An ntegrated fuzzy MCDM approach for suppler evaluaton and selecton E. Ertugrul Karsak * and Mehtap Dursun Industral Engneerng Department, Galatasaray Unversty, Ortakoy, Istanbul 34357, Turkey 2015 A fuzzy mult-crtera group decson makng approach that makes use of qualty functon deployment (QFD), fuson of fuzzy nformaton and 2-tuple lngustc representaton model s developed for suppler selecton. The proposed methodology seeks to establsh the relevant suppler assessment crtera whle also consderng the mpacts of nner dependence among them. Two nterrelated house of qualty matrces are constructed, and fuson of fuzzy nformaton and 2-tuple lngustc representaton model are employed to compute the weghts of suppler selecton crtera and subsequently the ratngs of supplers. The proposed method s apt to manage non-homogeneous nformaton n a decson settng wth multple nformaton sources. The decson framework presented n ths paper employs ordered weghted averagng (OWA) operator, and the aggregaton process s based on combnng nformaton by means of fuzzy sets on a basc lngustc term set. The proposed framework s llustrated through a case study conducted n a prvate hosptal n Istanbul. Keywords: suppler selecton; qualty functon deployment; mult-crtera decson makng; decson support; fuzzy methods; 2-tuple lngustc representaton 1. Introducton A supply chan s composed of a complex sequence of processng stages, rangng from raw materals supples, parts manufacturng, components and end-products assemblng, to the delvery of end products (Wu & Olson, 2008). In the context of supply chan management, suppler selecton decson s consdered as one of the key ssues faced by operatons and purchasng managers to reman compettve. Suppler selecton and management can be appled to a varety of supplers throughout a product s lfe cycle from ntal raw materal acquston to end-of-lfe servce provders. Thus, the breadth and dversty of supplers make the process even more cumbersome (Ba & Sarks, 2010). 1
As reported n De Boer et al. (2001), suppler selecton process has dfferent phases such as problem defnton, decson crtera formulaton, pre-qualfcaton of potental supplers, and makng a fnal choce. The qualty of the fnal choce largely depends on the qualty of all the steps nvolved n the selecton process. Due to shortened product lfe cycles, the search for new supplers s a contnuous prorty for companes n order to upgrade the varety and typology of ther products range. Decsonmakers are facng a wde varety of purchasng stuatons that lead to dfferent decsons (Assaou et al., 2007). Thus, the frst step n suppler selecton process nvolves determnng the ultmate problem and fndng out exactly what we want to acheve by selectng a suppler. Suppler selecton decsons are complcated by the fact that varous crtera must be consdered n decson makng process. The analyss of suppler selecton crtera has been the focus of many research works snce the 1960 s. In a study whch has become a reference for the majorty of papers on suppler selecton, Dckson (1966) dentfed 23 suppler attrbutes that managers consder when choosng a suppler. Today s logstcs envronment requres a low number of supplers as t s very dffcult to manage a hgh number (Assaou et al., 2007). Pre-qualfcaton of potental supplers s the process of reducng the set of all supplers to a smaller set of acceptable supplers. Therefore, pre-qualfcaton s a sortng process rather than a rankng process (De Boer et al., 2001). Most of the research studes n the area of suppler selecton have focused on determnng the best suppler to supply all needed tems. At the fnal choce stage, the ultmate suppler s dentfed whle consderng the system s constrants and takng nto account varous quanttatve and/or qualtatve crtera. Accordng to the vast lterature on suppler selecton, the followng propertes need to be consdered whle resolvng the suppler selecton problem (Chen et al., 2006). Frst, the suppler selecton process requres consderng multple conflctng crtera. Second, several decson-makers are oftentmes nvolved n the decson process. Thrd, decson-makng s often nfluenced by uncertanty n practce. Wth ts need to trade-off multple crtera exhbtng vagueness and mprecson, suppler selecton s a hghly mportant mult-crtera decson makng (MCDM) problem. The classcal MCDM methods that consder determnstc or random processes cannot effectvely address decson problems ncorporatng mprecse and lngustc nformaton. Fuzzy set theory s one of the effectve tools to deal wth uncertanty and vagueness. The objectve of ths study s to propose a fuzzy mult-crtera group decson makng approach based on the qualty functon deployment (QFD) methodology, fuson of fuzzy 2
nformaton, and 2-tuple lngustc representaton model for suppler selecton. In suppler selecton process, the company s ultmate am s to have access to supplers that ensure a certan qualty standard n terms of the characterstcs of the purchased products or servces (Bevlacqua et al., 2006). Achevng these objectves depends largely on consderng not only the relatonshps between purchased product features and suppler assessment crtera, but also the relatonshps between suppler assessment crtera dsregardng the unrealstc ndependence assumpton. Thus, constructng a house of qualty (HOQ), whch enables the relatonshps among the purchased product features and suppler assessment crtera as well as nner dependence of suppler assessment crtera to be consdered, s key to dentfy how well each suppler characterstc succeeds n meetng the requrements establshed for the product beng purchased. The proposed methodology ntally dentfes the features that the purchased product should possess n order to satsfy the company s needs, and then t seeks to establsh the relevant suppler assessment crtera. Fuson of fuzzy nformaton approach s used to manage nformaton assessed usng dfferent lngustc scales. In ths context, frst the nonhomogeneous fuzzy nformaton s made unform usng a lngustc term set as the unform representaton base, called basc lngustc term set (BLTS). Ths approach enables the sources that partcpate n the decson process express ther judgments by means of nformaton of a dfferent nature accordng to ther preferences (Herrera et al., 2000). The collectve performance values of the alternatves that are also fuzzy sets on BLTS are obtaned by means of an aggregaton operator. In ths paper, ordered weghted averagng (OWA) operator s employed as the aggregaton operator. Ths operator provdes an aggregaton whch les n between the and requrng all the crtera to be satsfed, and the or requrng at least one crteron to be satsfed. OWA operator dffers from the classcal weghted average n that coeffcents are bute but rather to an ordered poston. The aggregaton process s based on combnng nformaton by means of fuzzy sets on BLTS. Then, the collectve preference values are transformed nto lngustc 2-tuples whch enable to calculate both the weghts of suppler selecton crtera and the ratngs of supplers usng the QFD methodology that ncorporates nterrelated HOQ matrces. The 2-tuple fuzzy lngustc approach nherts the exstng characters of fuzzy lngustc assessment, and t also rectfes the problem of loss of nformaton of other fuzzy lngustc approaches (Herrera-Vedma et al., 2004). 3
The rest of the paper s organzed as follows: The followng secton presents a bref lterature revew on suppler selecton. In Secton 3, a concse treatment of the basc concepts of QFD s presented. Secton 4 and Secton 5 delneate the fuson of fuzzy nformaton approach and 2-tuple fuzzy lngustc representaton model, respectvely. Secton 6 presents the developed decson makng approach and provdes ts stepwse representaton. The mplementaton of the proposed framework for evaluatng medcal supplers of a prvate hosptal n Istanbul s provded n Secton 7. Fnally, concludng observatons and drectons for future research are gven n the last secton. 2. Lterature revew Suppler evaluaton s a management decson-makng process that addresses how organzatons select strategc supplers to enhance ther compettve advantage. Earler studes on suppler selecton focused on dentfyng the crtera used to select supplers. Dckson (1966) conducted one of the earlest works on suppler selecton and dentfed 23 suppler attrbutes that managers consder when choosng a suppler. Among these crtera, qualty, ontme delvery, and performance hstory were noted as the most sgnfcant ones. Another study conducted by Lehmann and O Shaughnessy (1974) found that the key crtera generally clamed to affect suppler selecton decsons were prce, reputaton of suppler, relablty, and delvery. Weber et al. (1991) classfed the artcles publshed between 1966 and 1990 accordng to the consdered crtera. Based on 74 papers, they concluded that suppler selecton s a mult-crtera problem, and prce, delvery, qualty, and producton faclty and locaton are the most frequently employed crtera. In lght of the mult-crtera nature of suppler selecton problem, t would appear that the applcaton of MCDM technques to the problem s a frutful area of research. Such technques would allow purchasers to systematcally examne the trade-offs among varous crtera when selectng specfc supplers. As frms become nvolved n strategc partnershps wth ther supplers, a new set of suppler selecton crtera, termed as soft crtera, need to be consdered n suppler selecton decsons. These crtera are subjectve factors that are dffcult to quantfy. Fuzzy set theory appears as an effectve tool to deal wth uncertanty nherent n suppler selecton process. Ths secton wll brefly revew the research works on suppler selecton that employ fuzzy MCDM technques and QFD-based methods. Several authors have used fuzzy MCDM technques such as fuzzy analytc herarchy process (AHP), fuzzy analytc network process (ANP), fuzzy technque for order preference 4
by smlarty to deal soluton (TOPSIS), fuzzy mult-crtera optmzaton and compromse soluton (VIKOR), fuzzy preference-rankng-organzaton-method-for-enrchment-ofevaluaton (PROMETHEE), fuzzy sutablty ndex, 2-tuple fuzzy lngustc representaton model, and grey approach. Bevlacqua and Petron (2002) proposed a methodology for suppler selecton based on the use of fuzzy sutablty ndex. Bottan and Rzz (2005) addressed the problem of suppler selecton n an e-procurement envronment. Fuzzy AHP was employed to determne the most vable suppler. Beneftng from TOPSIS, Chen et al. (2006) developed a methodology for solvng suppler selecton problems n fuzzy envronment. Chan and Kumar (2007) dentfed the decson crtera ncludng rsk factors for the development of an effcent system for global suppler selecton. Fuzzy extended AHP based methodology was used n the selecton procedure. Chan et al. (2008) employed a fuzzy modfed AHP approach to select the best global suppler. Wang (2008) used 2-tuple fuzzy lngustc representaton model to determne the overall suppler performance wth dynamc supply behavors. Chen and Wang (2009) provded an ntegrated VIKOR framework under fuzzy envronment for determnng the most approprate suppler and compromse soluton from a number of potental supplers n nformaton system/nformaton technology outsourcng project. Kavta et al. (2009) extended TOPSIS for nterval-valued ntutonstc fuzzy data. Wang (2010) developed a model based on 2-tuple fuzzy lngustc representaton model to evaluate the suppler performance. Vnodh et al. (2011) utlzed fuzzy ANP for suppler selecton process and presented a case study n an electroncs swtches manufacturng company. Recently, Baskaran et al. (2012) evaluated the Indan textle and clothng ndustry supplers employng grey approach. The sustanablty crtera are consdered n the evaluaton process. Chu and Varma (2012) suggested a herarchcal MCDM model under fuzzy envronment to evaluate and select supplers. Govndan et al. (2013) employed fuzzy TOPSIS for suppler selecton consderng envronmental, socal, and economc aspects of suppler fuzzy herarchcal TOPSIS for evaluatng supplers n detergent producton ndustry. Lately, Junor et al. (2014) appled fuzzy TOPSIS and fuzzy AHP to suppler selecton problem and compared the obtaned results. Integrated MCDM technques based approaches have also been developed to select the most approprate suppler. Haq and Kannan (2006) proposed an ntegrated suppler selecton and mult-echelon dstrbuton nventory model utlzng fuzzy AHP and genetc algorthm (GA). Sevkl et al. (2008) developed a suppler selecton approach that ntegrates AHP and fuzzy lnear programmng. Yang et al. (2008) ntroduced a fuzzy MADM method for suppler selecton problem. Frst, they used nterpretve structural modelng to obtan the relatonshps 5
among the sub-crtera. Then, they appled fuzzy AHP to compute the relatve weghts for each crteron. Fnally, they employed fuzzy ntegral to obtan the fuzzy synthetc performance and determned the rank order of alternatve supplers. Lang et al. (2009) presented a herarchcal suppler evaluaton framework combnng ANP and Choquet ntegral. Razm et al. (2009) proposed a hybrd model based on ANP to evaluate and select suppler under fuzzy envronment. The proposed approach was enhanced wth a non-lnear programmng model to elct weghts of comparsons from comparson matrces n the ANP structure. Ordoobad (2010) combned Taguch loss functon and AHP to develop a decson makng model for the selecton of the approprate suppler. Ravndran et al. (2010) ntroduced two-phase mult-crtera suppler selecton models ncorporatng suppler rsk. In phase 1, ntal set of suppler alternatves was reduced to a smaller set employng AHP. In phase 2, order quanttes are allocated among the supplers usng a mult-objectve optmzaton model. Chen and Yang (2011) combned constraned fuzzy AHP and fuzzy TOPSIS for suppler selecton. Lao and Kao (2011) proposed an ntegrated fuzzy TOPSIS and mult-choce goal programmng model to solve mult-sourcng et al. (2013) proposed a structured decson model for evaluatng supplers by ntegratng fuzzy AHP and grey relatonal analyss. Rodrguez et al. (2013) proposed a combnaton of AHP and TOPSIS n fuzzy envronment for the selecton of customzed equpment supplers. Shdpour et al. (2013) ntegrated fuzzy AHP, TOPSIS and mult-objectve lnear programmng to determne the most approprate confguraton product desgn, assembly process, and suppler of components n the new product development process. In a recent work, Sngh (2014) combned TOPSIS and mxed lnear nteger programmng for suppler selecton and order allocaton problem. Hasheman et al. (2014) ntegrated fuzzy AHP and fuzzy PROMETHEE for suppler evaluaton. Fuzzy AHP was used to determne the weght of the crtera and fuzzy PROMETHEE was employed for obtanng the fnal rankng of supplers. Lately, a few researchers have employed QFD n suppler selecton. Bevlacqua et al. (2006) constructed a house of qualty to dentfy the features that the purchased product should possess n order to satsfy the customers requrements. Then, the potental supplers were evaluated aganst the relevant suppler assessment crtera. N et al. (2007) developed a suppler selecton methodology based on QFD and data mnng technques. Amn and Razm (2009) presented a two-phase decson model for suppler management ncludng suppler selecton, evaluaton, and development. In the frst phase, QFD model was ntegrated wth a quanttatve model ntroduced by Ng (2008) to account for both qualtatve and quanttatve 6
crtera to select the approprate nternet servce provders. In the second phase, the selected nternet servce provders were evaluated from customer, performance, and competton perspectves. Bhattacharya et al. (2010) ntegrated AHP wth QFD to rank and subsequently select canddate-supplers under multple, conflctng nature crtera envronment. Ho et al. (2011) developed a combned QFD and AHP approach to measure the performance of alternatve supplers. Soroor et al. (2012) proposed a hybrd model, whch mplements fuzzy AHP and QFD to provde an ntellgent soluton to evaluate supplers. In a recent work, Alnezad et al. (2013) proposed a methodology for selectng the vendors n pharmaceutcal company. QFD was employed for selectng the vendors, where fuzzy AHP was used to determne the mportance weghts n QFD. Although prevously reported studes developed approaches for suppler selecton process, further studes are necessary to ntegrate mprecse nformaton concernng the mportance of purchased product features, relatonshp between purchased product features and suppler assessment crtera, and dependences between suppler assessment crtera nto the analyss. A sound decson ad for suppler selecton should also am to rectfy the problem of loss of nformaton when computng wth lngustc varables. In ths paper, a fuzzy multcrtera group decson makng approach based on QFD, fuson of fuzzy nformaton, and 2- tuple lngustc representaton model s developed. The weghts of suppler selecton crtera and the fnal rankng of supplers are obtaned beneftng from QFD methodology usng nterrelated HOQ matrces. The proposed approach uses the fuson method to manage nformaton assessed usng mult-granular lngustc nformaton. The non-homogeneous nformaton provded by decson-makers s unfed nto a specfc lngustc doman, named BLTS. The collectve performance values that are also fuzzy sets on BLTS are obtaned va OWA operator. Then, the collectve preference values are transformed nto lngustc 2-tuples. 3. Qualty functon deployment Qualty functon deployment (QFD) was frst mplemented at the Kobe Shpyards of Mtsubsh Heavy Industres Ltd. n 1972. After the frst mplementaton, Toyota and ts supplers further developed QFD n order to address desgn problems assocated wth automoble manufacturng (Iranmanesh & Thomson, 2008). Even though ts applcatons were followed by successful mplementatons throughout Japan, QFD was brought to the attenton of the U.S. frms ten years later. 7
In order to reman compettve n the global market, the mprovement of mature-perod product n a short tme and at a mnmum cost s one of the key factors. As far as the decsons for mature-perod product mprovement are concerned, the use of QFD has ganed extensve nternatonal support for helpng decson-makng n product plannng and mprovement (L et al., 2011). QFD s a crucal product development method dedcated to translatng customer requrements nto actvtes to develop products and servces (Carnevell & Mguel, 2008). QFD focuses on delverng value by takng nto account the customer needs, and then deployng ths nformaton throughout the development process (Karsak, 2004). It ensures a hgher qualty level that meets customer expectatons throughout each stage of product plannng. QFD allows for the company to allocate resources and to coordnate sklls based on customer needs, and thus, helps to decrease producton costs and reduce cycle tme. It evaluates the necessary decsons for change and development at the begnnng of the product desgn phase and mnmzes the correctons durng the entre development process (Karsak et al., 2003). QFD usually requres four matrces each correspondng to a stage of the product development cycle. These are product plannng, part deployment, process plannng, and producton/operaton plannng matrces, respectvely. The product plannng matrx translates customer needs (CNs) nto techncal attrbutes (TAs); the part deployment matrx translates mportant TAs nto product/part characterstcs; the process plannng matrx translates mportant product/part characterstcs nto manufacturng operatons; the producton/operaton plannng matrx translates mportant manufacturng operatons nto day-to-day operatons and controls (Shllto, 1994). In ths paper, we focus on the frst and the most wdely used of the four matrces, also called the house of qualty (HOQ). Relatonshps between CNs and TAs and among the TAs are defned by answerng a specfc queston correspondng to each cell n HOQ. The HOQ contans seven elements as shown n Fgure 1. [Insert Fgure 1 about here] The elements of the HOQ shown n Fgure 1 can be brefly descrbed as follows: (1) CNs: They are also known as customer attrbutes, customer requrements or demanded qualty. The ntal step n constructng the HOQ ncludes determnng, clarfyng, and specfyng the customer needs. As the ntal nput for the HOQ, the CNs hghlght the product 8
characterstcs that should be pad attenton to. The purpose of ths step s to capture the voce of the customer. (2) TAs: TAs are also named as desgn requrements, product features, engneerng attrbutes, engneerng characterstcs or substtute qualty characterstcs. They are the product requrements that relate drectly to the customer requrements. TAs descrbe the product n the language of the engneer; therefore, are sometmes referred to as the voce of the company. They are used to determne how well the company satsfes the CNs (Karsak et al., 2003). (3) Importance of CNs: Snce the collected and organzed data from the customers usually contan too many needs to deal wth smultaneously, they must be rated. The company should trade off one beneft aganst another, and work on the most mportant needs whle elmnatng relatvely unmportant ones (Karsak et al., 2003). (4) Relatonshps between CNs and TAs: The relatonshp matrx ndcates to what extent each TA affects each CN and s placed n the body of the HOQ (Alptekn & Karsak, 2011). In ths paper, lngustc varables are used to denote the relatonshps between CNs and TAs. (5) Compettve assessment matrx: Understandng how customers rate the competton can be a tremendous compettve advantage. The requred nformaton can be acqured through askng the customers to rate the performance of the company s and ts compettors products for each CN usng a predetermned scale. (6) Inner dependence among the TAs: The HOQ s roof matrx s used to specfy the nner dependences among TAs. Ths enables to account for the correlatons between TAs, whch n turn facltates nformed trade-offs. (7) Overall prortes of the TAs and addtonal goals: Here, the results obtaned from precedng steps are used to calculate a fnal rank order of TAs. 4. Fuson of fuzzy nformaton Fuson approach of fuzzy nformaton s proposed by Herrera et al. (2000). Ths approach s used to manage nformaton assessed usng dfferent lngustc scales n a decson makng problem wth multple nformaton sources. It enables the sources that partcpate n the decson process express ther judgments by means of non-homogeneous nformaton accordng to ther preferences (Herrera et al., 2000). In any lngustc approach, a crucal task for dealng wth lngustc nformaton s to determne the granularty of uncertanty,.e., the level of dscrmnaton among dfferent counts of uncertanty (Herrera and Martnez, 2000a). In group decson makng problems, dependng on ther cultural and educatonal backgrounds, 9
experts can have dfferent uncertanty degrees n qualfyng a phenomenon. Thus, the lngustc term set chosen to provde ther knowledge wll have more or less terms. When dfferent experts have dfferent uncertanty degrees over the alternatves, then the lngustc nformaton that manages the problem s assessed n dfferent lngustc domans wth dfferent granularty (Herrera and Martínez, 2001). The lngustc term set wth small cardnalty s useful for experts to express ther clear assessment nformaton whereas the lngustc term set wth large cardnalty presents experts more choces to express ther assessment nformaton. Hence, the research on group decson makng problems wth multgranularty lngustc nformaton s essental n modelng real world problems (Jang et al., 2008). Fuson approach of fuzzy nformaton conssts of obtanng a collectve performance profle on the alternatves accordng to the ndvdual performance profles. It s performed n two phases (Herrera et al., 2000):. Makng the nformaton unform,. Computng the collectve performance values. 4.1. Makng the nformaton unform The performance values expressed usng mult-granularty lngustc term sets are converted (under a transformaton functon) nto a specfc lngustc doman, whch s a BLTS denoted as S T, chosen so as not to mpose useless precson to the orgnal evaluatons and to allow an approprate dscrmnaton of the ntal performance values. The transformaton functon s defned as follows (Herrera et al., 2000): Let A = l l,..., l } and S = { s s,..., } be two lngustc term sets, such that g p. 0, 1 p T 0, 1 s g Then, the transformaton functon, τ AS T, s defned as τ τ γ AST AST k = : A F ( S ), ( l ) = {( sk, γ k )/ k { 0,1,..., g }, max mn{ μ ( y), μ ( y) } y T l sk l A, (1) where F ( S T ) s the set of fuzzy sets defned n S T, and μ (y) and μ (y) are the membershp functons of the fuzzy sets assocated wth the terms l and s k, respectvely. 10 l s k
The transformaton functon s also approprate to convert the standardzed fuzzy assessments nto a BLTS (Chuu, 2009). The max-mn operaton has been chosen n the defnton of the transformaton functon snce t s a classcal tool to set the matchng degree between fuzzy sets (Herrera et al., 2000). 4.2. Computng the collectve performance values The nput nformaton, whch was denoted by means of fuzzy sets, s expressed on a BLTS by the abovementoned transformaton functon. For each alternatve, a collectve performance value s obtaned by means of the aggregaton of the aforementoned fuzzy sets on the BLTS that represents the ndvdual performance values assgned to the altern nformaton source (Herrera et al., 2000). Ths collectve performance value s a new fuzzy set defned on a BLTS. Ths paper employs ordered weghted averagng (OWA) operator, ntally proposed by Yager (1988), as the aggregaton operator. Ths operator provdes aggregatons whch le between two extreme cases of MCDM problems that lead to the use of and and or operators to combne the crtera functon. OWA operator encompasses several operators snce t can mplement dfferent aggregaton rules by changng the order weghts. The OWA operator provdes a unfed framework for decson makng under uncertanty, n whch dfferent decson crtera such as maxmax, maxmn, equally lkely (Laplace) and Hurwcz crtera are characterzed by dfferent OWA operator weghts. To apply the OWA operator for decson makng, a crucal ssue s to determne ts weghts, whch can be accomplshed as follows: Let A { a a,..., } = 1, 2 a n be a set of values to be aggregated, OWA operator F s defned as T n F( a, a,..., a = wb = w b (2) 1 2 n ) = 1 where w = { w w,..., } s a weghtng vector, such that [ 0,1] 1, 2 w n the assocated ordered value vector where b b s the th largest value n A. w and w = 1, and b s The weghts of the OWA operator are calculated usng fuzzy lngustc quantfers, whch for a non-decreasng relatve quantfer Q, are gven by 11
( / n) Q( ( 1) / n), = 1 n w = Q,..., (3) The non-decreasng relatve quantfer, Q, s defned as (Herrera et al., 2000) Q ( y) 0 y a = b a 1, y < a,, a y b,, y > b, (4) wth a, b, y [ 0,1], and Q (y) ndcatng the degree to whch the proporton y s compatble wth the meanng of the quantfer t represents. Some non-decreasng relatve quantfers are dentfed by terms most, at least half, and as many as possble, wth parameters ( a, b) are (.3,0.8)(, 0,0.5), 0 and ( 0.5,1), respectvely. 5. 2-tuple fuzzy lngustc representaton model The 2-tuple lngustc model that was presented by Herrera and Martínez (2000b) s based on the concept of symbolc translaton. It s used for representng the lngustc assessment nformaton by means of a 2-tuple that s composed of a lngustc term and a number. It can be denoted as (,α ) s where s represents the lngustc label of the predefned lngustc term set S T, and α s a numercal value representng the symbolc translaton (Fan et al., 2009). The man advantages of ths representaton can be summarzed as the contnuous treatment of the lngustc doman, and the mnmzaton of the loss of nformaton and thus the lack of precson. The process of comparson between lngustc 2-tuples s carred out accordng to an ordnary lexcographc order as follows (Herrera & Martínez, 2001): Let r = ( ) and ( ) 1 s c,α 1 2 s d,α 2 If c < d then r 1 s smaller than r 2 ; If c = d then r = be two lngustc varables represented by 2-tuples. o If α 1 = α 2 then r 1 and r 2 represent the same nformaton; o If α 1 < α 2 then r 1 s smaller than r 2 ; o If α 1 > α 2 then r 1 s bgger than r 2. 12
In the followng, we defne a computatonal technque to operate wth the 2-tuples wthout loss of nformaton: Defnton 1 (Herrera & Martínez, 2000a): Let L ( γ γ,..., γ ) = be a fuzzy set defned n S T. A transformaton functon χ that transforms L nto a numercal value n the nterval of granularty of S T [ 0, g], s defned as 0, 1 g χ : F χ ( S ) [ 0, g], ( F( S )) = χ ( s, γ ), T T jγ j j= 0 ({ j j j = 0,1,..., g} ) = = β g γ j g j= 0 (5) ( T where F S ) s the set of fuzzy sets defned n S. Defnton 2 (Herrera & Martínez, 2000b): Let S { s s,..., } [ g] T = be a lngustc term set and β 0, a value supportng the result of a symbolc aggregaton operaton, then the 2-tuple that expresses the equvalent nformaton to β s obtaned wth the followng functon: 0, 1 s g [ g] S [ ) Δ: 0, 0.5,0.5, ( β ) [ ) s, = round Δ ( β ) = α = β, α 0.5, 0.5 (6) where round s the usual round operaton, s has the closest ndex label to β, and α s the value of the symbolc translaton. Proposton 1 (Herrera & Martínez, 2000b): Let S { s0, s1,..., sg} (,α ) s be a 2-tuple. There s a numercal value [ 0, g] R. = be a lngustc term set and 1 Δ functon such that from a 2-tuple t returns ts equvalent β Ths functon s defned as Δ Δ 1 1 : S [ 0.5,0.5) [ 0, g], ( s α ) = + α = β, (7) 13
Defnton 3 (Herrera-Vedma et al., 2004): Let x {( s α ),...,(, α )} 2-tuples and W { w,..., } computed as 1 w n = 1, 1 s n n be a set of lngustc = be ther assocated weghts. The 2-tuple weghted average w x s x w n n 1 Δ ( s ), α. w β. w = 1 = 1 α 1 n n = Δ = Δ n n (8) w w = 1 = 1 [( s, ),...,( s, α )] 1 Defnton 4 (Herrera-Vedma et al., 2004, Wang, 2010): Let x {( s α ),...,(, α )} w w of lngustc 2-tuples and W {( w α ),...,( w, α )} weghts. The 2-tuple lngustc weghted average functon: = 1, 1 s n n be a set = 1, 1 n n be ther lngustc 2-tuple assocated x l w s calculated wth the followng x w l n β. β w = 1 α 1 1 1 n n n n = Δ n (9) β w = 1 w w ([( s, )(, w, α )]...[( s, α )(, w, α )]) 1 1 wth β Δ ( s, α ) 1 w = and β Δ ( w, α ) w =. 6. Proposed decson makng algorthm Ths secton outlnes the fuzzy mult-crtera group decson makng algorthm that bulds on fuzzy QFD, fuson of fuzzy nformaton approach, and 2-tuple lngustc representaton model. In tradtonal QFD applcatons, the company has to dentfy ts customers expectatons and ther relatve mportance to determne the desgn characterstcs for whch resources should be allocated. On the other hand, when the HOQ s used n suppler selecton, the company starts wth the features that the outsourced product/servce must possess to meet certan requrements that the company has establshed, and then tres to dentfy whch of the supplers attrbutes have the greatest mpact on the achevement of ts establshed objectves (Bevlacqua et al., 2006). 14
The proposed algorthm computes the weghts of suppler selecton crtera and the ratngs of supplers usng two nterrelated HOQ matrces as depcted n Fgure 2. Furthermore, utlzaton of the fuson of fuzzy nformaton and the 2-tuple lngustc representaton model enables decson-makers to deal wth heterogeneous nformaton, and rectfy the problem of loss of nformaton encountered usng other fuzzy lngustc approaches. The proposed decson makng approach uses the OWA operator to aggregate decson makers preferences. The OWA operator s a common generalzaton of the three basc aggregaton operators,.e. max, mn, and the arthmetc mean. Unlke the arthmetc mean, the OWA operator combnes the nformaton through assgnng weghts to the values wth respect to ther ordered poston. [Insert Fgure 2 about here] The detaled stepwse representaton of the proposed fuzzy MCDM algorthm s gven below. Step 1. Construct a decson-makers commttee of Z ( z 1,2,..., Z ) = experts. Identfy the characterstcs that the product beng purchased must possess (CNs) n order to meet the company s needs and the crtera relevant to suppler assessment (TAs). Step 2. Construct the decson matrces for each decson-maker that denote the fuzzy assessment to determne the CN-TA relatonshp scores, the relatve mportance of CNs, and the degree of dependences among the TAs. Step 3. Let the fuzzy value assgned as the relatonshp score between the lth CN ( l = 1,2,..., L) and kth TA ( k = 1,2,..., K ), mportance weght of the lth CN, and degree of dependence of the ~ 1 2 klz klz klz klz 3 kth TA on the k th TA for the zth decson-maker be x = ( x, x, x ), ~ 1 2 w lz = ( wlz, wlz, wlz 3 ), and ~ 1 2 3 r kk z = ( rkk z, rkk z, rkk z ), respectvely. Convert x~ klz, w ~ lz, and ~ r kk z nto the basc lngustc scale S T by usng Equaton (1). The fuzzy assessment vector on S T, the mportance weght vector on S T respectvely denoted as F ( ~ x klz ), F ( w ~ lz ), and F ( r kk z ), and the degree of dependence vector on S T, whch are ~, can be represented as F F F ( ~ x ) = ( ( ~ x, s ), γ ( ~ x, s ),..., γ ( ~ x, s ), k, l z γ (10) klz klz 0 klz 1 klz 8, ( w~ ) = ( ( w~, s ), γ ( w~, s ),..., γ ( w~, s ), l z γ (11) lz lz 0 lz 1 lz 8, ( ~ r ) ( ( ~ r, s ), γ ( ~ r, s ),..., γ ( ~ r, s ), k, k z k k z = kk z 0 kk z 1 kk z 8, γ (12) 15
In ths study, the label set gven n Table 1 s used as the BLTS (Jang et al., 2008). [Insert Table 1 about here] Step 4. Aggregate F ( ~ x klz ), F ( w ~ lz ), and F ( ~ r kk z ) to yeld the fuzzy assessment vector F ( ~ x ) kl, the mportance weght vector F ( w ~ l ), and the degree of dependence vector F ( ~ r kk ). The aggregated parameters obtaned from the assessment data of Z experts can be calculated usng Equaton (2) as follows: ~ xkl ( sm) = φ Q ( γ ( ~ xkl sm ( ~ xkl, sm ),..., ( ~ 1, ), γ 2 γ xklz, sm )), k, l, m (13) w~ l ( sm ) = φ Q ( γ ( w l, sm ), ( w l, sm ),..., ( w 1 γ 2 γ lz, sm )), l, m (14) ~ rk k sm Q ( ~ rkk sm ( ~ rkk sm ( ~ ( ) = φ ( γ 1, ), γ 2, ),..., γ rkk z, sm )), k, k, m (15) where φ Q denotes the OWA operator whose weghts are computed usng the lngustc quantfer, Q. Then, the fuzzy assessment vector on S T wth respect to the lth CN, F ( ~ x kl ), the mportance weght vector on S T, F ( w ~ l ), and the degree of dependence vector on S T, F ( ~ r kk ), are defned as follows: F F F ~ γ ~ ~ ~ (16) ( x ) = ( ( x, s ), γ ( x, s ),..., γ ( x, s )), k l kl kl 0 kl 1 kl 8, ( w~ ) = ( ( w~, s ), γ ( w~, s ),..., ( w~, s ), l l γ (17) l 0 l 1 γ ( ~ r ) ( ( ~ r, s ), γ ( ~ r, s ),..., γ ( ~ r, s ), k k k k = kk 0 kk 1 kk 8, l 8 γ (18) Step 5. Compute the β values of F ( ~ x kl ), ( w l ) F ~ and F ~ ), and transform these values nto ( r k k lngustc 2-tuples by usng formulatons (5) and (6), respectvely. Step 6. Compute the orgnal relatonshp measure between the kth TA and the lth CN, Let ~ X * kl. D kk denote the degree of dependence of the kth TA on the k ' th TA. Accordng to Fung et al. (2002) and Tang et al. (2002), the orgnal relatonshp measure between the kth TA and the lth CN should be rewrtten as 16
K ~ X * = D ~ x kl k = 1 kk k l (19) where ~ X * kl s the orgnal relatonshp measure after consderaton of the nner dependence among TAs. Note that the correlaton matrx D s symmetrc. A desgn requrement has the strongest dependence on tself,.e. the kth and the k ' th TAs, then D = 0. kk D kk s assgned to be 1. If there s no dependence between Beneftng from Equaton (19), the orgnal relatonshp measure s obtaned employng 2- tuple lngustc weghted average. Step 7. Calculate the 2-tuple lngustc weghted average for each TA. Step 8. Construct the decson matrces for each decson-maker that denote the ratngs of each potental suppler wth respect to each TA. Step 9. Apply Steps 3-5 to the ratngs of each suppler obtaned at Step 8. Step 10. Calculate the 2-tuple lngustc weghted average for each suppler. The assocated weghts are consdered as the 2-tuple lngustc weghted average score for each TA computed at Step 7. Step 11. Rank the supplers usng the rules of comparson of 2-tuples gven n Secton 5. 7. Case study Growng health expendtures, ncreased qualty and competton n the health sector requre hosptals to use ther resources effcently. In order to llustrate the applcaton of the proposed decson makng method to medcal suppler selecton problem, a case study conducted n a prvate hosptal on the Asan sde of Istanbul s presented (Dursun Usta, 2013). The hosptal operates wth all major departments, and also ncludes facltes such as clncal laboratores, emergency servce, ntensve care unts and operatng room. Frst, through ntervewng the experts from the purchasng department of the hosptal, the exstng purchasng process of the hosptal was revewed and analyzed, and the problems encountered n suppler selecton were dscussed. It was reported that the purchasng department consdered only three major suppler selecton crtera, whch were cost, qualty, and delvery, and the supplers were evaluated on the bass of mean scores of these crtera values. The hosptal manager has been seekng to mprove the purchasng process n order to sharpen the hosptal s compettve edge n the sector. As a result of dscussons wth experts, fve fundamental characterstcs requred 17
of products purchased from medcal supplers (CNs) are determned. These can be lsted as cost (CN 1 ), qualty (CN 2 ), product conformty (CN 3 ), avalablty and customer support (CN 4 ), and effcacy of correctve acton (CN 5 ). Determnng the most preferred suppler depends on a number of dstnct features. Beneftng from the lterature on the evaluaton of supplers, nne crtera relevant to suppler assessment are dentfed as product volume (TA 1 ), delvery (TA 2 ), payment method (TA 3 ), supply varety (TA 4 ), relablty (TA 5 ), experence n the sector (TA 6 ), earler busness relatonshp (TA 7 ), management (TA 8 ), and geographcal locaton (TA 9 ). There are 12 supplers who are n contact wth the hosptal. The evaluaton s conducted by a commttee of fve decson-makers (DM 1, DM 2, DM 3, DM 4, DM 5 ) that ncludes purchasng manager of the hosptal, two feld experts from admnstratve personnel, and a doctor and a nurse from the emergency servce of the hosptal, who have all been workng for more than three years n the case hosptal. A questonnare s prepared concernng the evaluaton of characterstcs requred of products purchased from medcal supplers, suppler assessment crtera and suppler alternatves. The experts are asked to provde ther opnons on the mportance weghts of each CN, the mpact of each TA on each CN, the nner dependences of TAs, and the ratngs of supplers wth respect to each TA. DM 1, DM 2 and DM 3 used the lngustc term set very low (VL), low (L), moderate (M), hgh (H) and very hgh (VH) as shown n Fgure 3, whereas DM 4 and DM 5, who have medcal expertse and thus dfferent backgrounds compared wth other decson-makers, preferred to use a dfferent lngustc term set wth more choces to express ther assessment nformaton ncludng defntely low (DL), very low (VL), low (L), moderate (M), hgh (H), very hgh (VH) and defntely hgh (DH) as depcted n Fgure 4. [Insert Fgure 3 about here] [Insert Fgure 4 about here] The data related to medcal suppler selecton that s provded n the HOQ depcted n Fgure 5 and n Table 2 consst of assessments of fve decson-makers employng lngustc varables defned n Fgures 3 and 4. [Insert Fgure 5 about here] [Insert Table 2 about here] 18
The computatonal procedure s summarzed as follows: Frst, the fuzzy assessment correspondng to the mpact of each TA on each CN, the mportance of CNs, and the degree of dependences among TAs are converted nto the BLTS employng formulatons (10)-(12). Next, by usng the lngustc quantfer most and the formulatons (3) and (4), the OWA weghts for fve decson-makers are computed as ( ) w = 0,0.2,0.4,0.4,0. Then, the fuzzy assessment wth respect to the mpact of each TA on each CN, the mportance of CNs, and the dependences among TAs converted nto the BLTS are aggregated employng formulatons (13)-(18). The β values of these ratngs, mportance, and dependences are computed and transformed nto lngustc 2-tuples va formulatons (5) and (6) as delneated n Fgure 6. [Insert Fgure 6 about here] The orgnal relatonshp measure between TAs and CNs s computed employng Equaton (19) and 2-tuple lngustc weghted average. Then, the 2-tuple lngustc weghted averages for each TA are calculated. The results are represented n Table 3. [Insert Table 3 about here] The ratngs of each suppler converted nto the BLTS are aggregated and transformed nto lngustc 2-tuples as n Table 4. [Insert Table 4 about here] Fnally, the 2-tuple lngustc weghted average for each suppler s computed and the supplers are ranked as shown n Table 5. The rank order of the supplers s Sup 7 Sup 1 Sup 4 Sup 2 Sup 3 Sup 6 Sup 8 Sup 11 Sup 9 Sup 5 Sup 10 Sup 12. [Insert Table 5 about here] Accordng to the results of the analyss, suppler 7 s determned as the most sutable suppler, whch s followed by suppler 1, and then by suppler 4 and suppler 2. Supplers 10 and 12 are ranked at the bottom due to late delvery tme, nadequate experence n the sector, 19
unsatsfactory earler busness relatonshps, and mproper geographcal locaton. Pror to our analyss, the hosptal has been workng wth supplers 7, 1 and 2 usng ther own evaluaton system. The results obtaned from the proposed decson makng approach are smlar to the fndngs from real lfe selecton of supplers by the hosptal, whch has demonstrated the robustness of the methodology and promoted ts use as a decson ad for further suppler evaluaton and selecton stuatons faced by hosptal s management. Over the past decade, several researchers have used varous fuzzy MCDM technques for suppler selecton process. Whle fuzzy MCDM technques enable to consder mprecson and vagueness nherent n suppler evaluaton, they also ncorporate several shortcomngs. Defuzzfcaton has been commonly employed n a number of fuzzy MCDM methods. Freelng (1980) revealed that by reducng the whole analyss to a sngle number, much of the nformaton whch has been ntentonally kept throughout calculatons s lost. Thus, defuzzfcaton mght essentally contradct wth the key objectve of mnmzng the loss of nformaton throughout the analyss. Moreover, obtanng parwse comparsons n wdely used technques such as AHP and ANP may become qute complex especally when the number of attrbutes and/or alternatves ncreases. Apart from ths, Saaty and Tran (2007) clamed that uncertanty n the AHP was successfully remeded by usng ntermedate values n the 1 9 scale combned wth the verbal scale and that seemed to work better to obtan accurate results than usng fuzzy AHP. Fuzzy TOPSIS and fuzzy VIKOR assume mutual ndependence of attrbutes, whch can be hghly restrctve for suppler selecton decsons that usually ncorporate nner dependences among suppler attrbutes. The lack of a precse justfcaton for the values chosen for concordance and dscordance thresholds n fuzzy ELECTRE as well as the absence of a clear methodology for the weght assgnment n fuzzy PROMETHEE may pose lmtatons for ther use n suppler selecton. To the best of our knowledge, an earler study, whch s apt to account for the mpacts of relatonshps among the purchased product features and suppler selecton crtera as well as the correlatons among suppler selecton crtera whle also enablng to manage nonhomogeneous nformaton n a decson settng wth multple nformaton sources, does not exst n the suppler selecton lterature. In here, the suppler selecton methodology proposed n Bevlacqua et al. (2006), whch also made use of fuzzy QFD approach for suppler selecton, s employed for comparson purposes. However, dfferng from the methodology developed n ths paper, ther approach has nether consdered the nner dependences among suppler attrbutes that are denoted n the roof matrx of the HOQ nor enabled the use of dfferent semantc types by decson-makers. Thus, the data obtaned from the frst three 20
decson-makers (DM 1, DM 2 and DM 3 ), who use the same lngustc scale for preference judgments, are consdered to mplement Bevlacqua et al. s method and then compare the obtaned results wth those of the proposed method. Bevlacqua et al. (2006) ntally dentfed the features that the purchased product should possess n order to satsfy the company s needs, and then they attempted to determne the mportance of relevant suppler assessment crtera wthout consderng the correlatons between them. Afterwards, the mportance of suppler attrbutes and the ratngs of supplers wth respect to the related suppler attrbutes were employed to obtan the fnal rankngs of supplers on the bass of fuzzy sutablty ndex. Bevlacqua et al. s methodology provdes the rank-order of supplers as represented n Table 6. It s perceved that the rank-order derved from the proposed approach dffers from that of Bevlacqua et al. s method. In partcular, t s observed that hgher rankngs are obtaned for supplers 3, 4, 7 and 9, manly due to takng nto account the roof matrx n the proposed method. For example, suppler 7 s ranked frst accordng to the results of the proposed methodology, whereas t s ranked n the second place and suppler 1 s ranked frst when Bevlacqua et al. s method s employed. As the roof matrx that accounts for the dependences among TAs s consdered n the proposed approach, the mportance weghts of TAs 3 and 7 ncrease, and thus, suppler 7, whch has more favorable results compared wth suppler 1 for the respectve TAs, supersedes suppler 1. Lkewse, the proposed approach ranks suppler 4 as thrd and suppler 2 as fourth whle suppler 4 and suppler 2 are ranked ffth and thrd, respectvely, accordng to Bevlacqua et al. s method. The proposed model yelds a hgher rankng for suppler 4, whch has a superor performance wth respect to TAs 3 and 7 compared wth suppler 2, due to the ncrease n mportance weghts of the respectve TAs that results from consderng the correlatons among the TAs. Albet dfferences n the suppler rankngs obtaned from Bevlacqua et al. and the proposed approach due to the abovementoned reasons, n partcular resultng n dentfyng dfferent supplers as the best one as well as changes n rankngs n the top half of supplers, the results of Spearman s rank correlaton test for α = 0. 01 ( rs = 0.951 > rs, α = 0.703) ndcate a postve assocaton between the sets of rankngs of the two approaches. [Insert Table 6 about here] 21
8. Conclusons Consderng the global challenges n manufacturng envronment, organzatons are forced to optmze ther busness processes to reman compettve. To reach ths am, frms must work wth ts supply chan partners to mprove the chan s total performance. As the key process n the upstream chan and affectng all areas of an organzaton, the purchasng functon s ncreasngly seen as a strategc ssue n supply chan herarchy. Selectng the rght supplers sgnfcantly reduces the purchasng cost and mproves corporate compettveness. Suppler selecton problem, whch requres the consderaton of multple conflctng crtera ncorporatng vagueness and mprecson wth the nvolvement of a group of experts, s an mportant mult-crtera group decson makng problem. The classcal MCDM methods that consder determnstc or random processes cannot effectvely address suppler selecton problems snce fuzzness, mprecson and nteracton coexst n real-world. In ths paper, a fuzzy mult-crtera group decson makng algorthm s presented to rectfy the problems encountered when usng classcal decson makng methods n suppler selecton. The procedure used n ths paper consders the QFD plannng as a fuzzy mult-crtera group decson tool and constructs two nterrelated HOQ matrces to compute the weghts of suppler selecton crtera and the ratngs of supplers. It utlzes the fuson of fuzzy nformaton and the 2-tuple lngustc representaton model, whch enables decson-makers to tackle the problems of mult-granularty and loss of nformaton. The proposed methodology possesses a number of merts compared to some other MCDM technques presented n the lterature for suppler selecton. Frst, the developed method s a group decson makng process whch enables the group to dentfy and better apprecate the dfferences and smlartes of ther judgments. Second, the proposed approach s apt to ncorporate mprecse data nto the analyss usng fuzzy set theory. Thrd, ths methodology enables to consder the mpacts of relatonshps among the purchased product features and suppler selecton crtera, and also the correlatons among suppler selecton crtera for achevng hgher satsfacton to meet company s requrements. Fourth, the 2-tuple lngustc representaton model that nherts the exstng characters of fuzzy lngustc assessment and rectfes the problem of loss of nformaton faced wth other fuzzy lngustc approaches was used n the developed approach. Ffth, the proposed framework enables managers to deal wth heterogeneous nformaton, and thus, allows for the use of dfferent semantc types by decson-makers. Sxth, t employs the OWA operator as the aggregaton operator. OWA operator dffers from the classcal weghted average n that coeffcents are 22
not assocated drectly wth a partcular attrbute but rather wth an ordered poston. It encompasses several operators snce t can mplement dfferent aggregaton rules by changng the order weghts. Fnally, the decson makng approach set forth n ths paper dsregards the troublesome fuzzy number rankng process, whch may yeld nconsstent results for dfferent rankng methods, and as a result mproves the qualty of decson. Future research wll focus on mplementaton of the decson framework presented n here for real-world group decson makng problems n dverse dscplnes that can be represented usng HOQ structure. Incorporatng supply chan flexblty nto the analyss also remans as an ssue to be addressed n the future. Moreover, as ponted out n several recent works (Rezae & Ortt, 2012; Rezae & Ortt, 2013), suppler segmentaton has an mportant role n supply chan management. Suppler segmentaton that succeeds suppler selecton s the process of classfyng the supplers on the bass of ther smlartes. Ths classfcaton or segmentaton enables to choose the most sutable strateges for handlng dfferent segments of selected supplers. Therefore, further development of the proposed method for suppler segmentaton may also be consdered as a drecton for future research. References Alnezad, A., Sef, A., & Esfandar, N. (2013). Suppler evaluaton and selecton wth QFD and FAHP n a pharmaceutcal company. Internatonal Journal of Advanced Manufacturng Technology, 68, 355-364. Alptekn, S. E., & Karsak, E. E. (2011). An ntegrated decson framework for evaluatng and selectng e-learnng products. Appled Soft Computng, 11(3), 2990-2998. Assaou, N., Haouar, M., & Hassn, E. (2007). Suppler selecton and order lot szng modelng: a revew. Computers and Operatons Research, 34(12), 3516-3540. Amn, S. H,. & Razm, J. (2009). An ntegrated fuzzy model for suppler management: A case study of ISP selecton and evaluaton. Expert Systems wth Applcatons, 36, 8639-8648. Ba, C., & Sarks, J. (2010). Integratng sustanablty nto suppler selecton wth grey system and rough set methodologes. Internatonal Journal of Producton Economcs, 124, 252-264. Baskaran, V., Nachappan, S., & Rahman, S. (2012). Indan textle supplers sustanablty evaluaton usng the grey approach. Internatonal Journal of Producton Economcs, 135, 647-658. Bevlacqua, M., Carapca, F. E., & Gacchetta, G. (2006). A fuzzy-qfd approach to suppler selecton. Journal of Purchasng and Supply Management, 12, 14-27. 23