Fuzzy Decision Approach Based on QFD and FWA for Selection of Medical Suppliers

Transcription

1 , July 1-3, 2015, ondon,.k. Fuzzy Deciion Approach Baed on QFD and FWA for Selection of Medical Supplier Mehtap Durun and E. Ertugrul Karak Abtract The objective of thi paper i to develop a fuzzy multi-criteria group deciion making techniue that utilize the uality function deployment (QFD) methodology for upplier evaluation and election. The propoed deciion approach enable the deciion-maker to ue linguitic term, and thu, reduce their cognitive burden in the evaluation proce. Furthermore, the propoed algorithm allow for conidering the impact of inner dependence among upplier aement criteria. The lower and upper bound of the weight of upplier aement criteria and rating of upplier are computed by uing fuzzy weighted average (FWA), which enable the fuion of imprecie and ubjective information expreed a linguitic variable or fuzzy number and rectifie the problem of lo of information. The final ranking of upplier i obtained by employing a fuzzy number ranking method that i baed on area meaurement. The computational procedure of the propoed framework i illutrated through a cae tudy, and a comparative analyi with a well-known fuzzy deciion making approach ued lately for upplier election i performed. Index Term Supplier election, MCDM, deciion upport ytem, group deciion making, QFD, fuzzy weighted average. I I. INTRODCTION N order to harpen the competitive edge in a upply chain, a higher level of integration with upplier and cutomer i eential. Supplier management i conidered a one of the key iue of upply chain management ince cot of raw material and component part contitute the main cot item of a product [1]. Today, a ignificant number of manufacturer pend roughly half it revenue to purchae good and ervice, which make a company ucce dependent on it interaction with upplier. In a globally competitive environment, organization give particular importance to the identification and election of alternative upply ource. A well-elected et of upplier make a trategic difference to an organization' ability to reduce cot and improve uality of it end product. In an exhautive review of 74 article, Weber et al. [2] noted that 47 of the 74 article dicued more than one criterion. Thi demontrate the inherent multi-criteria nature of many upplier election deciion. The uncertainty of ubjective judgment i preent when Thi work ha been financially upported by Galataaray niverity Reearch Fund under Grant M. Durun i an Aitant Profeor of Indutrial Engineering, Galataaray niverity, Ortakoy, Itanbul 34357, Turkey (fax: ; mdurun@gu.edu.tr). E. E. Karak i a Profeor of Indutrial Engineering, Galataaray niverity, Ortakoy, Itanbul 34357, Turkey (fax: ; e- mail: ekarak@gu.edu.tr). carrying out a upplier election proce. Moreover, deciion making become more complicated when the available information i incomplete or imprecie. The claical multi-criteria deciion making (MCDM) method cannot effectively tackle deciion problem including ubjective information. In practice, deciion making in upplier election encompae a high degree of vaguene and impreciion. Fuzzy et theory et forth a ound deciion upport methodology to overcome the inherent uncertainty. Thi tudy focue on propoing a fuzzy multi-criteria group deciion making approach baed on the uality function deployment (QFD) concept for upplier election. QFD focue on delivering value by taking into account the cutomer need (CN), and then deploying thi information throughout the development proce [3]. The eence of QFD i to tranlate the deire of cutomer into technical attribute (TA), and ubeuently into part characteritic, proce plan and production reuirement. In upplier election proce, the company ultimate aim i to have acce to upplier that enure a certain uality tandard in term of the characteritic of the purchaed product or ervice [4]. Fulfilling thee aim depend largely on conidering not only the relationhip between purchaed product feature and upplier aement criteria, but alo the relationhip between upplier aement criteria diregarding the unrealitic independence aumption. Hence, contructing a houe of uality (HOQ), which allow for the relationhip among purchaed product feature and upplier aement criteria a well a inner dependence of upplier aement criteria to be conidered, i crucial in identifying how well each upplier characteritic ucceed in fulfilling the reuirement etablihed for the product being purchaed. The contribution of thi reearch to upplier election can be ummarized a follow. Firt, the propoed methodology i a group deciion making tool that enable to account for imprecie data uing fuzzy et theory. Further, the developed approach i apt to conider the impact of relationhip among the purchaed product feature and upplier election criteria a well a the inner dependence among upplier election criteria for achieving higher atifaction to meet company reuirement. Beide, the propoed framework employ the fuzzy weighted average (FWA) method that rectifie the problem of lo of information that occur when integrating imprecie and ubjective information. Furthermore, differing from previouly propoed FWA approach that doe not normalize fuzzy relationhip, the FWA method ued in thi paper produce normalized fuzzy importance rating for upplier

2 , July 1-3, 2015, ondon,.k. aement criteria while conidering inner dependence among upplier criteria. At lat, the propoed approach utilize a fuzzy number ranking method baed on area meaurement, which enable higher dicrimination among the fuzzy number to be ranked. In hort, conidering it effectivene in uantifying vaguene and impreciion in human judgment a well a all pertinent relationhip in the upplier election proce, the propoed deciion making approach appear a a ound alternative to exiting method. In the literature, there are a vat number of paper that employed different MCDM techniue for upplier election. Tam and Tummala [5] invetigated the feaibility of applying analytic hierachy proce (AHP) in upplier election for a telecommunication ytem. Bottani and Rizzi [6] addreed the problem of upplier election in an e-procurement environment. Fuzzy AHP wa employed to determine the mot viable upplier. Chen et al. [7] improved the concept of TOPSIS to develop a methodology for olving upplier election problem in fuzzy environment. Chan et al. [8] ued a fuzzy modified AHP approach to elect the bet global upplier. hu et al. [9] developed a methodology to evaluate upplier uing portfolio analyi baed on ANP and environmental factor. Awathi et al. [10] ued fuzzy TOPSIS for evaluating environmental performance of upplier. Sanayei et al. [11] propoed fuzzy VIKOR method to elect the uitable upplier in a upply chain ytem. Shemhadi et al. [12] handled upplier election a a multiple criteria group deciion making problem and developed a fuzzy VIKOR method to olve thi problem. More recently, Wu et al. [13] employed fuzzy TOPSIS to elect the mot appropriate upplier. Although fuzzy MCDM techniue enable to conider impreciion and vaguene inherent in upplier evaluation, they incorporate everal hortcoming. Defuzzification, which may caue lo of information, i commonly employed in fuzzy MCDM method uch a fuzzy AHP and fuzzy ANP. Apart from thi, uncertainty in the AHP i uccefully remedied by uing intermediate value in the 1 9 cale combined with the verbal cale and that eem to work better to obtain accurate reult than uing fuzzy AHP [14]. Fuzzy TOPSIS and fuzzy VIKOR aume mutual independence of attribute, which i highly retrictive for upplier election deciion. Moreover, fuzzy TOPSIS doe not conider the relative importance of the ditance to ideal and anti-ideal olution. Recently, QFD ha been utilized in upplier election. Bevilacua et al. [4] contructed an HOQ to identify the feature that the purchaed product hould poe in order to atify the cutomer reuirement. Then, the potential upplier were evaluated againt the relevant upplier aement criteria. Ho et al. [15] developed a combined QFD and AHP approach to meaure the performance of alternative upplier. Soroor et al. [16] combined fuzzy logic, AHP, and QFD for the evaluation of upplier. In a recent work, Durun and Karak [17] integrated QFD and fuzzy weighted average for upplier election proce. Even though prior reearche developed approache for upplier election proce, further tudie are reuired to incorporate imprecie information concerning the importance of purchaed product feature, relationhip between purchaed product feature and upplier aement criteria, and dependencie between upplier aement criteria into the analyi. The propoed methodology make ue of two interrelated HOQ matrice for upplier evaluation. In the firt HOQ, the characteritic reuired of product purchaed from medical upplier are taken into conideration to compute the lower and upper bound of the weight of upplier election criteria through the FWA method, which enable to rate the importance of upplier aement criteria in fuzzy environment accurately through α-level et. In the econd HOQ, the FWA method i utilized to compute the lower and upper bound of the upplier rating uing the weight of upplier election criteria obtained from the firt HOQ. The FWA method, which calculate both the weight of upplier election criteria and the rating of the upplier, enable to produce le imprecie and more realitic overall deirability level. II. FY WEIGHTED AVERAGE Conider the general fuzzy weighted average with criteria. Define W ~ p a the relative importance of criterion p (p = 1,, ) and X ~ pr a the rating of alternative r with repect to criterion p (p = 1,, ; r = 1,,). Then, the fuzzy weighted average can be defined a r p pr p p1 p1 W X W, r 1,..., (1) Since W ~ p and X ~ pr are fuzzy number, the weighted average ~ r i alo a fuzzy number. When the relative weight of cutomer need, the relationhip meaure between cutomer need and technical attribute, and the inner dependencie of technical attribute are denoted a fuzzy number, the computation of the overall prioritie of technical attribute fall into the category of fuzzy weighted average [18]. There are everal method developed for computing fuzzy weighted average [19-21]. In thi paper, the techniue propoed by Wang and Chin [21], which produce normalized fuzzy importance rating for TA, i employed. Exiting approache that do not normalize fuzzy relationhip between CN and TA may produce erroneou reult. According to Waerman [22], the relationhip between CN and TA need to be normalized; otherwie, the importance of TA cannot be correctly rated. Thi i alo valid for fuzzy relationhip. The ue of fuzzy arithmetic to perform fuzzy normalization or calculate FWA i alo inappropriate ince fuzzy arithmetic operation increae the fuzzine of normalized fuzzy relationhip and FWA, and make their upport interval much wider than actual one [21]. Wang and Chin method enable rating the importance of TA and upplier aement in fuzzy environment accurately through α-level et. They developed a pair of nonlinear programming model and two euivalent pair of linear programming model to find the α-cut of ~ r. The method can be ummarized a follow:

3 , July 1-3, 2015, ondon,.k. et X pr W p denote the fuzzy relative weight of CN p, denote the fuzzy relationhip meaure between TA r and cutomer need p, and kr denote the degree of dependence of the kth TA on the rth TA. Denote Wp, W p, X pr, X pr, and kr kr a the α-level et of the fuzzy relative weight, fuzzy relationhip, and fuzzy correlation, repectively. The normalized fuzzy relationhip can be calculated a follow: X pk kr ' k 1 X pr, p 1,..., ; r 1,..., X pk kl X pk kr l1 k1 k1 lr Once the normalized fuzzy relationhip are generated, the fuzzy weighted average of the normalized fuzzy relationhip can be formulated a ' r W px pr W p, r 1,2,..., (3) p1 p1 and the lower and upper bound of the α-cut of olved a ' r min px pr p1 ubject to Wp p Wp, p 1, 2,..., p 1 p1, p 0 ' r max px pr p1 ubject to Wp p Wp, p 1, 2,..., p 1 p1, p 0 where, 1 wp p1 ~ r (2) can be (4) (5) and p w p, according to the variable ubtitution of Charne and Cooper [23]. The α-cut of ~ r i the crip interval r, r obtained from formulation (4) and (5). By enumerating different α value, the memberhip function can be contructed. ~ r III. PROPOSED FY DECISION APPROACH Thi ection delineate the fuzzy multi-criteria group deciion making algorithm that build on fuzzy QFD methodology. In conventional QFD application, the company ha to identify it cutomer expectation and their relative importance to determine the deign characteritic for which reource hould be allocated. Alternatively, when the HOQ i ued in upplier election, the company commence with the feature that the outourced product/ervice mut poe to meet certain reuirement that the company ha etablihed, and then trie to identify which of the upplier attribute have the greatet impact on the achievement of it etablihed objective [4]. The propoed algorithm ue FWA method to compute the lower and upper bound of the weight of TA and the upplier aement uing two interrelated HOQ matrice. In addition, the propoed algorithm enable to conider the impact of inner dependence among TA. Furthermore, it employ a fuzzy number ranking method baed on area meaurement. Thi ranking method conider the loci of left and right pread at each α-level of a group of fuzzy number and the horizontal-axi location of the group of fuzzy number baed on their common maximizing and minimizing barrier imultaneouly. Thi in turn increae the ability of thi method to dicriminate among the number to be ranked, and thu yield better enitivity compared with other exiting ranking method [24]. The detailed tepwie repreentation of the propoed fuzzy MCDM algorithm i given below. Step 1. Contruct a deciion-maker committee of expert 1,2,...,. Identify the characteritic that the product being purchaed mut poe (CN) in order to meet the company need and the criteria relevant to upplier aement (TA). Step 2. Contruct the deciion matrice for each deciionmaker that denote the relative importance of CN, the fuzzy aement to determine the CN-TA relationhip core, the degree of dependencie among TA, and the rating of each potential upplier with repect to each TA. Step 3. et the fuzzy value aigned a the importance weight of the pth CN, relationhip core between the pth CN p1,2,...,and the rth TA r1,2,...,, degree of dependence of the kth TA on the rth TA, and rating of the jth upplier j1,2,...,nwith repect to the rth TA for the ~ th deciion-maker be W p W p, W p, W p, ~ X pr X pr, X pr, X pr, ~ kr kr, kr, kr, and ~ yrj yrj, yrj, yrj, repectively. Compute the aggregated importance weight of the pth CN W p, aggregated fuzzy aement of the relationhip core between the rth TA and the pth CN X pr,aggregated degree of dependence of the kth TA on the rth TA, kr

4 , July 1-3, 2015, ondon,.k. and aggregated rating of the jth upplier with repect to the rth TA y rj a follow: W p W p (6) 1 pr X pr (7) 1 X kr kr 1 (8) yrj y rj (9) 1 where 0,1 repreent the weight of the th deciionmaker and 1. 1 Step 4. Calculate the normalized fuzzy relationhip, and then compute the lower and upper bound of the weight for each TA by employing formulation (4) and (5). Step 5. Calculate the lower and upper bound for each upplier by utilizing formulation (4) and (5). Thi time, the relative importance expreed in formulation (4) and (5) are the lower and upper bound, repectively, of the weight for each TA calculated at Step 4. Step 6. Rank the upplier by employing Chen and Klein [24] ranking algorithm, which can be ummarized a follow: ~ ~ ~ ~ et 1, 2,...,,..., be arbitrary bounded fuzzy number, and h pecify the maximum height of ~, 1,2,...,. Suppoe h i eually divided into v interval uch that e eh / v, e 0,1,2,..., v. Chen and Klein [24] devied the following index for ranking fuzzy number. v v v I c c d e e e e0 e0 e0 v (10) where c mine, e and d maxe, e. e e The larger the ranking index I, the more preferred the fuzzy number i. IV. EVAATING MEDICA SPPIERS SING FY MCDM APPROACH In order to illutrate the application of the propoed deciion making method to medical upplier election problem, a cae tudy conducted in a private hopital on the Aian ide of Itanbul i preented [25]. The hopital operate with all major department, and poee facilitie uch a clinical laboratorie, emergency ervice, intenive care unit and operating room a well. Following the dicuion with expert from the purchaing department of the hopital, five fundamental characteritic reuired of product purchaed from medical upplie (CN) are determined. Thee can be lited a cot (CN 1 ), uality (CN 2 ), product conformity (CN 3 ), availability and cutomer upport (CN 4 ), and efficacy of corrective action (CN 5 ). Nine criteria relevant to upplier aement are identified a product volume (TA 1 ), delivery (TA 2 ), payment method (TA 3 ), upply variety (TA 4 ), reliability (TA 5 ), experience in the ector (TA 6 ), earlier buine relationhip (TA 7 ), management (TA 8 ), and geographical location (TA 9 ). There are 12 upplier who are in contact with the hopital. TABE I INGISTIC SCAE FOR THE EVAATION OF MEDICA SPPIERS. Very low/poor (V/VP) (0, 0, 0.25) ow/poor (/P) (0, 0.25, 0.50) Moderate/fair (M/F) (0.25, 0.50, 0.75) High/good (H/G) (0.50, 0.75, 1) Very high/good (VH/VG) (0.75, 1, 1) The evaluation i performed by a committee of three deciion-maker. The deciion-maker ue the linguitic cale defined in Table I to denote the level of importance of each CN, the impact of each TA on each CN, the inner dependencie of TA, and the rating of the upplier with repect to each TA. By uing E. (6)-(9), the deciion-maker evaluation are aggregated to obtain aggregated importance of each CN, aggregated impact of each TA on each CN, aggregated degree of dependence of TA, and aggregated rating of upplier. In here, one hall note that ince eual weight are allocated to each deciion-maker. The lower and upper bound of the weight of TA are computed via formulation (4) and (5). By employing formulation (4) and (5), the lower and upper bound for upplier rating are computed a given in Table II. Finally, the ranking index I for each upplier i calculated uing E. (10). The ranking indice are a I Sup , I Sup , I Sup , I Sup , I Sup , I Sup , I Sup , I Sup , I Sup , I Sup , I(Sup11)=0.5210, and I(Sup12)= Thu, the rank-order of the upplier i Sup1 Sup7 Sup2 Sup4 Sup3 Sup6 Sup8 Sup11 Sup5 Sup9 Sup10 Sup12. According to the reult of the analyi, upplier 1 i determined a the mot uitable upplier, which i followed by upplier 7, and then by upplier 2 and upplier 4. Supplier 10 and 12 are ranked at the bottom due to late delivery time, inadeuate experience in the ector, unatifactory earlier buine relationhip, and improper geographical location. The reult obtained from the propoed methodology are comparable to thoe already in ue by the hopital management, which reveal the robutne of the propoed methodology and promote it ue a a deciion aid for imminent upplier election ituation.

5 , July 1-3, 2015, ondon,.k. α TABE II OWER AND PPER BONDS OF THE SPPIER RATINGS. Supplier up Sup 1 up up Sup 2 up up Sup 3 up up Sup 4 up up Sup 5 up up Sup 6 up up Sup 7 up up Sup 8 up up Sup 9 up up Sup 10 up up Sup 11 up up Sup 12 up In order to demontrate the robutne of the propoed methodology, the reult are compared with thoe obtained by fuzzy VIKOR, which i a well-known MCDM approach previouly ued for upplier evaluation a well [11, 12]. The VIKOR method wa developed a an MCDM techniue to olve a dicrete multi-criteria problem with noncommenurable and conflicting criteria [26]. It focue on ranking and electing from a et of alternative in the preence of conflicting criteria, and determine compromie olution, providing a maximum group utility for the majority and a minimum of an individual regret for the opponent. VIKOR introduce the multi-criteria ranking index baed on the particular meaure of cloene to the ideal olution. In here, the fuzzy VIKOR method preented in Opricovic [26] i employed to evaluate medical upplier. To compare the reult with thoe of the propoed deciion framework, QFD methodology, which enable to incorporate the relationhip between CN and TA, and the inner dependencie among TA, i utilized to compute the weight of TA. The roof matrix of the HOQ i handled by uing the procedure propoed by Fung et al. [27]. The ranking of the upplier i obtained a Sup1~Sup2~Sup7 Sup4 Sup3 Sup6~Sup11 Sup8~Sup9 Sup5~Sup10 Sup12.

6 , July 1-3, 2015, ondon,.k. While fuzzy VIKOR identifie upplier 1, 2 and 7 a the top ranking upplier, which are in accordance with the propoed approach, the outcome of fuzzy VIKOR yield indifference between thoe upplier. In addition, fuzzy VIKOR reult in indifference between upplier 6 and 11, upplier 8 and 9 a well a upplier 5 and 10. One hall note that the fuzzy VIKOR method can neither provide a complete ranking of the upplier nor identify the bet upplier. On the other hand, the propoed deciion framework both yield a complete rank order and enable to determine the mot uitable upplier. V. CONCSIONS Thi paper preent a fuzzy multi-criteria group deciion making framework to rectify the problem encountered when uing traditional deciion making method in upplier election. It employ the FWA method developed by Wang and Chin [21]; however, it extend their reearch in everal apect. Firt, the methodology ued in thi paper conider QFD planning a a fuzzy multi-criteria group deciion making tool and make ue of two interrelated HOQ matrice to evaluate alternative upplier. In the firt HOQ, the characteritic reuired of product purchaed from medical upplie are taken into account a CN, and the upplier election criteria are conidered a TA. Then, the lower and upper bound of the weight of upplier election criteria are calculated through the FWA method, which enable to rate the importance of TA in fuzzy environment accurately through α-level et. In the econd HOQ, the FWA method i utilized to compute the lower and upper bound of the upplier rating uing the weight of upplier election criteria obtained from the firt HOQ. Finally, the rank-order of upplier i obtained by employing a fuzzy number ranking method baed on area meaurement, which overcome the hortcoming of other ranking method. It i worth noting that the deciion model preented here i not retricted to medical upplier election and could be applied to a upplier election problem in another dicipline without any difficulty. Future reearch may concentrate on implementing the propoed deciion framework to group deciion making problem in real-life acro divere dicipline that can be repreented in HOQ tructure. Moreover, a uer interface can be developed for uer who are novice in mathematical programming. REFERENCES [1] K. Goffin, M. Szwejczewki, and C. New, Managing upplier: when fewer can mean more, International Journal of Phyical Ditribution & ogitic Management, vol. 27, pp , [2] C. A. Weber, J. R. Current, and W. C. Benton, Vendor election criteria and method, European Journal of Operational Reearch, vol. 50, pp. 2-18, [3] E. E. Karak, Fuzzy multiple objective deciion making approach to prioritize deign reuirement in uality function deployment, International Journal of Production Reearch, vol. 42, pp , [4] M. 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