental and economicaspects to either comply with regulation or meet customerneeds Furthermore TOP has proactively invested both qual-ity and environmental management system such as quality

system of economic criteria ISO9001 and QC080000 andenvironmental criteria ISO14001 and OHSAS18001 TOP hasimplemented a continuous quality improvement programand constituted an international standard as a platform totraining staffs as well as suppliers Those activities eithersave the costs of customers involved with their supplierdevelopment program or strengthen TOPrsquos green brandimage

TOP has learned and accumulated plenty of green SCMdomain knowledge and capabilities as a main supplier ofLCD supply chain through the two-stage process of the rawmaterial quality verification and integration all of material inone product for each customerThus TOP reversely requeststhe suppliers to comply with its customer environmental andeconomic requirement Under the consensus of a multidisci-plinary group of decision makers with various points of viewand representing the different services of the company TOPrsquosmanagers and heads of departments have decided that prod-uct price ISO quality system and lead time are economiccriteria Green technology and environmental certificate areenvironmental criteria The managers of the departmentssuch as Employee Health and Safety Production QualityControl and Assessment and Purchasing were required tomake their evaluation respectively

In reality TOP must work with suppliers for green prod-uct development Quality control and supply ability of eco-nomic criteria are the most important customer requirementfactors which related to green products TOPrsquos managementteam continuously integrates resources to investigate greenproducts such as light lean production and energy savingto satisfy stakeholders TOP is keeping good relationshipwiththe suppliers that will benefit from the purchasingmaterials ifneeded Additionally TOP also maintains good relationshipwith customers who will provide TOP opportunities ininnovative product developing and meeting the needs ofcustomers easier

The case revealed that the green criteria such as environ-ment and sustainability do not yet play a crucial role withingreen supplier selection procedures in enterprise practiceDue to the environmental regulations suppliers must meetsome minimum requirements in order to be eligible to workwith focal firms on the supply chain After that most of thecompanies do not apply environmental criteria to discrimi-nate qualified suppliers instead customers require suppliersto provide information such as Certificate of Nonuse of

Mathematical Problems in Engineering 7

Table 3 Fuzzy pairwise comparison of economic and environmental criteria

Criteria 1198621

1198622

1198623

1198624

1198625

1198621

(10 10 10) (10 30 50) (50 70 90) (10 30 50) (10 10 30)1198622

(15 13 11) (10 10 10) (19 17 15) (15 13 11) (50 70 90)1198623

(19 17 15) (50 70 90) (10 10 10) (17 15 13) (17 15 13)1198624

(15 13 11) (10 30 50) (30 50 70) (10 10 10) (13 11 11)1198625

(13 11 11) (19 17 15) (30 50 70) (10 10 30) (10 10 10)

Table 4 Fuzzy weights of the economic and environmental criteria

Criteria Fuzzy weight1198621

(0123 0295 0699)1198622

(0089 0173 0371)1198623

(0087 0168 0330)1198624

(0076 0203 0456)1198625

(0074 0160 0371)

Controlled Substances Certificate of Nonuse of Other Con-trolled Substances Material Safety Data Sheet and TestReport of customer assigned items issued by SGS annuallyThose certificates concern quality of economic criterion andpollution control of environmental criterion

According to institutional theory implementation ofgreen SCM is due to mimetic and normative (competitiveand benchmarking)mechanisms Facing environmental pro-tection pressure and legitimacy isomorphism pressure enter-prises must comply with social expectation and maintainconsistency with external environment to survive Thus theenvironmental and economic dimensionsmust be consideredsimultaneously [5] Consequently the proposed method isapplied on the case of TOP following the steps below

Step 1 (identify a number of economic and environmental cri-teria) In this study the data used as input to implement theproposed green supplier selection and evaluate the methodwere collected by means of semistructured interviews withthe top managers and head of departments Four companymanagers were required to make their evaluation respec-tively according to their preferences for important weightsof selection criteria and ratings of green suppliers

Using Table 1 and discussions with a companyrsquos top man-agers and heads of departments five criteria of economicsand environment for green supplier selection were selectedEconomic criteria include product price (119862

1) ISO quality

system (1198622) and lead time (119862

3) Green technology (119862

4) and

environmental certificate (1198625) are environmental criteria

Step 2 (aggregate the important weights of the criteria)After the determination of the green supplier criteria eachof four company managers is asked to conduct a pairwisecomparison with regard to the different criteria using thefuzzy linguistic assessment variables (see Table 2 for thesevariables) The completed matrices for the required cell areshown in Table 3 Applying (5)ndash(8) the final weights of theeconomic and environmental criteria are obtained as shownin Table 4

Step 3 (aggregate the ratings of suppliers versus the criteria)After the determination of the suppliers assessment criteriafour company managers rate each supplier according to eachcriterion A linguistic rating set of S was used to express theopinions of the managers where S = (VP P F G VG) VP(Very Poor) = (00 01 02) P (Poor) = (01 03 05) F (Fair) =(03 05 07) G (Good) = (05 07 09) and VG (Very Good)= (08 09 10) Table 5 gives the aggregated suitability ratingsof four green suppliers (119860

1 1198602 1198603 and 119860

4) using (12)

Step 4 (normalized performance of suppliers versus criteria)For simplicity and practicality all of the fuzzy numbers in thispaper are defined in the closed interval [0 1] Consequentlythe normalization procedure is no longer needed

Step 5 (calculate normalized weighted rating) Using (14) thenormalized weighted ratings 119866

119894can be obtained as shown in

Table 6

Step 6 (calculate 119860+ 119860minus 119889+119894 and 119889minus

119894) As shown in Table 7

the distance of each green supplier from 119860+ and 119860minus can be

calculated by (15)sim(16)

Step 7 (obtain the closeness coefficient) The closeness coef-ficients of green suppliers can be calculated by (17) as shownin Table 8 Therefore the ranking order of the four greensuppliers is 119860

3gt 1198604gt 1198601gt 1198602 Consequently the best

green supplier is 1198603

6 Conclusion

While the types of industry vary the key strategies ofgreen supplier selection also are changed Nevertheless allindustries should concern suppliers from both economicand environmental aspects because suppliers could influencefirmsrsquo performance and stakeholders

Green supplier selection is an important and complicatedMCDM problem requiring evaluation of multiple economicand environmental criteria incorporating vagueness andimprecision with the involvement of a group of expertsAlthough numerous studies have used economic criteria inthe supplier selection process limited studies have consid-ered the economic and environmental criteria simultane-ously The implementation of green supply management wasnot well understood This paper has proposed an integratedfuzzy MCDM approach to support the green suppliers selec-tion and the evaluation process In the proposed approachboth economic and environmental criteria were consideredIn order to overcome the shortcomings of the existing fuzzy

8 Mathematical Problems in Engineering

Table 5 Aggregate of the green supplier ratings versus criteria

Criteria Green suppliers Company managers119903119894119895

1198631

1198632

1198633

1198634

1198621

1198601

VG G G VG (0650 0800 0950)1198602

F G G F (0400 0600 0800)1198603

G G G G (0500 0700 0900)1198604

G F G G (0450 0650 0850)

1198622

1198601

G G G G (0500 0700 0900)1198602

F F G F (0350 0550 0750)1198603

G G VG G (0575 0750 0925)1198604

VG G VG G (0650 0800 0950)

1198623

1198601

G F G F (0400 0600 0800)1198602

F F F G (0350 0550 0750)1198603

VG G VG G (0650 0800 0950)1198604

F G F F (0350 0550 0750)

1198624

1198601

F G G F (0400 0600 0800)1198602

G VG G G (0575 0750 0925)1198603

G VG VG G (0650 0800 0950)1198604

VG G VG G (0650 0800 0950)

1198625

1198601

G G G G (0500 0700 0900)1198602

VG G G VG (0650 0800 0950)1198603

G G G VG (0575 0750 0925)1198604

VG G G VG (0650 0800 0950)

Table 6 Normalized weighted ratings of each market segment

Green suppliers 119866119894

1198601

(0045 0138 0392)1198602

(0041 0129 0372)1198603

(0052 0151 0413)1198604

(0048 0143 0396)

Table 7 The distance of each green supplier from 119860+ and 119860minus

Green suppliers 119889+

119889minus

1198601

1422 04181198602

1440 03961198603

1402 04421198604

1416 0424

Table 8 Closeness coefficients of alternatives

Alternatives Closeness coefficient Ranking1198601

0227 31198602

0216 41198603

0240 11198604

0230 2

TOPSIS technique this study has integrated the fuzzy TOP-SIS technique with the fuzzy AHP method to determine theimportant weights of economic and environmental criteriaFinally the proposed approach was employed to solve a realproblem in the LEF industry The results showed that the

proposed approach is effective in supplier selection for thecompany The application also indicated that the computa-tional procedure is efficient and easy to use in practice Futureresearch should focus on developing an extension of fuzzyMCDM approach to segment the green suppliers based onthe economic and environmental aspects Different methodsmay be applied to select green suppliers and the results shouldbe compared with the proposed approach The proposedapproach can also be applied to other management problemswith similar settings

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

References

[1] Y-S Chen and C-H Chang ldquoThe determinants of green prod-uct development performance Green dynamic capabilitiesgreen transformational leadership and green creativityrdquo Journalof Business Ethics vol 116 no 1 pp 107ndash119 2013

[2] A H I Lee H-Y Kang C-F Hsu and H-C Hung ldquoA greensupplier selectionmodel for high-tech industryrdquo Expert Systemswith Applications vol 36 no 4 pp 7917ndash7927 2009

[3] K Govindan S Rajendran J Sarkis and P Murugesan ldquoMulticriteria decision making approaches for green supplier evalua-tion and selection a literature reviewrdquo Journal of Cleaner Pro-duction vol 98 pp 66ndash83 2015

Mathematical Problems in Engineering 9

[4] R J Kuo Y C Wang and F C Tien ldquoIntegration of artificialneural network and MADA methods for green supplier selec-tionrdquo Journal of Cleaner Production vol 18 no 12 pp 1161ndash11702010

[5] A Gunasekaran and D Gallear ldquoSpecial Issue on Sustainabledevelopment of manufacturing and servicesrdquo InternationalJournal of Production Economics vol 140 no 1 pp 1ndash6 2012

[6] J Sarkis Q Zhu and K-H Lai ldquoAn organizational theoreticreview of green supply chain management literaturerdquo Interna-tional Journal of Production Economics vol 130 no 1 pp 1ndash152011

[7] A Appolloni H Sun F Jia and X Li ldquoGreen Procurement inthe private sector a state of the art review between 1996 and2013rdquo Journal of Cleaner Production vol 85 pp 122ndash133 2014

[8] H C Pimenta and P D Ball ldquoAnalysis of environmentalsustainability practices across upstream supply chain manage-mentrdquo Procedia CIRP vol 26 pp 677ndash682 2015

[9] C-L Hwang andK YoonMultiple Attribute DecisionMakingmdashMethods and Applications A State of the Art Survey SpringerNew York NY USA 1981

[10] H-S Shih H-J Shyur and E S Lee ldquoAn extension of TOPSISfor group decision makingrdquoMathematical and Computer Mod-elling vol 45 no 7-8 pp 801ndash813 2007

[11] T L SaatyTheAnalytical Hierarchy Process McGraw-Hill NewYork NY USA 1980

[12] G Buyukozkan and G Cifci ldquoEvaluation of the green supplychain management practices a fuzzy ANP approachrdquo Produc-tion Planning and Control vol 23 no 6 pp 405ndash418 2012

[13] C-C Sun ldquoA performance evaluation model by integratingfuzzy AHP and fuzzy TOPSIS methodsrdquo Expert Systems withApplications vol 37 no 12 pp 7745ndash7754 2010

[14] W Xia and Z Wu ldquoSupplier selection with multiple criteria involume discount environmentsrdquoOmega vol 35 no 5 pp 494ndash504 2007

[15] I Chamodrakas D Batis and D Martakos ldquoSupplier selectionin electronic marketplaces using satisficing and fuzzy AHPrdquoExpert Systems with Applications vol 37 no 1 pp 490ndash4982010

[16] K Shaw R Shankar S S Yadav and L S Thakur ldquoSupplierselection using fuzzy AHP and fuzzy multi-objective linearprogramming for developing low carbon supply chainrdquo ExpertSystems with Applications vol 39 no 9 pp 8182ndash8192 2012

[17] O Kilincci and S A Onal ldquoFuzzy AHP approach for supplierselection in a washing machine companyrdquo Expert Systems withApplications vol 38 no 8 pp 9656ndash9664 2011

[18] A H I Lee ldquoA fuzzy supplier selection model with the consid-eration of benefits opportunities costs and risksrdquo Expert Sys-tems with Applications vol 36 no 2 pp 2879ndash2893 2009

[19] C Bai and J Sarkis ldquoGreen supplier development analyticalevaluation using rough set theoryrdquo Journal of Cleaner Produc-tion vol 18 no 12 pp 1200ndash1210 2010

[20] M Abdollahi M Arvan and J Razmi ldquoAn integrated approachfor supplier portfolio selection lean or agilerdquo Expert Systemswith Applications vol 42 no 1 pp 679ndash690 2015

[21] M S Memon Y H Lee and S I Mari ldquoGroup multi-criteriasupplier selection using combined grey systems theory anduncertainty theoryrdquo Expert Systems with Applications vol 42no 21 pp 7951ndash7959 2015

[22] S H Hashemi A Karimi and M Tavana ldquoAn integratedgreen supplier selection approachwith analytic network processand improved Grey relational analysisrdquo International Journal ofProduction Economics vol 159 pp 178ndash191 2015

[23] M Punniyamoorthy P Mathiyalagan and P Parthiban ldquoAstrategic model using structural equation modeling and fuzzylogic in supplier selectionrdquo Expert Systems with Applicationsvol 38 no 1 pp 458ndash474 2011

[24] R M Grisi L Guerra and G Naviglio ldquoSupplier performanceevaluation for green supply chainmanagementrdquo inBusiness Per-formanceMeasurement andManagement pp 149ndash163 SpringerBerlin Germany 2010

[25] F Mafakheri M Breton and A Ghoniem ldquoSupplier selection-order allocation a two-stage multiple criteria dynamic pro-gramming approachrdquo International Journal of Production Eco-nomics vol 132 no 1 pp 52ndash57 2011

[26] Y-J Chen ldquoStructured methodology for supplier selection andevaluation in a supply chainrdquo Information Sciences vol 181 no9 pp 1651ndash1670 2011

[27] W-PWang ldquoA fuzzy linguistic computing approach to supplierevaluationrdquo Applied Mathematical Modelling vol 34 no 10 pp3130ndash3141 2010

[28] M-L Tseng and A S F Chiu ldquoEvaluating firmrsquos green supplychain management in linguistic preferencesrdquo Journal of CleanerProduction vol 40 pp 22ndash31 2013

[29] Q Zhu Y Dou and J Sarkis ldquoA portfolio-based analysisfor green supplier management using the analytical networkprocessrdquo Supply Chain Management vol 15 no 4 pp 306ndash3192010

[30] G A Keskin S Ilhan and C Ozkan ldquoThe Fuzzy ARTalgorithm a categorization method for supplier evaluation andselectionrdquo Expert Systems with Applications vol 37 no 2 pp1235ndash1240 2010

[31] C-Y Shen and K-T Yu ldquoEnhancing the efficacy of supplierselection decision-making on the initial stage of new productdevelopment a hybrid fuzzy approach considering the strategicand operational factors simultaneouslyrdquo Expert Systems withApplications vol 36 no 8 pp 11271ndash11281 2009

[32] K Govindan R Khodaverdi and A Jafarian ldquoA fuzzy multicriteria approach for measuring sustainability performance ofa supplier based on triple bottom line approachrdquo Journal ofCleaner Production vol 47 pp 345ndash354 2013

[33] G Tuzkaya A Ozgen D Ozgen and U R Tuzkaya ldquoEnvi-ronmental performance evaluation of suppliers a hybrid fuzzymulti-criteria decision approachrdquo International Journal of Envi-ronmental ScienceampTechnology vol 6 no 3 pp 477ndash490 2009

[34] Q Zhu J Sarkis and K-H Lai ldquoInitiatives and outcomes ofgreen supply chain management implementation by Chinesemanufacturersrdquo Journal of Environmental Management vol 85no 1 pp 179ndash189 2007

[35] W-C Yeh and M-C Chuang ldquoUsing multi-objective geneticalgorithm for partner selection in green supply chain problemsrdquoExpert Systems with Applications vol 38 no 4 pp 4244ndash42532011

[36] A Awasthi S S Chauhan and S K Goyal ldquoA fuzzy multi-criteria approach for evaluating environmental performance ofsuppliersrdquo International Journal of Production Economics vol126 no 2 pp 370ndash378 2010

[37] J Sarkis ldquoManufacturingrsquos role in corporate environmentalsustainability-Concerns for the new millenniumrdquo InternationalJournal of Operations amp Production Management vol 21 no 5-6 pp 666ndash686 2001

[38] S MMirhedayatian M Azadi and R Farzipoor Saen ldquoA novelnetwork data envelopment analysis model for evaluating greensupply chain managementrdquo International Journal of ProductionEconomics vol 147 pp 544ndash554 2014

10 Mathematical Problems in Engineering

[39] C Wu and D Barnes ldquoAn integrated model for green partnerselection and supply chain constructionrdquo Journal of CleanerProduction vol 112 pp 2114ndash2132 2016

[40] G Bruno E Esposito A Genovese andR Passaro ldquoAHP-basedapproaches for supplier evaluation problems and perspectivesrdquoJournal of Purchasing and Supply Management vol 18 no 3 pp159ndash172 2012

[41] F R L Junior L Osiro and L C R Carpinetti ldquoA comparisonbetween Fuzzy AHP and Fuzzy TOPSIS methods to supplierselectionrdquo Applied Soft Computing vol 21 pp 194ndash209 2014

[42] A Kawa and W W Koczkodaj ldquoSupplier evaluation process bypairwise comparisonsrdquo Mathematical Problems in Engineeringvol 2015 Article ID 976742 9 pages 2015

[43] X Deng Y Hu Y Deng and S Mahadevan ldquoSupplier selectionusing AHP methodology extended by D numbersrdquo ExpertSystems with Applications vol 41 no 1 pp 156ndash167 2014

[44] N Xie and J Xin ldquoInterval grey numbers based multi-attributedecisionmakingmethod for supplier selectionrdquoKybernetes vol43 no 7 pp 1064ndash1078 2014

[45] J Lee H Cho and Y S Kim ldquoAssessing business impacts ofagility criterion and order allocation strategy in multi-criteriasupplier selectionrdquo Expert Systems with Applications vol 42 no3 pp 1136ndash1148 2015

[46] L Shen L Olfat K Govindan R Khodaverdi and A DiabatldquoA fuzzy multi criteria approach for evaluating green supplierrsquosperformance in green supply chain with linguistic preferencesrdquoResources Conservation and Recycling vol 74 pp 170ndash179 2012

[47] B Kanga Y Hu Y Deng and D Zhou ldquoA new methodologyof multicriteria decision-making in supplier selection based onZ-numbersrdquo Mathematical Problems in Engineering vol 2016Article ID 8475987 17 pages 2016

[48] N Asthana and M Gupta ldquoSupplier selection using artificialneural network and genetic algorithmrdquo International Journal ofIndian Culture and Business Management vol 11 no 4 pp 457ndash472 2015

[49] D Dubois and H Prade ldquoOperations on fuzzy numbersrdquo Inter-national Journal of Systems Science vol 9 no 6 pp 613ndash6261978

[50] A Kaufmann and M M Gupta Introduction to Fuzzy Arith-metic Theory and Applications The Arden Shakespeare 1991

[51] L A Zadeh ldquoThe concept of a linguistic variable and its appli-cation to approximate reasoningmdashIrdquo Information Sciences vol8 no 3 pp 199ndash249 1975

[52] L A Zadeh ldquoThe concept of a linguistic variable and its applica-tion to approximate reasoningmdashIIrdquo Information Sciences vol 8no 4 pp 301ndash357 1975

[53] D-Y Chang ldquoApplications of the extent analysis method onfuzzy AHPrdquo European Journal of Operational Research vol 95no 3 pp 649ndash655 1996

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical Problems in Engineering

Hindawi Publishing Corporationhttpwwwhindawicom

Differential EquationsInternational Journal of

Volume 2014

Applied MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical PhysicsAdvances in

Complex AnalysisJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

OptimizationJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Operations ResearchAdvances in

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Function Spaces

Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of Mathematics and Mathematical Sciences

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Algebra

Discrete Dynamics in Nature and Society

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Decision SciencesAdvances in

Discrete MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom

Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Stochastic AnalysisInternational Journal of

6 Mathematical Problems in Engineering

Table 2 Linguistic variables describing weights of the ldquoHOWsrdquo criteria

Linguistic scale for importance Triangular fuzzy scale119872 = (119897119898 119906)Just equal (10 10 10)Equal importance (10 10 30)Weak importance (10 30 50)Strong importance (30 50 70)Very strong importance (50 70 90)Extremely importance (70 90 90)If factor 119894 has one of the above numbers assigned to it when compared tofactor 119895 then 119895 has the reciprocal value when compared with 119894

Reciprocals of above119872minus1

1asymp (1119906

1 11198981 11198971)

47 Obtain the Closeness Coefficient Thecloseness coefficientof each green supplier which is usually defined to determinethe ranking order of all green suppliers is calculated asfollows

CC119894=

119889minus

119894

119889+

119894+ 119889minus

119894

(17)

A higher value of the closeness coefficient indicates thatan alternative is simultaneously closer to PIS and furtherfromNISThe closeness coefficient of each alternative is usedto determine the ranking order of all green suppliers andindicates the best one among a set of given feasible greensuppliers

5 Case Study

In this paper a comprehensive green supplier selectionmodel is proposed by considering the important criteria ineconomic and environmental aspects for evaluating greensuppliers The proposed method is applied on the case ofthe Taiwanese optical prism (TOP) manufacturing entity inLuminance Enhancement Film (LEF) industry to solve greensuppliers selection

TOP founded in late 2003 is the leading optical prismmanufacturer in Taiwan TOP focuses on advanced productdevelopment and quality improvement However TOP isnow dealing with the increase in competition Moreover theLCD product life cycle is very short qualified suppliers asTOP frequently have to provide innovative products withina limited lead time for customers verification to meet time-to-market as well Consequently with the purpose of main-taining the existing customers satisfaction and attractingnew international customers to improve market share theselection of quality constant green suppliers for long termcooperation is extremely essential for survival of TOP

When TOP confirmed its role and strategy as a greensupplier TOP needs to evaluate its core competences andidentify the gap between customer needs and consultantsuggestions TOP then restructures the ecological environ-ment of the industry TOP has employed the green SCMsimultaneously considering environmental and economicaspects to either comply with regulation or meet customerneeds Furthermore TOP has proactively invested both qual-ity and environmental management system such as quality

system of economic criteria ISO9001 and QC080000 andenvironmental criteria ISO14001 and OHSAS18001 TOP hasimplemented a continuous quality improvement programand constituted an international standard as a platform totraining staffs as well as suppliers Those activities eithersave the costs of customers involved with their supplierdevelopment program or strengthen TOPrsquos green brandimage

TOP has learned and accumulated plenty of green SCMdomain knowledge and capabilities as a main supplier ofLCD supply chain through the two-stage process of the rawmaterial quality verification and integration all of material inone product for each customerThus TOP reversely requeststhe suppliers to comply with its customer environmental andeconomic requirement Under the consensus of a multidisci-plinary group of decision makers with various points of viewand representing the different services of the company TOPrsquosmanagers and heads of departments have decided that prod-uct price ISO quality system and lead time are economiccriteria Green technology and environmental certificate areenvironmental criteria The managers of the departmentssuch as Employee Health and Safety Production QualityControl and Assessment and Purchasing were required tomake their evaluation respectively

In reality TOP must work with suppliers for green prod-uct development Quality control and supply ability of eco-nomic criteria are the most important customer requirementfactors which related to green products TOPrsquos managementteam continuously integrates resources to investigate greenproducts such as light lean production and energy savingto satisfy stakeholders TOP is keeping good relationshipwiththe suppliers that will benefit from the purchasingmaterials ifneeded Additionally TOP also maintains good relationshipwith customers who will provide TOP opportunities ininnovative product developing and meeting the needs ofcustomers easier

The case revealed that the green criteria such as environ-ment and sustainability do not yet play a crucial role withingreen supplier selection procedures in enterprise practiceDue to the environmental regulations suppliers must meetsome minimum requirements in order to be eligible to workwith focal firms on the supply chain After that most of thecompanies do not apply environmental criteria to discrimi-nate qualified suppliers instead customers require suppliersto provide information such as Certificate of Nonuse of

Mathematical Problems in Engineering 7

Table 3 Fuzzy pairwise comparison of economic and environmental criteria

Criteria 1198621

1198622

1198623

1198624

1198625

1198621

(10 10 10) (10 30 50) (50 70 90) (10 30 50) (10 10 30)1198622

(15 13 11) (10 10 10) (19 17 15) (15 13 11) (50 70 90)1198623

(19 17 15) (50 70 90) (10 10 10) (17 15 13) (17 15 13)1198624

(15 13 11) (10 30 50) (30 50 70) (10 10 10) (13 11 11)1198625

(13 11 11) (19 17 15) (30 50 70) (10 10 30) (10 10 10)

Table 4 Fuzzy weights of the economic and environmental criteria

Criteria Fuzzy weight1198621

(0123 0295 0699)1198622

(0089 0173 0371)1198623

(0087 0168 0330)1198624

(0076 0203 0456)1198625

(0074 0160 0371)

Controlled Substances Certificate of Nonuse of Other Con-trolled Substances Material Safety Data Sheet and TestReport of customer assigned items issued by SGS annuallyThose certificates concern quality of economic criterion andpollution control of environmental criterion

According to institutional theory implementation ofgreen SCM is due to mimetic and normative (competitiveand benchmarking)mechanisms Facing environmental pro-tection pressure and legitimacy isomorphism pressure enter-prises must comply with social expectation and maintainconsistency with external environment to survive Thus theenvironmental and economic dimensionsmust be consideredsimultaneously [5] Consequently the proposed method isapplied on the case of TOP following the steps below

Step 1 (identify a number of economic and environmental cri-teria) In this study the data used as input to implement theproposed green supplier selection and evaluate the methodwere collected by means of semistructured interviews withthe top managers and head of departments Four companymanagers were required to make their evaluation respec-tively according to their preferences for important weightsof selection criteria and ratings of green suppliers

Using Table 1 and discussions with a companyrsquos top man-agers and heads of departments five criteria of economicsand environment for green supplier selection were selectedEconomic criteria include product price (119862

1) ISO quality

system (1198622) and lead time (119862

3) Green technology (119862

4) and

environmental certificate (1198625) are environmental criteria

Step 2 (aggregate the important weights of the criteria)After the determination of the green supplier criteria eachof four company managers is asked to conduct a pairwisecomparison with regard to the different criteria using thefuzzy linguistic assessment variables (see Table 2 for thesevariables) The completed matrices for the required cell areshown in Table 3 Applying (5)ndash(8) the final weights of theeconomic and environmental criteria are obtained as shownin Table 4

Step 3 (aggregate the ratings of suppliers versus the criteria)After the determination of the suppliers assessment criteriafour company managers rate each supplier according to eachcriterion A linguistic rating set of S was used to express theopinions of the managers where S = (VP P F G VG) VP(Very Poor) = (00 01 02) P (Poor) = (01 03 05) F (Fair) =(03 05 07) G (Good) = (05 07 09) and VG (Very Good)= (08 09 10) Table 5 gives the aggregated suitability ratingsof four green suppliers (119860

1 1198602 1198603 and 119860

4) using (12)

Step 4 (normalized performance of suppliers versus criteria)For simplicity and practicality all of the fuzzy numbers in thispaper are defined in the closed interval [0 1] Consequentlythe normalization procedure is no longer needed

Step 5 (calculate normalized weighted rating) Using (14) thenormalized weighted ratings 119866

119894can be obtained as shown in

Table 6

Step 6 (calculate 119860+ 119860minus 119889+119894 and 119889minus

119894) As shown in Table 7

the distance of each green supplier from 119860+ and 119860minus can be

calculated by (15)sim(16)

Step 7 (obtain the closeness coefficient) The closeness coef-ficients of green suppliers can be calculated by (17) as shownin Table 8 Therefore the ranking order of the four greensuppliers is 119860

3gt 1198604gt 1198601gt 1198602 Consequently the best

green supplier is 1198603

6 Conclusion

While the types of industry vary the key strategies ofgreen supplier selection also are changed Nevertheless allindustries should concern suppliers from both economicand environmental aspects because suppliers could influencefirmsrsquo performance and stakeholders

Green supplier selection is an important and complicatedMCDM problem requiring evaluation of multiple economicand environmental criteria incorporating vagueness andimprecision with the involvement of a group of expertsAlthough numerous studies have used economic criteria inthe supplier selection process limited studies have consid-ered the economic and environmental criteria simultane-ously The implementation of green supply management wasnot well understood This paper has proposed an integratedfuzzy MCDM approach to support the green suppliers selec-tion and the evaluation process In the proposed approachboth economic and environmental criteria were consideredIn order to overcome the shortcomings of the existing fuzzy

8 Mathematical Problems in Engineering

Table 5 Aggregate of the green supplier ratings versus criteria

Criteria Green suppliers Company managers119903119894119895

1198631

1198632

1198633

1198634

1198621

1198601

VG G G VG (0650 0800 0950)1198602

F G G F (0400 0600 0800)1198603

G G G G (0500 0700 0900)1198604

G F G G (0450 0650 0850)

1198622

1198601

G G G G (0500 0700 0900)1198602

F F G F (0350 0550 0750)1198603

G G VG G (0575 0750 0925)1198604

VG G VG G (0650 0800 0950)

1198623

1198601

G F G F (0400 0600 0800)1198602

F F F G (0350 0550 0750)1198603

VG G VG G (0650 0800 0950)1198604

F G F F (0350 0550 0750)

1198624

1198601

F G G F (0400 0600 0800)1198602

G VG G G (0575 0750 0925)1198603

G VG VG G (0650 0800 0950)1198604

VG G VG G (0650 0800 0950)

1198625

1198601

G G G G (0500 0700 0900)1198602

VG G G VG (0650 0800 0950)1198603

G G G VG (0575 0750 0925)1198604

VG G G VG (0650 0800 0950)

Table 6 Normalized weighted ratings of each market segment

Green suppliers 119866119894

1198601

(0045 0138 0392)1198602

(0041 0129 0372)1198603

(0052 0151 0413)1198604

(0048 0143 0396)

Table 7 The distance of each green supplier from 119860+ and 119860minus

Green suppliers 119889+

119889minus

1198601

1422 04181198602

1440 03961198603

1402 04421198604

1416 0424

Table 8 Closeness coefficients of alternatives

Alternatives Closeness coefficient Ranking1198601

0227 31198602

0216 41198603

0240 11198604

0230 2

TOPSIS technique this study has integrated the fuzzy TOP-SIS technique with the fuzzy AHP method to determine theimportant weights of economic and environmental criteriaFinally the proposed approach was employed to solve a realproblem in the LEF industry The results showed that the

proposed approach is effective in supplier selection for thecompany The application also indicated that the computa-tional procedure is efficient and easy to use in practice Futureresearch should focus on developing an extension of fuzzyMCDM approach to segment the green suppliers based onthe economic and environmental aspects Different methodsmay be applied to select green suppliers and the results shouldbe compared with the proposed approach The proposedapproach can also be applied to other management problemswith similar settings

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

References

[1] Y-S Chen and C-H Chang ldquoThe determinants of green prod-uct development performance Green dynamic capabilitiesgreen transformational leadership and green creativityrdquo Journalof Business Ethics vol 116 no 1 pp 107ndash119 2013

[2] A H I Lee H-Y Kang C-F Hsu and H-C Hung ldquoA greensupplier selectionmodel for high-tech industryrdquo Expert Systemswith Applications vol 36 no 4 pp 7917ndash7927 2009

[3] K Govindan S Rajendran J Sarkis and P Murugesan ldquoMulticriteria decision making approaches for green supplier evalua-tion and selection a literature reviewrdquo Journal of Cleaner Pro-duction vol 98 pp 66ndash83 2015

Mathematical Problems in Engineering 9

[4] R J Kuo Y C Wang and F C Tien ldquoIntegration of artificialneural network and MADA methods for green supplier selec-tionrdquo Journal of Cleaner Production vol 18 no 12 pp 1161ndash11702010

[5] A Gunasekaran and D Gallear ldquoSpecial Issue on Sustainabledevelopment of manufacturing and servicesrdquo InternationalJournal of Production Economics vol 140 no 1 pp 1ndash6 2012

[6] J Sarkis Q Zhu and K-H Lai ldquoAn organizational theoreticreview of green supply chain management literaturerdquo Interna-tional Journal of Production Economics vol 130 no 1 pp 1ndash152011

[7] A Appolloni H Sun F Jia and X Li ldquoGreen Procurement inthe private sector a state of the art review between 1996 and2013rdquo Journal of Cleaner Production vol 85 pp 122ndash133 2014

[8] H C Pimenta and P D Ball ldquoAnalysis of environmentalsustainability practices across upstream supply chain manage-mentrdquo Procedia CIRP vol 26 pp 677ndash682 2015

[9] C-L Hwang andK YoonMultiple Attribute DecisionMakingmdashMethods and Applications A State of the Art Survey SpringerNew York NY USA 1981

[10] H-S Shih H-J Shyur and E S Lee ldquoAn extension of TOPSISfor group decision makingrdquoMathematical and Computer Mod-elling vol 45 no 7-8 pp 801ndash813 2007

[11] T L SaatyTheAnalytical Hierarchy Process McGraw-Hill NewYork NY USA 1980

[12] G Buyukozkan and G Cifci ldquoEvaluation of the green supplychain management practices a fuzzy ANP approachrdquo Produc-tion Planning and Control vol 23 no 6 pp 405ndash418 2012

[13] C-C Sun ldquoA performance evaluation model by integratingfuzzy AHP and fuzzy TOPSIS methodsrdquo Expert Systems withApplications vol 37 no 12 pp 7745ndash7754 2010

[14] W Xia and Z Wu ldquoSupplier selection with multiple criteria involume discount environmentsrdquoOmega vol 35 no 5 pp 494ndash504 2007

[15] I Chamodrakas D Batis and D Martakos ldquoSupplier selectionin electronic marketplaces using satisficing and fuzzy AHPrdquoExpert Systems with Applications vol 37 no 1 pp 490ndash4982010

[16] K Shaw R Shankar S S Yadav and L S Thakur ldquoSupplierselection using fuzzy AHP and fuzzy multi-objective linearprogramming for developing low carbon supply chainrdquo ExpertSystems with Applications vol 39 no 9 pp 8182ndash8192 2012

[17] O Kilincci and S A Onal ldquoFuzzy AHP approach for supplierselection in a washing machine companyrdquo Expert Systems withApplications vol 38 no 8 pp 9656ndash9664 2011

[18] A H I Lee ldquoA fuzzy supplier selection model with the consid-eration of benefits opportunities costs and risksrdquo Expert Sys-tems with Applications vol 36 no 2 pp 2879ndash2893 2009

[19] C Bai and J Sarkis ldquoGreen supplier development analyticalevaluation using rough set theoryrdquo Journal of Cleaner Produc-tion vol 18 no 12 pp 1200ndash1210 2010

[20] M Abdollahi M Arvan and J Razmi ldquoAn integrated approachfor supplier portfolio selection lean or agilerdquo Expert Systemswith Applications vol 42 no 1 pp 679ndash690 2015

[21] M S Memon Y H Lee and S I Mari ldquoGroup multi-criteriasupplier selection using combined grey systems theory anduncertainty theoryrdquo Expert Systems with Applications vol 42no 21 pp 7951ndash7959 2015

[22] S H Hashemi A Karimi and M Tavana ldquoAn integratedgreen supplier selection approachwith analytic network processand improved Grey relational analysisrdquo International Journal ofProduction Economics vol 159 pp 178ndash191 2015

[23] M Punniyamoorthy P Mathiyalagan and P Parthiban ldquoAstrategic model using structural equation modeling and fuzzylogic in supplier selectionrdquo Expert Systems with Applicationsvol 38 no 1 pp 458ndash474 2011

[24] R M Grisi L Guerra and G Naviglio ldquoSupplier performanceevaluation for green supply chainmanagementrdquo inBusiness Per-formanceMeasurement andManagement pp 149ndash163 SpringerBerlin Germany 2010

[25] F Mafakheri M Breton and A Ghoniem ldquoSupplier selection-order allocation a two-stage multiple criteria dynamic pro-gramming approachrdquo International Journal of Production Eco-nomics vol 132 no 1 pp 52ndash57 2011

[26] Y-J Chen ldquoStructured methodology for supplier selection andevaluation in a supply chainrdquo Information Sciences vol 181 no9 pp 1651ndash1670 2011

[27] W-PWang ldquoA fuzzy linguistic computing approach to supplierevaluationrdquo Applied Mathematical Modelling vol 34 no 10 pp3130ndash3141 2010

[28] M-L Tseng and A S F Chiu ldquoEvaluating firmrsquos green supplychain management in linguistic preferencesrdquo Journal of CleanerProduction vol 40 pp 22ndash31 2013

[29] Q Zhu Y Dou and J Sarkis ldquoA portfolio-based analysisfor green supplier management using the analytical networkprocessrdquo Supply Chain Management vol 15 no 4 pp 306ndash3192010

[30] G A Keskin S Ilhan and C Ozkan ldquoThe Fuzzy ARTalgorithm a categorization method for supplier evaluation andselectionrdquo Expert Systems with Applications vol 37 no 2 pp1235ndash1240 2010

[31] C-Y Shen and K-T Yu ldquoEnhancing the efficacy of supplierselection decision-making on the initial stage of new productdevelopment a hybrid fuzzy approach considering the strategicand operational factors simultaneouslyrdquo Expert Systems withApplications vol 36 no 8 pp 11271ndash11281 2009

[32] K Govindan R Khodaverdi and A Jafarian ldquoA fuzzy multicriteria approach for measuring sustainability performance ofa supplier based on triple bottom line approachrdquo Journal ofCleaner Production vol 47 pp 345ndash354 2013

[33] G Tuzkaya A Ozgen D Ozgen and U R Tuzkaya ldquoEnvi-ronmental performance evaluation of suppliers a hybrid fuzzymulti-criteria decision approachrdquo International Journal of Envi-ronmental ScienceampTechnology vol 6 no 3 pp 477ndash490 2009

[34] Q Zhu J Sarkis and K-H Lai ldquoInitiatives and outcomes ofgreen supply chain management implementation by Chinesemanufacturersrdquo Journal of Environmental Management vol 85no 1 pp 179ndash189 2007

[35] W-C Yeh and M-C Chuang ldquoUsing multi-objective geneticalgorithm for partner selection in green supply chain problemsrdquoExpert Systems with Applications vol 38 no 4 pp 4244ndash42532011

[36] A Awasthi S S Chauhan and S K Goyal ldquoA fuzzy multi-criteria approach for evaluating environmental performance ofsuppliersrdquo International Journal of Production Economics vol126 no 2 pp 370ndash378 2010

[37] J Sarkis ldquoManufacturingrsquos role in corporate environmentalsustainability-Concerns for the new millenniumrdquo InternationalJournal of Operations amp Production Management vol 21 no 5-6 pp 666ndash686 2001

[38] S MMirhedayatian M Azadi and R Farzipoor Saen ldquoA novelnetwork data envelopment analysis model for evaluating greensupply chain managementrdquo International Journal of ProductionEconomics vol 147 pp 544ndash554 2014

10 Mathematical Problems in Engineering

[39] C Wu and D Barnes ldquoAn integrated model for green partnerselection and supply chain constructionrdquo Journal of CleanerProduction vol 112 pp 2114ndash2132 2016

[40] G Bruno E Esposito A Genovese andR Passaro ldquoAHP-basedapproaches for supplier evaluation problems and perspectivesrdquoJournal of Purchasing and Supply Management vol 18 no 3 pp159ndash172 2012

[41] F R L Junior L Osiro and L C R Carpinetti ldquoA comparisonbetween Fuzzy AHP and Fuzzy TOPSIS methods to supplierselectionrdquo Applied Soft Computing vol 21 pp 194ndash209 2014

[42] A Kawa and W W Koczkodaj ldquoSupplier evaluation process bypairwise comparisonsrdquo Mathematical Problems in Engineeringvol 2015 Article ID 976742 9 pages 2015

[43] X Deng Y Hu Y Deng and S Mahadevan ldquoSupplier selectionusing AHP methodology extended by D numbersrdquo ExpertSystems with Applications vol 41 no 1 pp 156ndash167 2014

[44] N Xie and J Xin ldquoInterval grey numbers based multi-attributedecisionmakingmethod for supplier selectionrdquoKybernetes vol43 no 7 pp 1064ndash1078 2014

[45] J Lee H Cho and Y S Kim ldquoAssessing business impacts ofagility criterion and order allocation strategy in multi-criteriasupplier selectionrdquo Expert Systems with Applications vol 42 no3 pp 1136ndash1148 2015

[46] L Shen L Olfat K Govindan R Khodaverdi and A DiabatldquoA fuzzy multi criteria approach for evaluating green supplierrsquosperformance in green supply chain with linguistic preferencesrdquoResources Conservation and Recycling vol 74 pp 170ndash179 2012

[47] B Kanga Y Hu Y Deng and D Zhou ldquoA new methodologyof multicriteria decision-making in supplier selection based onZ-numbersrdquo Mathematical Problems in Engineering vol 2016Article ID 8475987 17 pages 2016

[48] N Asthana and M Gupta ldquoSupplier selection using artificialneural network and genetic algorithmrdquo International Journal ofIndian Culture and Business Management vol 11 no 4 pp 457ndash472 2015

[49] D Dubois and H Prade ldquoOperations on fuzzy numbersrdquo Inter-national Journal of Systems Science vol 9 no 6 pp 613ndash6261978

[50] A Kaufmann and M M Gupta Introduction to Fuzzy Arith-metic Theory and Applications The Arden Shakespeare 1991

[51] L A Zadeh ldquoThe concept of a linguistic variable and its appli-cation to approximate reasoningmdashIrdquo Information Sciences vol8 no 3 pp 199ndash249 1975

[52] L A Zadeh ldquoThe concept of a linguistic variable and its applica-tion to approximate reasoningmdashIIrdquo Information Sciences vol 8no 4 pp 301ndash357 1975

[53] D-Y Chang ldquoApplications of the extent analysis method onfuzzy AHPrdquo European Journal of Operational Research vol 95no 3 pp 649ndash655 1996

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical Problems in Engineering

Hindawi Publishing Corporationhttpwwwhindawicom

Differential EquationsInternational Journal of

Volume 2014

Applied MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical PhysicsAdvances in

Complex AnalysisJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

OptimizationJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Operations ResearchAdvances in

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Function Spaces

Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of Mathematics and Mathematical Sciences

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Algebra

Discrete Dynamics in Nature and Society

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Decision SciencesAdvances in

Discrete MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom

Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Stochastic AnalysisInternational Journal of

Mathematical Problems in Engineering 7

Table 3 Fuzzy pairwise comparison of economic and environmental criteria

Criteria 1198621

1198622

1198623

1198624

1198625

1198621

(10 10 10) (10 30 50) (50 70 90) (10 30 50) (10 10 30)1198622

(15 13 11) (10 10 10) (19 17 15) (15 13 11) (50 70 90)1198623

(19 17 15) (50 70 90) (10 10 10) (17 15 13) (17 15 13)1198624

(15 13 11) (10 30 50) (30 50 70) (10 10 10) (13 11 11)1198625

(13 11 11) (19 17 15) (30 50 70) (10 10 30) (10 10 10)

Table 4 Fuzzy weights of the economic and environmental criteria

Criteria Fuzzy weight1198621

(0123 0295 0699)1198622

(0089 0173 0371)1198623

(0087 0168 0330)1198624

(0076 0203 0456)1198625

(0074 0160 0371)

Controlled Substances Certificate of Nonuse of Other Con-trolled Substances Material Safety Data Sheet and TestReport of customer assigned items issued by SGS annuallyThose certificates concern quality of economic criterion andpollution control of environmental criterion

According to institutional theory implementation ofgreen SCM is due to mimetic and normative (competitiveand benchmarking)mechanisms Facing environmental pro-tection pressure and legitimacy isomorphism pressure enter-prises must comply with social expectation and maintainconsistency with external environment to survive Thus theenvironmental and economic dimensionsmust be consideredsimultaneously [5] Consequently the proposed method isapplied on the case of TOP following the steps below

Step 1 (identify a number of economic and environmental cri-teria) In this study the data used as input to implement theproposed green supplier selection and evaluate the methodwere collected by means of semistructured interviews withthe top managers and head of departments Four companymanagers were required to make their evaluation respec-tively according to their preferences for important weightsof selection criteria and ratings of green suppliers

Using Table 1 and discussions with a companyrsquos top man-agers and heads of departments five criteria of economicsand environment for green supplier selection were selectedEconomic criteria include product price (119862

1) ISO quality

system (1198622) and lead time (119862

3) Green technology (119862

4) and

environmental certificate (1198625) are environmental criteria

Step 2 (aggregate the important weights of the criteria)After the determination of the green supplier criteria eachof four company managers is asked to conduct a pairwisecomparison with regard to the different criteria using thefuzzy linguistic assessment variables (see Table 2 for thesevariables) The completed matrices for the required cell areshown in Table 3 Applying (5)ndash(8) the final weights of theeconomic and environmental criteria are obtained as shownin Table 4

Step 3 (aggregate the ratings of suppliers versus the criteria)After the determination of the suppliers assessment criteriafour company managers rate each supplier according to eachcriterion A linguistic rating set of S was used to express theopinions of the managers where S = (VP P F G VG) VP(Very Poor) = (00 01 02) P (Poor) = (01 03 05) F (Fair) =(03 05 07) G (Good) = (05 07 09) and VG (Very Good)= (08 09 10) Table 5 gives the aggregated suitability ratingsof four green suppliers (119860

1 1198602 1198603 and 119860

4) using (12)

Step 4 (normalized performance of suppliers versus criteria)For simplicity and practicality all of the fuzzy numbers in thispaper are defined in the closed interval [0 1] Consequentlythe normalization procedure is no longer needed

Step 5 (calculate normalized weighted rating) Using (14) thenormalized weighted ratings 119866

119894can be obtained as shown in

Table 6

Step 6 (calculate 119860+ 119860minus 119889+119894 and 119889minus

119894) As shown in Table 7

the distance of each green supplier from 119860+ and 119860minus can be

calculated by (15)sim(16)

Step 7 (obtain the closeness coefficient) The closeness coef-ficients of green suppliers can be calculated by (17) as shownin Table 8 Therefore the ranking order of the four greensuppliers is 119860

3gt 1198604gt 1198601gt 1198602 Consequently the best

green supplier is 1198603

6 Conclusion

While the types of industry vary the key strategies ofgreen supplier selection also are changed Nevertheless allindustries should concern suppliers from both economicand environmental aspects because suppliers could influencefirmsrsquo performance and stakeholders

Green supplier selection is an important and complicatedMCDM problem requiring evaluation of multiple economicand environmental criteria incorporating vagueness andimprecision with the involvement of a group of expertsAlthough numerous studies have used economic criteria inthe supplier selection process limited studies have consid-ered the economic and environmental criteria simultane-ously The implementation of green supply management wasnot well understood This paper has proposed an integratedfuzzy MCDM approach to support the green suppliers selec-tion and the evaluation process In the proposed approachboth economic and environmental criteria were consideredIn order to overcome the shortcomings of the existing fuzzy

8 Mathematical Problems in Engineering

Table 5 Aggregate of the green supplier ratings versus criteria

Criteria Green suppliers Company managers119903119894119895

1198631

1198632

1198633

1198634

1198621

1198601

VG G G VG (0650 0800 0950)1198602

F G G F (0400 0600 0800)1198603

G G G G (0500 0700 0900)1198604

G F G G (0450 0650 0850)

1198622

1198601

G G G G (0500 0700 0900)1198602

F F G F (0350 0550 0750)1198603

G G VG G (0575 0750 0925)1198604

VG G VG G (0650 0800 0950)

1198623

1198601

G F G F (0400 0600 0800)1198602

F F F G (0350 0550 0750)1198603

VG G VG G (0650 0800 0950)1198604

F G F F (0350 0550 0750)

1198624

1198601

F G G F (0400 0600 0800)1198602

G VG G G (0575 0750 0925)1198603

G VG VG G (0650 0800 0950)1198604

VG G VG G (0650 0800 0950)

1198625

1198601

G G G G (0500 0700 0900)1198602

VG G G VG (0650 0800 0950)1198603

G G G VG (0575 0750 0925)1198604

VG G G VG (0650 0800 0950)

Table 6 Normalized weighted ratings of each market segment

Green suppliers 119866119894

1198601

(0045 0138 0392)1198602

(0041 0129 0372)1198603

(0052 0151 0413)1198604

(0048 0143 0396)

Table 7 The distance of each green supplier from 119860+ and 119860minus

Green suppliers 119889+

119889minus

1198601

1422 04181198602

1440 03961198603

1402 04421198604

1416 0424

Table 8 Closeness coefficients of alternatives

Alternatives Closeness coefficient Ranking1198601

0227 31198602

0216 41198603

0240 11198604

0230 2

TOPSIS technique this study has integrated the fuzzy TOP-SIS technique with the fuzzy AHP method to determine theimportant weights of economic and environmental criteriaFinally the proposed approach was employed to solve a realproblem in the LEF industry The results showed that the

proposed approach is effective in supplier selection for thecompany The application also indicated that the computa-tional procedure is efficient and easy to use in practice Futureresearch should focus on developing an extension of fuzzyMCDM approach to segment the green suppliers based onthe economic and environmental aspects Different methodsmay be applied to select green suppliers and the results shouldbe compared with the proposed approach The proposedapproach can also be applied to other management problemswith similar settings

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

References

[1] Y-S Chen and C-H Chang ldquoThe determinants of green prod-uct development performance Green dynamic capabilitiesgreen transformational leadership and green creativityrdquo Journalof Business Ethics vol 116 no 1 pp 107ndash119 2013

[2] A H I Lee H-Y Kang C-F Hsu and H-C Hung ldquoA greensupplier selectionmodel for high-tech industryrdquo Expert Systemswith Applications vol 36 no 4 pp 7917ndash7927 2009

[3] K Govindan S Rajendran J Sarkis and P Murugesan ldquoMulticriteria decision making approaches for green supplier evalua-tion and selection a literature reviewrdquo Journal of Cleaner Pro-duction vol 98 pp 66ndash83 2015

Mathematical Problems in Engineering 9

[4] R J Kuo Y C Wang and F C Tien ldquoIntegration of artificialneural network and MADA methods for green supplier selec-tionrdquo Journal of Cleaner Production vol 18 no 12 pp 1161ndash11702010

[5] A Gunasekaran and D Gallear ldquoSpecial Issue on Sustainabledevelopment of manufacturing and servicesrdquo InternationalJournal of Production Economics vol 140 no 1 pp 1ndash6 2012

[6] J Sarkis Q Zhu and K-H Lai ldquoAn organizational theoreticreview of green supply chain management literaturerdquo Interna-tional Journal of Production Economics vol 130 no 1 pp 1ndash152011

[7] A Appolloni H Sun F Jia and X Li ldquoGreen Procurement inthe private sector a state of the art review between 1996 and2013rdquo Journal of Cleaner Production vol 85 pp 122ndash133 2014

[8] H C Pimenta and P D Ball ldquoAnalysis of environmentalsustainability practices across upstream supply chain manage-mentrdquo Procedia CIRP vol 26 pp 677ndash682 2015

[9] C-L Hwang andK YoonMultiple Attribute DecisionMakingmdashMethods and Applications A State of the Art Survey SpringerNew York NY USA 1981

[10] H-S Shih H-J Shyur and E S Lee ldquoAn extension of TOPSISfor group decision makingrdquoMathematical and Computer Mod-elling vol 45 no 7-8 pp 801ndash813 2007

[11] T L SaatyTheAnalytical Hierarchy Process McGraw-Hill NewYork NY USA 1980

[12] G Buyukozkan and G Cifci ldquoEvaluation of the green supplychain management practices a fuzzy ANP approachrdquo Produc-tion Planning and Control vol 23 no 6 pp 405ndash418 2012

[13] C-C Sun ldquoA performance evaluation model by integratingfuzzy AHP and fuzzy TOPSIS methodsrdquo Expert Systems withApplications vol 37 no 12 pp 7745ndash7754 2010

[14] W Xia and Z Wu ldquoSupplier selection with multiple criteria involume discount environmentsrdquoOmega vol 35 no 5 pp 494ndash504 2007

[15] I Chamodrakas D Batis and D Martakos ldquoSupplier selectionin electronic marketplaces using satisficing and fuzzy AHPrdquoExpert Systems with Applications vol 37 no 1 pp 490ndash4982010

[16] K Shaw R Shankar S S Yadav and L S Thakur ldquoSupplierselection using fuzzy AHP and fuzzy multi-objective linearprogramming for developing low carbon supply chainrdquo ExpertSystems with Applications vol 39 no 9 pp 8182ndash8192 2012

[17] O Kilincci and S A Onal ldquoFuzzy AHP approach for supplierselection in a washing machine companyrdquo Expert Systems withApplications vol 38 no 8 pp 9656ndash9664 2011

[18] A H I Lee ldquoA fuzzy supplier selection model with the consid-eration of benefits opportunities costs and risksrdquo Expert Sys-tems with Applications vol 36 no 2 pp 2879ndash2893 2009

[19] C Bai and J Sarkis ldquoGreen supplier development analyticalevaluation using rough set theoryrdquo Journal of Cleaner Produc-tion vol 18 no 12 pp 1200ndash1210 2010

[20] M Abdollahi M Arvan and J Razmi ldquoAn integrated approachfor supplier portfolio selection lean or agilerdquo Expert Systemswith Applications vol 42 no 1 pp 679ndash690 2015

[21] M S Memon Y H Lee and S I Mari ldquoGroup multi-criteriasupplier selection using combined grey systems theory anduncertainty theoryrdquo Expert Systems with Applications vol 42no 21 pp 7951ndash7959 2015

[22] S H Hashemi A Karimi and M Tavana ldquoAn integratedgreen supplier selection approachwith analytic network processand improved Grey relational analysisrdquo International Journal ofProduction Economics vol 159 pp 178ndash191 2015

[23] M Punniyamoorthy P Mathiyalagan and P Parthiban ldquoAstrategic model using structural equation modeling and fuzzylogic in supplier selectionrdquo Expert Systems with Applicationsvol 38 no 1 pp 458ndash474 2011

[24] R M Grisi L Guerra and G Naviglio ldquoSupplier performanceevaluation for green supply chainmanagementrdquo inBusiness Per-formanceMeasurement andManagement pp 149ndash163 SpringerBerlin Germany 2010

[25] F Mafakheri M Breton and A Ghoniem ldquoSupplier selection-order allocation a two-stage multiple criteria dynamic pro-gramming approachrdquo International Journal of Production Eco-nomics vol 132 no 1 pp 52ndash57 2011

[26] Y-J Chen ldquoStructured methodology for supplier selection andevaluation in a supply chainrdquo Information Sciences vol 181 no9 pp 1651ndash1670 2011

[27] W-PWang ldquoA fuzzy linguistic computing approach to supplierevaluationrdquo Applied Mathematical Modelling vol 34 no 10 pp3130ndash3141 2010

[28] M-L Tseng and A S F Chiu ldquoEvaluating firmrsquos green supplychain management in linguistic preferencesrdquo Journal of CleanerProduction vol 40 pp 22ndash31 2013

[29] Q Zhu Y Dou and J Sarkis ldquoA portfolio-based analysisfor green supplier management using the analytical networkprocessrdquo Supply Chain Management vol 15 no 4 pp 306ndash3192010

[30] G A Keskin S Ilhan and C Ozkan ldquoThe Fuzzy ARTalgorithm a categorization method for supplier evaluation andselectionrdquo Expert Systems with Applications vol 37 no 2 pp1235ndash1240 2010

[31] C-Y Shen and K-T Yu ldquoEnhancing the efficacy of supplierselection decision-making on the initial stage of new productdevelopment a hybrid fuzzy approach considering the strategicand operational factors simultaneouslyrdquo Expert Systems withApplications vol 36 no 8 pp 11271ndash11281 2009

[32] K Govindan R Khodaverdi and A Jafarian ldquoA fuzzy multicriteria approach for measuring sustainability performance ofa supplier based on triple bottom line approachrdquo Journal ofCleaner Production vol 47 pp 345ndash354 2013

[33] G Tuzkaya A Ozgen D Ozgen and U R Tuzkaya ldquoEnvi-ronmental performance evaluation of suppliers a hybrid fuzzymulti-criteria decision approachrdquo International Journal of Envi-ronmental ScienceampTechnology vol 6 no 3 pp 477ndash490 2009

[34] Q Zhu J Sarkis and K-H Lai ldquoInitiatives and outcomes ofgreen supply chain management implementation by Chinesemanufacturersrdquo Journal of Environmental Management vol 85no 1 pp 179ndash189 2007

[35] W-C Yeh and M-C Chuang ldquoUsing multi-objective geneticalgorithm for partner selection in green supply chain problemsrdquoExpert Systems with Applications vol 38 no 4 pp 4244ndash42532011

[36] A Awasthi S S Chauhan and S K Goyal ldquoA fuzzy multi-criteria approach for evaluating environmental performance ofsuppliersrdquo International Journal of Production Economics vol126 no 2 pp 370ndash378 2010

[37] J Sarkis ldquoManufacturingrsquos role in corporate environmentalsustainability-Concerns for the new millenniumrdquo InternationalJournal of Operations amp Production Management vol 21 no 5-6 pp 666ndash686 2001

[38] S MMirhedayatian M Azadi and R Farzipoor Saen ldquoA novelnetwork data envelopment analysis model for evaluating greensupply chain managementrdquo International Journal of ProductionEconomics vol 147 pp 544ndash554 2014

10 Mathematical Problems in Engineering

[39] C Wu and D Barnes ldquoAn integrated model for green partnerselection and supply chain constructionrdquo Journal of CleanerProduction vol 112 pp 2114ndash2132 2016

[40] G Bruno E Esposito A Genovese andR Passaro ldquoAHP-basedapproaches for supplier evaluation problems and perspectivesrdquoJournal of Purchasing and Supply Management vol 18 no 3 pp159ndash172 2012

[41] F R L Junior L Osiro and L C R Carpinetti ldquoA comparisonbetween Fuzzy AHP and Fuzzy TOPSIS methods to supplierselectionrdquo Applied Soft Computing vol 21 pp 194ndash209 2014

[42] A Kawa and W W Koczkodaj ldquoSupplier evaluation process bypairwise comparisonsrdquo Mathematical Problems in Engineeringvol 2015 Article ID 976742 9 pages 2015

[43] X Deng Y Hu Y Deng and S Mahadevan ldquoSupplier selectionusing AHP methodology extended by D numbersrdquo ExpertSystems with Applications vol 41 no 1 pp 156ndash167 2014

[44] N Xie and J Xin ldquoInterval grey numbers based multi-attributedecisionmakingmethod for supplier selectionrdquoKybernetes vol43 no 7 pp 1064ndash1078 2014

[45] J Lee H Cho and Y S Kim ldquoAssessing business impacts ofagility criterion and order allocation strategy in multi-criteriasupplier selectionrdquo Expert Systems with Applications vol 42 no3 pp 1136ndash1148 2015

[46] L Shen L Olfat K Govindan R Khodaverdi and A DiabatldquoA fuzzy multi criteria approach for evaluating green supplierrsquosperformance in green supply chain with linguistic preferencesrdquoResources Conservation and Recycling vol 74 pp 170ndash179 2012

[47] B Kanga Y Hu Y Deng and D Zhou ldquoA new methodologyof multicriteria decision-making in supplier selection based onZ-numbersrdquo Mathematical Problems in Engineering vol 2016Article ID 8475987 17 pages 2016

[48] N Asthana and M Gupta ldquoSupplier selection using artificialneural network and genetic algorithmrdquo International Journal ofIndian Culture and Business Management vol 11 no 4 pp 457ndash472 2015

[49] D Dubois and H Prade ldquoOperations on fuzzy numbersrdquo Inter-national Journal of Systems Science vol 9 no 6 pp 613ndash6261978

[50] A Kaufmann and M M Gupta Introduction to Fuzzy Arith-metic Theory and Applications The Arden Shakespeare 1991

[51] L A Zadeh ldquoThe concept of a linguistic variable and its appli-cation to approximate reasoningmdashIrdquo Information Sciences vol8 no 3 pp 199ndash249 1975

[52] L A Zadeh ldquoThe concept of a linguistic variable and its applica-tion to approximate reasoningmdashIIrdquo Information Sciences vol 8no 4 pp 301ndash357 1975

[53] D-Y Chang ldquoApplications of the extent analysis method onfuzzy AHPrdquo European Journal of Operational Research vol 95no 3 pp 649ndash655 1996

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical Problems in Engineering

Hindawi Publishing Corporationhttpwwwhindawicom

Differential EquationsInternational Journal of

Volume 2014

Applied MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical PhysicsAdvances in

Complex AnalysisJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

OptimizationJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Operations ResearchAdvances in

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Function Spaces

Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of Mathematics and Mathematical Sciences

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Algebra

Discrete Dynamics in Nature and Society

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Decision SciencesAdvances in

Discrete MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom

Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Stochastic AnalysisInternational Journal of

8 Mathematical Problems in Engineering

Table 5 Aggregate of the green supplier ratings versus criteria

Criteria Green suppliers Company managers119903119894119895

1198631

1198632

1198633

1198634

1198621

1198601

VG G G VG (0650 0800 0950)1198602

F G G F (0400 0600 0800)1198603

G G G G (0500 0700 0900)1198604

G F G G (0450 0650 0850)

1198622

1198601

G G G G (0500 0700 0900)1198602

F F G F (0350 0550 0750)1198603

G G VG G (0575 0750 0925)1198604

VG G VG G (0650 0800 0950)

1198623

1198601

G F G F (0400 0600 0800)1198602

F F F G (0350 0550 0750)1198603

VG G VG G (0650 0800 0950)1198604

F G F F (0350 0550 0750)

1198624

1198601

F G G F (0400 0600 0800)1198602

G VG G G (0575 0750 0925)1198603

G VG VG G (0650 0800 0950)1198604

VG G VG G (0650 0800 0950)

1198625

1198601

G G G G (0500 0700 0900)1198602

VG G G VG (0650 0800 0950)1198603

G G G VG (0575 0750 0925)1198604

VG G G VG (0650 0800 0950)

Table 6 Normalized weighted ratings of each market segment

Green suppliers 119866119894

1198601

(0045 0138 0392)1198602

(0041 0129 0372)1198603

(0052 0151 0413)1198604

(0048 0143 0396)

Table 7 The distance of each green supplier from 119860+ and 119860minus

Green suppliers 119889+

119889minus

1198601

1422 04181198602

1440 03961198603

1402 04421198604

1416 0424

Table 8 Closeness coefficients of alternatives

Alternatives Closeness coefficient Ranking1198601

0227 31198602

0216 41198603

0240 11198604

0230 2

TOPSIS technique this study has integrated the fuzzy TOP-SIS technique with the fuzzy AHP method to determine theimportant weights of economic and environmental criteriaFinally the proposed approach was employed to solve a realproblem in the LEF industry The results showed that the

proposed approach is effective in supplier selection for thecompany The application also indicated that the computa-tional procedure is efficient and easy to use in practice Futureresearch should focus on developing an extension of fuzzyMCDM approach to segment the green suppliers based onthe economic and environmental aspects Different methodsmay be applied to select green suppliers and the results shouldbe compared with the proposed approach The proposedapproach can also be applied to other management problemswith similar settings

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

References

[1] Y-S Chen and C-H Chang ldquoThe determinants of green prod-uct development performance Green dynamic capabilitiesgreen transformational leadership and green creativityrdquo Journalof Business Ethics vol 116 no 1 pp 107ndash119 2013

[2] A H I Lee H-Y Kang C-F Hsu and H-C Hung ldquoA greensupplier selectionmodel for high-tech industryrdquo Expert Systemswith Applications vol 36 no 4 pp 7917ndash7927 2009

[3] K Govindan S Rajendran J Sarkis and P Murugesan ldquoMulticriteria decision making approaches for green supplier evalua-tion and selection a literature reviewrdquo Journal of Cleaner Pro-duction vol 98 pp 66ndash83 2015

Mathematical Problems in Engineering 9

[4] R J Kuo Y C Wang and F C Tien ldquoIntegration of artificialneural network and MADA methods for green supplier selec-tionrdquo Journal of Cleaner Production vol 18 no 12 pp 1161ndash11702010

[5] A Gunasekaran and D Gallear ldquoSpecial Issue on Sustainabledevelopment of manufacturing and servicesrdquo InternationalJournal of Production Economics vol 140 no 1 pp 1ndash6 2012

[6] J Sarkis Q Zhu and K-H Lai ldquoAn organizational theoreticreview of green supply chain management literaturerdquo Interna-tional Journal of Production Economics vol 130 no 1 pp 1ndash152011

[7] A Appolloni H Sun F Jia and X Li ldquoGreen Procurement inthe private sector a state of the art review between 1996 and2013rdquo Journal of Cleaner Production vol 85 pp 122ndash133 2014

[8] H C Pimenta and P D Ball ldquoAnalysis of environmentalsustainability practices across upstream supply chain manage-mentrdquo Procedia CIRP vol 26 pp 677ndash682 2015

[9] C-L Hwang andK YoonMultiple Attribute DecisionMakingmdashMethods and Applications A State of the Art Survey SpringerNew York NY USA 1981

[10] H-S Shih H-J Shyur and E S Lee ldquoAn extension of TOPSISfor group decision makingrdquoMathematical and Computer Mod-elling vol 45 no 7-8 pp 801ndash813 2007

[11] T L SaatyTheAnalytical Hierarchy Process McGraw-Hill NewYork NY USA 1980

[12] G Buyukozkan and G Cifci ldquoEvaluation of the green supplychain management practices a fuzzy ANP approachrdquo Produc-tion Planning and Control vol 23 no 6 pp 405ndash418 2012

[13] C-C Sun ldquoA performance evaluation model by integratingfuzzy AHP and fuzzy TOPSIS methodsrdquo Expert Systems withApplications vol 37 no 12 pp 7745ndash7754 2010

[14] W Xia and Z Wu ldquoSupplier selection with multiple criteria involume discount environmentsrdquoOmega vol 35 no 5 pp 494ndash504 2007

[15] I Chamodrakas D Batis and D Martakos ldquoSupplier selectionin electronic marketplaces using satisficing and fuzzy AHPrdquoExpert Systems with Applications vol 37 no 1 pp 490ndash4982010

[16] K Shaw R Shankar S S Yadav and L S Thakur ldquoSupplierselection using fuzzy AHP and fuzzy multi-objective linearprogramming for developing low carbon supply chainrdquo ExpertSystems with Applications vol 39 no 9 pp 8182ndash8192 2012

[17] O Kilincci and S A Onal ldquoFuzzy AHP approach for supplierselection in a washing machine companyrdquo Expert Systems withApplications vol 38 no 8 pp 9656ndash9664 2011

[18] A H I Lee ldquoA fuzzy supplier selection model with the consid-eration of benefits opportunities costs and risksrdquo Expert Sys-tems with Applications vol 36 no 2 pp 2879ndash2893 2009

[19] C Bai and J Sarkis ldquoGreen supplier development analyticalevaluation using rough set theoryrdquo Journal of Cleaner Produc-tion vol 18 no 12 pp 1200ndash1210 2010

[20] M Abdollahi M Arvan and J Razmi ldquoAn integrated approachfor supplier portfolio selection lean or agilerdquo Expert Systemswith Applications vol 42 no 1 pp 679ndash690 2015

[21] M S Memon Y H Lee and S I Mari ldquoGroup multi-criteriasupplier selection using combined grey systems theory anduncertainty theoryrdquo Expert Systems with Applications vol 42no 21 pp 7951ndash7959 2015

[22] S H Hashemi A Karimi and M Tavana ldquoAn integratedgreen supplier selection approachwith analytic network processand improved Grey relational analysisrdquo International Journal ofProduction Economics vol 159 pp 178ndash191 2015

[23] M Punniyamoorthy P Mathiyalagan and P Parthiban ldquoAstrategic model using structural equation modeling and fuzzylogic in supplier selectionrdquo Expert Systems with Applicationsvol 38 no 1 pp 458ndash474 2011

[24] R M Grisi L Guerra and G Naviglio ldquoSupplier performanceevaluation for green supply chainmanagementrdquo inBusiness Per-formanceMeasurement andManagement pp 149ndash163 SpringerBerlin Germany 2010

[25] F Mafakheri M Breton and A Ghoniem ldquoSupplier selection-order allocation a two-stage multiple criteria dynamic pro-gramming approachrdquo International Journal of Production Eco-nomics vol 132 no 1 pp 52ndash57 2011

[26] Y-J Chen ldquoStructured methodology for supplier selection andevaluation in a supply chainrdquo Information Sciences vol 181 no9 pp 1651ndash1670 2011

[27] W-PWang ldquoA fuzzy linguistic computing approach to supplierevaluationrdquo Applied Mathematical Modelling vol 34 no 10 pp3130ndash3141 2010

[28] M-L Tseng and A S F Chiu ldquoEvaluating firmrsquos green supplychain management in linguistic preferencesrdquo Journal of CleanerProduction vol 40 pp 22ndash31 2013

[29] Q Zhu Y Dou and J Sarkis ldquoA portfolio-based analysisfor green supplier management using the analytical networkprocessrdquo Supply Chain Management vol 15 no 4 pp 306ndash3192010

[30] G A Keskin S Ilhan and C Ozkan ldquoThe Fuzzy ARTalgorithm a categorization method for supplier evaluation andselectionrdquo Expert Systems with Applications vol 37 no 2 pp1235ndash1240 2010

[31] C-Y Shen and K-T Yu ldquoEnhancing the efficacy of supplierselection decision-making on the initial stage of new productdevelopment a hybrid fuzzy approach considering the strategicand operational factors simultaneouslyrdquo Expert Systems withApplications vol 36 no 8 pp 11271ndash11281 2009

[32] K Govindan R Khodaverdi and A Jafarian ldquoA fuzzy multicriteria approach for measuring sustainability performance ofa supplier based on triple bottom line approachrdquo Journal ofCleaner Production vol 47 pp 345ndash354 2013

[33] G Tuzkaya A Ozgen D Ozgen and U R Tuzkaya ldquoEnvi-ronmental performance evaluation of suppliers a hybrid fuzzymulti-criteria decision approachrdquo International Journal of Envi-ronmental ScienceampTechnology vol 6 no 3 pp 477ndash490 2009

[34] Q Zhu J Sarkis and K-H Lai ldquoInitiatives and outcomes ofgreen supply chain management implementation by Chinesemanufacturersrdquo Journal of Environmental Management vol 85no 1 pp 179ndash189 2007

[35] W-C Yeh and M-C Chuang ldquoUsing multi-objective geneticalgorithm for partner selection in green supply chain problemsrdquoExpert Systems with Applications vol 38 no 4 pp 4244ndash42532011

[36] A Awasthi S S Chauhan and S K Goyal ldquoA fuzzy multi-criteria approach for evaluating environmental performance ofsuppliersrdquo International Journal of Production Economics vol126 no 2 pp 370ndash378 2010

[37] J Sarkis ldquoManufacturingrsquos role in corporate environmentalsustainability-Concerns for the new millenniumrdquo InternationalJournal of Operations amp Production Management vol 21 no 5-6 pp 666ndash686 2001

[38] S MMirhedayatian M Azadi and R Farzipoor Saen ldquoA novelnetwork data envelopment analysis model for evaluating greensupply chain managementrdquo International Journal of ProductionEconomics vol 147 pp 544ndash554 2014

10 Mathematical Problems in Engineering

[39] C Wu and D Barnes ldquoAn integrated model for green partnerselection and supply chain constructionrdquo Journal of CleanerProduction vol 112 pp 2114ndash2132 2016

[40] G Bruno E Esposito A Genovese andR Passaro ldquoAHP-basedapproaches for supplier evaluation problems and perspectivesrdquoJournal of Purchasing and Supply Management vol 18 no 3 pp159ndash172 2012

[41] F R L Junior L Osiro and L C R Carpinetti ldquoA comparisonbetween Fuzzy AHP and Fuzzy TOPSIS methods to supplierselectionrdquo Applied Soft Computing vol 21 pp 194ndash209 2014

[42] A Kawa and W W Koczkodaj ldquoSupplier evaluation process bypairwise comparisonsrdquo Mathematical Problems in Engineeringvol 2015 Article ID 976742 9 pages 2015

[43] X Deng Y Hu Y Deng and S Mahadevan ldquoSupplier selectionusing AHP methodology extended by D numbersrdquo ExpertSystems with Applications vol 41 no 1 pp 156ndash167 2014

[44] N Xie and J Xin ldquoInterval grey numbers based multi-attributedecisionmakingmethod for supplier selectionrdquoKybernetes vol43 no 7 pp 1064ndash1078 2014

[45] J Lee H Cho and Y S Kim ldquoAssessing business impacts ofagility criterion and order allocation strategy in multi-criteriasupplier selectionrdquo Expert Systems with Applications vol 42 no3 pp 1136ndash1148 2015

[46] L Shen L Olfat K Govindan R Khodaverdi and A DiabatldquoA fuzzy multi criteria approach for evaluating green supplierrsquosperformance in green supply chain with linguistic preferencesrdquoResources Conservation and Recycling vol 74 pp 170ndash179 2012

[47] B Kanga Y Hu Y Deng and D Zhou ldquoA new methodologyof multicriteria decision-making in supplier selection based onZ-numbersrdquo Mathematical Problems in Engineering vol 2016Article ID 8475987 17 pages 2016

[48] N Asthana and M Gupta ldquoSupplier selection using artificialneural network and genetic algorithmrdquo International Journal ofIndian Culture and Business Management vol 11 no 4 pp 457ndash472 2015

[49] D Dubois and H Prade ldquoOperations on fuzzy numbersrdquo Inter-national Journal of Systems Science vol 9 no 6 pp 613ndash6261978

[50] A Kaufmann and M M Gupta Introduction to Fuzzy Arith-metic Theory and Applications The Arden Shakespeare 1991

[51] L A Zadeh ldquoThe concept of a linguistic variable and its appli-cation to approximate reasoningmdashIrdquo Information Sciences vol8 no 3 pp 199ndash249 1975

[52] L A Zadeh ldquoThe concept of a linguistic variable and its applica-tion to approximate reasoningmdashIIrdquo Information Sciences vol 8no 4 pp 301ndash357 1975

[53] D-Y Chang ldquoApplications of the extent analysis method onfuzzy AHPrdquo European Journal of Operational Research vol 95no 3 pp 649ndash655 1996

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical Problems in Engineering

Hindawi Publishing Corporationhttpwwwhindawicom

Differential EquationsInternational Journal of

Volume 2014

Applied MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical PhysicsAdvances in

Complex AnalysisJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

OptimizationJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Operations ResearchAdvances in

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Function Spaces

Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of Mathematics and Mathematical Sciences

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Algebra

Discrete Dynamics in Nature and Society

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Decision SciencesAdvances in

Discrete MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom

Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Stochastic AnalysisInternational Journal of

Mathematical Problems in Engineering 9

[4] R J Kuo Y C Wang and F C Tien ldquoIntegration of artificialneural network and MADA methods for green supplier selec-tionrdquo Journal of Cleaner Production vol 18 no 12 pp 1161ndash11702010

[5] A Gunasekaran and D Gallear ldquoSpecial Issue on Sustainabledevelopment of manufacturing and servicesrdquo InternationalJournal of Production Economics vol 140 no 1 pp 1ndash6 2012

[6] J Sarkis Q Zhu and K-H Lai ldquoAn organizational theoreticreview of green supply chain management literaturerdquo Interna-tional Journal of Production Economics vol 130 no 1 pp 1ndash152011

[7] A Appolloni H Sun F Jia and X Li ldquoGreen Procurement inthe private sector a state of the art review between 1996 and2013rdquo Journal of Cleaner Production vol 85 pp 122ndash133 2014

[8] H C Pimenta and P D Ball ldquoAnalysis of environmentalsustainability practices across upstream supply chain manage-mentrdquo Procedia CIRP vol 26 pp 677ndash682 2015

[9] C-L Hwang andK YoonMultiple Attribute DecisionMakingmdashMethods and Applications A State of the Art Survey SpringerNew York NY USA 1981

[10] H-S Shih H-J Shyur and E S Lee ldquoAn extension of TOPSISfor group decision makingrdquoMathematical and Computer Mod-elling vol 45 no 7-8 pp 801ndash813 2007

[11] T L SaatyTheAnalytical Hierarchy Process McGraw-Hill NewYork NY USA 1980

[12] G Buyukozkan and G Cifci ldquoEvaluation of the green supplychain management practices a fuzzy ANP approachrdquo Produc-tion Planning and Control vol 23 no 6 pp 405ndash418 2012

[13] C-C Sun ldquoA performance evaluation model by integratingfuzzy AHP and fuzzy TOPSIS methodsrdquo Expert Systems withApplications vol 37 no 12 pp 7745ndash7754 2010

[14] W Xia and Z Wu ldquoSupplier selection with multiple criteria involume discount environmentsrdquoOmega vol 35 no 5 pp 494ndash504 2007

[15] I Chamodrakas D Batis and D Martakos ldquoSupplier selectionin electronic marketplaces using satisficing and fuzzy AHPrdquoExpert Systems with Applications vol 37 no 1 pp 490ndash4982010

[16] K Shaw R Shankar S S Yadav and L S Thakur ldquoSupplierselection using fuzzy AHP and fuzzy multi-objective linearprogramming for developing low carbon supply chainrdquo ExpertSystems with Applications vol 39 no 9 pp 8182ndash8192 2012

[17] O Kilincci and S A Onal ldquoFuzzy AHP approach for supplierselection in a washing machine companyrdquo Expert Systems withApplications vol 38 no 8 pp 9656ndash9664 2011

[18] A H I Lee ldquoA fuzzy supplier selection model with the consid-eration of benefits opportunities costs and risksrdquo Expert Sys-tems with Applications vol 36 no 2 pp 2879ndash2893 2009

[19] C Bai and J Sarkis ldquoGreen supplier development analyticalevaluation using rough set theoryrdquo Journal of Cleaner Produc-tion vol 18 no 12 pp 1200ndash1210 2010

[20] M Abdollahi M Arvan and J Razmi ldquoAn integrated approachfor supplier portfolio selection lean or agilerdquo Expert Systemswith Applications vol 42 no 1 pp 679ndash690 2015

[21] M S Memon Y H Lee and S I Mari ldquoGroup multi-criteriasupplier selection using combined grey systems theory anduncertainty theoryrdquo Expert Systems with Applications vol 42no 21 pp 7951ndash7959 2015

[22] S H Hashemi A Karimi and M Tavana ldquoAn integratedgreen supplier selection approachwith analytic network processand improved Grey relational analysisrdquo International Journal ofProduction Economics vol 159 pp 178ndash191 2015

[23] M Punniyamoorthy P Mathiyalagan and P Parthiban ldquoAstrategic model using structural equation modeling and fuzzylogic in supplier selectionrdquo Expert Systems with Applicationsvol 38 no 1 pp 458ndash474 2011

[24] R M Grisi L Guerra and G Naviglio ldquoSupplier performanceevaluation for green supply chainmanagementrdquo inBusiness Per-formanceMeasurement andManagement pp 149ndash163 SpringerBerlin Germany 2010

[25] F Mafakheri M Breton and A Ghoniem ldquoSupplier selection-order allocation a two-stage multiple criteria dynamic pro-gramming approachrdquo International Journal of Production Eco-nomics vol 132 no 1 pp 52ndash57 2011

[26] Y-J Chen ldquoStructured methodology for supplier selection andevaluation in a supply chainrdquo Information Sciences vol 181 no9 pp 1651ndash1670 2011

[27] W-PWang ldquoA fuzzy linguistic computing approach to supplierevaluationrdquo Applied Mathematical Modelling vol 34 no 10 pp3130ndash3141 2010

[28] M-L Tseng and A S F Chiu ldquoEvaluating firmrsquos green supplychain management in linguistic preferencesrdquo Journal of CleanerProduction vol 40 pp 22ndash31 2013

[29] Q Zhu Y Dou and J Sarkis ldquoA portfolio-based analysisfor green supplier management using the analytical networkprocessrdquo Supply Chain Management vol 15 no 4 pp 306ndash3192010

[30] G A Keskin S Ilhan and C Ozkan ldquoThe Fuzzy ARTalgorithm a categorization method for supplier evaluation andselectionrdquo Expert Systems with Applications vol 37 no 2 pp1235ndash1240 2010

[31] C-Y Shen and K-T Yu ldquoEnhancing the efficacy of supplierselection decision-making on the initial stage of new productdevelopment a hybrid fuzzy approach considering the strategicand operational factors simultaneouslyrdquo Expert Systems withApplications vol 36 no 8 pp 11271ndash11281 2009

[32] K Govindan R Khodaverdi and A Jafarian ldquoA fuzzy multicriteria approach for measuring sustainability performance ofa supplier based on triple bottom line approachrdquo Journal ofCleaner Production vol 47 pp 345ndash354 2013

[33] G Tuzkaya A Ozgen D Ozgen and U R Tuzkaya ldquoEnvi-ronmental performance evaluation of suppliers a hybrid fuzzymulti-criteria decision approachrdquo International Journal of Envi-ronmental ScienceampTechnology vol 6 no 3 pp 477ndash490 2009

[34] Q Zhu J Sarkis and K-H Lai ldquoInitiatives and outcomes ofgreen supply chain management implementation by Chinesemanufacturersrdquo Journal of Environmental Management vol 85no 1 pp 179ndash189 2007

[35] W-C Yeh and M-C Chuang ldquoUsing multi-objective geneticalgorithm for partner selection in green supply chain problemsrdquoExpert Systems with Applications vol 38 no 4 pp 4244ndash42532011

[36] A Awasthi S S Chauhan and S K Goyal ldquoA fuzzy multi-criteria approach for evaluating environmental performance ofsuppliersrdquo International Journal of Production Economics vol126 no 2 pp 370ndash378 2010

[37] J Sarkis ldquoManufacturingrsquos role in corporate environmentalsustainability-Concerns for the new millenniumrdquo InternationalJournal of Operations amp Production Management vol 21 no 5-6 pp 666ndash686 2001

[38] S MMirhedayatian M Azadi and R Farzipoor Saen ldquoA novelnetwork data envelopment analysis model for evaluating greensupply chain managementrdquo International Journal of ProductionEconomics vol 147 pp 544ndash554 2014

10 Mathematical Problems in Engineering

[39] C Wu and D Barnes ldquoAn integrated model for green partnerselection and supply chain constructionrdquo Journal of CleanerProduction vol 112 pp 2114ndash2132 2016

[40] G Bruno E Esposito A Genovese andR Passaro ldquoAHP-basedapproaches for supplier evaluation problems and perspectivesrdquoJournal of Purchasing and Supply Management vol 18 no 3 pp159ndash172 2012

[41] F R L Junior L Osiro and L C R Carpinetti ldquoA comparisonbetween Fuzzy AHP and Fuzzy TOPSIS methods to supplierselectionrdquo Applied Soft Computing vol 21 pp 194ndash209 2014

[42] A Kawa and W W Koczkodaj ldquoSupplier evaluation process bypairwise comparisonsrdquo Mathematical Problems in Engineeringvol 2015 Article ID 976742 9 pages 2015

[43] X Deng Y Hu Y Deng and S Mahadevan ldquoSupplier selectionusing AHP methodology extended by D numbersrdquo ExpertSystems with Applications vol 41 no 1 pp 156ndash167 2014

[44] N Xie and J Xin ldquoInterval grey numbers based multi-attributedecisionmakingmethod for supplier selectionrdquoKybernetes vol43 no 7 pp 1064ndash1078 2014

[45] J Lee H Cho and Y S Kim ldquoAssessing business impacts ofagility criterion and order allocation strategy in multi-criteriasupplier selectionrdquo Expert Systems with Applications vol 42 no3 pp 1136ndash1148 2015

[46] L Shen L Olfat K Govindan R Khodaverdi and A DiabatldquoA fuzzy multi criteria approach for evaluating green supplierrsquosperformance in green supply chain with linguistic preferencesrdquoResources Conservation and Recycling vol 74 pp 170ndash179 2012

[47] B Kanga Y Hu Y Deng and D Zhou ldquoA new methodologyof multicriteria decision-making in supplier selection based onZ-numbersrdquo Mathematical Problems in Engineering vol 2016Article ID 8475987 17 pages 2016

[48] N Asthana and M Gupta ldquoSupplier selection using artificialneural network and genetic algorithmrdquo International Journal ofIndian Culture and Business Management vol 11 no 4 pp 457ndash472 2015

[49] D Dubois and H Prade ldquoOperations on fuzzy numbersrdquo Inter-national Journal of Systems Science vol 9 no 6 pp 613ndash6261978

[50] A Kaufmann and M M Gupta Introduction to Fuzzy Arith-metic Theory and Applications The Arden Shakespeare 1991

[51] L A Zadeh ldquoThe concept of a linguistic variable and its appli-cation to approximate reasoningmdashIrdquo Information Sciences vol8 no 3 pp 199ndash249 1975

[52] L A Zadeh ldquoThe concept of a linguistic variable and its applica-tion to approximate reasoningmdashIIrdquo Information Sciences vol 8no 4 pp 301ndash357 1975

[53] D-Y Chang ldquoApplications of the extent analysis method onfuzzy AHPrdquo European Journal of Operational Research vol 95no 3 pp 649ndash655 1996

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical Problems in Engineering

Hindawi Publishing Corporationhttpwwwhindawicom

Differential EquationsInternational Journal of

Volume 2014

Applied MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical PhysicsAdvances in

Complex AnalysisJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

OptimizationJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Operations ResearchAdvances in

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Function Spaces

Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of Mathematics and Mathematical Sciences

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Algebra

Discrete Dynamics in Nature and Society

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Decision SciencesAdvances in

Discrete MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom

Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Stochastic AnalysisInternational Journal of

10 Mathematical Problems in Engineering

[39] C Wu and D Barnes ldquoAn integrated model for green partnerselection and supply chain constructionrdquo Journal of CleanerProduction vol 112 pp 2114ndash2132 2016

[40] G Bruno E Esposito A Genovese andR Passaro ldquoAHP-basedapproaches for supplier evaluation problems and perspectivesrdquoJournal of Purchasing and Supply Management vol 18 no 3 pp159ndash172 2012

[41] F R L Junior L Osiro and L C R Carpinetti ldquoA comparisonbetween Fuzzy AHP and Fuzzy TOPSIS methods to supplierselectionrdquo Applied Soft Computing vol 21 pp 194ndash209 2014

[42] A Kawa and W W Koczkodaj ldquoSupplier evaluation process bypairwise comparisonsrdquo Mathematical Problems in Engineeringvol 2015 Article ID 976742 9 pages 2015

[43] X Deng Y Hu Y Deng and S Mahadevan ldquoSupplier selectionusing AHP methodology extended by D numbersrdquo ExpertSystems with Applications vol 41 no 1 pp 156ndash167 2014

[44] N Xie and J Xin ldquoInterval grey numbers based multi-attributedecisionmakingmethod for supplier selectionrdquoKybernetes vol43 no 7 pp 1064ndash1078 2014

[45] J Lee H Cho and Y S Kim ldquoAssessing business impacts ofagility criterion and order allocation strategy in multi-criteriasupplier selectionrdquo Expert Systems with Applications vol 42 no3 pp 1136ndash1148 2015

[46] L Shen L Olfat K Govindan R Khodaverdi and A DiabatldquoA fuzzy multi criteria approach for evaluating green supplierrsquosperformance in green supply chain with linguistic preferencesrdquoResources Conservation and Recycling vol 74 pp 170ndash179 2012

[47] B Kanga Y Hu Y Deng and D Zhou ldquoA new methodologyof multicriteria decision-making in supplier selection based onZ-numbersrdquo Mathematical Problems in Engineering vol 2016Article ID 8475987 17 pages 2016

[48] N Asthana and M Gupta ldquoSupplier selection using artificialneural network and genetic algorithmrdquo International Journal ofIndian Culture and Business Management vol 11 no 4 pp 457ndash472 2015

[49] D Dubois and H Prade ldquoOperations on fuzzy numbersrdquo Inter-national Journal of Systems Science vol 9 no 6 pp 613ndash6261978

[50] A Kaufmann and M M Gupta Introduction to Fuzzy Arith-metic Theory and Applications The Arden Shakespeare 1991

[51] L A Zadeh ldquoThe concept of a linguistic variable and its appli-cation to approximate reasoningmdashIrdquo Information Sciences vol8 no 3 pp 199ndash249 1975

[52] L A Zadeh ldquoThe concept of a linguistic variable and its applica-tion to approximate reasoningmdashIIrdquo Information Sciences vol 8no 4 pp 301ndash357 1975

[53] D-Y Chang ldquoApplications of the extent analysis method onfuzzy AHPrdquo European Journal of Operational Research vol 95no 3 pp 649ndash655 1996

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical Problems in Engineering

Hindawi Publishing Corporationhttpwwwhindawicom

Differential EquationsInternational Journal of

Volume 2014

Applied MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical PhysicsAdvances in

Complex AnalysisJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

OptimizationJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Operations ResearchAdvances in

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Function Spaces

Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of Mathematics and Mathematical Sciences

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Algebra

Discrete Dynamics in Nature and Society

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Decision SciencesAdvances in

Discrete MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom

Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Stochastic AnalysisInternational Journal of

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical Problems in Engineering

Hindawi Publishing Corporationhttpwwwhindawicom

Differential EquationsInternational Journal of

Volume 2014

Applied MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical PhysicsAdvances in

Complex AnalysisJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

OptimizationJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Operations ResearchAdvances in

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Function Spaces

Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of Mathematics and Mathematical Sciences

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Algebra

Discrete Dynamics in Nature and Society

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Decision SciencesAdvances in

Discrete MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom

Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Stochastic AnalysisInternational Journal of