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Research ArticleFuzzy Multicriteria ABC Supplier Classification inGlobal Supply Chain
Petar Kefer1 Dragan D Milanovic2 Mirjana Misita2 and Aleksandar Zunjic2
1Omni Surfaces 40 Kodiak Cres Toronto ON Canada M3J 3G52Faculty of Mechanical Engineering Kraljice Marije 16 11000 Belgrade Serbia
Correspondence should be addressed to Mirjana Misita mmisitamasbgacrs
Received 13 April 2016 Revised 5 July 2016 Accepted 19 July 2016
Academic Editor Monica A Lopez-Campos
Copyright copy 2016 Petar Kefer et al This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited
The determination of the optimal purchasing strategy in enterprise that is a part of global supply chain could be performed in twosteps In step one a classification of potential suppliers is performed in order to determine the optimal portfolio of suppliers Thisis delivered by using the fuzzy multicriteria proposed ABC classification method Uncertainties in relative importance of criteriaand their values are described by linguistic expressions Modelling of linguistic expressions is based on the fuzzy sets theory In thesecond step ranking of optimal portfolio of suppliers is performed by using the modified ELECTRE method The obtained resultsrepresent valuable input for determining the long time purchasing strategy and building partnership with the best suppliers Thedeveloped two-stepmodel is verified on real life dataThe obtained results indicate good compliance with the opinionsmanagementin this type of industry It is worth to mention that the proposed model can be easily extended and adopted to the analysis of otherissues of management which could be applicable in different research areas
1 Introduction
During the usual activities in enterprises many products andservices originated out of enterprise are used In that mannerthe organization should ensure that purchased and usedproducts and services conform to specified requirements [1]In compliance with that an organization shall establish andapply criteria for evaluation selection and monitoring ofperformance and reevaluate suppliers (external providers)On the other hand distribution and procurement in thesame time are usually based on complex procedures involv-ing many management and control functions at variouslevels Strategies for better supplymanagementmust promotean effective and appropriate products and services supplyproviding products and services in requested quantities justin time and yet the inventory costs have to be as lowas possible Development of supply policy and appropriatestrategy have to be defined on the enterprise level or on thelevel of the whole supply chain which is a complex problem
Recent work majorly focuses on analytical and decisionmodelling [2] for supplier selection as well as on supplierdevelopment [3] Development of sophisticated models for
optimal supplier selection strategy [4] for different kind ofproducts requires time effort and resources which lead toan increase in inventory control costs and to an increasein total costs too In order to decrease inventory controlcosts in practice the first important step is to perform theclassification of potential suppliers into classes in compliancewith their ability to provide processes or products andservices in accordance with specified requirements Basedon the suppliers classification results management definesappropriate ways to manage and control specific suppliersand rank them for cooperation and building partner con-nections Building partnership should be based on obtainingrespect and trust with mutual benefit [5]
In practice one of the widely used techniques for classifi-cation of different items into classes (applicable to the classi-fication of suppliers too) is the ABC method which is basedon Pareto analysis [6]This method is easy to understand anduse in practice since in the conventional ABC classificationmethod inventory items are divided into three classes AB and C The values of deterministic classification criteriaare classified into descending row As it is known 5ndash10
Hindawi Publishing CorporationMathematical Problems in EngineeringVolume 2016 Article ID 9139483 11 pageshttpdxdoiorg10115520169139483
2 Mathematical Problems in Engineering
of analysed inventory items ranked at first place belong togroup A next 15 correspond to group B and the rest ofinventory items correspond to group C Selection of theclassification criterion depends on the kind of problem beingconsidered The issue of selection of suppliers may be statedas a multicriteria optimization task In literature there isa lot of papers that employ different methods for rankingand assessment of suppliers The most used methods areAnalytical Hierarchy Process (AHP) [7] Technique forOrderof Preference by Similarity to Ideal Solution (TOPSIS) [8]ELimination Et Choix Traduisant la REalite (ELECTRE) [9]or combination of two or more methods [10] In compliancewith the rank of suppliers decision makers may choose themost suitable suppliers work building partnership relations
The conventional ABC methodology may sometimes notbe appropriate to provide a good classification of inventoryitems in practice [11] If there is a need to make the clas-sification more sophisticated more than one classificationcriterion and imprecise data about items have to be usedThe classification task becomes a multicriteria classificationproblem in the presence of uncertainty
In this paper the authors focus on the supplier classifica-tion in global supply chain where number of suppliers is largedue to demands of global market The number and types ofthe selection criteria are not clearly defined in the literatureand there are no specific guidelines that treat this issue Thespecificity of construction industry products their variabledemand over time and in particular high cost indicatethe importance of suppliersrsquo classification problem A newfuzzy multicriteria ABC model for classification of suppliersin construction industry is proposed Three eliminatorycriteria are selected to make a base of potential suppliers (1)customer care (2) quality (ratio between price and specificperformances of products) and (3) delivery method (ratiobetween costs and delivery rate)
The objective of paper is to define the appropriate pur-chasing strategy in the global supply chain through two steps(1) classification of a large number of potential suppliers byapplying proposed fuzzymulticriteriaABC (2) the ranking ofclassifiedA group of suppliers (optimal portfolio of suppliers)by using the proposed model consisted from fuzzy AHP andfuzzy ELECTREmethods For the classification problem theproposed fuzzy multicriteria ABC methodology is suitablesince it treats uncertain criteria in appropriate way andit is easy and suitable for usage leading to determinationof optimal portfolio of suppliers This optimal portfolio ofsuppliers consisted of those who are suitable for furtherselection of the group that will be used for building partner-shipThemethods of multicriteria decisionmakingmethodsfuzzy AHP and fuzzy ELECTRE are used for ranking ofselected suppliers In this manner resources such as time andcosts of defining appropriate supply strategy may be reducedsignificantly and in the same time effectiveness of supplyprocess is increased In the final consequence this should leadto increase effectiveness of all business processes in globalsupply chain
Each of three considered criteria is described by using lin-guistic expressions specified by enterprisemanagement teamThese linguistic expressions are modelled using triangular
fuzzy numbers by analogy to Aleksic et al [12] Uncertaintyin criteria values used in supplier classification are mod-elled by fuzzy sets [13ndash15] The motivation for using thismethodology came from its suitability for handling impreciseand ambiguous data and it supports usage of decisionmaking methods which operate with such data It may besaid that fuzzy sets theory resembles the human reasoningin its use of approximate information and uncertainty togenerate decisions [16] In thismanner fuzzy sets have severaladvantages over theories that treat similar problems (a) theyare based on a natural language (b) they are conceptually easyto understand (c) they could be combined with conventionalmethods and techniques for dealing and reasoning withuncertain data and (d) they can capture most nonlinearrelations in problems of arbitrary complexity [17]
The paper is organized in the followingwayThe literaturereview is given in Section 2 Section 3 presents evaluationframework and modelling of uncertainties In Section 4the proposed algorithm is presented Section 5 is used forthe verification of the model using an illustrative exampleConclusions are presented in Section 6
2 Literature Review
A number of papers presented in the literature were dealingwith the problem of items classification in uncertain envi-ronments for inventory control purposes and proposed fuzzymulticriteria ABC classification approaches after realizingthe importance of considering multiple criteria in the ABCanalysis [18] In addition to the overall cost some othercriteria such as lead time inventory holding cost limitationof the warehouse space and order cost were recognized asbeing important for items classification
In the literature as well as in the practice determinationof the optimal portfolio of suppliers is based onmathematicalmodels Possibly there may be a lot of potential suppliers soin the first step the eliminatory criteria should be appliedBuilding partnersrsquo relations with suppliers should be per-formed after the portfolio of suitable suppliers is generatedHowever there is no wide literature which considers supplierselection when there is large number of potential suppliers
Techniques of artificial intelligence such as backprop-agation networks support vector machines and 119896-nearestneighbors may be used for ABC inventory classificationtaking into account several criteria [19] Also ABC classifi-cation may be supported by using different methods such asAnalytic Hierarchy Process and Data Envelopment Analysis[20] In some cases existing models may be analysed andimproved such as extension of theNg-model formulticriteriainventory ABC classification [20] In this way classificationmay be performed by respect to multicriteria and theirweights simultaneouslyThe criteria weightsmay be obtainedby using DEA [20] If criteria are uncertain such as thefact that demand frequency and costs are in focus fuzzyABC model for classification of items according to theirvalue may be applied [21] As the values of classificationcriteria are uncertain they may be described by triangularfuzzy numbers [15] and may be aggregated into one bymultiplying two corresponding criteria values In this way
Mathematical Problems in Engineering 3
value of aggregated classification criteria is described by fuzzynumber which may be defuzzified and classification may beperformed by application of conventional ABC In a case ofexisting variables with either nominal or nonnominal valuesand incorporated management experience and judgmenta fuzzy rule based approach to ABC classification may beapplied [22]
The values of the treated classification items should beranked according to the value of classification criterion inmonotonically decreasing string Typically items of classA represent about 5ndash10 of the total number of itemsapproximately next 15 of items correspond to the groupB and the rest of the items belong to the group C Theitems of class A are the most significant in the treatedissue respecting the classification criteria In treated problemof suppliersrsquo selection ABC method may be deployed fordetermining optimal portfolio of suppliers (classifiedAgroupof suppliers) Optimal portfolio of suppliers should be rankedin order to propose optimal purchasing strategy throughbuilding potential partnership with the best ranked suppliersOptimal portfolio of suppliers may be ranked by applyingdifferent supplier selection models [23] Amongst manymethodologies ELECTRE may be seen as a proven asset formulticriteria decision analysis finding applications in widescientific fields [24] When the issue of supplier selection isin focus the determination of preference of alternatives maybe set as a group decision making problem [25] ELECTREmethod may be used for dealing with multicriteria decisionproblems such as determination of master contractor whenthere are several subcontractors [26] In this case index ofpreference is modified and it is calculated as a product offuzzy triangular numbers ELECTREmay bemodified in waythat the value of criteria for each supplier may be assessedby three decision makers whose assessments are modelledby fuzzy numbers [27] In this proposed fuzzy ELECTREHamming distance is used for comparing the suppliers on thetreated criteria
In compliance with the results of good practice it maybe noticed that the evaluation criteria used for the supplierselection often do not have the same relative importanceTherelative importance does not depend on supplier and it is notsubordinated to change over time Usually decision makersdeliver better opinions by using linguistic expressions thanprecise numbers Itmay be suggested that it is closer to humanthinking to compare relative importance of each pair ofcriteria than to perform direct assessment Respecting thesefacts many authors determine relative importance throughthe fuzzy AHP framework [28] Handling of uncertaintiesmay be performed by using extent analysis [29]
3 Evaluation Framework andModelling of Uncertainties
Step 1 Potential suppliers may be formally presented as a setof indices 120580 = 1 119894 119868 where 119868 is the total number ofsuppliers and 119894 is the index of the possible supplier In thiscase a set of suppliers is defined according to results of goodpractice
Step 2 Evaluation criteria are presented by set of indices 120581 =1 119896 119870 where 119870 is the total number of criteria and119896 is index of criterion The number and type of criteria aredefined by the management team based on the experiencethe results of benchmarking and current information aboutsuppliers which are presented in reports
Step 3 Management team of the enterprise is formallypresented by set of indices 120576 = 1 119890 119864 where 119864 isthe total number of the decision makers and 119890 is the index ofdecision maker In the considered problem the managementteam of treated enterprise which exists within the global sup-ply chain consisted of purchasing manager main managerplantmanager and financialmanager It may be assumed thatthe decision makers have different importance for evaluationand selection of suppliersrsquo problem The decision makerrsquosweight is denoted as 120596
119890 119890 = 1 119864 These weights are given
with respect to the results of good practice For consideredproblem the weights of decision makers are 03 03 02 and02 respectively
Step 4 The relative importance of each pair of criteria isassessed by each decision maker The decision maker usespredefined linguistic expressions which are modelled bytriangular fuzzy numbers (TFNs) The aggregated values ofthe fuzzy pairwisematrix of the relative importance of criteriaare calculated by using Fuzzy Averaging Ordered Method(FOWA) [30] The weights vector is given by extent analysesmethod [29] The criteria weights are described by precisevalues
Step 5 The possible suppliers should be evaluated accordingto the predefined period of time Usually it is a period ofone year In general the time period is divided into smalltime intervals In other words the assessment of suppliers isperformed in discreet time periods Time period is presentedby set of indices 120591 = 1 119905 119879 where 119879 is the totalnumber of discretized intervals and 119905 is the index of timeinterval
Step 6 The criterion value for supplier is assessed by eachdecision maker for each time period 119905 Decision makersuse predefined linguistic expressions which are modelled byTFNs The aggregated values of criteria values for suppliersover time period are given by using fuzzy averaging method
Step 7 The crisp values of decision matrix are given byapplying moment method [15]
Step 8 Classification of possible suppliers with respect to allcriteria and their weights is performed by the proposed ABCmodel
Step 9 Fuzzy decision matrix of suppliers which belong togroup A is stated The rank of these suppliers is determinedby fuzzy ELECTRE method
31 Modelling of Uncertainties Rating of the relative impor-tance of evaluation criteria and their values are based on
4 Mathematical Problems in Engineering
uncertain and imprecise knowledge of decision makersModelling of these uncertainties is based on fuzzy set theory[13 15] which is a suitable mathematical tool for presentinguncertain numbers in quantitativeway Fuzzy set is defined byits membership function which can be obtained in differentways [14] The uncertainties which exist in real problemsare often modelled by TFNs because they offer a goodcompromise between descriptive power and computationalsimplicityThe number of TFNs assigned to the uncertaintiesinto the relative importance of criteria and criteria valuesis defined by management team of global supply chain Thedomain of defined TFNs is defined on the real line whichbelong to different intervals In the literature there are norules or suggestions on how to determine the domain andgranularity of fuzzy numbers
311 Modelling of Criteria Relative Importance The relativeimportance of evaluation criteria is unchangeable during theconsidered period of time The assessment of relative impor-tance of each pair of identified criteria is performed by eachdecision maker They use predefined linguistic expressionswhich are modelled by TFNs 119890
The domains of these TFNs are defined real line into interval[1 5]The value 1 denotes that criterion 119896 over criterion 1198961015840 hasequal importance Value 5means that the relative importanceof criterion 119896 over criterion 1198961015840 has the most importance
If the strong relative importance of criterion 1198961015840 overcriterion 119896 holds then the pairwise comparison scale canbe represented by the fuzzy number 119890
1198961198961015840 = (
119890
1198961015840119896)minus1
=
(1119906119890
1198961015840119896 1119898119890
1198961015840119896 1119897119890
1198961015840119896)
32 Modelling of Criteria Values In the practice uncertaincriteria values are assessed bymanagement team at the globalsupply chain level for each time intervalTheir judgments arebased on evidence data results of good practice experienceand so forth It could be assumed that management teammakes decision by consensus In this paper fuzzy rating ofuncertain criteria values at the time interval level is describedby linguistic expressions which can be represented as TFNsV119905119894119896= (119910 119871
119905
119894119896119872119905
119894119896 119880119905
119894119896) Values in the domain of these TFNs
are defined on measurement scale which belong to areal setwithin the interval [0 1] Value 0 and 1 denote that criterion119896 for each supplier at the time interval level is at the lowestvalue and the highest value respectively
Specifically seven linguistic expressions which are mod-elled by TFNs are used
Very low (119910 0 0 025)Low (119910 01 02 03)Fairly medium moderate (119910 015 03 045)Moderate (119910 035 05 065)
Fairly high (119910 055 07 085)High (119910 07 08 09)Very high (119910 075 1 1)
4 The Proposed Algorithm
The algorithm of the proposed model is presented as follows
Step 1 Fuzzy assessment of the relative importance of eachcriteria pair is presented in matrix form
[119890
1198961198961015840]119870times119870
(1)
Step 2 The aggregated value of each pair of criteria iscalculated
1198961198961015840 =
119864
sum
119890=1
120596119890sdot 119890
1198961198961015840 (2)
The fuzzy pairwise comparison matrix of the relative impor-tance of criteria is constructed
[1198961198961015840]119870times119870
(3)
The weights vector is determined by using the concept ofextent analysis [29] which is presented in the followingmanner The value of fuzzy synthetic extent 119878
119896 with respect
to the 119896th criterion is defined as follows
119896= (
119870
sum
1198961015840=1
1198971198961198961015840
119870
sum
1198961015840=1
1198981198961198961015840
119870
sum
1198961015840=1
1198971198961198961015840)
sdot (
119870
sum
119896=1
119870
sum
1198961015840=1
1198971198961198961015840
119870
sum
119896=1
119870
sum
1198961015840=1
1198981198961198961015840
119870
sum
119896=1
119870
sum
1198961015840=1
1199061198961198961015840)
(4)
The weights vector is represented as follows
119882119901= ((Bel (
1)) (Bel (
119896)) (Bel (
119870))) (5)
The measure of belief according to which TFN 119896 is bigger
than all other TFNs 1198961015840 is denoted as Bel(
119896) This value
is obtained by applying the method for fuzzy numberscomparison [31 32] These values are crisp
The normalized weights vector is given by using linearnormalization procedure for benefit type criteria [33]
Step 3 The fuzzy rating of criterion 119896 for each supplier atthe time interval level 119905 is performed by each decisionmakerThese values are presented by TFNs V119905
119894119896
Step 4 Thevalue of criterion 119896 for each supplier for the wholetime period V
119894119896 is obtained by using the fuzzy averaging
method
V119894119896=1
119879sdot
119879
sum
119905=1
V119905119894119896 (6)
Mathematical Problems in Engineering 5
Step 5 The weighted fuzzy criterion value 119894119896 is calculated
as follows
119894119896= 119908119896sdot V119894119896 (7)
Step 6 The class A of items is determined as followsClass A contains suppliers that have high rated criteria
customer care quality and delivery method The highestvalues of identified criteria are represented by crisp values1199081 1199082 1199083 respectively According to fuzzy algebra rules
these crisp values should be represented by TFNs (1199081 1)
(1199082 1) and (119908
3 1) respectively In order to determine
whether a supplier belongs to class A the Euclidian distanceof supplier 119894 119894 = 1 119868 represented by (
1198941 1198942 1198943) from the
highest criteria values is calculated as follows
dist (119894 ref119860) = defuzz
radic
3
sum
119896=1
(119908119896minus 119894119896)2
(8)
As 119894119896are fuzzy numbers their distance to ref119860 is also a fuzzy
number The supports of fuzzy numbers dist(119894 ref119860) can bedescribed in discrete forms by discrete with membershipdegree min
119896=1119870(120583119894119896
(119910))Once the distances of all possible suppliers from ref119860 are
calculated they are ranked in the ascending orderThefirst 5ndash10 of the corresponding ranked suppliers are classified intoclass A
Step 7 The class C of items is determined as followsSuppliers that have low criteria values belong to class C
The reference point ref119862 is defined as the arranged tripletcrisp values (0 0 0) for care about clients quality anddelivery method
The weighted ref119862 is also represented as arranged triplet(0 0 0) Similarly as in the previous step a fuzzy distancebetween supplier 119894 119894 = 1 119868 and weighted ref119862 iscalculated as follows
dist (119894 ref119862) = defuzz
radic
3
sum
119896=1
(0 minus 119894119896)2
(9)
The distances have to be ranked in the ascending order Thefirst 80 distances correspond to suppliers which belong toclass C
Step 8 Suppliers that are not classified either into class A orinto class C form class B
Step 9 Theweighted decision matrix for suppliers from classof A is constructed
Step 10 The sets of concordance 1198781198941198941015840 and the sets of discor-
dance 1198731198781198941198941015840 are determined in the following way If
1198941015840119896ge
119894119896 (119894 1198941015840
= 1 1198681) then criteria 119896 belongs to the set of
concordance The total number of suppliers of class A isdenoted as 119868
(iii) 1198981198941198941015840 = 1 for those pair of alternatives (119894 1198941015840) where 119888
1198941198941015840 ge
119888119904119903and 1198991198941198941015840 le 119899119904119903
Step 13 Rank of suppliers of group A with respect to allcriteria and their weights is determined according to theconcordance matrix The best supplier is one with greatestnumber in the concordance matrix
5 Illustrative Example
Illustrative example is presented as a verification for theproposed model The large group of potential suppliers isanalysed for the ABC classification since all of supplierscould deliver needed products and they are geographicallydistributed all over the world It is worth to mention thatanalysed enterprise is performing suppliersrsquo selection inbuilding and civil engineering industry
6 Mathematical Problems in Engineering
Fuzzy assessment according to the Step 1 should beperformed
[[[[[
[
1 1 1 11
1198721
1198671
1198721
119871
1
1198711
1198721
1198721
119867
1 1 1 1 1119872 1 119871
1 1 1 1
]]]]]
]
(14)
Aggregated values of judgements of decision makers areobtained by FOWA This procedure is presented on criteria2 and 3 (Step 2)
The values of discordance matrix are calculated in same wayThe matrix of discordance is as follows
119873 =
[[[[[
[
mdash 1 1 1
0583 mdash 0759 1
0340 0433 mdash 1
0623 0579 0790 mdash
]]]]]
]
(21)
The mean value of concordance coefficient 119888119904119903and coefficient
of disconcordance 119899119904119903are calculated in the following way (see
(13))
119888119904119903=
1
4 sdot (4 minus 1)
4
sum
119894=1
4
sum
119894=1
1198881198941198941015840 =
1
12sdot 6 = 05
119899119904119903=
1
4 sdot (4 minus 1)
119868
sum
119894=1
119868
sum
119894=1
1198991198941198941015840 =
1
12sdot 9107 = 0759
(22)
Thematrix of consistent domination is obtained according toStep 12 of the proposed algorithm such as
119872 =
[[[[[
[
mdash 0 0 0
0 mdash 1 0
1 1 mdash 0
1 1 0 mdash
]]]]]
]
(23)
The rank of suppliers of group A is given by using procedure(Step 13 of the proposed algorithm) The obtained rank ispresented in Table 5
51 Discussion There are no specific guidelines for determin-ing the classification criteria in suppliersrsquo selection problemso these criteria vary in different economy branches In thispaper three eliminatory criteria are chosen based on theresults of good practice in order to make a base of potentialsuppliers The analysed criteria are (1) customer care (2)quality (ratio between price and specific performances ofproducts) and (3) delivery method (ratio between costs anddelivery rate) In global supply chains there is large number
of potential suppliers so determining the optimal portfolioof suppliers is very important task since it may save timedecrease costs and provide input for defining optimal supplystrategy Comparing this model to application of developedABC models [19 21] it may be stated that main implicationof this model is using the new approach in classification todetermine A and C class The proposed model takes intoaccount the type of criteria for suppliers selection so it maybe assumed that it represents its main advantage
Based on the obtained ranking results by applying themodified ELECTRE method (see Table 5) it may be con-cluded that suppliers (119894 = 41) and (119894 = 36) have the sameimportance for the treated enterprise as a part of global supplychain With respect to the obtained result the managementteam may define different supply strategy for short-timeperiod (one year) such as exclusive purchasing form one ofthe selected suppliers The selection of adequate purchasingstrategy has a crucial influence on profit of enterprise withinglobal supply chain as well as on its market position
In the same time the obtained results present inputdata for development of the methodology for selectingsuppliers in different environment supply conditions andexternal circumstances This methodology should includevarious aspects of technical economic social organizationalmarket-oriented and environmental character By using thementioned methodology management team can choose thebest supplier that is suitable for building long-term and stablecooperationThis cooperation can potentially include provid-ing capabilities for innovation and development reliability inother partnerships preparedness to share risk and profit withthe company
The proposed model is focused on the real-world sit-uation in domain determining short-time and long-timepurchasing strategy With regard to paper which treats theproblemof supplier assessment andwhich can be found in theliterature this paper pioneers the application of classificationfor building optimal portfolio of suppliers and their rankingand selection within the supply chain management
Research implications of this paper may be presented asa comparison with similar papers that have used ELECTREmethod for solving similar problems as well as with papersthat have used ABC classification The weight of criteriaand preference rating can be stated as fuzzy group decisionmaking problems
Aggregation of relative weights of criteria importance isperformed by using FOWA operator comparing it to pro-cedure proposed by Marbini and Tavana [27] or procedureproposed by Alencar et al [25] In practice it is reasonableto expect that decision makers have different weights soFOWA operator seems to be more suitable The time interval
10 Mathematical Problems in Engineering
for assessment of preference rating is divided in sub-timeintervals compared to other models where an assessment isperformedduring thewhole time interval [25 27] It is knownthat it is more precise to make assessment in shorter timeinterval
6 Conclusion
Quick and continuous changes occurring in the businessenvironment lead to opening issues in the organization andadaptation in different type of industries One of the mostimportant management tasks is determining of purchasingstrategy for the short-time and long-time period respec-tively This is because purchasing strategy has significantinfluence on successful establishment of global supply chainAs it is known in the global supply chain there are numerouspotential suppliers so that the considered problem is verycomplex
The theoretical contributions of this paper are presentedas follows In the first place conventional assessment ofsuppliers is performed with respect to quality and priceSometimes the other influencing criteria are disregardedThe evaluation criteria are selected according to the literaturereview which is conducted
Secondly it is appropriate to use linguistic terms insteadof numerical values for describing uncertainties into (1) therelative importance of each pair of criteria and (2) criteriavalues which exist in the considered problem Modelling oflinguistic variables is based on the fuzzy set theory Weightsvector of criteria is obtained by applying extent analysisapproach The fuzzy AHP may be considered as suitable forcapturing the vagueness of human thinking style and in thesame time it may be effectively employed for solving theissue of determining criteria weights in the supplier selectionproblem
The large number of potential suppliers in global supplychain enhances the complexity of the process of supplierselection In that manner it is necessary before delivery ofthe process of selection to deliver the process of suppliersrsquoclassification This may be denoted as the third contributionof the paper since a new fuzzymulticriteriaABC classificationof suppliers is proposed The effectiveness of the proposedalgorithm is tested using real-world data of 42 suppliers thatoperate in different geographical locations all over the worldThe classification obtained using the algorithm is in goodagreement with the judgment of the management team of theconsidered global supply chain
The fourth contribution makes the ranking of the suppli-ers denoted as group A The ranking is conducted by usingthe fuzzy ELECTRE proposed in this paper Modification ofELECTRE may be presented as (1) determination of sets onconcordance and sets of discordance [31] and (2) calculationof coefficient of discordance
Beside abovementioned various advantages the proposedmodel has some constraints It may be seen that there is thelack of research foundation in the literature which relatesto selection of criteria that are used for suppliersrsquo selectionin building and civil engineering industry Those criteriamay vary from constrains of supplierrsquos capacity aggregated
quality duty taxes and risk factors to political stability andso forth These extensions could undoubtedly increase thecomputational complexities The second constraint relates toABC method since it may be deployed only if 119896 is less orequal to 3 ELECTRE should be expanded with more criteriain order to determine purchasing strategy for long time andin the same time to establish partnership with supplier
This paper focuses on the complex circumstances alarge number of suppliers from different countries multipledecision makers involved in decision process and multipleuncertainties The established mathematical model can helpboth practitioners and researchers to further utilize anddeploy the purchasing strategy in global supply chain
Competing Interests
The authors declare that they have no competing interests
References
[1] ISO 90012015 Quality management systemsmdashRequirements[2] G Bruno E Esposito A Genovese andM Simpson ldquoApplying
supplier selection methodologies in a multi-stakeholder envi-ronment a case study and a critical assessmentrdquo Expert Systemswith Applications vol 43 pp 271ndash285 2016
[3] A C Trapp and J Sarkis ldquoIdentifying robust portfolios of sup-pliers a sustainability selection and development perspectiverdquoJournal of Cleaner Production vol 112 part 3 pp 2088ndash21002016
[4] P Amorim E Curcio B Almada-Lobo A P Barbosa-Povoaand I E Grossmann ldquoSupplier selection in the processed foodindustry under uncertaintyrdquo European Journal of OperationalResearch vol 252 no 3 pp 801ndash814 2016
[5] P H Andersen C Ellegaard andH Kragh ldquoIrsquom yourman howsuppliers gain strategic status in buying companiesrdquo Journal ofPurchasing and Supply Management vol 22 no 2 pp 72ndash812014
[6] B Du S Guo X Huang Y Li and J Guo ldquoA Pareto supplierselection algorithm for minimum the life cycle cost of complexproduct systemrdquo Expert Systems with Applications vol 42 no9 pp 4253ndash4264 2015
[7] T L Saaty ldquoHow to make a decision the analytic hierarchyprocessrdquo European Journal Operation-al Research vol 48 no1 pp 9ndash26 1990
[8] C-L Hwang and K Yoon Multiple Attribute Decision MakingMethods and Applications vol 186 of Lecture Notes in Economicsand Mathematical Systems Springer Heidelberg Germany1981
[9] B Roy ldquoClassement et choix en presence de points de vue mul-tiples (Lamethode ELECTRE)rdquoRevue Francaise drsquoInformatiqueet de Recherche Operationnelle vol 2 no 8 pp 57ndash75 1968
[10] D Tadic D D Milanovic M Misita and B Tadic ldquoNewintegrated approach to the problem of ranking and supplierselection under uncertaintiesrdquo Proceedings of the Institution ofMechanical Engineers Part B Journal of Engineering Manufac-ture vol 225 no 9 pp 1713ndash1724 2011
[11] HAGuvenir andE Erel ldquoMulticriteria inventory classificationusing a genetic algorithmrdquo European Journal of OperationalResearch vol 105 no 1 pp 29ndash37 1998
Mathematical Problems in Engineering 11
[12] A Aleksic M Stefanovic D Tadic and S Arsovski ldquoA fuzzymodel for assessment of organization vulnerabilityrdquo Measure-ment vol 51 no 1 pp 214ndash223 2014
[13] G J Klir and T A Folger Fuzzy Sets Uncertainty and Informa-tion Prentice Hall Upper Saddle River NJ USA 1988
[14] W Pedrycz and F Gomide An Introduction to Fuzzy SetsAnalysis and Design MIT Press Cambridge Mass USA 1997
[15] H-J Zimmermann Fuzzy Set Theorymdashand Its ApplicationsKluwer Academic Boston Mass USA 4th edition 2001
[16] P Kaur and S Chakrabortyb ldquoA new approach to vendorselection problem with impact factor as an indirect measure ofqualityrdquo Journal ofModernMathematics and Statistics vol 1 no1 pp 8ndash14 2007
[17] H M Fazel Zarandi B I Turksen and S Saghiri ldquoSupplychain crisp and fuzzy aspectsrdquo International Journal of AppliedMathematics and Computer Science vol 12 no 3 pp 423ndash4352002
[18] B E Flores andDCWhybark ldquoImplementingmultiple criteriaABC analysisrdquo Journal of OperationsManagement vol 7 no 1-2pp 79ndash85 1987
[19] M-C Yu ldquoMulti-criteria ABC analysis using artificial-intelligence-based classification techniquesrdquo Expert Systemswith Applications vol 38 no 4 pp 3416ndash3421 2011
[20] A Hadi-Vencheh and A Mohamadghasemi ldquoA fuzzy AHP-DEA approach for multiple criteria ABC inventory classifica-tionrdquo Expert Systems with Applications vol 38 no 4 pp 3346ndash3352 2011
[21] J Puente D de la Fuente P Priore and R Pino ldquoAbc classi-fication with uncertain data A fuzzy model vs a probabilisticmodelrdquoApplied Artificial Intelligence vol 16 no 6 pp 443ndash4562002
[22] C-W Chu G-S Liang and C-T Liao ldquoControlling inventoryby combiningABC analysis and fuzzy classificationrdquoComputersamp Industrial Engineering vol 55 no 4 pp 841ndash851 2008
[23] W Ho X Xu and P K Dey ldquoMulti-criteria decision makingapproaches for supplier evaluation and selection a literaturereviewrdquo European Journal of Operational Research vol 202 no1 pp 16ndash24 2010
[24] K Govindan and M B Jepsen ldquoELECTRE a comprehensiveliterature review onmethodologies and applicationsrdquo EuropeanJournal of Operational Research vol 250 no 1 pp 1ndash29 2016
[25] L H Alencar A T de Almeida and D C Morais ldquoAmulticriteria group decision model aggregating the preferencesof decision-makers based on electre methodsrdquo Pesquisa Opera-cional vol 30 no 3 pp 687ndash702 2010
[26] G AMontazer H Q Saremi andM Ramezani ldquoDesign a newmixed expert decision aiding system using fuzzy ELECTRE IIImethod for vendor selectionrdquo Expert Systems with Applicationsvol 36 no 8 pp 10837ndash10847 2009
[27] A H Marbini and M Tavana ldquoAn extension of the ElectreI method for group decision-making under a fuzzy environ-mentrdquo Omega vol 39 no 4 pp 373ndash386 2011
[28] D Tadic A T Gumus S Arsovski A Aleksic and MStefanovic ldquoAn evaluation of quality goals by using fuzzy AHPand fuzzy TOPSIS methodologyrdquo Journal of Intelligent amp FuzzySystems vol 25 no 3 pp 547ndash556 2013
[29] D-Y Chang ldquoApplications of the extent analysis method onfuzzy AHPrdquo European Journal of Operational Research vol 95no 3 pp 649ndash655 1996
[30] J MMerigo andM Casanovas ldquoUsing fuzzy numbers in heavyaggregation operatorsrdquo International Journal of InformationTechnology vol 4 no 4 pp 267ndash272 2008
[31] SM Baas andHKwakernaak ldquoRating and ranking ofmultiple-aspect alternatives using fuzzy setsrdquo Automatica vol 13 no 1pp 47ndash58 1977
[32] D Dubois and H Prade ldquoDecision-making under fuzzinessrdquoin Advances in Fuzzy Set Theory and Applications pp 279ndash302North-Holland Amsterdam Netherlands 1979
[33] J C Pomerol and S Barba-RomeoMulticriteria Decision Man-agement Principles and Practice Kluwer Nijhoff PublishingBoston Mass USA 2000
[34] C-T Chen ldquoExtensions of the TOPSIS for group decision-making under fuzzy environmentrdquo Fuzzy Sets and Systems vol114 no 1 pp 1ndash9 2000
of analysed inventory items ranked at first place belong togroup A next 15 correspond to group B and the rest ofinventory items correspond to group C Selection of theclassification criterion depends on the kind of problem beingconsidered The issue of selection of suppliers may be statedas a multicriteria optimization task In literature there isa lot of papers that employ different methods for rankingand assessment of suppliers The most used methods areAnalytical Hierarchy Process (AHP) [7] Technique forOrderof Preference by Similarity to Ideal Solution (TOPSIS) [8]ELimination Et Choix Traduisant la REalite (ELECTRE) [9]or combination of two or more methods [10] In compliancewith the rank of suppliers decision makers may choose themost suitable suppliers work building partnership relations
The conventional ABC methodology may sometimes notbe appropriate to provide a good classification of inventoryitems in practice [11] If there is a need to make the clas-sification more sophisticated more than one classificationcriterion and imprecise data about items have to be usedThe classification task becomes a multicriteria classificationproblem in the presence of uncertainty
In this paper the authors focus on the supplier classifica-tion in global supply chain where number of suppliers is largedue to demands of global market The number and types ofthe selection criteria are not clearly defined in the literatureand there are no specific guidelines that treat this issue Thespecificity of construction industry products their variabledemand over time and in particular high cost indicatethe importance of suppliersrsquo classification problem A newfuzzy multicriteria ABC model for classification of suppliersin construction industry is proposed Three eliminatorycriteria are selected to make a base of potential suppliers (1)customer care (2) quality (ratio between price and specificperformances of products) and (3) delivery method (ratiobetween costs and delivery rate)
The objective of paper is to define the appropriate pur-chasing strategy in the global supply chain through two steps(1) classification of a large number of potential suppliers byapplying proposed fuzzymulticriteriaABC (2) the ranking ofclassifiedA group of suppliers (optimal portfolio of suppliers)by using the proposed model consisted from fuzzy AHP andfuzzy ELECTREmethods For the classification problem theproposed fuzzy multicriteria ABC methodology is suitablesince it treats uncertain criteria in appropriate way andit is easy and suitable for usage leading to determinationof optimal portfolio of suppliers This optimal portfolio ofsuppliers consisted of those who are suitable for furtherselection of the group that will be used for building partner-shipThemethods of multicriteria decisionmakingmethodsfuzzy AHP and fuzzy ELECTRE are used for ranking ofselected suppliers In this manner resources such as time andcosts of defining appropriate supply strategy may be reducedsignificantly and in the same time effectiveness of supplyprocess is increased In the final consequence this should leadto increase effectiveness of all business processes in globalsupply chain
Each of three considered criteria is described by using lin-guistic expressions specified by enterprisemanagement teamThese linguistic expressions are modelled using triangular
fuzzy numbers by analogy to Aleksic et al [12] Uncertaintyin criteria values used in supplier classification are mod-elled by fuzzy sets [13ndash15] The motivation for using thismethodology came from its suitability for handling impreciseand ambiguous data and it supports usage of decisionmaking methods which operate with such data It may besaid that fuzzy sets theory resembles the human reasoningin its use of approximate information and uncertainty togenerate decisions [16] In thismanner fuzzy sets have severaladvantages over theories that treat similar problems (a) theyare based on a natural language (b) they are conceptually easyto understand (c) they could be combined with conventionalmethods and techniques for dealing and reasoning withuncertain data and (d) they can capture most nonlinearrelations in problems of arbitrary complexity [17]
The paper is organized in the followingwayThe literaturereview is given in Section 2 Section 3 presents evaluationframework and modelling of uncertainties In Section 4the proposed algorithm is presented Section 5 is used forthe verification of the model using an illustrative exampleConclusions are presented in Section 6
2 Literature Review
A number of papers presented in the literature were dealingwith the problem of items classification in uncertain envi-ronments for inventory control purposes and proposed fuzzymulticriteria ABC classification approaches after realizingthe importance of considering multiple criteria in the ABCanalysis [18] In addition to the overall cost some othercriteria such as lead time inventory holding cost limitationof the warehouse space and order cost were recognized asbeing important for items classification
In the literature as well as in the practice determinationof the optimal portfolio of suppliers is based onmathematicalmodels Possibly there may be a lot of potential suppliers soin the first step the eliminatory criteria should be appliedBuilding partnersrsquo relations with suppliers should be per-formed after the portfolio of suitable suppliers is generatedHowever there is no wide literature which considers supplierselection when there is large number of potential suppliers
Techniques of artificial intelligence such as backprop-agation networks support vector machines and 119896-nearestneighbors may be used for ABC inventory classificationtaking into account several criteria [19] Also ABC classifi-cation may be supported by using different methods such asAnalytic Hierarchy Process and Data Envelopment Analysis[20] In some cases existing models may be analysed andimproved such as extension of theNg-model formulticriteriainventory ABC classification [20] In this way classificationmay be performed by respect to multicriteria and theirweights simultaneouslyThe criteria weightsmay be obtainedby using DEA [20] If criteria are uncertain such as thefact that demand frequency and costs are in focus fuzzyABC model for classification of items according to theirvalue may be applied [21] As the values of classificationcriteria are uncertain they may be described by triangularfuzzy numbers [15] and may be aggregated into one bymultiplying two corresponding criteria values In this way
Mathematical Problems in Engineering 3
value of aggregated classification criteria is described by fuzzynumber which may be defuzzified and classification may beperformed by application of conventional ABC In a case ofexisting variables with either nominal or nonnominal valuesand incorporated management experience and judgmenta fuzzy rule based approach to ABC classification may beapplied [22]
The values of the treated classification items should beranked according to the value of classification criterion inmonotonically decreasing string Typically items of classA represent about 5ndash10 of the total number of itemsapproximately next 15 of items correspond to the groupB and the rest of the items belong to the group C Theitems of class A are the most significant in the treatedissue respecting the classification criteria In treated problemof suppliersrsquo selection ABC method may be deployed fordetermining optimal portfolio of suppliers (classifiedAgroupof suppliers) Optimal portfolio of suppliers should be rankedin order to propose optimal purchasing strategy throughbuilding potential partnership with the best ranked suppliersOptimal portfolio of suppliers may be ranked by applyingdifferent supplier selection models [23] Amongst manymethodologies ELECTRE may be seen as a proven asset formulticriteria decision analysis finding applications in widescientific fields [24] When the issue of supplier selection isin focus the determination of preference of alternatives maybe set as a group decision making problem [25] ELECTREmethod may be used for dealing with multicriteria decisionproblems such as determination of master contractor whenthere are several subcontractors [26] In this case index ofpreference is modified and it is calculated as a product offuzzy triangular numbers ELECTREmay bemodified in waythat the value of criteria for each supplier may be assessedby three decision makers whose assessments are modelledby fuzzy numbers [27] In this proposed fuzzy ELECTREHamming distance is used for comparing the suppliers on thetreated criteria
In compliance with the results of good practice it maybe noticed that the evaluation criteria used for the supplierselection often do not have the same relative importanceTherelative importance does not depend on supplier and it is notsubordinated to change over time Usually decision makersdeliver better opinions by using linguistic expressions thanprecise numbers Itmay be suggested that it is closer to humanthinking to compare relative importance of each pair ofcriteria than to perform direct assessment Respecting thesefacts many authors determine relative importance throughthe fuzzy AHP framework [28] Handling of uncertaintiesmay be performed by using extent analysis [29]
3 Evaluation Framework andModelling of Uncertainties
Step 1 Potential suppliers may be formally presented as a setof indices 120580 = 1 119894 119868 where 119868 is the total number ofsuppliers and 119894 is the index of the possible supplier In thiscase a set of suppliers is defined according to results of goodpractice
Step 2 Evaluation criteria are presented by set of indices 120581 =1 119896 119870 where 119870 is the total number of criteria and119896 is index of criterion The number and type of criteria aredefined by the management team based on the experiencethe results of benchmarking and current information aboutsuppliers which are presented in reports
Step 3 Management team of the enterprise is formallypresented by set of indices 120576 = 1 119890 119864 where 119864 isthe total number of the decision makers and 119890 is the index ofdecision maker In the considered problem the managementteam of treated enterprise which exists within the global sup-ply chain consisted of purchasing manager main managerplantmanager and financialmanager It may be assumed thatthe decision makers have different importance for evaluationand selection of suppliersrsquo problem The decision makerrsquosweight is denoted as 120596
119890 119890 = 1 119864 These weights are given
with respect to the results of good practice For consideredproblem the weights of decision makers are 03 03 02 and02 respectively
Step 4 The relative importance of each pair of criteria isassessed by each decision maker The decision maker usespredefined linguistic expressions which are modelled bytriangular fuzzy numbers (TFNs) The aggregated values ofthe fuzzy pairwisematrix of the relative importance of criteriaare calculated by using Fuzzy Averaging Ordered Method(FOWA) [30] The weights vector is given by extent analysesmethod [29] The criteria weights are described by precisevalues
Step 5 The possible suppliers should be evaluated accordingto the predefined period of time Usually it is a period ofone year In general the time period is divided into smalltime intervals In other words the assessment of suppliers isperformed in discreet time periods Time period is presentedby set of indices 120591 = 1 119905 119879 where 119879 is the totalnumber of discretized intervals and 119905 is the index of timeinterval
Step 6 The criterion value for supplier is assessed by eachdecision maker for each time period 119905 Decision makersuse predefined linguistic expressions which are modelled byTFNs The aggregated values of criteria values for suppliersover time period are given by using fuzzy averaging method
Step 7 The crisp values of decision matrix are given byapplying moment method [15]
Step 8 Classification of possible suppliers with respect to allcriteria and their weights is performed by the proposed ABCmodel
Step 9 Fuzzy decision matrix of suppliers which belong togroup A is stated The rank of these suppliers is determinedby fuzzy ELECTRE method
31 Modelling of Uncertainties Rating of the relative impor-tance of evaluation criteria and their values are based on
4 Mathematical Problems in Engineering
uncertain and imprecise knowledge of decision makersModelling of these uncertainties is based on fuzzy set theory[13 15] which is a suitable mathematical tool for presentinguncertain numbers in quantitativeway Fuzzy set is defined byits membership function which can be obtained in differentways [14] The uncertainties which exist in real problemsare often modelled by TFNs because they offer a goodcompromise between descriptive power and computationalsimplicityThe number of TFNs assigned to the uncertaintiesinto the relative importance of criteria and criteria valuesis defined by management team of global supply chain Thedomain of defined TFNs is defined on the real line whichbelong to different intervals In the literature there are norules or suggestions on how to determine the domain andgranularity of fuzzy numbers
311 Modelling of Criteria Relative Importance The relativeimportance of evaluation criteria is unchangeable during theconsidered period of time The assessment of relative impor-tance of each pair of identified criteria is performed by eachdecision maker They use predefined linguistic expressionswhich are modelled by TFNs 119890
The domains of these TFNs are defined real line into interval[1 5]The value 1 denotes that criterion 119896 over criterion 1198961015840 hasequal importance Value 5means that the relative importanceof criterion 119896 over criterion 1198961015840 has the most importance
If the strong relative importance of criterion 1198961015840 overcriterion 119896 holds then the pairwise comparison scale canbe represented by the fuzzy number 119890
1198961198961015840 = (
119890
1198961015840119896)minus1
=
(1119906119890
1198961015840119896 1119898119890
1198961015840119896 1119897119890
1198961015840119896)
32 Modelling of Criteria Values In the practice uncertaincriteria values are assessed bymanagement team at the globalsupply chain level for each time intervalTheir judgments arebased on evidence data results of good practice experienceand so forth It could be assumed that management teammakes decision by consensus In this paper fuzzy rating ofuncertain criteria values at the time interval level is describedby linguistic expressions which can be represented as TFNsV119905119894119896= (119910 119871
119905
119894119896119872119905
119894119896 119880119905
119894119896) Values in the domain of these TFNs
are defined on measurement scale which belong to areal setwithin the interval [0 1] Value 0 and 1 denote that criterion119896 for each supplier at the time interval level is at the lowestvalue and the highest value respectively
Specifically seven linguistic expressions which are mod-elled by TFNs are used
Very low (119910 0 0 025)Low (119910 01 02 03)Fairly medium moderate (119910 015 03 045)Moderate (119910 035 05 065)
Fairly high (119910 055 07 085)High (119910 07 08 09)Very high (119910 075 1 1)
4 The Proposed Algorithm
The algorithm of the proposed model is presented as follows
Step 1 Fuzzy assessment of the relative importance of eachcriteria pair is presented in matrix form
[119890
1198961198961015840]119870times119870
(1)
Step 2 The aggregated value of each pair of criteria iscalculated
1198961198961015840 =
119864
sum
119890=1
120596119890sdot 119890
1198961198961015840 (2)
The fuzzy pairwise comparison matrix of the relative impor-tance of criteria is constructed
[1198961198961015840]119870times119870
(3)
The weights vector is determined by using the concept ofextent analysis [29] which is presented in the followingmanner The value of fuzzy synthetic extent 119878
119896 with respect
to the 119896th criterion is defined as follows
119896= (
119870
sum
1198961015840=1
1198971198961198961015840
119870
sum
1198961015840=1
1198981198961198961015840
119870
sum
1198961015840=1
1198971198961198961015840)
sdot (
119870
sum
119896=1
119870
sum
1198961015840=1
1198971198961198961015840
119870
sum
119896=1
119870
sum
1198961015840=1
1198981198961198961015840
119870
sum
119896=1
119870
sum
1198961015840=1
1199061198961198961015840)
(4)
The weights vector is represented as follows
119882119901= ((Bel (
1)) (Bel (
119896)) (Bel (
119870))) (5)
The measure of belief according to which TFN 119896 is bigger
than all other TFNs 1198961015840 is denoted as Bel(
119896) This value
is obtained by applying the method for fuzzy numberscomparison [31 32] These values are crisp
The normalized weights vector is given by using linearnormalization procedure for benefit type criteria [33]
Step 3 The fuzzy rating of criterion 119896 for each supplier atthe time interval level 119905 is performed by each decisionmakerThese values are presented by TFNs V119905
119894119896
Step 4 Thevalue of criterion 119896 for each supplier for the wholetime period V
119894119896 is obtained by using the fuzzy averaging
method
V119894119896=1
119879sdot
119879
sum
119905=1
V119905119894119896 (6)
Mathematical Problems in Engineering 5
Step 5 The weighted fuzzy criterion value 119894119896 is calculated
as follows
119894119896= 119908119896sdot V119894119896 (7)
Step 6 The class A of items is determined as followsClass A contains suppliers that have high rated criteria
customer care quality and delivery method The highestvalues of identified criteria are represented by crisp values1199081 1199082 1199083 respectively According to fuzzy algebra rules
these crisp values should be represented by TFNs (1199081 1)
(1199082 1) and (119908
3 1) respectively In order to determine
whether a supplier belongs to class A the Euclidian distanceof supplier 119894 119894 = 1 119868 represented by (
1198941 1198942 1198943) from the
highest criteria values is calculated as follows
dist (119894 ref119860) = defuzz
radic
3
sum
119896=1
(119908119896minus 119894119896)2
(8)
As 119894119896are fuzzy numbers their distance to ref119860 is also a fuzzy
number The supports of fuzzy numbers dist(119894 ref119860) can bedescribed in discrete forms by discrete with membershipdegree min
119896=1119870(120583119894119896
(119910))Once the distances of all possible suppliers from ref119860 are
calculated they are ranked in the ascending orderThefirst 5ndash10 of the corresponding ranked suppliers are classified intoclass A
Step 7 The class C of items is determined as followsSuppliers that have low criteria values belong to class C
The reference point ref119862 is defined as the arranged tripletcrisp values (0 0 0) for care about clients quality anddelivery method
The weighted ref119862 is also represented as arranged triplet(0 0 0) Similarly as in the previous step a fuzzy distancebetween supplier 119894 119894 = 1 119868 and weighted ref119862 iscalculated as follows
dist (119894 ref119862) = defuzz
radic
3
sum
119896=1
(0 minus 119894119896)2
(9)
The distances have to be ranked in the ascending order Thefirst 80 distances correspond to suppliers which belong toclass C
Step 8 Suppliers that are not classified either into class A orinto class C form class B
Step 9 Theweighted decision matrix for suppliers from classof A is constructed
Step 10 The sets of concordance 1198781198941198941015840 and the sets of discor-
dance 1198731198781198941198941015840 are determined in the following way If
1198941015840119896ge
119894119896 (119894 1198941015840
= 1 1198681) then criteria 119896 belongs to the set of
concordance The total number of suppliers of class A isdenoted as 119868
(iii) 1198981198941198941015840 = 1 for those pair of alternatives (119894 1198941015840) where 119888
1198941198941015840 ge
119888119904119903and 1198991198941198941015840 le 119899119904119903
Step 13 Rank of suppliers of group A with respect to allcriteria and their weights is determined according to theconcordance matrix The best supplier is one with greatestnumber in the concordance matrix
5 Illustrative Example
Illustrative example is presented as a verification for theproposed model The large group of potential suppliers isanalysed for the ABC classification since all of supplierscould deliver needed products and they are geographicallydistributed all over the world It is worth to mention thatanalysed enterprise is performing suppliersrsquo selection inbuilding and civil engineering industry
6 Mathematical Problems in Engineering
Fuzzy assessment according to the Step 1 should beperformed
[[[[[
[
1 1 1 11
1198721
1198671
1198721
119871
1
1198711
1198721
1198721
119867
1 1 1 1 1119872 1 119871
1 1 1 1
]]]]]
]
(14)
Aggregated values of judgements of decision makers areobtained by FOWA This procedure is presented on criteria2 and 3 (Step 2)
The values of discordance matrix are calculated in same wayThe matrix of discordance is as follows
119873 =
[[[[[
[
mdash 1 1 1
0583 mdash 0759 1
0340 0433 mdash 1
0623 0579 0790 mdash
]]]]]
]
(21)
The mean value of concordance coefficient 119888119904119903and coefficient
of disconcordance 119899119904119903are calculated in the following way (see
(13))
119888119904119903=
1
4 sdot (4 minus 1)
4
sum
119894=1
4
sum
119894=1
1198881198941198941015840 =
1
12sdot 6 = 05
119899119904119903=
1
4 sdot (4 minus 1)
119868
sum
119894=1
119868
sum
119894=1
1198991198941198941015840 =
1
12sdot 9107 = 0759
(22)
Thematrix of consistent domination is obtained according toStep 12 of the proposed algorithm such as
119872 =
[[[[[
[
mdash 0 0 0
0 mdash 1 0
1 1 mdash 0
1 1 0 mdash
]]]]]
]
(23)
The rank of suppliers of group A is given by using procedure(Step 13 of the proposed algorithm) The obtained rank ispresented in Table 5
51 Discussion There are no specific guidelines for determin-ing the classification criteria in suppliersrsquo selection problemso these criteria vary in different economy branches In thispaper three eliminatory criteria are chosen based on theresults of good practice in order to make a base of potentialsuppliers The analysed criteria are (1) customer care (2)quality (ratio between price and specific performances ofproducts) and (3) delivery method (ratio between costs anddelivery rate) In global supply chains there is large number
of potential suppliers so determining the optimal portfolioof suppliers is very important task since it may save timedecrease costs and provide input for defining optimal supplystrategy Comparing this model to application of developedABC models [19 21] it may be stated that main implicationof this model is using the new approach in classification todetermine A and C class The proposed model takes intoaccount the type of criteria for suppliers selection so it maybe assumed that it represents its main advantage
Based on the obtained ranking results by applying themodified ELECTRE method (see Table 5) it may be con-cluded that suppliers (119894 = 41) and (119894 = 36) have the sameimportance for the treated enterprise as a part of global supplychain With respect to the obtained result the managementteam may define different supply strategy for short-timeperiod (one year) such as exclusive purchasing form one ofthe selected suppliers The selection of adequate purchasingstrategy has a crucial influence on profit of enterprise withinglobal supply chain as well as on its market position
In the same time the obtained results present inputdata for development of the methodology for selectingsuppliers in different environment supply conditions andexternal circumstances This methodology should includevarious aspects of technical economic social organizationalmarket-oriented and environmental character By using thementioned methodology management team can choose thebest supplier that is suitable for building long-term and stablecooperationThis cooperation can potentially include provid-ing capabilities for innovation and development reliability inother partnerships preparedness to share risk and profit withthe company
The proposed model is focused on the real-world sit-uation in domain determining short-time and long-timepurchasing strategy With regard to paper which treats theproblemof supplier assessment andwhich can be found in theliterature this paper pioneers the application of classificationfor building optimal portfolio of suppliers and their rankingand selection within the supply chain management
Research implications of this paper may be presented asa comparison with similar papers that have used ELECTREmethod for solving similar problems as well as with papersthat have used ABC classification The weight of criteriaand preference rating can be stated as fuzzy group decisionmaking problems
Aggregation of relative weights of criteria importance isperformed by using FOWA operator comparing it to pro-cedure proposed by Marbini and Tavana [27] or procedureproposed by Alencar et al [25] In practice it is reasonableto expect that decision makers have different weights soFOWA operator seems to be more suitable The time interval
10 Mathematical Problems in Engineering
for assessment of preference rating is divided in sub-timeintervals compared to other models where an assessment isperformedduring thewhole time interval [25 27] It is knownthat it is more precise to make assessment in shorter timeinterval
6 Conclusion
Quick and continuous changes occurring in the businessenvironment lead to opening issues in the organization andadaptation in different type of industries One of the mostimportant management tasks is determining of purchasingstrategy for the short-time and long-time period respec-tively This is because purchasing strategy has significantinfluence on successful establishment of global supply chainAs it is known in the global supply chain there are numerouspotential suppliers so that the considered problem is verycomplex
The theoretical contributions of this paper are presentedas follows In the first place conventional assessment ofsuppliers is performed with respect to quality and priceSometimes the other influencing criteria are disregardedThe evaluation criteria are selected according to the literaturereview which is conducted
Secondly it is appropriate to use linguistic terms insteadof numerical values for describing uncertainties into (1) therelative importance of each pair of criteria and (2) criteriavalues which exist in the considered problem Modelling oflinguistic variables is based on the fuzzy set theory Weightsvector of criteria is obtained by applying extent analysisapproach The fuzzy AHP may be considered as suitable forcapturing the vagueness of human thinking style and in thesame time it may be effectively employed for solving theissue of determining criteria weights in the supplier selectionproblem
The large number of potential suppliers in global supplychain enhances the complexity of the process of supplierselection In that manner it is necessary before delivery ofthe process of selection to deliver the process of suppliersrsquoclassification This may be denoted as the third contributionof the paper since a new fuzzymulticriteriaABC classificationof suppliers is proposed The effectiveness of the proposedalgorithm is tested using real-world data of 42 suppliers thatoperate in different geographical locations all over the worldThe classification obtained using the algorithm is in goodagreement with the judgment of the management team of theconsidered global supply chain
The fourth contribution makes the ranking of the suppli-ers denoted as group A The ranking is conducted by usingthe fuzzy ELECTRE proposed in this paper Modification ofELECTRE may be presented as (1) determination of sets onconcordance and sets of discordance [31] and (2) calculationof coefficient of discordance
Beside abovementioned various advantages the proposedmodel has some constraints It may be seen that there is thelack of research foundation in the literature which relatesto selection of criteria that are used for suppliersrsquo selectionin building and civil engineering industry Those criteriamay vary from constrains of supplierrsquos capacity aggregated
quality duty taxes and risk factors to political stability andso forth These extensions could undoubtedly increase thecomputational complexities The second constraint relates toABC method since it may be deployed only if 119896 is less orequal to 3 ELECTRE should be expanded with more criteriain order to determine purchasing strategy for long time andin the same time to establish partnership with supplier
This paper focuses on the complex circumstances alarge number of suppliers from different countries multipledecision makers involved in decision process and multipleuncertainties The established mathematical model can helpboth practitioners and researchers to further utilize anddeploy the purchasing strategy in global supply chain
Competing Interests
The authors declare that they have no competing interests
References
[1] ISO 90012015 Quality management systemsmdashRequirements[2] G Bruno E Esposito A Genovese andM Simpson ldquoApplying
supplier selection methodologies in a multi-stakeholder envi-ronment a case study and a critical assessmentrdquo Expert Systemswith Applications vol 43 pp 271ndash285 2016
[3] A C Trapp and J Sarkis ldquoIdentifying robust portfolios of sup-pliers a sustainability selection and development perspectiverdquoJournal of Cleaner Production vol 112 part 3 pp 2088ndash21002016
[4] P Amorim E Curcio B Almada-Lobo A P Barbosa-Povoaand I E Grossmann ldquoSupplier selection in the processed foodindustry under uncertaintyrdquo European Journal of OperationalResearch vol 252 no 3 pp 801ndash814 2016
[5] P H Andersen C Ellegaard andH Kragh ldquoIrsquom yourman howsuppliers gain strategic status in buying companiesrdquo Journal ofPurchasing and Supply Management vol 22 no 2 pp 72ndash812014
[6] B Du S Guo X Huang Y Li and J Guo ldquoA Pareto supplierselection algorithm for minimum the life cycle cost of complexproduct systemrdquo Expert Systems with Applications vol 42 no9 pp 4253ndash4264 2015
[7] T L Saaty ldquoHow to make a decision the analytic hierarchyprocessrdquo European Journal Operation-al Research vol 48 no1 pp 9ndash26 1990
[8] C-L Hwang and K Yoon Multiple Attribute Decision MakingMethods and Applications vol 186 of Lecture Notes in Economicsand Mathematical Systems Springer Heidelberg Germany1981
[9] B Roy ldquoClassement et choix en presence de points de vue mul-tiples (Lamethode ELECTRE)rdquoRevue Francaise drsquoInformatiqueet de Recherche Operationnelle vol 2 no 8 pp 57ndash75 1968
[10] D Tadic D D Milanovic M Misita and B Tadic ldquoNewintegrated approach to the problem of ranking and supplierselection under uncertaintiesrdquo Proceedings of the Institution ofMechanical Engineers Part B Journal of Engineering Manufac-ture vol 225 no 9 pp 1713ndash1724 2011
[11] HAGuvenir andE Erel ldquoMulticriteria inventory classificationusing a genetic algorithmrdquo European Journal of OperationalResearch vol 105 no 1 pp 29ndash37 1998
Mathematical Problems in Engineering 11
[12] A Aleksic M Stefanovic D Tadic and S Arsovski ldquoA fuzzymodel for assessment of organization vulnerabilityrdquo Measure-ment vol 51 no 1 pp 214ndash223 2014
[13] G J Klir and T A Folger Fuzzy Sets Uncertainty and Informa-tion Prentice Hall Upper Saddle River NJ USA 1988
[14] W Pedrycz and F Gomide An Introduction to Fuzzy SetsAnalysis and Design MIT Press Cambridge Mass USA 1997
[15] H-J Zimmermann Fuzzy Set Theorymdashand Its ApplicationsKluwer Academic Boston Mass USA 4th edition 2001
[16] P Kaur and S Chakrabortyb ldquoA new approach to vendorselection problem with impact factor as an indirect measure ofqualityrdquo Journal ofModernMathematics and Statistics vol 1 no1 pp 8ndash14 2007
[17] H M Fazel Zarandi B I Turksen and S Saghiri ldquoSupplychain crisp and fuzzy aspectsrdquo International Journal of AppliedMathematics and Computer Science vol 12 no 3 pp 423ndash4352002
[18] B E Flores andDCWhybark ldquoImplementingmultiple criteriaABC analysisrdquo Journal of OperationsManagement vol 7 no 1-2pp 79ndash85 1987
[19] M-C Yu ldquoMulti-criteria ABC analysis using artificial-intelligence-based classification techniquesrdquo Expert Systemswith Applications vol 38 no 4 pp 3416ndash3421 2011
[20] A Hadi-Vencheh and A Mohamadghasemi ldquoA fuzzy AHP-DEA approach for multiple criteria ABC inventory classifica-tionrdquo Expert Systems with Applications vol 38 no 4 pp 3346ndash3352 2011
[21] J Puente D de la Fuente P Priore and R Pino ldquoAbc classi-fication with uncertain data A fuzzy model vs a probabilisticmodelrdquoApplied Artificial Intelligence vol 16 no 6 pp 443ndash4562002
[22] C-W Chu G-S Liang and C-T Liao ldquoControlling inventoryby combiningABC analysis and fuzzy classificationrdquoComputersamp Industrial Engineering vol 55 no 4 pp 841ndash851 2008
[23] W Ho X Xu and P K Dey ldquoMulti-criteria decision makingapproaches for supplier evaluation and selection a literaturereviewrdquo European Journal of Operational Research vol 202 no1 pp 16ndash24 2010
[24] K Govindan and M B Jepsen ldquoELECTRE a comprehensiveliterature review onmethodologies and applicationsrdquo EuropeanJournal of Operational Research vol 250 no 1 pp 1ndash29 2016
[25] L H Alencar A T de Almeida and D C Morais ldquoAmulticriteria group decision model aggregating the preferencesof decision-makers based on electre methodsrdquo Pesquisa Opera-cional vol 30 no 3 pp 687ndash702 2010
[26] G AMontazer H Q Saremi andM Ramezani ldquoDesign a newmixed expert decision aiding system using fuzzy ELECTRE IIImethod for vendor selectionrdquo Expert Systems with Applicationsvol 36 no 8 pp 10837ndash10847 2009
[27] A H Marbini and M Tavana ldquoAn extension of the ElectreI method for group decision-making under a fuzzy environ-mentrdquo Omega vol 39 no 4 pp 373ndash386 2011
[28] D Tadic A T Gumus S Arsovski A Aleksic and MStefanovic ldquoAn evaluation of quality goals by using fuzzy AHPand fuzzy TOPSIS methodologyrdquo Journal of Intelligent amp FuzzySystems vol 25 no 3 pp 547ndash556 2013
[29] D-Y Chang ldquoApplications of the extent analysis method onfuzzy AHPrdquo European Journal of Operational Research vol 95no 3 pp 649ndash655 1996
[30] J MMerigo andM Casanovas ldquoUsing fuzzy numbers in heavyaggregation operatorsrdquo International Journal of InformationTechnology vol 4 no 4 pp 267ndash272 2008
[31] SM Baas andHKwakernaak ldquoRating and ranking ofmultiple-aspect alternatives using fuzzy setsrdquo Automatica vol 13 no 1pp 47ndash58 1977
[32] D Dubois and H Prade ldquoDecision-making under fuzzinessrdquoin Advances in Fuzzy Set Theory and Applications pp 279ndash302North-Holland Amsterdam Netherlands 1979
[33] J C Pomerol and S Barba-RomeoMulticriteria Decision Man-agement Principles and Practice Kluwer Nijhoff PublishingBoston Mass USA 2000
[34] C-T Chen ldquoExtensions of the TOPSIS for group decision-making under fuzzy environmentrdquo Fuzzy Sets and Systems vol114 no 1 pp 1ndash9 2000
value of aggregated classification criteria is described by fuzzynumber which may be defuzzified and classification may beperformed by application of conventional ABC In a case ofexisting variables with either nominal or nonnominal valuesand incorporated management experience and judgmenta fuzzy rule based approach to ABC classification may beapplied [22]
The values of the treated classification items should beranked according to the value of classification criterion inmonotonically decreasing string Typically items of classA represent about 5ndash10 of the total number of itemsapproximately next 15 of items correspond to the groupB and the rest of the items belong to the group C Theitems of class A are the most significant in the treatedissue respecting the classification criteria In treated problemof suppliersrsquo selection ABC method may be deployed fordetermining optimal portfolio of suppliers (classifiedAgroupof suppliers) Optimal portfolio of suppliers should be rankedin order to propose optimal purchasing strategy throughbuilding potential partnership with the best ranked suppliersOptimal portfolio of suppliers may be ranked by applyingdifferent supplier selection models [23] Amongst manymethodologies ELECTRE may be seen as a proven asset formulticriteria decision analysis finding applications in widescientific fields [24] When the issue of supplier selection isin focus the determination of preference of alternatives maybe set as a group decision making problem [25] ELECTREmethod may be used for dealing with multicriteria decisionproblems such as determination of master contractor whenthere are several subcontractors [26] In this case index ofpreference is modified and it is calculated as a product offuzzy triangular numbers ELECTREmay bemodified in waythat the value of criteria for each supplier may be assessedby three decision makers whose assessments are modelledby fuzzy numbers [27] In this proposed fuzzy ELECTREHamming distance is used for comparing the suppliers on thetreated criteria
In compliance with the results of good practice it maybe noticed that the evaluation criteria used for the supplierselection often do not have the same relative importanceTherelative importance does not depend on supplier and it is notsubordinated to change over time Usually decision makersdeliver better opinions by using linguistic expressions thanprecise numbers Itmay be suggested that it is closer to humanthinking to compare relative importance of each pair ofcriteria than to perform direct assessment Respecting thesefacts many authors determine relative importance throughthe fuzzy AHP framework [28] Handling of uncertaintiesmay be performed by using extent analysis [29]
3 Evaluation Framework andModelling of Uncertainties
Step 1 Potential suppliers may be formally presented as a setof indices 120580 = 1 119894 119868 where 119868 is the total number ofsuppliers and 119894 is the index of the possible supplier In thiscase a set of suppliers is defined according to results of goodpractice
Step 2 Evaluation criteria are presented by set of indices 120581 =1 119896 119870 where 119870 is the total number of criteria and119896 is index of criterion The number and type of criteria aredefined by the management team based on the experiencethe results of benchmarking and current information aboutsuppliers which are presented in reports
Step 3 Management team of the enterprise is formallypresented by set of indices 120576 = 1 119890 119864 where 119864 isthe total number of the decision makers and 119890 is the index ofdecision maker In the considered problem the managementteam of treated enterprise which exists within the global sup-ply chain consisted of purchasing manager main managerplantmanager and financialmanager It may be assumed thatthe decision makers have different importance for evaluationand selection of suppliersrsquo problem The decision makerrsquosweight is denoted as 120596
119890 119890 = 1 119864 These weights are given
with respect to the results of good practice For consideredproblem the weights of decision makers are 03 03 02 and02 respectively
Step 4 The relative importance of each pair of criteria isassessed by each decision maker The decision maker usespredefined linguistic expressions which are modelled bytriangular fuzzy numbers (TFNs) The aggregated values ofthe fuzzy pairwisematrix of the relative importance of criteriaare calculated by using Fuzzy Averaging Ordered Method(FOWA) [30] The weights vector is given by extent analysesmethod [29] The criteria weights are described by precisevalues
Step 5 The possible suppliers should be evaluated accordingto the predefined period of time Usually it is a period ofone year In general the time period is divided into smalltime intervals In other words the assessment of suppliers isperformed in discreet time periods Time period is presentedby set of indices 120591 = 1 119905 119879 where 119879 is the totalnumber of discretized intervals and 119905 is the index of timeinterval
Step 6 The criterion value for supplier is assessed by eachdecision maker for each time period 119905 Decision makersuse predefined linguistic expressions which are modelled byTFNs The aggregated values of criteria values for suppliersover time period are given by using fuzzy averaging method
Step 7 The crisp values of decision matrix are given byapplying moment method [15]
Step 8 Classification of possible suppliers with respect to allcriteria and their weights is performed by the proposed ABCmodel
Step 9 Fuzzy decision matrix of suppliers which belong togroup A is stated The rank of these suppliers is determinedby fuzzy ELECTRE method
31 Modelling of Uncertainties Rating of the relative impor-tance of evaluation criteria and their values are based on
4 Mathematical Problems in Engineering
uncertain and imprecise knowledge of decision makersModelling of these uncertainties is based on fuzzy set theory[13 15] which is a suitable mathematical tool for presentinguncertain numbers in quantitativeway Fuzzy set is defined byits membership function which can be obtained in differentways [14] The uncertainties which exist in real problemsare often modelled by TFNs because they offer a goodcompromise between descriptive power and computationalsimplicityThe number of TFNs assigned to the uncertaintiesinto the relative importance of criteria and criteria valuesis defined by management team of global supply chain Thedomain of defined TFNs is defined on the real line whichbelong to different intervals In the literature there are norules or suggestions on how to determine the domain andgranularity of fuzzy numbers
311 Modelling of Criteria Relative Importance The relativeimportance of evaluation criteria is unchangeable during theconsidered period of time The assessment of relative impor-tance of each pair of identified criteria is performed by eachdecision maker They use predefined linguistic expressionswhich are modelled by TFNs 119890
The domains of these TFNs are defined real line into interval[1 5]The value 1 denotes that criterion 119896 over criterion 1198961015840 hasequal importance Value 5means that the relative importanceof criterion 119896 over criterion 1198961015840 has the most importance
If the strong relative importance of criterion 1198961015840 overcriterion 119896 holds then the pairwise comparison scale canbe represented by the fuzzy number 119890
1198961198961015840 = (
119890
1198961015840119896)minus1
=
(1119906119890
1198961015840119896 1119898119890
1198961015840119896 1119897119890
1198961015840119896)
32 Modelling of Criteria Values In the practice uncertaincriteria values are assessed bymanagement team at the globalsupply chain level for each time intervalTheir judgments arebased on evidence data results of good practice experienceand so forth It could be assumed that management teammakes decision by consensus In this paper fuzzy rating ofuncertain criteria values at the time interval level is describedby linguistic expressions which can be represented as TFNsV119905119894119896= (119910 119871
119905
119894119896119872119905
119894119896 119880119905
119894119896) Values in the domain of these TFNs
are defined on measurement scale which belong to areal setwithin the interval [0 1] Value 0 and 1 denote that criterion119896 for each supplier at the time interval level is at the lowestvalue and the highest value respectively
Specifically seven linguistic expressions which are mod-elled by TFNs are used
Very low (119910 0 0 025)Low (119910 01 02 03)Fairly medium moderate (119910 015 03 045)Moderate (119910 035 05 065)
Fairly high (119910 055 07 085)High (119910 07 08 09)Very high (119910 075 1 1)
4 The Proposed Algorithm
The algorithm of the proposed model is presented as follows
Step 1 Fuzzy assessment of the relative importance of eachcriteria pair is presented in matrix form
[119890
1198961198961015840]119870times119870
(1)
Step 2 The aggregated value of each pair of criteria iscalculated
1198961198961015840 =
119864
sum
119890=1
120596119890sdot 119890
1198961198961015840 (2)
The fuzzy pairwise comparison matrix of the relative impor-tance of criteria is constructed
[1198961198961015840]119870times119870
(3)
The weights vector is determined by using the concept ofextent analysis [29] which is presented in the followingmanner The value of fuzzy synthetic extent 119878
119896 with respect
to the 119896th criterion is defined as follows
119896= (
119870
sum
1198961015840=1
1198971198961198961015840
119870
sum
1198961015840=1
1198981198961198961015840
119870
sum
1198961015840=1
1198971198961198961015840)
sdot (
119870
sum
119896=1
119870
sum
1198961015840=1
1198971198961198961015840
119870
sum
119896=1
119870
sum
1198961015840=1
1198981198961198961015840
119870
sum
119896=1
119870
sum
1198961015840=1
1199061198961198961015840)
(4)
The weights vector is represented as follows
119882119901= ((Bel (
1)) (Bel (
119896)) (Bel (
119870))) (5)
The measure of belief according to which TFN 119896 is bigger
than all other TFNs 1198961015840 is denoted as Bel(
119896) This value
is obtained by applying the method for fuzzy numberscomparison [31 32] These values are crisp
The normalized weights vector is given by using linearnormalization procedure for benefit type criteria [33]
Step 3 The fuzzy rating of criterion 119896 for each supplier atthe time interval level 119905 is performed by each decisionmakerThese values are presented by TFNs V119905
119894119896
Step 4 Thevalue of criterion 119896 for each supplier for the wholetime period V
119894119896 is obtained by using the fuzzy averaging
method
V119894119896=1
119879sdot
119879
sum
119905=1
V119905119894119896 (6)
Mathematical Problems in Engineering 5
Step 5 The weighted fuzzy criterion value 119894119896 is calculated
as follows
119894119896= 119908119896sdot V119894119896 (7)
Step 6 The class A of items is determined as followsClass A contains suppliers that have high rated criteria
customer care quality and delivery method The highestvalues of identified criteria are represented by crisp values1199081 1199082 1199083 respectively According to fuzzy algebra rules
these crisp values should be represented by TFNs (1199081 1)
(1199082 1) and (119908
3 1) respectively In order to determine
whether a supplier belongs to class A the Euclidian distanceof supplier 119894 119894 = 1 119868 represented by (
1198941 1198942 1198943) from the
highest criteria values is calculated as follows
dist (119894 ref119860) = defuzz
radic
3
sum
119896=1
(119908119896minus 119894119896)2
(8)
As 119894119896are fuzzy numbers their distance to ref119860 is also a fuzzy
number The supports of fuzzy numbers dist(119894 ref119860) can bedescribed in discrete forms by discrete with membershipdegree min
119896=1119870(120583119894119896
(119910))Once the distances of all possible suppliers from ref119860 are
calculated they are ranked in the ascending orderThefirst 5ndash10 of the corresponding ranked suppliers are classified intoclass A
Step 7 The class C of items is determined as followsSuppliers that have low criteria values belong to class C
The reference point ref119862 is defined as the arranged tripletcrisp values (0 0 0) for care about clients quality anddelivery method
The weighted ref119862 is also represented as arranged triplet(0 0 0) Similarly as in the previous step a fuzzy distancebetween supplier 119894 119894 = 1 119868 and weighted ref119862 iscalculated as follows
dist (119894 ref119862) = defuzz
radic
3
sum
119896=1
(0 minus 119894119896)2
(9)
The distances have to be ranked in the ascending order Thefirst 80 distances correspond to suppliers which belong toclass C
Step 8 Suppliers that are not classified either into class A orinto class C form class B
Step 9 Theweighted decision matrix for suppliers from classof A is constructed
Step 10 The sets of concordance 1198781198941198941015840 and the sets of discor-
dance 1198731198781198941198941015840 are determined in the following way If
1198941015840119896ge
119894119896 (119894 1198941015840
= 1 1198681) then criteria 119896 belongs to the set of
concordance The total number of suppliers of class A isdenoted as 119868
(iii) 1198981198941198941015840 = 1 for those pair of alternatives (119894 1198941015840) where 119888
1198941198941015840 ge
119888119904119903and 1198991198941198941015840 le 119899119904119903
Step 13 Rank of suppliers of group A with respect to allcriteria and their weights is determined according to theconcordance matrix The best supplier is one with greatestnumber in the concordance matrix
5 Illustrative Example
Illustrative example is presented as a verification for theproposed model The large group of potential suppliers isanalysed for the ABC classification since all of supplierscould deliver needed products and they are geographicallydistributed all over the world It is worth to mention thatanalysed enterprise is performing suppliersrsquo selection inbuilding and civil engineering industry
6 Mathematical Problems in Engineering
Fuzzy assessment according to the Step 1 should beperformed
[[[[[
[
1 1 1 11
1198721
1198671
1198721
119871
1
1198711
1198721
1198721
119867
1 1 1 1 1119872 1 119871
1 1 1 1
]]]]]
]
(14)
Aggregated values of judgements of decision makers areobtained by FOWA This procedure is presented on criteria2 and 3 (Step 2)
The values of discordance matrix are calculated in same wayThe matrix of discordance is as follows
119873 =
[[[[[
[
mdash 1 1 1
0583 mdash 0759 1
0340 0433 mdash 1
0623 0579 0790 mdash
]]]]]
]
(21)
The mean value of concordance coefficient 119888119904119903and coefficient
of disconcordance 119899119904119903are calculated in the following way (see
(13))
119888119904119903=
1
4 sdot (4 minus 1)
4
sum
119894=1
4
sum
119894=1
1198881198941198941015840 =
1
12sdot 6 = 05
119899119904119903=
1
4 sdot (4 minus 1)
119868
sum
119894=1
119868
sum
119894=1
1198991198941198941015840 =
1
12sdot 9107 = 0759
(22)
Thematrix of consistent domination is obtained according toStep 12 of the proposed algorithm such as
119872 =
[[[[[
[
mdash 0 0 0
0 mdash 1 0
1 1 mdash 0
1 1 0 mdash
]]]]]
]
(23)
The rank of suppliers of group A is given by using procedure(Step 13 of the proposed algorithm) The obtained rank ispresented in Table 5
51 Discussion There are no specific guidelines for determin-ing the classification criteria in suppliersrsquo selection problemso these criteria vary in different economy branches In thispaper three eliminatory criteria are chosen based on theresults of good practice in order to make a base of potentialsuppliers The analysed criteria are (1) customer care (2)quality (ratio between price and specific performances ofproducts) and (3) delivery method (ratio between costs anddelivery rate) In global supply chains there is large number
of potential suppliers so determining the optimal portfolioof suppliers is very important task since it may save timedecrease costs and provide input for defining optimal supplystrategy Comparing this model to application of developedABC models [19 21] it may be stated that main implicationof this model is using the new approach in classification todetermine A and C class The proposed model takes intoaccount the type of criteria for suppliers selection so it maybe assumed that it represents its main advantage
Based on the obtained ranking results by applying themodified ELECTRE method (see Table 5) it may be con-cluded that suppliers (119894 = 41) and (119894 = 36) have the sameimportance for the treated enterprise as a part of global supplychain With respect to the obtained result the managementteam may define different supply strategy for short-timeperiod (one year) such as exclusive purchasing form one ofthe selected suppliers The selection of adequate purchasingstrategy has a crucial influence on profit of enterprise withinglobal supply chain as well as on its market position
In the same time the obtained results present inputdata for development of the methodology for selectingsuppliers in different environment supply conditions andexternal circumstances This methodology should includevarious aspects of technical economic social organizationalmarket-oriented and environmental character By using thementioned methodology management team can choose thebest supplier that is suitable for building long-term and stablecooperationThis cooperation can potentially include provid-ing capabilities for innovation and development reliability inother partnerships preparedness to share risk and profit withthe company
The proposed model is focused on the real-world sit-uation in domain determining short-time and long-timepurchasing strategy With regard to paper which treats theproblemof supplier assessment andwhich can be found in theliterature this paper pioneers the application of classificationfor building optimal portfolio of suppliers and their rankingand selection within the supply chain management
Research implications of this paper may be presented asa comparison with similar papers that have used ELECTREmethod for solving similar problems as well as with papersthat have used ABC classification The weight of criteriaand preference rating can be stated as fuzzy group decisionmaking problems
Aggregation of relative weights of criteria importance isperformed by using FOWA operator comparing it to pro-cedure proposed by Marbini and Tavana [27] or procedureproposed by Alencar et al [25] In practice it is reasonableto expect that decision makers have different weights soFOWA operator seems to be more suitable The time interval
10 Mathematical Problems in Engineering
for assessment of preference rating is divided in sub-timeintervals compared to other models where an assessment isperformedduring thewhole time interval [25 27] It is knownthat it is more precise to make assessment in shorter timeinterval
6 Conclusion
Quick and continuous changes occurring in the businessenvironment lead to opening issues in the organization andadaptation in different type of industries One of the mostimportant management tasks is determining of purchasingstrategy for the short-time and long-time period respec-tively This is because purchasing strategy has significantinfluence on successful establishment of global supply chainAs it is known in the global supply chain there are numerouspotential suppliers so that the considered problem is verycomplex
The theoretical contributions of this paper are presentedas follows In the first place conventional assessment ofsuppliers is performed with respect to quality and priceSometimes the other influencing criteria are disregardedThe evaluation criteria are selected according to the literaturereview which is conducted
Secondly it is appropriate to use linguistic terms insteadof numerical values for describing uncertainties into (1) therelative importance of each pair of criteria and (2) criteriavalues which exist in the considered problem Modelling oflinguistic variables is based on the fuzzy set theory Weightsvector of criteria is obtained by applying extent analysisapproach The fuzzy AHP may be considered as suitable forcapturing the vagueness of human thinking style and in thesame time it may be effectively employed for solving theissue of determining criteria weights in the supplier selectionproblem
The large number of potential suppliers in global supplychain enhances the complexity of the process of supplierselection In that manner it is necessary before delivery ofthe process of selection to deliver the process of suppliersrsquoclassification This may be denoted as the third contributionof the paper since a new fuzzymulticriteriaABC classificationof suppliers is proposed The effectiveness of the proposedalgorithm is tested using real-world data of 42 suppliers thatoperate in different geographical locations all over the worldThe classification obtained using the algorithm is in goodagreement with the judgment of the management team of theconsidered global supply chain
The fourth contribution makes the ranking of the suppli-ers denoted as group A The ranking is conducted by usingthe fuzzy ELECTRE proposed in this paper Modification ofELECTRE may be presented as (1) determination of sets onconcordance and sets of discordance [31] and (2) calculationof coefficient of discordance
Beside abovementioned various advantages the proposedmodel has some constraints It may be seen that there is thelack of research foundation in the literature which relatesto selection of criteria that are used for suppliersrsquo selectionin building and civil engineering industry Those criteriamay vary from constrains of supplierrsquos capacity aggregated
quality duty taxes and risk factors to political stability andso forth These extensions could undoubtedly increase thecomputational complexities The second constraint relates toABC method since it may be deployed only if 119896 is less orequal to 3 ELECTRE should be expanded with more criteriain order to determine purchasing strategy for long time andin the same time to establish partnership with supplier
This paper focuses on the complex circumstances alarge number of suppliers from different countries multipledecision makers involved in decision process and multipleuncertainties The established mathematical model can helpboth practitioners and researchers to further utilize anddeploy the purchasing strategy in global supply chain
Competing Interests
The authors declare that they have no competing interests
References
[1] ISO 90012015 Quality management systemsmdashRequirements[2] G Bruno E Esposito A Genovese andM Simpson ldquoApplying
supplier selection methodologies in a multi-stakeholder envi-ronment a case study and a critical assessmentrdquo Expert Systemswith Applications vol 43 pp 271ndash285 2016
[3] A C Trapp and J Sarkis ldquoIdentifying robust portfolios of sup-pliers a sustainability selection and development perspectiverdquoJournal of Cleaner Production vol 112 part 3 pp 2088ndash21002016
[4] P Amorim E Curcio B Almada-Lobo A P Barbosa-Povoaand I E Grossmann ldquoSupplier selection in the processed foodindustry under uncertaintyrdquo European Journal of OperationalResearch vol 252 no 3 pp 801ndash814 2016
[5] P H Andersen C Ellegaard andH Kragh ldquoIrsquom yourman howsuppliers gain strategic status in buying companiesrdquo Journal ofPurchasing and Supply Management vol 22 no 2 pp 72ndash812014
[6] B Du S Guo X Huang Y Li and J Guo ldquoA Pareto supplierselection algorithm for minimum the life cycle cost of complexproduct systemrdquo Expert Systems with Applications vol 42 no9 pp 4253ndash4264 2015
[7] T L Saaty ldquoHow to make a decision the analytic hierarchyprocessrdquo European Journal Operation-al Research vol 48 no1 pp 9ndash26 1990
[8] C-L Hwang and K Yoon Multiple Attribute Decision MakingMethods and Applications vol 186 of Lecture Notes in Economicsand Mathematical Systems Springer Heidelberg Germany1981
[9] B Roy ldquoClassement et choix en presence de points de vue mul-tiples (Lamethode ELECTRE)rdquoRevue Francaise drsquoInformatiqueet de Recherche Operationnelle vol 2 no 8 pp 57ndash75 1968
[10] D Tadic D D Milanovic M Misita and B Tadic ldquoNewintegrated approach to the problem of ranking and supplierselection under uncertaintiesrdquo Proceedings of the Institution ofMechanical Engineers Part B Journal of Engineering Manufac-ture vol 225 no 9 pp 1713ndash1724 2011
[11] HAGuvenir andE Erel ldquoMulticriteria inventory classificationusing a genetic algorithmrdquo European Journal of OperationalResearch vol 105 no 1 pp 29ndash37 1998
Mathematical Problems in Engineering 11
[12] A Aleksic M Stefanovic D Tadic and S Arsovski ldquoA fuzzymodel for assessment of organization vulnerabilityrdquo Measure-ment vol 51 no 1 pp 214ndash223 2014
[13] G J Klir and T A Folger Fuzzy Sets Uncertainty and Informa-tion Prentice Hall Upper Saddle River NJ USA 1988
[14] W Pedrycz and F Gomide An Introduction to Fuzzy SetsAnalysis and Design MIT Press Cambridge Mass USA 1997
[15] H-J Zimmermann Fuzzy Set Theorymdashand Its ApplicationsKluwer Academic Boston Mass USA 4th edition 2001
[16] P Kaur and S Chakrabortyb ldquoA new approach to vendorselection problem with impact factor as an indirect measure ofqualityrdquo Journal ofModernMathematics and Statistics vol 1 no1 pp 8ndash14 2007
[17] H M Fazel Zarandi B I Turksen and S Saghiri ldquoSupplychain crisp and fuzzy aspectsrdquo International Journal of AppliedMathematics and Computer Science vol 12 no 3 pp 423ndash4352002
[18] B E Flores andDCWhybark ldquoImplementingmultiple criteriaABC analysisrdquo Journal of OperationsManagement vol 7 no 1-2pp 79ndash85 1987
[19] M-C Yu ldquoMulti-criteria ABC analysis using artificial-intelligence-based classification techniquesrdquo Expert Systemswith Applications vol 38 no 4 pp 3416ndash3421 2011
[20] A Hadi-Vencheh and A Mohamadghasemi ldquoA fuzzy AHP-DEA approach for multiple criteria ABC inventory classifica-tionrdquo Expert Systems with Applications vol 38 no 4 pp 3346ndash3352 2011
[21] J Puente D de la Fuente P Priore and R Pino ldquoAbc classi-fication with uncertain data A fuzzy model vs a probabilisticmodelrdquoApplied Artificial Intelligence vol 16 no 6 pp 443ndash4562002
[22] C-W Chu G-S Liang and C-T Liao ldquoControlling inventoryby combiningABC analysis and fuzzy classificationrdquoComputersamp Industrial Engineering vol 55 no 4 pp 841ndash851 2008
[23] W Ho X Xu and P K Dey ldquoMulti-criteria decision makingapproaches for supplier evaluation and selection a literaturereviewrdquo European Journal of Operational Research vol 202 no1 pp 16ndash24 2010
[24] K Govindan and M B Jepsen ldquoELECTRE a comprehensiveliterature review onmethodologies and applicationsrdquo EuropeanJournal of Operational Research vol 250 no 1 pp 1ndash29 2016
[25] L H Alencar A T de Almeida and D C Morais ldquoAmulticriteria group decision model aggregating the preferencesof decision-makers based on electre methodsrdquo Pesquisa Opera-cional vol 30 no 3 pp 687ndash702 2010
[26] G AMontazer H Q Saremi andM Ramezani ldquoDesign a newmixed expert decision aiding system using fuzzy ELECTRE IIImethod for vendor selectionrdquo Expert Systems with Applicationsvol 36 no 8 pp 10837ndash10847 2009
[27] A H Marbini and M Tavana ldquoAn extension of the ElectreI method for group decision-making under a fuzzy environ-mentrdquo Omega vol 39 no 4 pp 373ndash386 2011
[28] D Tadic A T Gumus S Arsovski A Aleksic and MStefanovic ldquoAn evaluation of quality goals by using fuzzy AHPand fuzzy TOPSIS methodologyrdquo Journal of Intelligent amp FuzzySystems vol 25 no 3 pp 547ndash556 2013
[29] D-Y Chang ldquoApplications of the extent analysis method onfuzzy AHPrdquo European Journal of Operational Research vol 95no 3 pp 649ndash655 1996
[30] J MMerigo andM Casanovas ldquoUsing fuzzy numbers in heavyaggregation operatorsrdquo International Journal of InformationTechnology vol 4 no 4 pp 267ndash272 2008
[31] SM Baas andHKwakernaak ldquoRating and ranking ofmultiple-aspect alternatives using fuzzy setsrdquo Automatica vol 13 no 1pp 47ndash58 1977
[32] D Dubois and H Prade ldquoDecision-making under fuzzinessrdquoin Advances in Fuzzy Set Theory and Applications pp 279ndash302North-Holland Amsterdam Netherlands 1979
[33] J C Pomerol and S Barba-RomeoMulticriteria Decision Man-agement Principles and Practice Kluwer Nijhoff PublishingBoston Mass USA 2000
[34] C-T Chen ldquoExtensions of the TOPSIS for group decision-making under fuzzy environmentrdquo Fuzzy Sets and Systems vol114 no 1 pp 1ndash9 2000
uncertain and imprecise knowledge of decision makersModelling of these uncertainties is based on fuzzy set theory[13 15] which is a suitable mathematical tool for presentinguncertain numbers in quantitativeway Fuzzy set is defined byits membership function which can be obtained in differentways [14] The uncertainties which exist in real problemsare often modelled by TFNs because they offer a goodcompromise between descriptive power and computationalsimplicityThe number of TFNs assigned to the uncertaintiesinto the relative importance of criteria and criteria valuesis defined by management team of global supply chain Thedomain of defined TFNs is defined on the real line whichbelong to different intervals In the literature there are norules or suggestions on how to determine the domain andgranularity of fuzzy numbers
311 Modelling of Criteria Relative Importance The relativeimportance of evaluation criteria is unchangeable during theconsidered period of time The assessment of relative impor-tance of each pair of identified criteria is performed by eachdecision maker They use predefined linguistic expressionswhich are modelled by TFNs 119890
The domains of these TFNs are defined real line into interval[1 5]The value 1 denotes that criterion 119896 over criterion 1198961015840 hasequal importance Value 5means that the relative importanceof criterion 119896 over criterion 1198961015840 has the most importance
If the strong relative importance of criterion 1198961015840 overcriterion 119896 holds then the pairwise comparison scale canbe represented by the fuzzy number 119890
1198961198961015840 = (
119890
1198961015840119896)minus1
=
(1119906119890
1198961015840119896 1119898119890
1198961015840119896 1119897119890
1198961015840119896)
32 Modelling of Criteria Values In the practice uncertaincriteria values are assessed bymanagement team at the globalsupply chain level for each time intervalTheir judgments arebased on evidence data results of good practice experienceand so forth It could be assumed that management teammakes decision by consensus In this paper fuzzy rating ofuncertain criteria values at the time interval level is describedby linguistic expressions which can be represented as TFNsV119905119894119896= (119910 119871
119905
119894119896119872119905
119894119896 119880119905
119894119896) Values in the domain of these TFNs
are defined on measurement scale which belong to areal setwithin the interval [0 1] Value 0 and 1 denote that criterion119896 for each supplier at the time interval level is at the lowestvalue and the highest value respectively
Specifically seven linguistic expressions which are mod-elled by TFNs are used
Very low (119910 0 0 025)Low (119910 01 02 03)Fairly medium moderate (119910 015 03 045)Moderate (119910 035 05 065)
Fairly high (119910 055 07 085)High (119910 07 08 09)Very high (119910 075 1 1)
4 The Proposed Algorithm
The algorithm of the proposed model is presented as follows
Step 1 Fuzzy assessment of the relative importance of eachcriteria pair is presented in matrix form
[119890
1198961198961015840]119870times119870
(1)
Step 2 The aggregated value of each pair of criteria iscalculated
1198961198961015840 =
119864
sum
119890=1
120596119890sdot 119890
1198961198961015840 (2)
The fuzzy pairwise comparison matrix of the relative impor-tance of criteria is constructed
[1198961198961015840]119870times119870
(3)
The weights vector is determined by using the concept ofextent analysis [29] which is presented in the followingmanner The value of fuzzy synthetic extent 119878
119896 with respect
to the 119896th criterion is defined as follows
119896= (
119870
sum
1198961015840=1
1198971198961198961015840
119870
sum
1198961015840=1
1198981198961198961015840
119870
sum
1198961015840=1
1198971198961198961015840)
sdot (
119870
sum
119896=1
119870
sum
1198961015840=1
1198971198961198961015840
119870
sum
119896=1
119870
sum
1198961015840=1
1198981198961198961015840
119870
sum
119896=1
119870
sum
1198961015840=1
1199061198961198961015840)
(4)
The weights vector is represented as follows
119882119901= ((Bel (
1)) (Bel (
119896)) (Bel (
119870))) (5)
The measure of belief according to which TFN 119896 is bigger
than all other TFNs 1198961015840 is denoted as Bel(
119896) This value
is obtained by applying the method for fuzzy numberscomparison [31 32] These values are crisp
The normalized weights vector is given by using linearnormalization procedure for benefit type criteria [33]
Step 3 The fuzzy rating of criterion 119896 for each supplier atthe time interval level 119905 is performed by each decisionmakerThese values are presented by TFNs V119905
119894119896
Step 4 Thevalue of criterion 119896 for each supplier for the wholetime period V
119894119896 is obtained by using the fuzzy averaging
method
V119894119896=1
119879sdot
119879
sum
119905=1
V119905119894119896 (6)
Mathematical Problems in Engineering 5
Step 5 The weighted fuzzy criterion value 119894119896 is calculated
as follows
119894119896= 119908119896sdot V119894119896 (7)
Step 6 The class A of items is determined as followsClass A contains suppliers that have high rated criteria
customer care quality and delivery method The highestvalues of identified criteria are represented by crisp values1199081 1199082 1199083 respectively According to fuzzy algebra rules
these crisp values should be represented by TFNs (1199081 1)
(1199082 1) and (119908
3 1) respectively In order to determine
whether a supplier belongs to class A the Euclidian distanceof supplier 119894 119894 = 1 119868 represented by (
1198941 1198942 1198943) from the
highest criteria values is calculated as follows
dist (119894 ref119860) = defuzz
radic
3
sum
119896=1
(119908119896minus 119894119896)2
(8)
As 119894119896are fuzzy numbers their distance to ref119860 is also a fuzzy
number The supports of fuzzy numbers dist(119894 ref119860) can bedescribed in discrete forms by discrete with membershipdegree min
119896=1119870(120583119894119896
(119910))Once the distances of all possible suppliers from ref119860 are
calculated they are ranked in the ascending orderThefirst 5ndash10 of the corresponding ranked suppliers are classified intoclass A
Step 7 The class C of items is determined as followsSuppliers that have low criteria values belong to class C
The reference point ref119862 is defined as the arranged tripletcrisp values (0 0 0) for care about clients quality anddelivery method
The weighted ref119862 is also represented as arranged triplet(0 0 0) Similarly as in the previous step a fuzzy distancebetween supplier 119894 119894 = 1 119868 and weighted ref119862 iscalculated as follows
dist (119894 ref119862) = defuzz
radic
3
sum
119896=1
(0 minus 119894119896)2
(9)
The distances have to be ranked in the ascending order Thefirst 80 distances correspond to suppliers which belong toclass C
Step 8 Suppliers that are not classified either into class A orinto class C form class B
Step 9 Theweighted decision matrix for suppliers from classof A is constructed
Step 10 The sets of concordance 1198781198941198941015840 and the sets of discor-
dance 1198731198781198941198941015840 are determined in the following way If
1198941015840119896ge
119894119896 (119894 1198941015840
= 1 1198681) then criteria 119896 belongs to the set of
concordance The total number of suppliers of class A isdenoted as 119868
(iii) 1198981198941198941015840 = 1 for those pair of alternatives (119894 1198941015840) where 119888
1198941198941015840 ge
119888119904119903and 1198991198941198941015840 le 119899119904119903
Step 13 Rank of suppliers of group A with respect to allcriteria and their weights is determined according to theconcordance matrix The best supplier is one with greatestnumber in the concordance matrix
5 Illustrative Example
Illustrative example is presented as a verification for theproposed model The large group of potential suppliers isanalysed for the ABC classification since all of supplierscould deliver needed products and they are geographicallydistributed all over the world It is worth to mention thatanalysed enterprise is performing suppliersrsquo selection inbuilding and civil engineering industry
6 Mathematical Problems in Engineering
Fuzzy assessment according to the Step 1 should beperformed
[[[[[
[
1 1 1 11
1198721
1198671
1198721
119871
1
1198711
1198721
1198721
119867
1 1 1 1 1119872 1 119871
1 1 1 1
]]]]]
]
(14)
Aggregated values of judgements of decision makers areobtained by FOWA This procedure is presented on criteria2 and 3 (Step 2)
The values of discordance matrix are calculated in same wayThe matrix of discordance is as follows
119873 =
[[[[[
[
mdash 1 1 1
0583 mdash 0759 1
0340 0433 mdash 1
0623 0579 0790 mdash
]]]]]
]
(21)
The mean value of concordance coefficient 119888119904119903and coefficient
of disconcordance 119899119904119903are calculated in the following way (see
(13))
119888119904119903=
1
4 sdot (4 minus 1)
4
sum
119894=1
4
sum
119894=1
1198881198941198941015840 =
1
12sdot 6 = 05
119899119904119903=
1
4 sdot (4 minus 1)
119868
sum
119894=1
119868
sum
119894=1
1198991198941198941015840 =
1
12sdot 9107 = 0759
(22)
Thematrix of consistent domination is obtained according toStep 12 of the proposed algorithm such as
119872 =
[[[[[
[
mdash 0 0 0
0 mdash 1 0
1 1 mdash 0
1 1 0 mdash
]]]]]
]
(23)
The rank of suppliers of group A is given by using procedure(Step 13 of the proposed algorithm) The obtained rank ispresented in Table 5
51 Discussion There are no specific guidelines for determin-ing the classification criteria in suppliersrsquo selection problemso these criteria vary in different economy branches In thispaper three eliminatory criteria are chosen based on theresults of good practice in order to make a base of potentialsuppliers The analysed criteria are (1) customer care (2)quality (ratio between price and specific performances ofproducts) and (3) delivery method (ratio between costs anddelivery rate) In global supply chains there is large number
of potential suppliers so determining the optimal portfolioof suppliers is very important task since it may save timedecrease costs and provide input for defining optimal supplystrategy Comparing this model to application of developedABC models [19 21] it may be stated that main implicationof this model is using the new approach in classification todetermine A and C class The proposed model takes intoaccount the type of criteria for suppliers selection so it maybe assumed that it represents its main advantage
Based on the obtained ranking results by applying themodified ELECTRE method (see Table 5) it may be con-cluded that suppliers (119894 = 41) and (119894 = 36) have the sameimportance for the treated enterprise as a part of global supplychain With respect to the obtained result the managementteam may define different supply strategy for short-timeperiod (one year) such as exclusive purchasing form one ofthe selected suppliers The selection of adequate purchasingstrategy has a crucial influence on profit of enterprise withinglobal supply chain as well as on its market position
In the same time the obtained results present inputdata for development of the methodology for selectingsuppliers in different environment supply conditions andexternal circumstances This methodology should includevarious aspects of technical economic social organizationalmarket-oriented and environmental character By using thementioned methodology management team can choose thebest supplier that is suitable for building long-term and stablecooperationThis cooperation can potentially include provid-ing capabilities for innovation and development reliability inother partnerships preparedness to share risk and profit withthe company
The proposed model is focused on the real-world sit-uation in domain determining short-time and long-timepurchasing strategy With regard to paper which treats theproblemof supplier assessment andwhich can be found in theliterature this paper pioneers the application of classificationfor building optimal portfolio of suppliers and their rankingand selection within the supply chain management
Research implications of this paper may be presented asa comparison with similar papers that have used ELECTREmethod for solving similar problems as well as with papersthat have used ABC classification The weight of criteriaand preference rating can be stated as fuzzy group decisionmaking problems
Aggregation of relative weights of criteria importance isperformed by using FOWA operator comparing it to pro-cedure proposed by Marbini and Tavana [27] or procedureproposed by Alencar et al [25] In practice it is reasonableto expect that decision makers have different weights soFOWA operator seems to be more suitable The time interval
10 Mathematical Problems in Engineering
for assessment of preference rating is divided in sub-timeintervals compared to other models where an assessment isperformedduring thewhole time interval [25 27] It is knownthat it is more precise to make assessment in shorter timeinterval
6 Conclusion
Quick and continuous changes occurring in the businessenvironment lead to opening issues in the organization andadaptation in different type of industries One of the mostimportant management tasks is determining of purchasingstrategy for the short-time and long-time period respec-tively This is because purchasing strategy has significantinfluence on successful establishment of global supply chainAs it is known in the global supply chain there are numerouspotential suppliers so that the considered problem is verycomplex
The theoretical contributions of this paper are presentedas follows In the first place conventional assessment ofsuppliers is performed with respect to quality and priceSometimes the other influencing criteria are disregardedThe evaluation criteria are selected according to the literaturereview which is conducted
Secondly it is appropriate to use linguistic terms insteadof numerical values for describing uncertainties into (1) therelative importance of each pair of criteria and (2) criteriavalues which exist in the considered problem Modelling oflinguistic variables is based on the fuzzy set theory Weightsvector of criteria is obtained by applying extent analysisapproach The fuzzy AHP may be considered as suitable forcapturing the vagueness of human thinking style and in thesame time it may be effectively employed for solving theissue of determining criteria weights in the supplier selectionproblem
The large number of potential suppliers in global supplychain enhances the complexity of the process of supplierselection In that manner it is necessary before delivery ofthe process of selection to deliver the process of suppliersrsquoclassification This may be denoted as the third contributionof the paper since a new fuzzymulticriteriaABC classificationof suppliers is proposed The effectiveness of the proposedalgorithm is tested using real-world data of 42 suppliers thatoperate in different geographical locations all over the worldThe classification obtained using the algorithm is in goodagreement with the judgment of the management team of theconsidered global supply chain
The fourth contribution makes the ranking of the suppli-ers denoted as group A The ranking is conducted by usingthe fuzzy ELECTRE proposed in this paper Modification ofELECTRE may be presented as (1) determination of sets onconcordance and sets of discordance [31] and (2) calculationof coefficient of discordance
Beside abovementioned various advantages the proposedmodel has some constraints It may be seen that there is thelack of research foundation in the literature which relatesto selection of criteria that are used for suppliersrsquo selectionin building and civil engineering industry Those criteriamay vary from constrains of supplierrsquos capacity aggregated
quality duty taxes and risk factors to political stability andso forth These extensions could undoubtedly increase thecomputational complexities The second constraint relates toABC method since it may be deployed only if 119896 is less orequal to 3 ELECTRE should be expanded with more criteriain order to determine purchasing strategy for long time andin the same time to establish partnership with supplier
This paper focuses on the complex circumstances alarge number of suppliers from different countries multipledecision makers involved in decision process and multipleuncertainties The established mathematical model can helpboth practitioners and researchers to further utilize anddeploy the purchasing strategy in global supply chain
Competing Interests
The authors declare that they have no competing interests
References
[1] ISO 90012015 Quality management systemsmdashRequirements[2] G Bruno E Esposito A Genovese andM Simpson ldquoApplying
supplier selection methodologies in a multi-stakeholder envi-ronment a case study and a critical assessmentrdquo Expert Systemswith Applications vol 43 pp 271ndash285 2016
[3] A C Trapp and J Sarkis ldquoIdentifying robust portfolios of sup-pliers a sustainability selection and development perspectiverdquoJournal of Cleaner Production vol 112 part 3 pp 2088ndash21002016
[4] P Amorim E Curcio B Almada-Lobo A P Barbosa-Povoaand I E Grossmann ldquoSupplier selection in the processed foodindustry under uncertaintyrdquo European Journal of OperationalResearch vol 252 no 3 pp 801ndash814 2016
[5] P H Andersen C Ellegaard andH Kragh ldquoIrsquom yourman howsuppliers gain strategic status in buying companiesrdquo Journal ofPurchasing and Supply Management vol 22 no 2 pp 72ndash812014
[6] B Du S Guo X Huang Y Li and J Guo ldquoA Pareto supplierselection algorithm for minimum the life cycle cost of complexproduct systemrdquo Expert Systems with Applications vol 42 no9 pp 4253ndash4264 2015
[7] T L Saaty ldquoHow to make a decision the analytic hierarchyprocessrdquo European Journal Operation-al Research vol 48 no1 pp 9ndash26 1990
[8] C-L Hwang and K Yoon Multiple Attribute Decision MakingMethods and Applications vol 186 of Lecture Notes in Economicsand Mathematical Systems Springer Heidelberg Germany1981
[9] B Roy ldquoClassement et choix en presence de points de vue mul-tiples (Lamethode ELECTRE)rdquoRevue Francaise drsquoInformatiqueet de Recherche Operationnelle vol 2 no 8 pp 57ndash75 1968
[10] D Tadic D D Milanovic M Misita and B Tadic ldquoNewintegrated approach to the problem of ranking and supplierselection under uncertaintiesrdquo Proceedings of the Institution ofMechanical Engineers Part B Journal of Engineering Manufac-ture vol 225 no 9 pp 1713ndash1724 2011
[11] HAGuvenir andE Erel ldquoMulticriteria inventory classificationusing a genetic algorithmrdquo European Journal of OperationalResearch vol 105 no 1 pp 29ndash37 1998
Mathematical Problems in Engineering 11
[12] A Aleksic M Stefanovic D Tadic and S Arsovski ldquoA fuzzymodel for assessment of organization vulnerabilityrdquo Measure-ment vol 51 no 1 pp 214ndash223 2014
[13] G J Klir and T A Folger Fuzzy Sets Uncertainty and Informa-tion Prentice Hall Upper Saddle River NJ USA 1988
[14] W Pedrycz and F Gomide An Introduction to Fuzzy SetsAnalysis and Design MIT Press Cambridge Mass USA 1997
[15] H-J Zimmermann Fuzzy Set Theorymdashand Its ApplicationsKluwer Academic Boston Mass USA 4th edition 2001
[16] P Kaur and S Chakrabortyb ldquoA new approach to vendorselection problem with impact factor as an indirect measure ofqualityrdquo Journal ofModernMathematics and Statistics vol 1 no1 pp 8ndash14 2007
[17] H M Fazel Zarandi B I Turksen and S Saghiri ldquoSupplychain crisp and fuzzy aspectsrdquo International Journal of AppliedMathematics and Computer Science vol 12 no 3 pp 423ndash4352002
[18] B E Flores andDCWhybark ldquoImplementingmultiple criteriaABC analysisrdquo Journal of OperationsManagement vol 7 no 1-2pp 79ndash85 1987
[19] M-C Yu ldquoMulti-criteria ABC analysis using artificial-intelligence-based classification techniquesrdquo Expert Systemswith Applications vol 38 no 4 pp 3416ndash3421 2011
[20] A Hadi-Vencheh and A Mohamadghasemi ldquoA fuzzy AHP-DEA approach for multiple criteria ABC inventory classifica-tionrdquo Expert Systems with Applications vol 38 no 4 pp 3346ndash3352 2011
[21] J Puente D de la Fuente P Priore and R Pino ldquoAbc classi-fication with uncertain data A fuzzy model vs a probabilisticmodelrdquoApplied Artificial Intelligence vol 16 no 6 pp 443ndash4562002
[22] C-W Chu G-S Liang and C-T Liao ldquoControlling inventoryby combiningABC analysis and fuzzy classificationrdquoComputersamp Industrial Engineering vol 55 no 4 pp 841ndash851 2008
[23] W Ho X Xu and P K Dey ldquoMulti-criteria decision makingapproaches for supplier evaluation and selection a literaturereviewrdquo European Journal of Operational Research vol 202 no1 pp 16ndash24 2010
[24] K Govindan and M B Jepsen ldquoELECTRE a comprehensiveliterature review onmethodologies and applicationsrdquo EuropeanJournal of Operational Research vol 250 no 1 pp 1ndash29 2016
[25] L H Alencar A T de Almeida and D C Morais ldquoAmulticriteria group decision model aggregating the preferencesof decision-makers based on electre methodsrdquo Pesquisa Opera-cional vol 30 no 3 pp 687ndash702 2010
[26] G AMontazer H Q Saremi andM Ramezani ldquoDesign a newmixed expert decision aiding system using fuzzy ELECTRE IIImethod for vendor selectionrdquo Expert Systems with Applicationsvol 36 no 8 pp 10837ndash10847 2009
[27] A H Marbini and M Tavana ldquoAn extension of the ElectreI method for group decision-making under a fuzzy environ-mentrdquo Omega vol 39 no 4 pp 373ndash386 2011
[28] D Tadic A T Gumus S Arsovski A Aleksic and MStefanovic ldquoAn evaluation of quality goals by using fuzzy AHPand fuzzy TOPSIS methodologyrdquo Journal of Intelligent amp FuzzySystems vol 25 no 3 pp 547ndash556 2013
[29] D-Y Chang ldquoApplications of the extent analysis method onfuzzy AHPrdquo European Journal of Operational Research vol 95no 3 pp 649ndash655 1996
[30] J MMerigo andM Casanovas ldquoUsing fuzzy numbers in heavyaggregation operatorsrdquo International Journal of InformationTechnology vol 4 no 4 pp 267ndash272 2008
[31] SM Baas andHKwakernaak ldquoRating and ranking ofmultiple-aspect alternatives using fuzzy setsrdquo Automatica vol 13 no 1pp 47ndash58 1977
[32] D Dubois and H Prade ldquoDecision-making under fuzzinessrdquoin Advances in Fuzzy Set Theory and Applications pp 279ndash302North-Holland Amsterdam Netherlands 1979
[33] J C Pomerol and S Barba-RomeoMulticriteria Decision Man-agement Principles and Practice Kluwer Nijhoff PublishingBoston Mass USA 2000
[34] C-T Chen ldquoExtensions of the TOPSIS for group decision-making under fuzzy environmentrdquo Fuzzy Sets and Systems vol114 no 1 pp 1ndash9 2000
Step 5 The weighted fuzzy criterion value 119894119896 is calculated
as follows
119894119896= 119908119896sdot V119894119896 (7)
Step 6 The class A of items is determined as followsClass A contains suppliers that have high rated criteria
customer care quality and delivery method The highestvalues of identified criteria are represented by crisp values1199081 1199082 1199083 respectively According to fuzzy algebra rules
these crisp values should be represented by TFNs (1199081 1)
(1199082 1) and (119908
3 1) respectively In order to determine
whether a supplier belongs to class A the Euclidian distanceof supplier 119894 119894 = 1 119868 represented by (
1198941 1198942 1198943) from the
highest criteria values is calculated as follows
dist (119894 ref119860) = defuzz
radic
3
sum
119896=1
(119908119896minus 119894119896)2
(8)
As 119894119896are fuzzy numbers their distance to ref119860 is also a fuzzy
number The supports of fuzzy numbers dist(119894 ref119860) can bedescribed in discrete forms by discrete with membershipdegree min
119896=1119870(120583119894119896
(119910))Once the distances of all possible suppliers from ref119860 are
calculated they are ranked in the ascending orderThefirst 5ndash10 of the corresponding ranked suppliers are classified intoclass A
Step 7 The class C of items is determined as followsSuppliers that have low criteria values belong to class C
The reference point ref119862 is defined as the arranged tripletcrisp values (0 0 0) for care about clients quality anddelivery method
The weighted ref119862 is also represented as arranged triplet(0 0 0) Similarly as in the previous step a fuzzy distancebetween supplier 119894 119894 = 1 119868 and weighted ref119862 iscalculated as follows
dist (119894 ref119862) = defuzz
radic
3
sum
119896=1
(0 minus 119894119896)2
(9)
The distances have to be ranked in the ascending order Thefirst 80 distances correspond to suppliers which belong toclass C
Step 8 Suppliers that are not classified either into class A orinto class C form class B
Step 9 Theweighted decision matrix for suppliers from classof A is constructed
Step 10 The sets of concordance 1198781198941198941015840 and the sets of discor-
dance 1198731198781198941198941015840 are determined in the following way If
1198941015840119896ge
119894119896 (119894 1198941015840
= 1 1198681) then criteria 119896 belongs to the set of
concordance The total number of suppliers of class A isdenoted as 119868
(iii) 1198981198941198941015840 = 1 for those pair of alternatives (119894 1198941015840) where 119888
1198941198941015840 ge
119888119904119903and 1198991198941198941015840 le 119899119904119903
Step 13 Rank of suppliers of group A with respect to allcriteria and their weights is determined according to theconcordance matrix The best supplier is one with greatestnumber in the concordance matrix
5 Illustrative Example
Illustrative example is presented as a verification for theproposed model The large group of potential suppliers isanalysed for the ABC classification since all of supplierscould deliver needed products and they are geographicallydistributed all over the world It is worth to mention thatanalysed enterprise is performing suppliersrsquo selection inbuilding and civil engineering industry
6 Mathematical Problems in Engineering
Fuzzy assessment according to the Step 1 should beperformed
[[[[[
[
1 1 1 11
1198721
1198671
1198721
119871
1
1198711
1198721
1198721
119867
1 1 1 1 1119872 1 119871
1 1 1 1
]]]]]
]
(14)
Aggregated values of judgements of decision makers areobtained by FOWA This procedure is presented on criteria2 and 3 (Step 2)
The values of discordance matrix are calculated in same wayThe matrix of discordance is as follows
119873 =
[[[[[
[
mdash 1 1 1
0583 mdash 0759 1
0340 0433 mdash 1
0623 0579 0790 mdash
]]]]]
]
(21)
The mean value of concordance coefficient 119888119904119903and coefficient
of disconcordance 119899119904119903are calculated in the following way (see
(13))
119888119904119903=
1
4 sdot (4 minus 1)
4
sum
119894=1
4
sum
119894=1
1198881198941198941015840 =
1
12sdot 6 = 05
119899119904119903=
1
4 sdot (4 minus 1)
119868
sum
119894=1
119868
sum
119894=1
1198991198941198941015840 =
1
12sdot 9107 = 0759
(22)
Thematrix of consistent domination is obtained according toStep 12 of the proposed algorithm such as
119872 =
[[[[[
[
mdash 0 0 0
0 mdash 1 0
1 1 mdash 0
1 1 0 mdash
]]]]]
]
(23)
The rank of suppliers of group A is given by using procedure(Step 13 of the proposed algorithm) The obtained rank ispresented in Table 5
51 Discussion There are no specific guidelines for determin-ing the classification criteria in suppliersrsquo selection problemso these criteria vary in different economy branches In thispaper three eliminatory criteria are chosen based on theresults of good practice in order to make a base of potentialsuppliers The analysed criteria are (1) customer care (2)quality (ratio between price and specific performances ofproducts) and (3) delivery method (ratio between costs anddelivery rate) In global supply chains there is large number
of potential suppliers so determining the optimal portfolioof suppliers is very important task since it may save timedecrease costs and provide input for defining optimal supplystrategy Comparing this model to application of developedABC models [19 21] it may be stated that main implicationof this model is using the new approach in classification todetermine A and C class The proposed model takes intoaccount the type of criteria for suppliers selection so it maybe assumed that it represents its main advantage
Based on the obtained ranking results by applying themodified ELECTRE method (see Table 5) it may be con-cluded that suppliers (119894 = 41) and (119894 = 36) have the sameimportance for the treated enterprise as a part of global supplychain With respect to the obtained result the managementteam may define different supply strategy for short-timeperiod (one year) such as exclusive purchasing form one ofthe selected suppliers The selection of adequate purchasingstrategy has a crucial influence on profit of enterprise withinglobal supply chain as well as on its market position
In the same time the obtained results present inputdata for development of the methodology for selectingsuppliers in different environment supply conditions andexternal circumstances This methodology should includevarious aspects of technical economic social organizationalmarket-oriented and environmental character By using thementioned methodology management team can choose thebest supplier that is suitable for building long-term and stablecooperationThis cooperation can potentially include provid-ing capabilities for innovation and development reliability inother partnerships preparedness to share risk and profit withthe company
The proposed model is focused on the real-world sit-uation in domain determining short-time and long-timepurchasing strategy With regard to paper which treats theproblemof supplier assessment andwhich can be found in theliterature this paper pioneers the application of classificationfor building optimal portfolio of suppliers and their rankingand selection within the supply chain management
Research implications of this paper may be presented asa comparison with similar papers that have used ELECTREmethod for solving similar problems as well as with papersthat have used ABC classification The weight of criteriaand preference rating can be stated as fuzzy group decisionmaking problems
Aggregation of relative weights of criteria importance isperformed by using FOWA operator comparing it to pro-cedure proposed by Marbini and Tavana [27] or procedureproposed by Alencar et al [25] In practice it is reasonableto expect that decision makers have different weights soFOWA operator seems to be more suitable The time interval
10 Mathematical Problems in Engineering
for assessment of preference rating is divided in sub-timeintervals compared to other models where an assessment isperformedduring thewhole time interval [25 27] It is knownthat it is more precise to make assessment in shorter timeinterval
6 Conclusion
Quick and continuous changes occurring in the businessenvironment lead to opening issues in the organization andadaptation in different type of industries One of the mostimportant management tasks is determining of purchasingstrategy for the short-time and long-time period respec-tively This is because purchasing strategy has significantinfluence on successful establishment of global supply chainAs it is known in the global supply chain there are numerouspotential suppliers so that the considered problem is verycomplex
The theoretical contributions of this paper are presentedas follows In the first place conventional assessment ofsuppliers is performed with respect to quality and priceSometimes the other influencing criteria are disregardedThe evaluation criteria are selected according to the literaturereview which is conducted
Secondly it is appropriate to use linguistic terms insteadof numerical values for describing uncertainties into (1) therelative importance of each pair of criteria and (2) criteriavalues which exist in the considered problem Modelling oflinguistic variables is based on the fuzzy set theory Weightsvector of criteria is obtained by applying extent analysisapproach The fuzzy AHP may be considered as suitable forcapturing the vagueness of human thinking style and in thesame time it may be effectively employed for solving theissue of determining criteria weights in the supplier selectionproblem
The large number of potential suppliers in global supplychain enhances the complexity of the process of supplierselection In that manner it is necessary before delivery ofthe process of selection to deliver the process of suppliersrsquoclassification This may be denoted as the third contributionof the paper since a new fuzzymulticriteriaABC classificationof suppliers is proposed The effectiveness of the proposedalgorithm is tested using real-world data of 42 suppliers thatoperate in different geographical locations all over the worldThe classification obtained using the algorithm is in goodagreement with the judgment of the management team of theconsidered global supply chain
The fourth contribution makes the ranking of the suppli-ers denoted as group A The ranking is conducted by usingthe fuzzy ELECTRE proposed in this paper Modification ofELECTRE may be presented as (1) determination of sets onconcordance and sets of discordance [31] and (2) calculationof coefficient of discordance
Beside abovementioned various advantages the proposedmodel has some constraints It may be seen that there is thelack of research foundation in the literature which relatesto selection of criteria that are used for suppliersrsquo selectionin building and civil engineering industry Those criteriamay vary from constrains of supplierrsquos capacity aggregated
quality duty taxes and risk factors to political stability andso forth These extensions could undoubtedly increase thecomputational complexities The second constraint relates toABC method since it may be deployed only if 119896 is less orequal to 3 ELECTRE should be expanded with more criteriain order to determine purchasing strategy for long time andin the same time to establish partnership with supplier
This paper focuses on the complex circumstances alarge number of suppliers from different countries multipledecision makers involved in decision process and multipleuncertainties The established mathematical model can helpboth practitioners and researchers to further utilize anddeploy the purchasing strategy in global supply chain
Competing Interests
The authors declare that they have no competing interests
References
[1] ISO 90012015 Quality management systemsmdashRequirements[2] G Bruno E Esposito A Genovese andM Simpson ldquoApplying
supplier selection methodologies in a multi-stakeholder envi-ronment a case study and a critical assessmentrdquo Expert Systemswith Applications vol 43 pp 271ndash285 2016
[3] A C Trapp and J Sarkis ldquoIdentifying robust portfolios of sup-pliers a sustainability selection and development perspectiverdquoJournal of Cleaner Production vol 112 part 3 pp 2088ndash21002016
[4] P Amorim E Curcio B Almada-Lobo A P Barbosa-Povoaand I E Grossmann ldquoSupplier selection in the processed foodindustry under uncertaintyrdquo European Journal of OperationalResearch vol 252 no 3 pp 801ndash814 2016
[5] P H Andersen C Ellegaard andH Kragh ldquoIrsquom yourman howsuppliers gain strategic status in buying companiesrdquo Journal ofPurchasing and Supply Management vol 22 no 2 pp 72ndash812014
[6] B Du S Guo X Huang Y Li and J Guo ldquoA Pareto supplierselection algorithm for minimum the life cycle cost of complexproduct systemrdquo Expert Systems with Applications vol 42 no9 pp 4253ndash4264 2015
[7] T L Saaty ldquoHow to make a decision the analytic hierarchyprocessrdquo European Journal Operation-al Research vol 48 no1 pp 9ndash26 1990
[8] C-L Hwang and K Yoon Multiple Attribute Decision MakingMethods and Applications vol 186 of Lecture Notes in Economicsand Mathematical Systems Springer Heidelberg Germany1981
[9] B Roy ldquoClassement et choix en presence de points de vue mul-tiples (Lamethode ELECTRE)rdquoRevue Francaise drsquoInformatiqueet de Recherche Operationnelle vol 2 no 8 pp 57ndash75 1968
[10] D Tadic D D Milanovic M Misita and B Tadic ldquoNewintegrated approach to the problem of ranking and supplierselection under uncertaintiesrdquo Proceedings of the Institution ofMechanical Engineers Part B Journal of Engineering Manufac-ture vol 225 no 9 pp 1713ndash1724 2011
[11] HAGuvenir andE Erel ldquoMulticriteria inventory classificationusing a genetic algorithmrdquo European Journal of OperationalResearch vol 105 no 1 pp 29ndash37 1998
Mathematical Problems in Engineering 11
[12] A Aleksic M Stefanovic D Tadic and S Arsovski ldquoA fuzzymodel for assessment of organization vulnerabilityrdquo Measure-ment vol 51 no 1 pp 214ndash223 2014
[13] G J Klir and T A Folger Fuzzy Sets Uncertainty and Informa-tion Prentice Hall Upper Saddle River NJ USA 1988
[14] W Pedrycz and F Gomide An Introduction to Fuzzy SetsAnalysis and Design MIT Press Cambridge Mass USA 1997
[15] H-J Zimmermann Fuzzy Set Theorymdashand Its ApplicationsKluwer Academic Boston Mass USA 4th edition 2001
[16] P Kaur and S Chakrabortyb ldquoA new approach to vendorselection problem with impact factor as an indirect measure ofqualityrdquo Journal ofModernMathematics and Statistics vol 1 no1 pp 8ndash14 2007
[17] H M Fazel Zarandi B I Turksen and S Saghiri ldquoSupplychain crisp and fuzzy aspectsrdquo International Journal of AppliedMathematics and Computer Science vol 12 no 3 pp 423ndash4352002
[18] B E Flores andDCWhybark ldquoImplementingmultiple criteriaABC analysisrdquo Journal of OperationsManagement vol 7 no 1-2pp 79ndash85 1987
[19] M-C Yu ldquoMulti-criteria ABC analysis using artificial-intelligence-based classification techniquesrdquo Expert Systemswith Applications vol 38 no 4 pp 3416ndash3421 2011
[20] A Hadi-Vencheh and A Mohamadghasemi ldquoA fuzzy AHP-DEA approach for multiple criteria ABC inventory classifica-tionrdquo Expert Systems with Applications vol 38 no 4 pp 3346ndash3352 2011
[21] J Puente D de la Fuente P Priore and R Pino ldquoAbc classi-fication with uncertain data A fuzzy model vs a probabilisticmodelrdquoApplied Artificial Intelligence vol 16 no 6 pp 443ndash4562002
[22] C-W Chu G-S Liang and C-T Liao ldquoControlling inventoryby combiningABC analysis and fuzzy classificationrdquoComputersamp Industrial Engineering vol 55 no 4 pp 841ndash851 2008
[23] W Ho X Xu and P K Dey ldquoMulti-criteria decision makingapproaches for supplier evaluation and selection a literaturereviewrdquo European Journal of Operational Research vol 202 no1 pp 16ndash24 2010
[24] K Govindan and M B Jepsen ldquoELECTRE a comprehensiveliterature review onmethodologies and applicationsrdquo EuropeanJournal of Operational Research vol 250 no 1 pp 1ndash29 2016
[25] L H Alencar A T de Almeida and D C Morais ldquoAmulticriteria group decision model aggregating the preferencesof decision-makers based on electre methodsrdquo Pesquisa Opera-cional vol 30 no 3 pp 687ndash702 2010
[26] G AMontazer H Q Saremi andM Ramezani ldquoDesign a newmixed expert decision aiding system using fuzzy ELECTRE IIImethod for vendor selectionrdquo Expert Systems with Applicationsvol 36 no 8 pp 10837ndash10847 2009
[27] A H Marbini and M Tavana ldquoAn extension of the ElectreI method for group decision-making under a fuzzy environ-mentrdquo Omega vol 39 no 4 pp 373ndash386 2011
[28] D Tadic A T Gumus S Arsovski A Aleksic and MStefanovic ldquoAn evaluation of quality goals by using fuzzy AHPand fuzzy TOPSIS methodologyrdquo Journal of Intelligent amp FuzzySystems vol 25 no 3 pp 547ndash556 2013
[29] D-Y Chang ldquoApplications of the extent analysis method onfuzzy AHPrdquo European Journal of Operational Research vol 95no 3 pp 649ndash655 1996
[30] J MMerigo andM Casanovas ldquoUsing fuzzy numbers in heavyaggregation operatorsrdquo International Journal of InformationTechnology vol 4 no 4 pp 267ndash272 2008
[31] SM Baas andHKwakernaak ldquoRating and ranking ofmultiple-aspect alternatives using fuzzy setsrdquo Automatica vol 13 no 1pp 47ndash58 1977
[32] D Dubois and H Prade ldquoDecision-making under fuzzinessrdquoin Advances in Fuzzy Set Theory and Applications pp 279ndash302North-Holland Amsterdam Netherlands 1979
[33] J C Pomerol and S Barba-RomeoMulticriteria Decision Man-agement Principles and Practice Kluwer Nijhoff PublishingBoston Mass USA 2000
[34] C-T Chen ldquoExtensions of the TOPSIS for group decision-making under fuzzy environmentrdquo Fuzzy Sets and Systems vol114 no 1 pp 1ndash9 2000
The values of discordance matrix are calculated in same wayThe matrix of discordance is as follows
119873 =
[[[[[
[
mdash 1 1 1
0583 mdash 0759 1
0340 0433 mdash 1
0623 0579 0790 mdash
]]]]]
]
(21)
The mean value of concordance coefficient 119888119904119903and coefficient
of disconcordance 119899119904119903are calculated in the following way (see
(13))
119888119904119903=
1
4 sdot (4 minus 1)
4
sum
119894=1
4
sum
119894=1
1198881198941198941015840 =
1
12sdot 6 = 05
119899119904119903=
1
4 sdot (4 minus 1)
119868
sum
119894=1
119868
sum
119894=1
1198991198941198941015840 =
1
12sdot 9107 = 0759
(22)
Thematrix of consistent domination is obtained according toStep 12 of the proposed algorithm such as
119872 =
[[[[[
[
mdash 0 0 0
0 mdash 1 0
1 1 mdash 0
1 1 0 mdash
]]]]]
]
(23)
The rank of suppliers of group A is given by using procedure(Step 13 of the proposed algorithm) The obtained rank ispresented in Table 5
51 Discussion There are no specific guidelines for determin-ing the classification criteria in suppliersrsquo selection problemso these criteria vary in different economy branches In thispaper three eliminatory criteria are chosen based on theresults of good practice in order to make a base of potentialsuppliers The analysed criteria are (1) customer care (2)quality (ratio between price and specific performances ofproducts) and (3) delivery method (ratio between costs anddelivery rate) In global supply chains there is large number
of potential suppliers so determining the optimal portfolioof suppliers is very important task since it may save timedecrease costs and provide input for defining optimal supplystrategy Comparing this model to application of developedABC models [19 21] it may be stated that main implicationof this model is using the new approach in classification todetermine A and C class The proposed model takes intoaccount the type of criteria for suppliers selection so it maybe assumed that it represents its main advantage
Based on the obtained ranking results by applying themodified ELECTRE method (see Table 5) it may be con-cluded that suppliers (119894 = 41) and (119894 = 36) have the sameimportance for the treated enterprise as a part of global supplychain With respect to the obtained result the managementteam may define different supply strategy for short-timeperiod (one year) such as exclusive purchasing form one ofthe selected suppliers The selection of adequate purchasingstrategy has a crucial influence on profit of enterprise withinglobal supply chain as well as on its market position
In the same time the obtained results present inputdata for development of the methodology for selectingsuppliers in different environment supply conditions andexternal circumstances This methodology should includevarious aspects of technical economic social organizationalmarket-oriented and environmental character By using thementioned methodology management team can choose thebest supplier that is suitable for building long-term and stablecooperationThis cooperation can potentially include provid-ing capabilities for innovation and development reliability inother partnerships preparedness to share risk and profit withthe company
The proposed model is focused on the real-world sit-uation in domain determining short-time and long-timepurchasing strategy With regard to paper which treats theproblemof supplier assessment andwhich can be found in theliterature this paper pioneers the application of classificationfor building optimal portfolio of suppliers and their rankingand selection within the supply chain management
Research implications of this paper may be presented asa comparison with similar papers that have used ELECTREmethod for solving similar problems as well as with papersthat have used ABC classification The weight of criteriaand preference rating can be stated as fuzzy group decisionmaking problems
Aggregation of relative weights of criteria importance isperformed by using FOWA operator comparing it to pro-cedure proposed by Marbini and Tavana [27] or procedureproposed by Alencar et al [25] In practice it is reasonableto expect that decision makers have different weights soFOWA operator seems to be more suitable The time interval
10 Mathematical Problems in Engineering
for assessment of preference rating is divided in sub-timeintervals compared to other models where an assessment isperformedduring thewhole time interval [25 27] It is knownthat it is more precise to make assessment in shorter timeinterval
6 Conclusion
Quick and continuous changes occurring in the businessenvironment lead to opening issues in the organization andadaptation in different type of industries One of the mostimportant management tasks is determining of purchasingstrategy for the short-time and long-time period respec-tively This is because purchasing strategy has significantinfluence on successful establishment of global supply chainAs it is known in the global supply chain there are numerouspotential suppliers so that the considered problem is verycomplex
The theoretical contributions of this paper are presentedas follows In the first place conventional assessment ofsuppliers is performed with respect to quality and priceSometimes the other influencing criteria are disregardedThe evaluation criteria are selected according to the literaturereview which is conducted
Secondly it is appropriate to use linguistic terms insteadof numerical values for describing uncertainties into (1) therelative importance of each pair of criteria and (2) criteriavalues which exist in the considered problem Modelling oflinguistic variables is based on the fuzzy set theory Weightsvector of criteria is obtained by applying extent analysisapproach The fuzzy AHP may be considered as suitable forcapturing the vagueness of human thinking style and in thesame time it may be effectively employed for solving theissue of determining criteria weights in the supplier selectionproblem
The large number of potential suppliers in global supplychain enhances the complexity of the process of supplierselection In that manner it is necessary before delivery ofthe process of selection to deliver the process of suppliersrsquoclassification This may be denoted as the third contributionof the paper since a new fuzzymulticriteriaABC classificationof suppliers is proposed The effectiveness of the proposedalgorithm is tested using real-world data of 42 suppliers thatoperate in different geographical locations all over the worldThe classification obtained using the algorithm is in goodagreement with the judgment of the management team of theconsidered global supply chain
The fourth contribution makes the ranking of the suppli-ers denoted as group A The ranking is conducted by usingthe fuzzy ELECTRE proposed in this paper Modification ofELECTRE may be presented as (1) determination of sets onconcordance and sets of discordance [31] and (2) calculationof coefficient of discordance
Beside abovementioned various advantages the proposedmodel has some constraints It may be seen that there is thelack of research foundation in the literature which relatesto selection of criteria that are used for suppliersrsquo selectionin building and civil engineering industry Those criteriamay vary from constrains of supplierrsquos capacity aggregated
quality duty taxes and risk factors to political stability andso forth These extensions could undoubtedly increase thecomputational complexities The second constraint relates toABC method since it may be deployed only if 119896 is less orequal to 3 ELECTRE should be expanded with more criteriain order to determine purchasing strategy for long time andin the same time to establish partnership with supplier
This paper focuses on the complex circumstances alarge number of suppliers from different countries multipledecision makers involved in decision process and multipleuncertainties The established mathematical model can helpboth practitioners and researchers to further utilize anddeploy the purchasing strategy in global supply chain
Competing Interests
The authors declare that they have no competing interests
References
[1] ISO 90012015 Quality management systemsmdashRequirements[2] G Bruno E Esposito A Genovese andM Simpson ldquoApplying
supplier selection methodologies in a multi-stakeholder envi-ronment a case study and a critical assessmentrdquo Expert Systemswith Applications vol 43 pp 271ndash285 2016
[3] A C Trapp and J Sarkis ldquoIdentifying robust portfolios of sup-pliers a sustainability selection and development perspectiverdquoJournal of Cleaner Production vol 112 part 3 pp 2088ndash21002016
[4] P Amorim E Curcio B Almada-Lobo A P Barbosa-Povoaand I E Grossmann ldquoSupplier selection in the processed foodindustry under uncertaintyrdquo European Journal of OperationalResearch vol 252 no 3 pp 801ndash814 2016
[5] P H Andersen C Ellegaard andH Kragh ldquoIrsquom yourman howsuppliers gain strategic status in buying companiesrdquo Journal ofPurchasing and Supply Management vol 22 no 2 pp 72ndash812014
[6] B Du S Guo X Huang Y Li and J Guo ldquoA Pareto supplierselection algorithm for minimum the life cycle cost of complexproduct systemrdquo Expert Systems with Applications vol 42 no9 pp 4253ndash4264 2015
[7] T L Saaty ldquoHow to make a decision the analytic hierarchyprocessrdquo European Journal Operation-al Research vol 48 no1 pp 9ndash26 1990
[8] C-L Hwang and K Yoon Multiple Attribute Decision MakingMethods and Applications vol 186 of Lecture Notes in Economicsand Mathematical Systems Springer Heidelberg Germany1981
[9] B Roy ldquoClassement et choix en presence de points de vue mul-tiples (Lamethode ELECTRE)rdquoRevue Francaise drsquoInformatiqueet de Recherche Operationnelle vol 2 no 8 pp 57ndash75 1968
[10] D Tadic D D Milanovic M Misita and B Tadic ldquoNewintegrated approach to the problem of ranking and supplierselection under uncertaintiesrdquo Proceedings of the Institution ofMechanical Engineers Part B Journal of Engineering Manufac-ture vol 225 no 9 pp 1713ndash1724 2011
[11] HAGuvenir andE Erel ldquoMulticriteria inventory classificationusing a genetic algorithmrdquo European Journal of OperationalResearch vol 105 no 1 pp 29ndash37 1998
Mathematical Problems in Engineering 11
[12] A Aleksic M Stefanovic D Tadic and S Arsovski ldquoA fuzzymodel for assessment of organization vulnerabilityrdquo Measure-ment vol 51 no 1 pp 214ndash223 2014
[13] G J Klir and T A Folger Fuzzy Sets Uncertainty and Informa-tion Prentice Hall Upper Saddle River NJ USA 1988
[14] W Pedrycz and F Gomide An Introduction to Fuzzy SetsAnalysis and Design MIT Press Cambridge Mass USA 1997
[15] H-J Zimmermann Fuzzy Set Theorymdashand Its ApplicationsKluwer Academic Boston Mass USA 4th edition 2001
[16] P Kaur and S Chakrabortyb ldquoA new approach to vendorselection problem with impact factor as an indirect measure ofqualityrdquo Journal ofModernMathematics and Statistics vol 1 no1 pp 8ndash14 2007
[17] H M Fazel Zarandi B I Turksen and S Saghiri ldquoSupplychain crisp and fuzzy aspectsrdquo International Journal of AppliedMathematics and Computer Science vol 12 no 3 pp 423ndash4352002
[18] B E Flores andDCWhybark ldquoImplementingmultiple criteriaABC analysisrdquo Journal of OperationsManagement vol 7 no 1-2pp 79ndash85 1987
[19] M-C Yu ldquoMulti-criteria ABC analysis using artificial-intelligence-based classification techniquesrdquo Expert Systemswith Applications vol 38 no 4 pp 3416ndash3421 2011
[20] A Hadi-Vencheh and A Mohamadghasemi ldquoA fuzzy AHP-DEA approach for multiple criteria ABC inventory classifica-tionrdquo Expert Systems with Applications vol 38 no 4 pp 3346ndash3352 2011
[21] J Puente D de la Fuente P Priore and R Pino ldquoAbc classi-fication with uncertain data A fuzzy model vs a probabilisticmodelrdquoApplied Artificial Intelligence vol 16 no 6 pp 443ndash4562002
[22] C-W Chu G-S Liang and C-T Liao ldquoControlling inventoryby combiningABC analysis and fuzzy classificationrdquoComputersamp Industrial Engineering vol 55 no 4 pp 841ndash851 2008
[23] W Ho X Xu and P K Dey ldquoMulti-criteria decision makingapproaches for supplier evaluation and selection a literaturereviewrdquo European Journal of Operational Research vol 202 no1 pp 16ndash24 2010
[24] K Govindan and M B Jepsen ldquoELECTRE a comprehensiveliterature review onmethodologies and applicationsrdquo EuropeanJournal of Operational Research vol 250 no 1 pp 1ndash29 2016
[25] L H Alencar A T de Almeida and D C Morais ldquoAmulticriteria group decision model aggregating the preferencesof decision-makers based on electre methodsrdquo Pesquisa Opera-cional vol 30 no 3 pp 687ndash702 2010
[26] G AMontazer H Q Saremi andM Ramezani ldquoDesign a newmixed expert decision aiding system using fuzzy ELECTRE IIImethod for vendor selectionrdquo Expert Systems with Applicationsvol 36 no 8 pp 10837ndash10847 2009
[27] A H Marbini and M Tavana ldquoAn extension of the ElectreI method for group decision-making under a fuzzy environ-mentrdquo Omega vol 39 no 4 pp 373ndash386 2011
[28] D Tadic A T Gumus S Arsovski A Aleksic and MStefanovic ldquoAn evaluation of quality goals by using fuzzy AHPand fuzzy TOPSIS methodologyrdquo Journal of Intelligent amp FuzzySystems vol 25 no 3 pp 547ndash556 2013
[29] D-Y Chang ldquoApplications of the extent analysis method onfuzzy AHPrdquo European Journal of Operational Research vol 95no 3 pp 649ndash655 1996
[30] J MMerigo andM Casanovas ldquoUsing fuzzy numbers in heavyaggregation operatorsrdquo International Journal of InformationTechnology vol 4 no 4 pp 267ndash272 2008
[31] SM Baas andHKwakernaak ldquoRating and ranking ofmultiple-aspect alternatives using fuzzy setsrdquo Automatica vol 13 no 1pp 47ndash58 1977
[32] D Dubois and H Prade ldquoDecision-making under fuzzinessrdquoin Advances in Fuzzy Set Theory and Applications pp 279ndash302North-Holland Amsterdam Netherlands 1979
[33] J C Pomerol and S Barba-RomeoMulticriteria Decision Man-agement Principles and Practice Kluwer Nijhoff PublishingBoston Mass USA 2000
[34] C-T Chen ldquoExtensions of the TOPSIS for group decision-making under fuzzy environmentrdquo Fuzzy Sets and Systems vol114 no 1 pp 1ndash9 2000
The values of discordance matrix are calculated in same wayThe matrix of discordance is as follows
119873 =
[[[[[
[
mdash 1 1 1
0583 mdash 0759 1
0340 0433 mdash 1
0623 0579 0790 mdash
]]]]]
]
(21)
The mean value of concordance coefficient 119888119904119903and coefficient
of disconcordance 119899119904119903are calculated in the following way (see
(13))
119888119904119903=
1
4 sdot (4 minus 1)
4
sum
119894=1
4
sum
119894=1
1198881198941198941015840 =
1
12sdot 6 = 05
119899119904119903=
1
4 sdot (4 minus 1)
119868
sum
119894=1
119868
sum
119894=1
1198991198941198941015840 =
1
12sdot 9107 = 0759
(22)
Thematrix of consistent domination is obtained according toStep 12 of the proposed algorithm such as
119872 =
[[[[[
[
mdash 0 0 0
0 mdash 1 0
1 1 mdash 0
1 1 0 mdash
]]]]]
]
(23)
The rank of suppliers of group A is given by using procedure(Step 13 of the proposed algorithm) The obtained rank ispresented in Table 5
51 Discussion There are no specific guidelines for determin-ing the classification criteria in suppliersrsquo selection problemso these criteria vary in different economy branches In thispaper three eliminatory criteria are chosen based on theresults of good practice in order to make a base of potentialsuppliers The analysed criteria are (1) customer care (2)quality (ratio between price and specific performances ofproducts) and (3) delivery method (ratio between costs anddelivery rate) In global supply chains there is large number
of potential suppliers so determining the optimal portfolioof suppliers is very important task since it may save timedecrease costs and provide input for defining optimal supplystrategy Comparing this model to application of developedABC models [19 21] it may be stated that main implicationof this model is using the new approach in classification todetermine A and C class The proposed model takes intoaccount the type of criteria for suppliers selection so it maybe assumed that it represents its main advantage
Based on the obtained ranking results by applying themodified ELECTRE method (see Table 5) it may be con-cluded that suppliers (119894 = 41) and (119894 = 36) have the sameimportance for the treated enterprise as a part of global supplychain With respect to the obtained result the managementteam may define different supply strategy for short-timeperiod (one year) such as exclusive purchasing form one ofthe selected suppliers The selection of adequate purchasingstrategy has a crucial influence on profit of enterprise withinglobal supply chain as well as on its market position
In the same time the obtained results present inputdata for development of the methodology for selectingsuppliers in different environment supply conditions andexternal circumstances This methodology should includevarious aspects of technical economic social organizationalmarket-oriented and environmental character By using thementioned methodology management team can choose thebest supplier that is suitable for building long-term and stablecooperationThis cooperation can potentially include provid-ing capabilities for innovation and development reliability inother partnerships preparedness to share risk and profit withthe company
The proposed model is focused on the real-world sit-uation in domain determining short-time and long-timepurchasing strategy With regard to paper which treats theproblemof supplier assessment andwhich can be found in theliterature this paper pioneers the application of classificationfor building optimal portfolio of suppliers and their rankingand selection within the supply chain management
Research implications of this paper may be presented asa comparison with similar papers that have used ELECTREmethod for solving similar problems as well as with papersthat have used ABC classification The weight of criteriaand preference rating can be stated as fuzzy group decisionmaking problems
Aggregation of relative weights of criteria importance isperformed by using FOWA operator comparing it to pro-cedure proposed by Marbini and Tavana [27] or procedureproposed by Alencar et al [25] In practice it is reasonableto expect that decision makers have different weights soFOWA operator seems to be more suitable The time interval
10 Mathematical Problems in Engineering
for assessment of preference rating is divided in sub-timeintervals compared to other models where an assessment isperformedduring thewhole time interval [25 27] It is knownthat it is more precise to make assessment in shorter timeinterval
6 Conclusion
Quick and continuous changes occurring in the businessenvironment lead to opening issues in the organization andadaptation in different type of industries One of the mostimportant management tasks is determining of purchasingstrategy for the short-time and long-time period respec-tively This is because purchasing strategy has significantinfluence on successful establishment of global supply chainAs it is known in the global supply chain there are numerouspotential suppliers so that the considered problem is verycomplex
The theoretical contributions of this paper are presentedas follows In the first place conventional assessment ofsuppliers is performed with respect to quality and priceSometimes the other influencing criteria are disregardedThe evaluation criteria are selected according to the literaturereview which is conducted
Secondly it is appropriate to use linguistic terms insteadof numerical values for describing uncertainties into (1) therelative importance of each pair of criteria and (2) criteriavalues which exist in the considered problem Modelling oflinguistic variables is based on the fuzzy set theory Weightsvector of criteria is obtained by applying extent analysisapproach The fuzzy AHP may be considered as suitable forcapturing the vagueness of human thinking style and in thesame time it may be effectively employed for solving theissue of determining criteria weights in the supplier selectionproblem
The large number of potential suppliers in global supplychain enhances the complexity of the process of supplierselection In that manner it is necessary before delivery ofthe process of selection to deliver the process of suppliersrsquoclassification This may be denoted as the third contributionof the paper since a new fuzzymulticriteriaABC classificationof suppliers is proposed The effectiveness of the proposedalgorithm is tested using real-world data of 42 suppliers thatoperate in different geographical locations all over the worldThe classification obtained using the algorithm is in goodagreement with the judgment of the management team of theconsidered global supply chain
The fourth contribution makes the ranking of the suppli-ers denoted as group A The ranking is conducted by usingthe fuzzy ELECTRE proposed in this paper Modification ofELECTRE may be presented as (1) determination of sets onconcordance and sets of discordance [31] and (2) calculationof coefficient of discordance
Beside abovementioned various advantages the proposedmodel has some constraints It may be seen that there is thelack of research foundation in the literature which relatesto selection of criteria that are used for suppliersrsquo selectionin building and civil engineering industry Those criteriamay vary from constrains of supplierrsquos capacity aggregated
quality duty taxes and risk factors to political stability andso forth These extensions could undoubtedly increase thecomputational complexities The second constraint relates toABC method since it may be deployed only if 119896 is less orequal to 3 ELECTRE should be expanded with more criteriain order to determine purchasing strategy for long time andin the same time to establish partnership with supplier
This paper focuses on the complex circumstances alarge number of suppliers from different countries multipledecision makers involved in decision process and multipleuncertainties The established mathematical model can helpboth practitioners and researchers to further utilize anddeploy the purchasing strategy in global supply chain
Competing Interests
The authors declare that they have no competing interests
References
[1] ISO 90012015 Quality management systemsmdashRequirements[2] G Bruno E Esposito A Genovese andM Simpson ldquoApplying
supplier selection methodologies in a multi-stakeholder envi-ronment a case study and a critical assessmentrdquo Expert Systemswith Applications vol 43 pp 271ndash285 2016
[3] A C Trapp and J Sarkis ldquoIdentifying robust portfolios of sup-pliers a sustainability selection and development perspectiverdquoJournal of Cleaner Production vol 112 part 3 pp 2088ndash21002016
[4] P Amorim E Curcio B Almada-Lobo A P Barbosa-Povoaand I E Grossmann ldquoSupplier selection in the processed foodindustry under uncertaintyrdquo European Journal of OperationalResearch vol 252 no 3 pp 801ndash814 2016
[5] P H Andersen C Ellegaard andH Kragh ldquoIrsquom yourman howsuppliers gain strategic status in buying companiesrdquo Journal ofPurchasing and Supply Management vol 22 no 2 pp 72ndash812014
[6] B Du S Guo X Huang Y Li and J Guo ldquoA Pareto supplierselection algorithm for minimum the life cycle cost of complexproduct systemrdquo Expert Systems with Applications vol 42 no9 pp 4253ndash4264 2015
[7] T L Saaty ldquoHow to make a decision the analytic hierarchyprocessrdquo European Journal Operation-al Research vol 48 no1 pp 9ndash26 1990
[8] C-L Hwang and K Yoon Multiple Attribute Decision MakingMethods and Applications vol 186 of Lecture Notes in Economicsand Mathematical Systems Springer Heidelberg Germany1981
[9] B Roy ldquoClassement et choix en presence de points de vue mul-tiples (Lamethode ELECTRE)rdquoRevue Francaise drsquoInformatiqueet de Recherche Operationnelle vol 2 no 8 pp 57ndash75 1968
[10] D Tadic D D Milanovic M Misita and B Tadic ldquoNewintegrated approach to the problem of ranking and supplierselection under uncertaintiesrdquo Proceedings of the Institution ofMechanical Engineers Part B Journal of Engineering Manufac-ture vol 225 no 9 pp 1713ndash1724 2011
[11] HAGuvenir andE Erel ldquoMulticriteria inventory classificationusing a genetic algorithmrdquo European Journal of OperationalResearch vol 105 no 1 pp 29ndash37 1998
Mathematical Problems in Engineering 11
[12] A Aleksic M Stefanovic D Tadic and S Arsovski ldquoA fuzzymodel for assessment of organization vulnerabilityrdquo Measure-ment vol 51 no 1 pp 214ndash223 2014
[13] G J Klir and T A Folger Fuzzy Sets Uncertainty and Informa-tion Prentice Hall Upper Saddle River NJ USA 1988
[14] W Pedrycz and F Gomide An Introduction to Fuzzy SetsAnalysis and Design MIT Press Cambridge Mass USA 1997
[15] H-J Zimmermann Fuzzy Set Theorymdashand Its ApplicationsKluwer Academic Boston Mass USA 4th edition 2001
[16] P Kaur and S Chakrabortyb ldquoA new approach to vendorselection problem with impact factor as an indirect measure ofqualityrdquo Journal ofModernMathematics and Statistics vol 1 no1 pp 8ndash14 2007
[17] H M Fazel Zarandi B I Turksen and S Saghiri ldquoSupplychain crisp and fuzzy aspectsrdquo International Journal of AppliedMathematics and Computer Science vol 12 no 3 pp 423ndash4352002
[18] B E Flores andDCWhybark ldquoImplementingmultiple criteriaABC analysisrdquo Journal of OperationsManagement vol 7 no 1-2pp 79ndash85 1987
[19] M-C Yu ldquoMulti-criteria ABC analysis using artificial-intelligence-based classification techniquesrdquo Expert Systemswith Applications vol 38 no 4 pp 3416ndash3421 2011
[20] A Hadi-Vencheh and A Mohamadghasemi ldquoA fuzzy AHP-DEA approach for multiple criteria ABC inventory classifica-tionrdquo Expert Systems with Applications vol 38 no 4 pp 3346ndash3352 2011
[21] J Puente D de la Fuente P Priore and R Pino ldquoAbc classi-fication with uncertain data A fuzzy model vs a probabilisticmodelrdquoApplied Artificial Intelligence vol 16 no 6 pp 443ndash4562002
[22] C-W Chu G-S Liang and C-T Liao ldquoControlling inventoryby combiningABC analysis and fuzzy classificationrdquoComputersamp Industrial Engineering vol 55 no 4 pp 841ndash851 2008
[23] W Ho X Xu and P K Dey ldquoMulti-criteria decision makingapproaches for supplier evaluation and selection a literaturereviewrdquo European Journal of Operational Research vol 202 no1 pp 16ndash24 2010
[24] K Govindan and M B Jepsen ldquoELECTRE a comprehensiveliterature review onmethodologies and applicationsrdquo EuropeanJournal of Operational Research vol 250 no 1 pp 1ndash29 2016
[25] L H Alencar A T de Almeida and D C Morais ldquoAmulticriteria group decision model aggregating the preferencesof decision-makers based on electre methodsrdquo Pesquisa Opera-cional vol 30 no 3 pp 687ndash702 2010
[26] G AMontazer H Q Saremi andM Ramezani ldquoDesign a newmixed expert decision aiding system using fuzzy ELECTRE IIImethod for vendor selectionrdquo Expert Systems with Applicationsvol 36 no 8 pp 10837ndash10847 2009
[27] A H Marbini and M Tavana ldquoAn extension of the ElectreI method for group decision-making under a fuzzy environ-mentrdquo Omega vol 39 no 4 pp 373ndash386 2011
[28] D Tadic A T Gumus S Arsovski A Aleksic and MStefanovic ldquoAn evaluation of quality goals by using fuzzy AHPand fuzzy TOPSIS methodologyrdquo Journal of Intelligent amp FuzzySystems vol 25 no 3 pp 547ndash556 2013
[29] D-Y Chang ldquoApplications of the extent analysis method onfuzzy AHPrdquo European Journal of Operational Research vol 95no 3 pp 649ndash655 1996
[30] J MMerigo andM Casanovas ldquoUsing fuzzy numbers in heavyaggregation operatorsrdquo International Journal of InformationTechnology vol 4 no 4 pp 267ndash272 2008
[31] SM Baas andHKwakernaak ldquoRating and ranking ofmultiple-aspect alternatives using fuzzy setsrdquo Automatica vol 13 no 1pp 47ndash58 1977
[32] D Dubois and H Prade ldquoDecision-making under fuzzinessrdquoin Advances in Fuzzy Set Theory and Applications pp 279ndash302North-Holland Amsterdam Netherlands 1979
[33] J C Pomerol and S Barba-RomeoMulticriteria Decision Man-agement Principles and Practice Kluwer Nijhoff PublishingBoston Mass USA 2000
[34] C-T Chen ldquoExtensions of the TOPSIS for group decision-making under fuzzy environmentrdquo Fuzzy Sets and Systems vol114 no 1 pp 1ndash9 2000
The values of discordance matrix are calculated in same wayThe matrix of discordance is as follows
119873 =
[[[[[
[
mdash 1 1 1
0583 mdash 0759 1
0340 0433 mdash 1
0623 0579 0790 mdash
]]]]]
]
(21)
The mean value of concordance coefficient 119888119904119903and coefficient
of disconcordance 119899119904119903are calculated in the following way (see
(13))
119888119904119903=
1
4 sdot (4 minus 1)
4
sum
119894=1
4
sum
119894=1
1198881198941198941015840 =
1
12sdot 6 = 05
119899119904119903=
1
4 sdot (4 minus 1)
119868
sum
119894=1
119868
sum
119894=1
1198991198941198941015840 =
1
12sdot 9107 = 0759
(22)
Thematrix of consistent domination is obtained according toStep 12 of the proposed algorithm such as
119872 =
[[[[[
[
mdash 0 0 0
0 mdash 1 0
1 1 mdash 0
1 1 0 mdash
]]]]]
]
(23)
The rank of suppliers of group A is given by using procedure(Step 13 of the proposed algorithm) The obtained rank ispresented in Table 5
51 Discussion There are no specific guidelines for determin-ing the classification criteria in suppliersrsquo selection problemso these criteria vary in different economy branches In thispaper three eliminatory criteria are chosen based on theresults of good practice in order to make a base of potentialsuppliers The analysed criteria are (1) customer care (2)quality (ratio between price and specific performances ofproducts) and (3) delivery method (ratio between costs anddelivery rate) In global supply chains there is large number
of potential suppliers so determining the optimal portfolioof suppliers is very important task since it may save timedecrease costs and provide input for defining optimal supplystrategy Comparing this model to application of developedABC models [19 21] it may be stated that main implicationof this model is using the new approach in classification todetermine A and C class The proposed model takes intoaccount the type of criteria for suppliers selection so it maybe assumed that it represents its main advantage
Based on the obtained ranking results by applying themodified ELECTRE method (see Table 5) it may be con-cluded that suppliers (119894 = 41) and (119894 = 36) have the sameimportance for the treated enterprise as a part of global supplychain With respect to the obtained result the managementteam may define different supply strategy for short-timeperiod (one year) such as exclusive purchasing form one ofthe selected suppliers The selection of adequate purchasingstrategy has a crucial influence on profit of enterprise withinglobal supply chain as well as on its market position
In the same time the obtained results present inputdata for development of the methodology for selectingsuppliers in different environment supply conditions andexternal circumstances This methodology should includevarious aspects of technical economic social organizationalmarket-oriented and environmental character By using thementioned methodology management team can choose thebest supplier that is suitable for building long-term and stablecooperationThis cooperation can potentially include provid-ing capabilities for innovation and development reliability inother partnerships preparedness to share risk and profit withthe company
The proposed model is focused on the real-world sit-uation in domain determining short-time and long-timepurchasing strategy With regard to paper which treats theproblemof supplier assessment andwhich can be found in theliterature this paper pioneers the application of classificationfor building optimal portfolio of suppliers and their rankingand selection within the supply chain management
Research implications of this paper may be presented asa comparison with similar papers that have used ELECTREmethod for solving similar problems as well as with papersthat have used ABC classification The weight of criteriaand preference rating can be stated as fuzzy group decisionmaking problems
Aggregation of relative weights of criteria importance isperformed by using FOWA operator comparing it to pro-cedure proposed by Marbini and Tavana [27] or procedureproposed by Alencar et al [25] In practice it is reasonableto expect that decision makers have different weights soFOWA operator seems to be more suitable The time interval
10 Mathematical Problems in Engineering
for assessment of preference rating is divided in sub-timeintervals compared to other models where an assessment isperformedduring thewhole time interval [25 27] It is knownthat it is more precise to make assessment in shorter timeinterval
6 Conclusion
Quick and continuous changes occurring in the businessenvironment lead to opening issues in the organization andadaptation in different type of industries One of the mostimportant management tasks is determining of purchasingstrategy for the short-time and long-time period respec-tively This is because purchasing strategy has significantinfluence on successful establishment of global supply chainAs it is known in the global supply chain there are numerouspotential suppliers so that the considered problem is verycomplex
The theoretical contributions of this paper are presentedas follows In the first place conventional assessment ofsuppliers is performed with respect to quality and priceSometimes the other influencing criteria are disregardedThe evaluation criteria are selected according to the literaturereview which is conducted
Secondly it is appropriate to use linguistic terms insteadof numerical values for describing uncertainties into (1) therelative importance of each pair of criteria and (2) criteriavalues which exist in the considered problem Modelling oflinguistic variables is based on the fuzzy set theory Weightsvector of criteria is obtained by applying extent analysisapproach The fuzzy AHP may be considered as suitable forcapturing the vagueness of human thinking style and in thesame time it may be effectively employed for solving theissue of determining criteria weights in the supplier selectionproblem
The large number of potential suppliers in global supplychain enhances the complexity of the process of supplierselection In that manner it is necessary before delivery ofthe process of selection to deliver the process of suppliersrsquoclassification This may be denoted as the third contributionof the paper since a new fuzzymulticriteriaABC classificationof suppliers is proposed The effectiveness of the proposedalgorithm is tested using real-world data of 42 suppliers thatoperate in different geographical locations all over the worldThe classification obtained using the algorithm is in goodagreement with the judgment of the management team of theconsidered global supply chain
The fourth contribution makes the ranking of the suppli-ers denoted as group A The ranking is conducted by usingthe fuzzy ELECTRE proposed in this paper Modification ofELECTRE may be presented as (1) determination of sets onconcordance and sets of discordance [31] and (2) calculationof coefficient of discordance
Beside abovementioned various advantages the proposedmodel has some constraints It may be seen that there is thelack of research foundation in the literature which relatesto selection of criteria that are used for suppliersrsquo selectionin building and civil engineering industry Those criteriamay vary from constrains of supplierrsquos capacity aggregated
quality duty taxes and risk factors to political stability andso forth These extensions could undoubtedly increase thecomputational complexities The second constraint relates toABC method since it may be deployed only if 119896 is less orequal to 3 ELECTRE should be expanded with more criteriain order to determine purchasing strategy for long time andin the same time to establish partnership with supplier
This paper focuses on the complex circumstances alarge number of suppliers from different countries multipledecision makers involved in decision process and multipleuncertainties The established mathematical model can helpboth practitioners and researchers to further utilize anddeploy the purchasing strategy in global supply chain
Competing Interests
The authors declare that they have no competing interests
References
[1] ISO 90012015 Quality management systemsmdashRequirements[2] G Bruno E Esposito A Genovese andM Simpson ldquoApplying
supplier selection methodologies in a multi-stakeholder envi-ronment a case study and a critical assessmentrdquo Expert Systemswith Applications vol 43 pp 271ndash285 2016
[3] A C Trapp and J Sarkis ldquoIdentifying robust portfolios of sup-pliers a sustainability selection and development perspectiverdquoJournal of Cleaner Production vol 112 part 3 pp 2088ndash21002016
[4] P Amorim E Curcio B Almada-Lobo A P Barbosa-Povoaand I E Grossmann ldquoSupplier selection in the processed foodindustry under uncertaintyrdquo European Journal of OperationalResearch vol 252 no 3 pp 801ndash814 2016
[5] P H Andersen C Ellegaard andH Kragh ldquoIrsquom yourman howsuppliers gain strategic status in buying companiesrdquo Journal ofPurchasing and Supply Management vol 22 no 2 pp 72ndash812014
[6] B Du S Guo X Huang Y Li and J Guo ldquoA Pareto supplierselection algorithm for minimum the life cycle cost of complexproduct systemrdquo Expert Systems with Applications vol 42 no9 pp 4253ndash4264 2015
[7] T L Saaty ldquoHow to make a decision the analytic hierarchyprocessrdquo European Journal Operation-al Research vol 48 no1 pp 9ndash26 1990
[8] C-L Hwang and K Yoon Multiple Attribute Decision MakingMethods and Applications vol 186 of Lecture Notes in Economicsand Mathematical Systems Springer Heidelberg Germany1981
[9] B Roy ldquoClassement et choix en presence de points de vue mul-tiples (Lamethode ELECTRE)rdquoRevue Francaise drsquoInformatiqueet de Recherche Operationnelle vol 2 no 8 pp 57ndash75 1968
[10] D Tadic D D Milanovic M Misita and B Tadic ldquoNewintegrated approach to the problem of ranking and supplierselection under uncertaintiesrdquo Proceedings of the Institution ofMechanical Engineers Part B Journal of Engineering Manufac-ture vol 225 no 9 pp 1713ndash1724 2011
[11] HAGuvenir andE Erel ldquoMulticriteria inventory classificationusing a genetic algorithmrdquo European Journal of OperationalResearch vol 105 no 1 pp 29ndash37 1998
Mathematical Problems in Engineering 11
[12] A Aleksic M Stefanovic D Tadic and S Arsovski ldquoA fuzzymodel for assessment of organization vulnerabilityrdquo Measure-ment vol 51 no 1 pp 214ndash223 2014
[13] G J Klir and T A Folger Fuzzy Sets Uncertainty and Informa-tion Prentice Hall Upper Saddle River NJ USA 1988
[14] W Pedrycz and F Gomide An Introduction to Fuzzy SetsAnalysis and Design MIT Press Cambridge Mass USA 1997
[15] H-J Zimmermann Fuzzy Set Theorymdashand Its ApplicationsKluwer Academic Boston Mass USA 4th edition 2001
[16] P Kaur and S Chakrabortyb ldquoA new approach to vendorselection problem with impact factor as an indirect measure ofqualityrdquo Journal ofModernMathematics and Statistics vol 1 no1 pp 8ndash14 2007
[17] H M Fazel Zarandi B I Turksen and S Saghiri ldquoSupplychain crisp and fuzzy aspectsrdquo International Journal of AppliedMathematics and Computer Science vol 12 no 3 pp 423ndash4352002
[18] B E Flores andDCWhybark ldquoImplementingmultiple criteriaABC analysisrdquo Journal of OperationsManagement vol 7 no 1-2pp 79ndash85 1987
[19] M-C Yu ldquoMulti-criteria ABC analysis using artificial-intelligence-based classification techniquesrdquo Expert Systemswith Applications vol 38 no 4 pp 3416ndash3421 2011
[20] A Hadi-Vencheh and A Mohamadghasemi ldquoA fuzzy AHP-DEA approach for multiple criteria ABC inventory classifica-tionrdquo Expert Systems with Applications vol 38 no 4 pp 3346ndash3352 2011
[21] J Puente D de la Fuente P Priore and R Pino ldquoAbc classi-fication with uncertain data A fuzzy model vs a probabilisticmodelrdquoApplied Artificial Intelligence vol 16 no 6 pp 443ndash4562002
[22] C-W Chu G-S Liang and C-T Liao ldquoControlling inventoryby combiningABC analysis and fuzzy classificationrdquoComputersamp Industrial Engineering vol 55 no 4 pp 841ndash851 2008
[23] W Ho X Xu and P K Dey ldquoMulti-criteria decision makingapproaches for supplier evaluation and selection a literaturereviewrdquo European Journal of Operational Research vol 202 no1 pp 16ndash24 2010
[24] K Govindan and M B Jepsen ldquoELECTRE a comprehensiveliterature review onmethodologies and applicationsrdquo EuropeanJournal of Operational Research vol 250 no 1 pp 1ndash29 2016
[25] L H Alencar A T de Almeida and D C Morais ldquoAmulticriteria group decision model aggregating the preferencesof decision-makers based on electre methodsrdquo Pesquisa Opera-cional vol 30 no 3 pp 687ndash702 2010
[26] G AMontazer H Q Saremi andM Ramezani ldquoDesign a newmixed expert decision aiding system using fuzzy ELECTRE IIImethod for vendor selectionrdquo Expert Systems with Applicationsvol 36 no 8 pp 10837ndash10847 2009
[27] A H Marbini and M Tavana ldquoAn extension of the ElectreI method for group decision-making under a fuzzy environ-mentrdquo Omega vol 39 no 4 pp 373ndash386 2011
[28] D Tadic A T Gumus S Arsovski A Aleksic and MStefanovic ldquoAn evaluation of quality goals by using fuzzy AHPand fuzzy TOPSIS methodologyrdquo Journal of Intelligent amp FuzzySystems vol 25 no 3 pp 547ndash556 2013
[29] D-Y Chang ldquoApplications of the extent analysis method onfuzzy AHPrdquo European Journal of Operational Research vol 95no 3 pp 649ndash655 1996
[30] J MMerigo andM Casanovas ldquoUsing fuzzy numbers in heavyaggregation operatorsrdquo International Journal of InformationTechnology vol 4 no 4 pp 267ndash272 2008
[31] SM Baas andHKwakernaak ldquoRating and ranking ofmultiple-aspect alternatives using fuzzy setsrdquo Automatica vol 13 no 1pp 47ndash58 1977
[32] D Dubois and H Prade ldquoDecision-making under fuzzinessrdquoin Advances in Fuzzy Set Theory and Applications pp 279ndash302North-Holland Amsterdam Netherlands 1979
[33] J C Pomerol and S Barba-RomeoMulticriteria Decision Man-agement Principles and Practice Kluwer Nijhoff PublishingBoston Mass USA 2000
[34] C-T Chen ldquoExtensions of the TOPSIS for group decision-making under fuzzy environmentrdquo Fuzzy Sets and Systems vol114 no 1 pp 1ndash9 2000
The values of discordance matrix are calculated in same wayThe matrix of discordance is as follows
119873 =
[[[[[
[
mdash 1 1 1
0583 mdash 0759 1
0340 0433 mdash 1
0623 0579 0790 mdash
]]]]]
]
(21)
The mean value of concordance coefficient 119888119904119903and coefficient
of disconcordance 119899119904119903are calculated in the following way (see
(13))
119888119904119903=
1
4 sdot (4 minus 1)
4
sum
119894=1
4
sum
119894=1
1198881198941198941015840 =
1
12sdot 6 = 05
119899119904119903=
1
4 sdot (4 minus 1)
119868
sum
119894=1
119868
sum
119894=1
1198991198941198941015840 =
1
12sdot 9107 = 0759
(22)
Thematrix of consistent domination is obtained according toStep 12 of the proposed algorithm such as
119872 =
[[[[[
[
mdash 0 0 0
0 mdash 1 0
1 1 mdash 0
1 1 0 mdash
]]]]]
]
(23)
The rank of suppliers of group A is given by using procedure(Step 13 of the proposed algorithm) The obtained rank ispresented in Table 5
51 Discussion There are no specific guidelines for determin-ing the classification criteria in suppliersrsquo selection problemso these criteria vary in different economy branches In thispaper three eliminatory criteria are chosen based on theresults of good practice in order to make a base of potentialsuppliers The analysed criteria are (1) customer care (2)quality (ratio between price and specific performances ofproducts) and (3) delivery method (ratio between costs anddelivery rate) In global supply chains there is large number
of potential suppliers so determining the optimal portfolioof suppliers is very important task since it may save timedecrease costs and provide input for defining optimal supplystrategy Comparing this model to application of developedABC models [19 21] it may be stated that main implicationof this model is using the new approach in classification todetermine A and C class The proposed model takes intoaccount the type of criteria for suppliers selection so it maybe assumed that it represents its main advantage
Based on the obtained ranking results by applying themodified ELECTRE method (see Table 5) it may be con-cluded that suppliers (119894 = 41) and (119894 = 36) have the sameimportance for the treated enterprise as a part of global supplychain With respect to the obtained result the managementteam may define different supply strategy for short-timeperiod (one year) such as exclusive purchasing form one ofthe selected suppliers The selection of adequate purchasingstrategy has a crucial influence on profit of enterprise withinglobal supply chain as well as on its market position
In the same time the obtained results present inputdata for development of the methodology for selectingsuppliers in different environment supply conditions andexternal circumstances This methodology should includevarious aspects of technical economic social organizationalmarket-oriented and environmental character By using thementioned methodology management team can choose thebest supplier that is suitable for building long-term and stablecooperationThis cooperation can potentially include provid-ing capabilities for innovation and development reliability inother partnerships preparedness to share risk and profit withthe company
The proposed model is focused on the real-world sit-uation in domain determining short-time and long-timepurchasing strategy With regard to paper which treats theproblemof supplier assessment andwhich can be found in theliterature this paper pioneers the application of classificationfor building optimal portfolio of suppliers and their rankingand selection within the supply chain management
Research implications of this paper may be presented asa comparison with similar papers that have used ELECTREmethod for solving similar problems as well as with papersthat have used ABC classification The weight of criteriaand preference rating can be stated as fuzzy group decisionmaking problems
Aggregation of relative weights of criteria importance isperformed by using FOWA operator comparing it to pro-cedure proposed by Marbini and Tavana [27] or procedureproposed by Alencar et al [25] In practice it is reasonableto expect that decision makers have different weights soFOWA operator seems to be more suitable The time interval
10 Mathematical Problems in Engineering
for assessment of preference rating is divided in sub-timeintervals compared to other models where an assessment isperformedduring thewhole time interval [25 27] It is knownthat it is more precise to make assessment in shorter timeinterval
6 Conclusion
Quick and continuous changes occurring in the businessenvironment lead to opening issues in the organization andadaptation in different type of industries One of the mostimportant management tasks is determining of purchasingstrategy for the short-time and long-time period respec-tively This is because purchasing strategy has significantinfluence on successful establishment of global supply chainAs it is known in the global supply chain there are numerouspotential suppliers so that the considered problem is verycomplex
The theoretical contributions of this paper are presentedas follows In the first place conventional assessment ofsuppliers is performed with respect to quality and priceSometimes the other influencing criteria are disregardedThe evaluation criteria are selected according to the literaturereview which is conducted
Secondly it is appropriate to use linguistic terms insteadof numerical values for describing uncertainties into (1) therelative importance of each pair of criteria and (2) criteriavalues which exist in the considered problem Modelling oflinguistic variables is based on the fuzzy set theory Weightsvector of criteria is obtained by applying extent analysisapproach The fuzzy AHP may be considered as suitable forcapturing the vagueness of human thinking style and in thesame time it may be effectively employed for solving theissue of determining criteria weights in the supplier selectionproblem
The large number of potential suppliers in global supplychain enhances the complexity of the process of supplierselection In that manner it is necessary before delivery ofthe process of selection to deliver the process of suppliersrsquoclassification This may be denoted as the third contributionof the paper since a new fuzzymulticriteriaABC classificationof suppliers is proposed The effectiveness of the proposedalgorithm is tested using real-world data of 42 suppliers thatoperate in different geographical locations all over the worldThe classification obtained using the algorithm is in goodagreement with the judgment of the management team of theconsidered global supply chain
The fourth contribution makes the ranking of the suppli-ers denoted as group A The ranking is conducted by usingthe fuzzy ELECTRE proposed in this paper Modification ofELECTRE may be presented as (1) determination of sets onconcordance and sets of discordance [31] and (2) calculationof coefficient of discordance
Beside abovementioned various advantages the proposedmodel has some constraints It may be seen that there is thelack of research foundation in the literature which relatesto selection of criteria that are used for suppliersrsquo selectionin building and civil engineering industry Those criteriamay vary from constrains of supplierrsquos capacity aggregated
quality duty taxes and risk factors to political stability andso forth These extensions could undoubtedly increase thecomputational complexities The second constraint relates toABC method since it may be deployed only if 119896 is less orequal to 3 ELECTRE should be expanded with more criteriain order to determine purchasing strategy for long time andin the same time to establish partnership with supplier
This paper focuses on the complex circumstances alarge number of suppliers from different countries multipledecision makers involved in decision process and multipleuncertainties The established mathematical model can helpboth practitioners and researchers to further utilize anddeploy the purchasing strategy in global supply chain
Competing Interests
The authors declare that they have no competing interests
References
[1] ISO 90012015 Quality management systemsmdashRequirements[2] G Bruno E Esposito A Genovese andM Simpson ldquoApplying
supplier selection methodologies in a multi-stakeholder envi-ronment a case study and a critical assessmentrdquo Expert Systemswith Applications vol 43 pp 271ndash285 2016
[3] A C Trapp and J Sarkis ldquoIdentifying robust portfolios of sup-pliers a sustainability selection and development perspectiverdquoJournal of Cleaner Production vol 112 part 3 pp 2088ndash21002016
[4] P Amorim E Curcio B Almada-Lobo A P Barbosa-Povoaand I E Grossmann ldquoSupplier selection in the processed foodindustry under uncertaintyrdquo European Journal of OperationalResearch vol 252 no 3 pp 801ndash814 2016
[5] P H Andersen C Ellegaard andH Kragh ldquoIrsquom yourman howsuppliers gain strategic status in buying companiesrdquo Journal ofPurchasing and Supply Management vol 22 no 2 pp 72ndash812014
[6] B Du S Guo X Huang Y Li and J Guo ldquoA Pareto supplierselection algorithm for minimum the life cycle cost of complexproduct systemrdquo Expert Systems with Applications vol 42 no9 pp 4253ndash4264 2015
[7] T L Saaty ldquoHow to make a decision the analytic hierarchyprocessrdquo European Journal Operation-al Research vol 48 no1 pp 9ndash26 1990
[8] C-L Hwang and K Yoon Multiple Attribute Decision MakingMethods and Applications vol 186 of Lecture Notes in Economicsand Mathematical Systems Springer Heidelberg Germany1981
[9] B Roy ldquoClassement et choix en presence de points de vue mul-tiples (Lamethode ELECTRE)rdquoRevue Francaise drsquoInformatiqueet de Recherche Operationnelle vol 2 no 8 pp 57ndash75 1968
[10] D Tadic D D Milanovic M Misita and B Tadic ldquoNewintegrated approach to the problem of ranking and supplierselection under uncertaintiesrdquo Proceedings of the Institution ofMechanical Engineers Part B Journal of Engineering Manufac-ture vol 225 no 9 pp 1713ndash1724 2011
[11] HAGuvenir andE Erel ldquoMulticriteria inventory classificationusing a genetic algorithmrdquo European Journal of OperationalResearch vol 105 no 1 pp 29ndash37 1998
Mathematical Problems in Engineering 11
[12] A Aleksic M Stefanovic D Tadic and S Arsovski ldquoA fuzzymodel for assessment of organization vulnerabilityrdquo Measure-ment vol 51 no 1 pp 214ndash223 2014
[13] G J Klir and T A Folger Fuzzy Sets Uncertainty and Informa-tion Prentice Hall Upper Saddle River NJ USA 1988
[14] W Pedrycz and F Gomide An Introduction to Fuzzy SetsAnalysis and Design MIT Press Cambridge Mass USA 1997
[15] H-J Zimmermann Fuzzy Set Theorymdashand Its ApplicationsKluwer Academic Boston Mass USA 4th edition 2001
[16] P Kaur and S Chakrabortyb ldquoA new approach to vendorselection problem with impact factor as an indirect measure ofqualityrdquo Journal ofModernMathematics and Statistics vol 1 no1 pp 8ndash14 2007
[17] H M Fazel Zarandi B I Turksen and S Saghiri ldquoSupplychain crisp and fuzzy aspectsrdquo International Journal of AppliedMathematics and Computer Science vol 12 no 3 pp 423ndash4352002
[18] B E Flores andDCWhybark ldquoImplementingmultiple criteriaABC analysisrdquo Journal of OperationsManagement vol 7 no 1-2pp 79ndash85 1987
[19] M-C Yu ldquoMulti-criteria ABC analysis using artificial-intelligence-based classification techniquesrdquo Expert Systemswith Applications vol 38 no 4 pp 3416ndash3421 2011
[20] A Hadi-Vencheh and A Mohamadghasemi ldquoA fuzzy AHP-DEA approach for multiple criteria ABC inventory classifica-tionrdquo Expert Systems with Applications vol 38 no 4 pp 3346ndash3352 2011
[21] J Puente D de la Fuente P Priore and R Pino ldquoAbc classi-fication with uncertain data A fuzzy model vs a probabilisticmodelrdquoApplied Artificial Intelligence vol 16 no 6 pp 443ndash4562002
[22] C-W Chu G-S Liang and C-T Liao ldquoControlling inventoryby combiningABC analysis and fuzzy classificationrdquoComputersamp Industrial Engineering vol 55 no 4 pp 841ndash851 2008
[23] W Ho X Xu and P K Dey ldquoMulti-criteria decision makingapproaches for supplier evaluation and selection a literaturereviewrdquo European Journal of Operational Research vol 202 no1 pp 16ndash24 2010
[24] K Govindan and M B Jepsen ldquoELECTRE a comprehensiveliterature review onmethodologies and applicationsrdquo EuropeanJournal of Operational Research vol 250 no 1 pp 1ndash29 2016
[25] L H Alencar A T de Almeida and D C Morais ldquoAmulticriteria group decision model aggregating the preferencesof decision-makers based on electre methodsrdquo Pesquisa Opera-cional vol 30 no 3 pp 687ndash702 2010
[26] G AMontazer H Q Saremi andM Ramezani ldquoDesign a newmixed expert decision aiding system using fuzzy ELECTRE IIImethod for vendor selectionrdquo Expert Systems with Applicationsvol 36 no 8 pp 10837ndash10847 2009
[27] A H Marbini and M Tavana ldquoAn extension of the ElectreI method for group decision-making under a fuzzy environ-mentrdquo Omega vol 39 no 4 pp 373ndash386 2011
[28] D Tadic A T Gumus S Arsovski A Aleksic and MStefanovic ldquoAn evaluation of quality goals by using fuzzy AHPand fuzzy TOPSIS methodologyrdquo Journal of Intelligent amp FuzzySystems vol 25 no 3 pp 547ndash556 2013
[29] D-Y Chang ldquoApplications of the extent analysis method onfuzzy AHPrdquo European Journal of Operational Research vol 95no 3 pp 649ndash655 1996
[30] J MMerigo andM Casanovas ldquoUsing fuzzy numbers in heavyaggregation operatorsrdquo International Journal of InformationTechnology vol 4 no 4 pp 267ndash272 2008
[31] SM Baas andHKwakernaak ldquoRating and ranking ofmultiple-aspect alternatives using fuzzy setsrdquo Automatica vol 13 no 1pp 47ndash58 1977
[32] D Dubois and H Prade ldquoDecision-making under fuzzinessrdquoin Advances in Fuzzy Set Theory and Applications pp 279ndash302North-Holland Amsterdam Netherlands 1979
[33] J C Pomerol and S Barba-RomeoMulticriteria Decision Man-agement Principles and Practice Kluwer Nijhoff PublishingBoston Mass USA 2000
[34] C-T Chen ldquoExtensions of the TOPSIS for group decision-making under fuzzy environmentrdquo Fuzzy Sets and Systems vol114 no 1 pp 1ndash9 2000
for assessment of preference rating is divided in sub-timeintervals compared to other models where an assessment isperformedduring thewhole time interval [25 27] It is knownthat it is more precise to make assessment in shorter timeinterval
6 Conclusion
Quick and continuous changes occurring in the businessenvironment lead to opening issues in the organization andadaptation in different type of industries One of the mostimportant management tasks is determining of purchasingstrategy for the short-time and long-time period respec-tively This is because purchasing strategy has significantinfluence on successful establishment of global supply chainAs it is known in the global supply chain there are numerouspotential suppliers so that the considered problem is verycomplex
The theoretical contributions of this paper are presentedas follows In the first place conventional assessment ofsuppliers is performed with respect to quality and priceSometimes the other influencing criteria are disregardedThe evaluation criteria are selected according to the literaturereview which is conducted
Secondly it is appropriate to use linguistic terms insteadof numerical values for describing uncertainties into (1) therelative importance of each pair of criteria and (2) criteriavalues which exist in the considered problem Modelling oflinguistic variables is based on the fuzzy set theory Weightsvector of criteria is obtained by applying extent analysisapproach The fuzzy AHP may be considered as suitable forcapturing the vagueness of human thinking style and in thesame time it may be effectively employed for solving theissue of determining criteria weights in the supplier selectionproblem
The large number of potential suppliers in global supplychain enhances the complexity of the process of supplierselection In that manner it is necessary before delivery ofthe process of selection to deliver the process of suppliersrsquoclassification This may be denoted as the third contributionof the paper since a new fuzzymulticriteriaABC classificationof suppliers is proposed The effectiveness of the proposedalgorithm is tested using real-world data of 42 suppliers thatoperate in different geographical locations all over the worldThe classification obtained using the algorithm is in goodagreement with the judgment of the management team of theconsidered global supply chain
The fourth contribution makes the ranking of the suppli-ers denoted as group A The ranking is conducted by usingthe fuzzy ELECTRE proposed in this paper Modification ofELECTRE may be presented as (1) determination of sets onconcordance and sets of discordance [31] and (2) calculationof coefficient of discordance
Beside abovementioned various advantages the proposedmodel has some constraints It may be seen that there is thelack of research foundation in the literature which relatesto selection of criteria that are used for suppliersrsquo selectionin building and civil engineering industry Those criteriamay vary from constrains of supplierrsquos capacity aggregated
quality duty taxes and risk factors to political stability andso forth These extensions could undoubtedly increase thecomputational complexities The second constraint relates toABC method since it may be deployed only if 119896 is less orequal to 3 ELECTRE should be expanded with more criteriain order to determine purchasing strategy for long time andin the same time to establish partnership with supplier
This paper focuses on the complex circumstances alarge number of suppliers from different countries multipledecision makers involved in decision process and multipleuncertainties The established mathematical model can helpboth practitioners and researchers to further utilize anddeploy the purchasing strategy in global supply chain
Competing Interests
The authors declare that they have no competing interests
References
[1] ISO 90012015 Quality management systemsmdashRequirements[2] G Bruno E Esposito A Genovese andM Simpson ldquoApplying
supplier selection methodologies in a multi-stakeholder envi-ronment a case study and a critical assessmentrdquo Expert Systemswith Applications vol 43 pp 271ndash285 2016
[3] A C Trapp and J Sarkis ldquoIdentifying robust portfolios of sup-pliers a sustainability selection and development perspectiverdquoJournal of Cleaner Production vol 112 part 3 pp 2088ndash21002016
[4] P Amorim E Curcio B Almada-Lobo A P Barbosa-Povoaand I E Grossmann ldquoSupplier selection in the processed foodindustry under uncertaintyrdquo European Journal of OperationalResearch vol 252 no 3 pp 801ndash814 2016
[5] P H Andersen C Ellegaard andH Kragh ldquoIrsquom yourman howsuppliers gain strategic status in buying companiesrdquo Journal ofPurchasing and Supply Management vol 22 no 2 pp 72ndash812014
[6] B Du S Guo X Huang Y Li and J Guo ldquoA Pareto supplierselection algorithm for minimum the life cycle cost of complexproduct systemrdquo Expert Systems with Applications vol 42 no9 pp 4253ndash4264 2015
[7] T L Saaty ldquoHow to make a decision the analytic hierarchyprocessrdquo European Journal Operation-al Research vol 48 no1 pp 9ndash26 1990
[8] C-L Hwang and K Yoon Multiple Attribute Decision MakingMethods and Applications vol 186 of Lecture Notes in Economicsand Mathematical Systems Springer Heidelberg Germany1981
[9] B Roy ldquoClassement et choix en presence de points de vue mul-tiples (Lamethode ELECTRE)rdquoRevue Francaise drsquoInformatiqueet de Recherche Operationnelle vol 2 no 8 pp 57ndash75 1968
[10] D Tadic D D Milanovic M Misita and B Tadic ldquoNewintegrated approach to the problem of ranking and supplierselection under uncertaintiesrdquo Proceedings of the Institution ofMechanical Engineers Part B Journal of Engineering Manufac-ture vol 225 no 9 pp 1713ndash1724 2011
[11] HAGuvenir andE Erel ldquoMulticriteria inventory classificationusing a genetic algorithmrdquo European Journal of OperationalResearch vol 105 no 1 pp 29ndash37 1998
Mathematical Problems in Engineering 11
[12] A Aleksic M Stefanovic D Tadic and S Arsovski ldquoA fuzzymodel for assessment of organization vulnerabilityrdquo Measure-ment vol 51 no 1 pp 214ndash223 2014
[13] G J Klir and T A Folger Fuzzy Sets Uncertainty and Informa-tion Prentice Hall Upper Saddle River NJ USA 1988
[14] W Pedrycz and F Gomide An Introduction to Fuzzy SetsAnalysis and Design MIT Press Cambridge Mass USA 1997
[15] H-J Zimmermann Fuzzy Set Theorymdashand Its ApplicationsKluwer Academic Boston Mass USA 4th edition 2001
[16] P Kaur and S Chakrabortyb ldquoA new approach to vendorselection problem with impact factor as an indirect measure ofqualityrdquo Journal ofModernMathematics and Statistics vol 1 no1 pp 8ndash14 2007
[17] H M Fazel Zarandi B I Turksen and S Saghiri ldquoSupplychain crisp and fuzzy aspectsrdquo International Journal of AppliedMathematics and Computer Science vol 12 no 3 pp 423ndash4352002
[18] B E Flores andDCWhybark ldquoImplementingmultiple criteriaABC analysisrdquo Journal of OperationsManagement vol 7 no 1-2pp 79ndash85 1987
[19] M-C Yu ldquoMulti-criteria ABC analysis using artificial-intelligence-based classification techniquesrdquo Expert Systemswith Applications vol 38 no 4 pp 3416ndash3421 2011
[20] A Hadi-Vencheh and A Mohamadghasemi ldquoA fuzzy AHP-DEA approach for multiple criteria ABC inventory classifica-tionrdquo Expert Systems with Applications vol 38 no 4 pp 3346ndash3352 2011
[21] J Puente D de la Fuente P Priore and R Pino ldquoAbc classi-fication with uncertain data A fuzzy model vs a probabilisticmodelrdquoApplied Artificial Intelligence vol 16 no 6 pp 443ndash4562002
[22] C-W Chu G-S Liang and C-T Liao ldquoControlling inventoryby combiningABC analysis and fuzzy classificationrdquoComputersamp Industrial Engineering vol 55 no 4 pp 841ndash851 2008
[23] W Ho X Xu and P K Dey ldquoMulti-criteria decision makingapproaches for supplier evaluation and selection a literaturereviewrdquo European Journal of Operational Research vol 202 no1 pp 16ndash24 2010
[24] K Govindan and M B Jepsen ldquoELECTRE a comprehensiveliterature review onmethodologies and applicationsrdquo EuropeanJournal of Operational Research vol 250 no 1 pp 1ndash29 2016
[25] L H Alencar A T de Almeida and D C Morais ldquoAmulticriteria group decision model aggregating the preferencesof decision-makers based on electre methodsrdquo Pesquisa Opera-cional vol 30 no 3 pp 687ndash702 2010
[26] G AMontazer H Q Saremi andM Ramezani ldquoDesign a newmixed expert decision aiding system using fuzzy ELECTRE IIImethod for vendor selectionrdquo Expert Systems with Applicationsvol 36 no 8 pp 10837ndash10847 2009
[27] A H Marbini and M Tavana ldquoAn extension of the ElectreI method for group decision-making under a fuzzy environ-mentrdquo Omega vol 39 no 4 pp 373ndash386 2011
[28] D Tadic A T Gumus S Arsovski A Aleksic and MStefanovic ldquoAn evaluation of quality goals by using fuzzy AHPand fuzzy TOPSIS methodologyrdquo Journal of Intelligent amp FuzzySystems vol 25 no 3 pp 547ndash556 2013
[29] D-Y Chang ldquoApplications of the extent analysis method onfuzzy AHPrdquo European Journal of Operational Research vol 95no 3 pp 649ndash655 1996
[30] J MMerigo andM Casanovas ldquoUsing fuzzy numbers in heavyaggregation operatorsrdquo International Journal of InformationTechnology vol 4 no 4 pp 267ndash272 2008
[31] SM Baas andHKwakernaak ldquoRating and ranking ofmultiple-aspect alternatives using fuzzy setsrdquo Automatica vol 13 no 1pp 47ndash58 1977
[32] D Dubois and H Prade ldquoDecision-making under fuzzinessrdquoin Advances in Fuzzy Set Theory and Applications pp 279ndash302North-Holland Amsterdam Netherlands 1979
[33] J C Pomerol and S Barba-RomeoMulticriteria Decision Man-agement Principles and Practice Kluwer Nijhoff PublishingBoston Mass USA 2000
[34] C-T Chen ldquoExtensions of the TOPSIS for group decision-making under fuzzy environmentrdquo Fuzzy Sets and Systems vol114 no 1 pp 1ndash9 2000
[12] A Aleksic M Stefanovic D Tadic and S Arsovski ldquoA fuzzymodel for assessment of organization vulnerabilityrdquo Measure-ment vol 51 no 1 pp 214ndash223 2014
[13] G J Klir and T A Folger Fuzzy Sets Uncertainty and Informa-tion Prentice Hall Upper Saddle River NJ USA 1988
[14] W Pedrycz and F Gomide An Introduction to Fuzzy SetsAnalysis and Design MIT Press Cambridge Mass USA 1997
[15] H-J Zimmermann Fuzzy Set Theorymdashand Its ApplicationsKluwer Academic Boston Mass USA 4th edition 2001
[16] P Kaur and S Chakrabortyb ldquoA new approach to vendorselection problem with impact factor as an indirect measure ofqualityrdquo Journal ofModernMathematics and Statistics vol 1 no1 pp 8ndash14 2007
[17] H M Fazel Zarandi B I Turksen and S Saghiri ldquoSupplychain crisp and fuzzy aspectsrdquo International Journal of AppliedMathematics and Computer Science vol 12 no 3 pp 423ndash4352002
[18] B E Flores andDCWhybark ldquoImplementingmultiple criteriaABC analysisrdquo Journal of OperationsManagement vol 7 no 1-2pp 79ndash85 1987
[19] M-C Yu ldquoMulti-criteria ABC analysis using artificial-intelligence-based classification techniquesrdquo Expert Systemswith Applications vol 38 no 4 pp 3416ndash3421 2011
[20] A Hadi-Vencheh and A Mohamadghasemi ldquoA fuzzy AHP-DEA approach for multiple criteria ABC inventory classifica-tionrdquo Expert Systems with Applications vol 38 no 4 pp 3346ndash3352 2011
[21] J Puente D de la Fuente P Priore and R Pino ldquoAbc classi-fication with uncertain data A fuzzy model vs a probabilisticmodelrdquoApplied Artificial Intelligence vol 16 no 6 pp 443ndash4562002
[22] C-W Chu G-S Liang and C-T Liao ldquoControlling inventoryby combiningABC analysis and fuzzy classificationrdquoComputersamp Industrial Engineering vol 55 no 4 pp 841ndash851 2008
[23] W Ho X Xu and P K Dey ldquoMulti-criteria decision makingapproaches for supplier evaluation and selection a literaturereviewrdquo European Journal of Operational Research vol 202 no1 pp 16ndash24 2010
[24] K Govindan and M B Jepsen ldquoELECTRE a comprehensiveliterature review onmethodologies and applicationsrdquo EuropeanJournal of Operational Research vol 250 no 1 pp 1ndash29 2016
[25] L H Alencar A T de Almeida and D C Morais ldquoAmulticriteria group decision model aggregating the preferencesof decision-makers based on electre methodsrdquo Pesquisa Opera-cional vol 30 no 3 pp 687ndash702 2010
[26] G AMontazer H Q Saremi andM Ramezani ldquoDesign a newmixed expert decision aiding system using fuzzy ELECTRE IIImethod for vendor selectionrdquo Expert Systems with Applicationsvol 36 no 8 pp 10837ndash10847 2009
[27] A H Marbini and M Tavana ldquoAn extension of the ElectreI method for group decision-making under a fuzzy environ-mentrdquo Omega vol 39 no 4 pp 373ndash386 2011
[28] D Tadic A T Gumus S Arsovski A Aleksic and MStefanovic ldquoAn evaluation of quality goals by using fuzzy AHPand fuzzy TOPSIS methodologyrdquo Journal of Intelligent amp FuzzySystems vol 25 no 3 pp 547ndash556 2013
[29] D-Y Chang ldquoApplications of the extent analysis method onfuzzy AHPrdquo European Journal of Operational Research vol 95no 3 pp 649ndash655 1996
[30] J MMerigo andM Casanovas ldquoUsing fuzzy numbers in heavyaggregation operatorsrdquo International Journal of InformationTechnology vol 4 no 4 pp 267ndash272 2008
[31] SM Baas andHKwakernaak ldquoRating and ranking ofmultiple-aspect alternatives using fuzzy setsrdquo Automatica vol 13 no 1pp 47ndash58 1977
[32] D Dubois and H Prade ldquoDecision-making under fuzzinessrdquoin Advances in Fuzzy Set Theory and Applications pp 279ndash302North-Holland Amsterdam Netherlands 1979
[33] J C Pomerol and S Barba-RomeoMulticriteria Decision Man-agement Principles and Practice Kluwer Nijhoff PublishingBoston Mass USA 2000
[34] C-T Chen ldquoExtensions of the TOPSIS for group decision-making under fuzzy environmentrdquo Fuzzy Sets and Systems vol114 no 1 pp 1ndash9 2000