International Journal of Industrial Engineering Computations

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1 Internatonal Journal of Industral ngneerng Coputatons 3 (2012) Contents lsts avalable at GrowngScence Internatonal Journal of Industral ngneerng Coputatons hoepage: Suppler evaluaton n anufacturng envronent usng coprose rankng ethod wth grey nterval nubers Prasenjt Chatterjee *a, and Rupsa Chatterjee b a MCKV Insttute of ngneerng, Lluah, Howah , Inda b Unversty College of Scence & Technology, Unversty of Calcutta, Kolkata , Inda A R T I C L I N F O A B S T R A C T Artcle hstory: Receved 1 June 2011 Receved n revsed for Noveber, 26, 2011 Accepted 14 Deceber 2011 Avalable onlne 20 Deceber 2011 Keywords: Suppler selecton Mult-crtera decson akng Coprose rankng ethod Grey nterval nuber Grey Suppler selecton ndex valuaton of proper suppler for anufacturng organzatons s one of the ost challengng probles n real te anufacturng envronent due to a wde varety of custoer deands. It has becoe ore and ore coplcated to eet the challenges of nternatonal copettveness and as the decson akers need to assess a wde range of alternatve supplers based on a set of conflctng crtera. Thus, the an objectve of suppler selecton s to select hghly potental suppler through whch all the set goals regardng the purchasng and anufacturng actvty can be acheved. Because of these reasons, suppler selecton has got consderable attenton by the acadecans and researchers. Ths paper presents a cobned ult-crtera decson akng ethodology for suppler evaluaton for gven ndustral applcatons. The proposed ethodology s based on a coprose rankng ethod cobned wth Grey Interval Nubers consderng dfferent cardnal and ordnal crtera and ther relatve portance. A suppler selecton ndex s also proposed to help evaluaton and rankng the alternatve supplers. Two exaples are llustrated to deonstrate the potentalty and applcablty of the proposed ethod Growng Scence Ltd. All rghts reserved 1. Introducton Suppler selecton s a contnuous procedure for acqurng necessary coponent aterals to support producton process as well as for the desred output of an organzaton. It has been a well known fact that the cost of purchased raw aterals or coponent parts or servces donates the fnal product cost by approxately 60%. Also, t has been a ajor setback for the anufacturng organzaton, f the receved aterals or servces are not as per standards as t drectly affects the fnal output of the sad organzaton. Thus, suppler selecton proble s one of the ost portant decsons for organzatons to ake a good aount of proft and for a successful supply chan syste. There are any selecton crtera dentfed by the prevous researchers, but t s not necessary that all the crtera fulfll the requreents of the organzaton durng purchasng actvty. For exaple, the suppler cost of product ay be lowest but qualty ay be nferor. On the other hand, the suppler product ay have hgh qualty but the delvery perforance ay be the worst. Accordng to Wu and Olson (2008), a proper balance aong the avalable crtera s to be taken nto account whle selectng the best suppler. Also accordng to Aleda (2007) n ths globalze ndustral era, each organzaton * Correspondng author. Tel.: al: (P. Chatterjee) 2012 Growng Scence Ltd. All rghts reserved. do: /j.jec

2 394 wants to grab apprecable aount of arket share by provdng qualty product at low cost and also quck after sales servce. 2. Revew of the past researches Varous approaches lke the analytc herarchy process (AHP), analytc network process (ANP), data envelopent analyss (DA), fuzzy set theory, atheatcal prograng, case-based reasonng (CBR), sple ult-attrbute ratng technque (SMART) have already been proposed by the past researchers to solve the proble of proper suppler selecton. Mult-crtera decson akng (MCDM) ethods gve an effectve fraework for suppler coparson based on the evaluaton of ultple conflctng crtera. Kaslnga and Lee (1996) proposed a xed-nteger prograng odel to select supplers and deterne the order quanttes. Weber et al. (1998) descrbed the noncooperatve suppler negotaton strateges where the selecton of one suppler results n another beng left out of the soluton. Ghodsypour and Bren (1998) ntegrated the analytcal herarchy process and lnear prograng to consder both tangble and ntangble factors n choosng the best supplers and placng the optal order quanttes aong the such that the total value of purchasng (TVP) becoes axu. Kuar et al (2000) developed a fuzzy ult-objectve nteger prograng odel for suppler selecton probles. In the proposed odel, varous nput paraeters are treated as vague wth a lnear ebershp functon of fuzzy type. Lu et al. (2000) proposed a splfed DA odel to evaluate the overall perforances of supplers wth respect to three nput and two output crtera. Tallur and Narashan (2003) proposed a ax n productvty based approach that derves the suppler perforance varablty easures, whch are then utlzed n a nonparaetrc statstcal technque n dentfyng suppler groups for effectve selecton. Lu and Ha (2005) presented a novel weghtng procedure n place of AHP s pared coparson for selectng supplers. Bayazt (2006) proposed an ANP odel to tackle the suppler selecton proble. Perçn (2006) appled an ntegrated AHP GP approach for suppler selecton. Chou et al. (2007) attepted to present a fuzzy decsonakng approach to deal wth the suppler selecton proble n supply chan syste. Here, lngustc values are used to assess the ratngs and weghts for selecton factors. P and Low (2007) provded an accurate and easer ethod for quantfyng the suppler s attrbutes to qualty losses usng a Taguch loss functon, and then these qualty losses are transferred nto a varable for decson-akng by analytcal herarchy process (AHP). Chou and Chang (2008) presented a strategy-algned fuzzy sple ult-attrbute ratng technque (SMART) for solvng the suppler/vendor selecton proble fro the perspectve of strategc anageent of the supply chan. Sanaye et al (2010) proposed a herarchy MCDM odel based on fuzzy sets theory and VIKOR ethod to deal wth the suppler selecton probles n the supply chan syste. Feng et al (2011) developed a ult-objectve algorth based on Tabu search for solvng the suppler selecton proble. xtensve coputatonal experents were also conducted to test the perforance of the proposed algorth. Lao and Kao (2011) proposed an ntegrated fuzzy TOPSIS (technques for order preference by slarty to deal soluton) and ult-choce goal prograng (MCGP) approach to solve the suppler selecton proble. Although a good aount of research works have already been carred out by the past researchers on suppler selecton, there s stll a need for a sple as well as systeatc atheatcal approach to gude the decson-akers n takng a proper suppler selecton decson. In ths research work, an attept s ade to dscover the potentaltes and applcablty of the Coprose Rankng Method cobned wth Grey Interval Nubers for real te uncertan envronents whle selectng the ost sutable supplers for two dfferent ndustral stuatons. A Grey suppler selecton ndex s also proposed to rank the alternatve supplers. Two real-te exaples are cted to deonstrate and copare the relatve perforances of the proposed approach wth that used by the past researchers. The frst exaple deals wth the selecton of the ost approprate suppler for an agrcultural and constructon equpent anufacturng fr (Rao, 2007) whereas, the second exaple consders the choce of the best suted suppler for an ndustral organzaton (Ln et al., 2007).

3 3. Coprose rankng ethod P. Chatterjee and R. Chatterjee / Internatonal Journal of Industral ngneerng Coputatons 3 (2012) 395 The VIKOR (the Serban nae s Vlse Krterjuska Optzacja Koprosno Resenje whch eans ult-crtera optzaton (MCO) and coprose soluton) ethod was anly establshed by Zeleny (2002) and later advocated by Oprcovc and Tzeng (2002, 2003, 2004, 2007). Ths ethod s developed to solve MCDM probles wth conflctng and non-coensurable (attrbutes wth dfferent unts) crtera, assung that coprose can be acceptable for conflct resoluton, when the decson aker wants a soluton that s the closest to the deal soluton and the alternatves can be evaluated accordng to all the establshed crtera. It focuses on rankng and selectng the best alternatve fro a set of alternatves wth conflctng crtera, and on proposng coprose soluton (one or ore). The coprose soluton s a feasble soluton, whch s the closest to the deal soluton, and a coprose eans an agreeent establshed by utual concessons ade between the alternatves. A detaled descrpton of the ethod s avalable n (Chatterjee et al., 2009). 4. Grey Interval Nubers Most of the real te ult-attrbute decson-akng probles can not be deterned or predcted wth certan and exact attrbute values, but t can be expressed n ters of fuzzy values or wth values n soe ntervals. So, t becoes necessary to extend the applcatons fro whte nuber (crsp values) to grey nubers s necessary for real-world applcatons. Grey nuber s bascally a concept of grey theory, developed by Deng (19982) to deal wth the nsuffcent and ncoplete nforaton. Whte nuber, grey nuber and black nuber are three classfcatons to dstngush the uncertanty level of nforaton. X and x ЄR, then X whch has two real nubers x (the lower lt of Let = [ x, x] = { x x x x X ) and x (the upper lt of X ) s defned as follows (Deng, 1988, Ln et al., 2008): a). If x and x, then X s called the black nuber whch eans t has no eanngful nforaton. b). lse f x = x, then X s called the whte nuber whch eans wth coplete nforaton. c). Otherwse, X = [ x, x] s called the grey nuber whch eans nsuffcent and uncertan nforaton. A detal descrpton about the dfferent operatons related to Grey nterval nubers can be found n Ln et al. (2008). 5. Matheatcal odellng of the proposed coprose rankng ethod wth grey nterval nubers (VIKOR-G) The an dea of Coprose Rankng Method wth Grey Interval Nubers (VIKOR-G) ethod s based on the real condtons of decson-akng stuatons and applcatons of the Grey systes theory and Grey decson-akng systes (Deng, 1988). The followng ultple attrbute ert for coprose rankng s developed fro the L p -etrc as used n the tradtonal coprose prograng ethod. L ( w [( ) ]/ [( ) ( ) ]) M p, = j j ax j j ax j n j= 1 p 1/p 1 p ; = 1,2,..., N (1) where M s the nuber of crtera and N s the nuber of alternatves. The j values (for = 1,2,..., N; j = 1,2,...,M) ndcate the values of crtera for dfferent alternatves. In the VIKOR ethod, L 1,

4 396 and L, are used to forulate the rankng easure. The procedural steps for the VIKOR-G ethod are enlsted as follows Step 1: Identfy the ajor suppler selecton crtera for the gven proble and short-lst alternatves on the bass of the dentfed crtera satsfyng the requreents. A quanttatve or qualtatve value s assgned to each dentfed crteron to construct the Grey decson atrx X. x 11 x x 1 x x... x X = = x n1 x n2... x n [ x 11, 11] [ x 12, 12 ]... [ x 1, 1 ] [ x 21, 21] [ x 22, 22 ]... [ x 2, 2 ] ,, [ x, ] [ x, ]... [ x n, ] n1 n1 where xj s the nterval perforance value of th alternatve on j th crteron, n s the nuber of alternatves copared and s the nuber of crtera. The value of x s deterned by j (the lower lt) and x j (the upper lt). Step 2: After short-lstng the alternatves and developent of the ntal decson atrx, deterne the best, ( j ) ax and (x j ) ax and the worst, ( j ) n and (x j ) n values of all the crtera. Step 3: The relatve portance of the consdered crtera are deterned usng any subjectve or objectve weghtng ethod. n2 n2 n (2) Step 4: Calculate the and values for j and x j respectvely as follows. M ( ) ( ) ( ) = L 1,j = w / j = 1 j j ax j j ax j n (3) M ( ) ( ) ( ) = L 1,j = w / x x j = 1 j x j x ax j j ax j (4) n q. (3) and q. (4) are applcable to benefcal crtera (whose hgher values are desrable for a gven applcaton). For non-benefcal crtera (whose lower values are preferable for a gven applcaton), [( j ) ax j ] and [(x j ) ax x j ] n q. (3) and q. (4) are to be replaced by [ j ( j ) n ] and [x j (x j ) n ] respectvely. Step 5: Calculate 1 = [ ] 2 + (5) Step 6: Calculate F values for F = L F = L,, = Max = Max Step 7: Calculate F 1 F = [ F + F ] 2 of of and eleents. { w [( ) ] [( ) ( ) ]} j j j / j j j=1,2,..., M ax ax n { w [( x ) x ]/ [( x ) ( x ) ]} j=1,2,..., M j j ax j j ax j n (6) (7) (8)

5 P. Chatterjee and R. Chatterjee / Internatonal Journal of Industral ngneerng Coputatons 3 (2012) 397 Step 8: Calculate the value of suppler selecton ndex (P ). P = v (( -n ) / ( -ax -n )) + (1 v) ((F F -n ) / (F -ax F -n )), (9) where -ax and -n are the axu and nu values of respectvely, and F -ax and F -n are the axu and nu values of F respectvely. v s ntroduced as weght of the strategy of the ajorty of attrbutes (or the axu group utlty ). The value of v les n the range of 0 to 1. Norally, the value of v s taken as 0.5. The coprose can be selected wth votng by ajorty (v > 0.5), wth consensus (v = 0.5) or wth veto (v < 0.5). Step 9: Arrange the alternatve supplers n the ascendng order, accordng to the values of "suppler selecton ndex (P ). Coprose rankng lst for a gven v can be obtaned by rankng wth the P easure. The best alternatve suppler s the one havng the nu P value. The proposed VIKOR-G ethod s an effectve ult-crtera decson akng tool, specfcally applcable to those stuatons when the decson aker s not able, or does not know to express hs/her preference at the begnnng of the decson akng process. The obtaned coprose soluton can be accepted by the decson aker because t provdes a axu group utlty of the ajorty and a nu ndvdual regret of the opponent. The coprose solutons can be the base for negotatons, nvolvng the decson aker s preference on crtera weghts (Rao, 2008). The VIKOR-G results depend on the deal soluton, whch stands only for a gven set of alternatves. Incluson (or excluson) of an alternatve can affect the VIKOR-G rankng of the new set of alternatves. 6. Illustratve exaple 1 Ths exaple deals wth the selecton of the ost approprate suppler for an agrcultural and constructon equpent anufacturng fr (Rao, 2007). The organzaton has dvded all ts purchased parts nto 18 coodty groups, lke hydraulc valves, fasteners, electrcal coponents etc. To collect data n each coodty group, the copany frst lsted all the parts suppled by each suppler to obtan the supply varety of the vendors. If a suppler supples ore than one coodty group, the supply varety of ths suppler n each group s the su of the nuber of parts n all the groups. Here fve crtera were consdered,.e. prce, qualty, delvery perforance, dstance and supply varety. Aong these fve crtera, prce and dstance are non-benefcal attrbutes where saller values are often preferable, whereas qualty, delvery perforance and supply varety are the benefcal attrbutes where hgher values are desrable. ghteen supplers coprsng are consdered as the alternatves. Thus, the MCDM proble conssts of 18 alternatve supplers and 5 suppler selecton crtera. The orgnal decson atrx (Rao, 2008) s expressed n Grey ntervals as shown n Table 1. Now ths suppler selecton proble for the agrcultural and constructon equpent anufacturng fr s solved usng the proposed VIKOR-G ethod. At frst, Grey decson atrx s developed fro orgnal decson atrx. The nterval range of grey nuber depends on the uncertanty of the obtaned nforaton fro each subcontractor and depends on the decson aker. Then the best and the worst values of all the crtera are dentfed. Rao (2008) eployed the AHP ethod to deterne the weghts of the consdered crtera, as w P = , w Q = , w DP = and w D = and w SV = These crtera weghts are used here for all the analyss. Now, the values of and F are calculated usng qs. (3), (4), (5) and (6) respectvely, as gven n Table 2. Table 2 also exhbts the values of suppler selecton ndex (P ). for v = 0.5 and the coprose rankng lst of the consdered alternatve supplers. The canddate supplers are arranged n ascendng order, accordng to the values of P. The best choce of suppler s suppler 15. Suppler 17 s the second choce and the last choce s suppler 14. Rao (2008) obtaned a rankng of the alternatve supplers as by applyng TOPSIS ethod, whereas, usng the proposed VIKOR-G ethod, the coprose rankng of supplers s

6 It s observed that n the VIKOR-G ethod, the best choce of suppler s suppler alternatve 17. Table 1 Quanttatve data expressed n Grey ntervals Suppler Prce (P) Qualty (Q) Delvery Perforance (DP) Dstance (D) Supply Varety (SV) A closer look at the values of attrbutes and ther portance for supplers 10 and 17 reveals that suppler 17 s superor than suppler 10 wth respect to attrbutes prce and qualty and these two are the ost portant attrbutes as per the weghts gven by Rao (2007). Table 2, F and P values for exaple 1 Suppler F F F P Rank

7 P. Chatterjee and R. Chatterjee / Internatonal Journal of Industral ngneerng Coputatons 3 (2012) 399 Lu (2000) also suggested that suppler alternatves 17, 1, 10, 12, 15 are the only effcent supplers, so proposng suppler 17 as the best choce s justfed. Whle calculatng P values, the value of v s usually taken as 0.5 (Rao, 2008), but actually ts value les between 0 and 1. Table 3 shows the coprose rankngs of the alternatve supplers for two extree values of v = 0.1 and v = 0.9. Table 3 Rankng of supplers for exaple 1 for dfferent values of v Suppler P (v = 0.9) Rank P (v = 0.1) Rank In both these cases, the best choce of suppler (suppler alternatve 17) does not change, although the rankng of the alternatve suppler changes slghtly, whch suggest that VIKOR-G ethod can be successfully appled for dealng wth coplex suppler selecton probles. Fg. 1 copares the rankng perforance of the proposed VIKOR-G ethod wth respect to TOPSIS ethod proposed by Rao (2008). Rank VIKOR-G TOPSIS A1 A2 A3 A4 A5 A6 A7 A8 A9 A10 A11 A12 Alternatve Suppler A13 A14 A15 A16 A17 A18 Fg. 1. Coparatve rankngs of alternatve supplers for exaple 1

8 Illustratve exaple 2 The second exaple (Ln et al., 2007) deals wth the selecton of the ost approprate subcontractor for an engneerng corporaton to deonstrate the potentalty, feasblty and applcablty of the proposed ethod. The perforance of each subcontractor was evaluated on the bass of four crtera,.e. Relablty (RA), Schedule-control ablty (SA), Manageent ablty (MA), and Labor qualty (LQ). The relablty of subcontractors s evaluated by ther reputaton, records and fnancal condton. The schedule-control ablty s easured by subcontractors effcency and oblzaton. Manageent ablty (MA) s assessed by the qualty, safety, and envronental anageent level of each subcontractor. Labor qualty (LQ) s evaluated by the workers skll level, coordnaton and cooperaton of subcontractors. So all the four crtera are benefcal n nature where hgher values are desrable. Four supplers naely S 1, S 2, S 3, and S 4 were consdered as the alternatves. Thus, the MCDM proble conssts of 4 alternatve supplers and 4 suppler selecton crtera, as shown n Table 4. Table 4 Quanttatve data expressed n Grey ntervals (Ln et al., 2007) Suppler RA SA MA LQ At frst, the best and the worst values of all the crtera are dentfed. Ln et al. (2007) deterned the weghts of the consdered crtera, as w RA = 0.2,w SA = 0.25, w MA = 0.20 and w LQ = These crtera weghts are used here for all the analyss. Now, the values of and F are calculated usng qs. (3), (4), (5) and (6) respectvely, as gven n Table 5. Table 5 also exhbts the values of suppler selecton ndex P for v = 0.5 and the coprose rankng lst of the consdered alternatve supplers. The canddate supplers are arranged n ascendng order, accordng to the values of the suppler selecton ndex P. The best choce of suppler s suppler 3. Suppler 1 s the second choce and the last choce s suppler 4. Usng the ethod as proposed by Ln et al. (2007), a rankng of the alternatve supplers obtaned as , whereas, usng the proposed VIKOR-G ethod, the coprose rankng of supplers s , whch exactly corroborates wth that of Ln et al. (2007). Table 5, F and P values for exaple 2 Suppler F F F P Rank Table 6 shows the coprose rankngs of the alternatve supplers for two extree values of v = 0.1 and v = 0.9. In both these cases, the best choce of suppler (suppler alternatve 15) does not change, although the rankng of the alternatve suppler ay change slghtly. Fg. 2 copares the rankng perforance of the proposed ethod wth respect to Ln et al. (2007).

9 P. Chatterjee and R. Chatterjee / Internatonal Journal of Industral ngneerng Coputatons 3 (2012) 401 Table 6 Rankng of supplers for exaple 2 for dfferent values of v Suppler P (v = 0.9) Rank P (v = 0.1) Rank VIKOR- G Rank 2 1 A1 A2 A3 A4 Alternatve Suppler Fg. 2 Coparatve rankngs of alternatve supplers for exaple 2 8. Conclusons Owng to the ncreasng coplexty n decson akng, the uncertanty of evaluaton ncreases. In real te anufacturng envronent, the decson aker ay not always be able to gve precse evaluatons to the alternatves on every crteron. However, they can gve an approxate range of evaluaton based on ther knowledge and cognton. Under ths stuaton, t becoes necessary to develop such decson akng odels whch can easly handle the uncertan nforaton. In ths paper, the concept Grey Interval Nuber ntegrated has been used wth the Coprose Rankng Method VIKOR, to propose a decson akng fraework and a Grey suppler selecton ndex whch can effectvely handle the uncertan nforaton and rank the alternatve supplers. The two cted exaples deonstrate the potentalty, applcablty and splcty of the proposed VIKOR-G ethod n solvng suppler selecton decson-akng probles, nvolvng uncertan and qualtatve as well as quanttatve crtera. The proposed ethod can ncorporate the decson aker s preferences regardng the relatve portance of dfferent crtera. The easures of the quanttatve and qualtatve crtera and ther relatve portance are used together to rank the alternatves under uncertan envronent, provdng a better evaluaton of the alternatves. The VIKOR-G ethod can ake a coprose rankng aong the alternatves. The results derved usng the proposed VIKOR- G ethod show an excellent correlaton wth those obtaned by the past researchers, whch specfcally prove the global applcablty of these two ethods whle solvng such type of coplex suppler selecton probles. The proposed VIKOR-G ethod can also be used for any type of decson-akng proble, nvolvng any nuber of quanttatve and qualtatve crtera and any nuber of alternatves under uncertan and ncoplete envronent. References Aleda, A.T. (2007). Mult crtera decson odel for outsourcng contracts selecton based on utlty functon and LCTR ethod. Coputers & Operatons Research, 34, Bayazt, O. (2006). Use of analytc network process n vendor selecton decsons. Bencharkng: An Internatonal Journal, 13 (5),

10 402 Chatterjee, P., Athawale V. M., & Chakraborty, S.(2009). Selecton of aterals usng coprose rankng and outrankng ethods. Materals and Desgn, 30, Chou, S.Y., & Chang, Y.H. (2008). A decson support syste for suppler selecton based on a strategy-algned fuzzy SMART approach. xpert Systes wth Applcatons, 34, Chou, S.Y., Shen, C.Y., & Chang,Y.H. (2007). Vendor selecton n a odfed re-buy stuaton usng a strategy-algned fuzzy approach. Internatonal Journal Producton Research, 5, Deng, J. L. ( 1982,).Control proble of grey syste. Syste and Control Letters, 5, Deng, J. L. (1988). Introducton to Grey Syste Theory. The Journal of Grey Theory, 1, Feng B, Fan Z-P. & YanzhL, A. (2011). Decson ethod for suppler selecton n ult-servce outsourcng, Internatonal Journal of Producton conocs. 132, Ghodsypour, S.H. & Bren, O.(1998). A decson support syste for suppler selecton usng an ntegrated analytc herarchy process and lnear prograng. Internatonal Journal Producton conocs, 56-57, Kaslnga, R.G., & Lee, C.P.(1996). Selecton of vendors-a xed-nteger prograng approach. Coputers & Industral ngneerng, 31, Kuar, M., Vrat, P., & Shankar, R.(2000). A fuzzy prograng approach for vendor selecton proble n a supply chan. Internatonal Journal of Producton conocs, 101, Lao C-N., & Kao H-P.(2011). An ntegrated fuzzy TOPSIS and MCGP approach to suppler selecton n supply chan anageent. xpert Systes wth Applcatons, 38, Ln, Y-H., Lee, P-C., & Tng, H-I.(2008). Dynac ult-attrbute decson akng odel wth grey nuber evaluatons. xpert Systes wth Applcatons, 35, Lu, F.H.F., & Ha, H.L.(2005). The votng analytc herarchy process ethod for selectng suppler. Internatonal Journal Producton conocs, 97, Lu, F., Dng, F.Y., & Lall, V. (2000).Usng Data nvelopent Analyss to copare vendors for vendor selecton and perforance proveent. Supply Chan Manageent, An Internatonal Journal, 5, Oprcovc, S., & Tzeng, G.H.(2007). xtended VIKOR ethod n coparson wth outrankng ethods. uropean Journal of Operatonal Research, 178, Oprcovc, S., & Tzeng, G.H.(2004). Coprose soluton by MCDM ethods: a coparatve analyss of VIKOR and TOPSIS. uropean Journal of Operatonal Research, 156, Oprcovc, S., & Tzeng, G.H.(2003). Fuzzy ult crtera odel for post-earthquake land-use plannng. Natural Hazards Revew, 4, Oprcovc, S., & Tzeng, G.H.(2002). Mult crtera plannng of post-earthquake sustanable reconstructon. Coputer Aded Cvl Infrastructure ngneerng, 17, P, W.N., & Low, C.(2007). Suppler evaluaton and selecton va Taguch loss functons and an AHP. Internatonal Journal of Advanced Manufacturng Technology, 27, Perçn, S. (2006). An applcaton of the ntegrated AHP PGP odel n suppler selecton. Measurng Busness xcellence 10 (4), Rao, R.V. (2008). A decson akng ethodology for ateral selecton usng an proved coprose rankng ethod. Materals and Desgn, 29, Rao, R.V. (2007). Decson akng n the anufacturng envronent usng graph theory and fuzzy ultple attrbute decson akng ethods. London: Sprnger-Verlag. Sanaye A., Fard M. S., & Yazdankhah A.(2010). Group decson akng process for suppler selecton wth VIKOR under fuzzy envronent. xpert Systes wth Applcatons 37, Tallur, S., & Narashan, R.(2003). Vendor evaluaton wth perforance varablty: A ax-n approach. uropean Journal of Operatonal Research, 146, Weber, C.A., Current, J.R.,& Desa, A.(1998). Non-cooperatve negotaton strateges for vendor selecton. uropean Journal of Operatonal Research, 108, Wu, D., & Olson, D.L (2008). A coparson of stochastc donance and stochastc DA for vendor evaluaton. Internatonal Journal of Producton Research, 46, Zeleny, M. (2002). Multple crtera decson akng. New York: McGraw Hll Publshers.

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