Research Article An Integrated Model of Material Supplier Selection and Order Allocation Using Fuzzy Extended AHP and Multiobjective Programming

Transcription

1 Hidawi Publishig Corporatio Matheatical Probles i Egieerig Volue 2013, Article ID , 14 pages Research Article A Itegrated Model of Material Supplier Selectio ad Order Allocatio Usig Fuzzy Exteded AHP ad Multiobjective Prograig Zhi Li, 1 W. K. Wog, 1 ad C. K. Kwog 2 1 Istitute of Textiles ad Clothig, The Hog Kog Polytechic Uiversity, Hugho, Kowloo, Hog Kog 2 Departet of Idustrial ad Systes Egieerig, The Hog Kog Polytechic Uiversity, Hugho, Kowloo, Hog Kog Correspodece should be addressed to W. K. Wog; tcwogca@iet.polyu.edu.hk Received 15 October 2012; Accepted 14 Deceber 2012 Acadeic Editor: Yag Tag Copyright 2013 Zhi Li et al. This is a ope access article distributed uder the Creative Coos Attributio Licese, which perits urestricted use, distributio, ad reproductio i ay ediu, provided the origial work is properly cited. This paper presets a supplier selectio ad order allocatio (SSOA) odel to solve the proble of a ultiperiod supplier selectio ad the order allocatio i the eviroet of short product life cycle ad frequet aterial purchasig, for exaple, fast fashio eviroet i apparel idustry. At the first stage, with cosideratio of ultiple decisio criteria ad the fuzziess of the data ivolved i decidig the prefereces of ultiple decisio variables i supplier selectio, the fuzzy extet aalytic hierarchy process (FEAHP) is adopted. I the secod stage, supplier raks are iputted ito a order allocatio odel that ais at iiizig the risk of aterial purchasig ad iiizig the total aterial purchasig costs usig a dyaic prograig approach, subject to costraits o deteriistic custoer dead ad deteriistic supplier capacity. Nuerical exaples are preseted, ad coputatioal results are reported. 1. Itroductio Most aufacturers owadays face cutthroat copetitio i the ever-chagig arket, which leads to establishet of etwork orgaizatios. Supply chai aageet offers a itegrated decisio-akig fraework to adiister such orgaizatios. Oe of the key fuctios of supply chai aageet is the purchasig strategy. For a geeral producer, purchased ites (e.g., raw aterials) ca accout for 60% of total sales; purchasig shares orally accout for 50% to 90% of total turover i a idustrial copay [1]. Therefore, it is iportat to aage the process of supplier selectio ad the strategy of order allocatio i order to costruct a copetitive ad effective purchasig fuctio. Suitable suppliers ca give a copay a copetitive edge ad are istruetal to cost reductio ad iproveet i product quality. Various techiques have bee preseted to effectively evaluate ad select suppliers. For order allocatio proble, aterial purchasig aagers firstly deterie the optial aterials quatities purchased fro each supplier durig the purchasig period. A itegrated atheatical prograig odel has the bee established to solve supplier selectio ad order allocatio probles based o various assuptios adaptig to real-world productio Supplier Selectio. To deal with supplier selectio, ay ethodologies have bee proposed, icludig categorical ethods, case-based reasoig systes [2], statistical odels [1], total cost of owership odels [3], atheatical prograig, techiques for order preferece by siilarity to a ideal solutio (TOPSISs) [4], ad aalytic hierarchy processes (AHP) [5]. Aog these ethods, the aalytic hierarchy process (AHPs), first proposed by Saaty (1977), is a popular ultiple criteria decisio-akig techique [6] cobiig qualitative with quatitative criteria. It is used to rak potetial suppliers i a hierarchy syste [7, 8]. However, the AHP frequetly fails to adequately accoodate the iheret ucertaity ad iprecisio associated with appig decisio-akers perceptios o extracted ubers. It is difficult to respod to prefereces of decisio-akers by assigig precise uerical values. As a result, the fuzzy

2 2 Matheatical Probles i Egieerig aalytic hierarchy process (FAHP) is proposed [9, 10] which icorporates both the fuzzy ets theory ad the AHP. To prioritize decisio variables, Cha ad Kuar [11] proposed the fuzzy extet aalytic hierarchy process (FEAHP) which is used i differet types of proble [12, 13]. I additio, order allocatio is aother iportat topic, especially i a ultiplesupplier eviroet Order Allocatio. Foraterialpurchasigprocess,after choosig suitable suppliers, order allocatio is the ext iportat stage to deterie the optial aterials quatities purchased fro each supplier, especially i a ultiplesupplier eviroet. Various techiques have bee developed to solve the optial order allocatio proble, icludig liear prograig [14], oliear prograig [15, 16], ixed-iteger prograig [17], ad artificial itelligece techique [18 23]. These ethods aily focused o sigle objective optiizatio, that is, iiize cost. However, i a real-world supply chai eviroet, the decisio-aker ust cosider ucertai factors alog the supply chai. To reduce the risk, ay scholars [24 26] proposed ultiobjective optiizatio odels to idetify appealig tradeoffs betwee two or ore coflictig objectives ivolved i the order allocatio process. Furtherore, to deal with ucertaity, Xu ad Nozick [27] proposedatwo-stageixediteger stochastic prograig odel, which quatified the tradeoff betwee the risk ad cost o the basis of orderig, thus deteriig optial supplier sourcig decisios for varyig levels of risk tolerace. To solve the ultiperiod order allocatio proble, dyaic prograig has bee utilized. Wager ad Whiti [28] eployed a dyaic prograig solutio algorith to solve a dyaic lot-sizig proble with the objective of iiizig the total cost, uder tie-varyig deads for a sigle ite, ivetory holdig charges, ad setup costs. Baset ad Leug [29] exteded the odel, which has bee proposed by Wager ad Whiti, to a ulti-ite order allocatio proble, with ultiple suppliers durig a ultiperiod plaig horizo. Alidaee ad Kocheberger [30] solved the sigle-sik, fixed charge trasportatio proble by usig a dyaic prograig ethod which is able to deterie optial order quatities fro a set of potetial suppliers to achieve the iiizatio of cost based o the total aterials deads. Li et al. [31]copared periodically purchasig fro the spot arket with sigig a log-ter cotract with a sigle supplier with cosideratio of fluctuat stochastic dead ad price. Sawik [32]ivestigated the proble of ultiperiod supplier selectio ad order allocatio i ake-to-order eviroet ad proposed a ixed-iteger prograig approach to icorporate risk that uses coditioal value-at-risk via sceario aalysis, which is capable of optiizig the dyaic supply portfolio by calculatig value-at-risk of cost per part ad iiizig expected worst-case cost per part siultaeously. Based o the aforeetioed discussio, few studies [33, 34] have ivestigated aterial purchasig probles by itegratig supplier evaluatio ad order allocatio together. Specifically, research o aterial purchasig probles with cosideratio of the features of the fast fashio eviroet such as iprecise supplier evaluatio easure ad ultiperiod ad ultiobjective order allocatio, has ot bee reported so far. The ai purpose of this paper is to develop a supplier selectio ad order allocatio (SSOA) odel, which is a effective ulticriteria decisio-akig odel, to hadle aterial purchasig. Various features i fast fashio eviroet will be cosidered, icludig iprecise supplier evaluatio easure, ultiple order allocatio objectives, varyig purchasig prices, supplier capacities, ad custoer deads i differet periods. The SSOA odel will cobie FEAHP with ultiobjective dyaic liear prograig techique to geerate effective aterial purchasig solutios. The rest of this paper is orgaized as follows. Sectio 2 presets the atheatical odel of optial order allocatio basedosupplierrakigs.isectio 3, a supply selectio (rakig) ad order allocatio odel is developed. I Sectio 4, experietal results to validate the perforace oftheproposedodelarepreseted.coclusiosaredraw ad future research is suggested i Sectio Proble Descriptio To eet custoers deads ad ake a healthy profit, a aufacturer ust ake a effective sourcig pla based o custoers orders. I the textile idustry, aufacturers always eed to source coo aterials (e.g., white fabric) fro suppliers over a plaig horizo of differet periods i order to ecourage copetitio aog suppliers ad esure access to a wide variety of goods or services. Therefore, selectio of suitable suppliers ad a optial order allocatio pla becoe crucial. This study proposes a odel to hadle optial order allocatio based o supplier rakig. Theassuptiosofthisstudyareasfollows. (1) Each supplier ca provide aterials for aufacturers, ad suppliers have differet productio capacities. (2) Maufacturers ca get iforatio o each supplier i ters of productio capacity ad price at the begiig of each plaig horizo. (3) There is o ivetory of aterials, ad aufacturers eed to purchase all aterials for productio. Let I = {1,...,N} represet the set of N suppliers, J= {1,...,M}the set of M custoer orders, ad T = {1,...,H} the set of T plaig periods. x it deotes the order quatity fro supplier i. c it deotes the capacity of supplier i (i I)i period t. p it deotes the uit price of the aterial purchased fro supplier i (i I)iperiodt T. D t represets aufacturers deads for aterials based o custoers orders, kow ahead of aterial purchasig. r i represets the relative risk idex of supplier i, which idicates that a higher value of r i ca geerate a higher real purchasig risk. Supplier rakig ad order allocatio ivestigated i this research ca be forulated as follows: T i E (x it ) = i ( p it x it ), (1) t=1

3 Matheatical Probles i Egieerig 3 T i F (x it ) = i ( r i x it ), (2) t=1 s.t., (0 x it c it ), i,t, (3) x it =D t, i. (4) Forula (1) iiizes the total purchasig costs of aterials for all custoers orders. Forula (2) iiizes the total purchasig risks (e.g., delay risk ad defect risk). Forula (3) represets that the order quatities are ot ore tha the supplier s axiu capacity i ay purchasig periods.forula (4) requires that the supply ust satisfy the deads of aufacturers. 3. Methodologies for Supplier Selectio ad Order Allocatio This paper proposes a effective supplier selectio (rakig) ad order allocatio (SSOA) odel based o the FEAHP ad dyaic prograig (DP). This odel coprises a FEAHP-based supplier/criteria rakig process ad a DPbased order allocatio process (Figure 1). The details of the SSOA odel are described as follows The FEAHP Method. The AHP has bee widely used to address ulticriteria decisio-akig probles. It oly requires a discrete scale fro oe to ie. However, hua judgeet is ucertai of criteria s prefereces. The liguistic assesset of hua feeligs ad judgeet is vague ad caot be represeted reasoably i precise ubers. Hece, triagular fuzzy ubers are used to decide the priority of decisio variables. Sythetic extet aalysis is used to decide thefialpriorityweightsbasedotriagularfuzzyubers Triagular Fuzzy Nubers ad Represetatio of Prefereces. A fuzzy set [35, 36] is characterized by a ebership fuctio, which assigs to each object a grade of ebership ragig fro 0 to 1. The geeral ters large, ediu ad sall are used i fuzzy set to capture a rage of uerical values. If l,, ad u, respectively, deote the sallest possible value, the ost proisig value, ad the largest possible value that describe a fuzzy evet, the triagular fuzzy uber (TFN) ca be deoted as a vector (l,, u),wherel u. Whe l==u, it is a ofuzzy uber by covetio. The ebership fuctio ca be defied as (x 1) ( 1), { 1 x, μ (x M) = (u x) { (u ), x u, { 0 otherwise. TFNs M 1, M 3, M 5, M 7,adM 9 are used to represet the pairwise copariso of decisio variables fro equal to absolutely preferred, ad TFNs M 2, M 4, M 6,adM 8 represet the iddle preferece values aog the. Figure2 (5) Liguistic variables Table 1: Triagular fuzzy ubers. Positive triagular fuzzy uber Positive reciprocal triagular fuzzy uber Extreely strog (8, 9, 9) (1/9, 1/9, 1/8) Iterediate (7, 8, 9) (1/9, 1/8, 1/7) Very strog (6, 7, 8) (1/8, 1/7, 1/6) Iterediate (5, 6, 7) (1/7, 1/6, 1/5) Strog (4, 5, 6) (1/6, 1/5, 1/4) Iterediate (3, 4, 5) (1/5, 1/4, 1/3) Moderately strog (2, 3, 4) (1/4, 1/3, 1/2) Iterediate (1, 2, 3) (1/3, 1/2, 1) Equally strog (1, 1, 2) (1/2, 1, 1) shows the ebership fuctios of the TFNs, M i =(l i, i, u i ),wherei = 1,2,...,9,adl i, i,u i are the lower, iddle, ad upper values of the fuzzy uber M i,respectively Fuzzy Extet Aalytic Hierarchy Process (FEAHP). The FEAHP was origially itroduced by Chag (1996). Soe calculatio steps are essetial ad explaied as follows. Let X = {x 1,x 2,x 3,...,x } be a object set ad G = {g 1,g 2,g 3,...,g } a goal set. Accordig to Chag s ethod, each object is take, ad extet aalysis of each goal is perfored. Therefore, extet aalysis values for each object ca be obtaied with the followig sigs: M 1 g i,m 2 g i,...,m g i, i = 1,2,...,,whereM j g i (j = 1,2,...,) are the triagular fuzzy ubers (TFNs). Step 1. Costructig a hierarchical structure with decisio eleets, decisio-akers are required to ake pairwise coparisos betwee decisio alteratives ad criteria usig a ie-poit scale (Table 1). All atrices are developed, ad all pairwise coparisos are obtaied fro each decisioaker. Step 2. The fuzzy sythetic extet value with respect to the ith object is defied as: S j = j=1 M j g i [ M j ] g i j=1 [ ] 1. (6) To obtai j=1 Mj g i, the fuzzy additio operatio of extet aalysis values for a particular atrix is perfored as j=1 M j g i = ( j=1 l j, j=1 j, j=1 u j ). (7) To obtai [ j=1 Mj g i ], the fuzzy additio operatio of M j g i (j=1,2,...,)valuesisperforedas M j g i =( j=1 l i, i, u i ). (8)

4 4 Matheatical Probles i Egieerig Cadidate suppliers FEAHP-based supplier selectio process Selected suppliers ad their risk idexes Maufacturer s purchasig dead DP-based order allocatio process Supplier s capacity Purchasig order allocatio solutio Figure 1: The processes of SSOA Fairly Very Equal Moderate strog strog Absolute M 1 M 2 M 3 M 4 M 5 M 6 M 7 M 8 M 9 V (M 2 M 1 ) 1 M 2 M 1 D l 2 2 l 1 d u 2 1 u Figure 2: The ebership fuctios of triagular fuzzy ubers. Figure 3: The itersectio betwee M 1 ad M 2. Ad the iverse of the previous vector is coputed as [ M j ] g i j=1 [ ] 1 = ( 1 u, i 1 1, i l ). (9) i Step 3. As M 1 =(l 1, 1,u 1 ) ad M 2 =(l 2, 2,u 2 ) are two triagular fuzzy ubers, the degree of M 2 =(l 2, 2,u 2 ) M 1 =(l 1, 1,u 1 ) possibility of is defied as V(M 2 M 1 )=sup {i (μ M1 (x),μ M2 (y))} (10) y x cabeexpressedasfollows: V(M 2 M 1 )=hgt(m 2 M 1 )=μ M2 (d) { 1, if 2 1, = l { 1 u 2, otherwise. { ( 2 u 2 ) ( 1 l 1 ) (11) Equatio (11) (Figure 3) idicates that d is the ordiate of the highest itersectio poit D betwee μ M1 ad μ M2. To copare M 1 ad M 2,thevaluesofV(M 2 M 1 ) ad V(M 1 M 2 ) are eeded. Step 4. The degree of possibility that the covex fuzzy uber is greater tha k covex fuzzy M i (,2,...,k)ubers ca be defied by V(M M 1,M 2,...,M k ) =V[(M M 1 ) ad (M M 2 ),...,ad (M M k )] = i V(M M i ), (,2,3,...,k). (12) Assue that d(a i )=i V(S i S k ) for k = 1,2,...,; k =1. The, the weight vector is give by W =(d (A 1 ),d (A 2 ),...,d (A )) τ, (13) where A i (,2,3,...,)are eleets. Step 5. Via oralizatio, the oralized weight vectors are W = (d (A 1 ),d(a 2 ),...,d(a )) τ, (14) where W is a ofuzzy uber. The upward copositio of these weights (fro the lowest to the top level) geerates the rakig scores (weights) of eleets at the lowest level (i.e., suppliers) i fulfillig the topost objective (i.e., suppliers rakig) FEAHP-Based Supplier Rakig. As discussed i the itroductio, supplier rakig gives decisio-akers a

5 Matheatical Probles i Egieerig 5 effective techique to choose suitable suppliers. I this research, supplier rakig is ipleeted by the FEAHP ethod. The procedure is detailed as follows. Step 1 (defie criteria for supplier selectio). To defie effective criteria for supplier selectio, this research collects proisig cadidate criteria based o existig research results (Dickso 1966; Cha ad Kuar [11] 2007), ad ay additioal criteria deeed iportat for aufacturers are icluded. O the basis of the cadidate criteria selected, structured iterviews are used to evaluate these criteria by three seior specialists, icludig a seior desiger ad two purchasig aagers deoted by (R1), (R2), ad (R3), respectively. To evaluate cadidate criteria, the respodets are requested to use the liguistic assesset of hua feeligs (Table 1). Upo receivig the iputs of the respodets, the criteria are idetified ad averaged. If there are too ay criteria, the pairwise copariso ca becoe a difficult ad tiecosuig process. To overcoe these probles, the criteria saveragevalueitop5isselected.ithispaper,the5 fial criteria are (1) overall cost of products (C 1 ); (2) quality of product (C 2 ); (3) risk factors (C 3 ); (4) a supplier s profile (C 4 ); (5) service perforace of a supplier (C 5 ). Step 2 (defie subcriteria for supplier selectio). To evaluate suppliers ore precisely, each selected criterio i Step 1 eeds to be further represeted by several subcriteria. The idetificatio ad selectio of these subcriteria ca be ipleeted as described i Step 1. If the subcriteria are still obscure, they ca be re-represeted by sub-subcriteria usig thesaeprocess. Step 3 (structure the hierarchical odel ad each criterio s weight). I this step, the FEAHP hierarchy odel is built, ad the weight of each supplier selectio odel is calculated. The developed FEAHP odel, based o the idetified criteria, subcriteria ad subcriteria s subcriteria, has five levels: goals, criteria, subcriteria, subcriteria s subcriteria, ad cadidates. Figure4 shows the 5-level hierarchy for supplier selectio. The goal of supplier selectio for aufacturers is idetified o the first level. The secod level (criteria) cotais 5 criteria etioed i Step 1. The third ad fourth levels cosist of subcriteria ad subcriteria s subcriteria (subcriteria s subcriteria are ot cosidered i this paper s uerical experietatio). The lowest level of the hierarchy cotais alteratives. That is, differet suppliers are evaluated i order to pick the best oes. As show i Figure 4, differet suppliers are used to represet the arbitrary oes which aufacturers wish to evaluate. The FEAHP odel (Figure 4) is geerally applicable to ay type of supplier selectio by aufacturers as it covers ay iportat factors ad their related criteria, subcriteria, ad subcriteria s subcriteria. I order to obtai the priority weight of each criterio o eachlevel,asecodstructureisdoeiasiilaraer as Step 1. The iterview cosistig of factors o each level of the FEAHP odel is used to collect the judgets of pairwise coparisos fro all evaluatio tea ebers. This judgets is perfored usig pairwise coparisos, which are elaborated isectio A exaple of the pairwise copariso atrix is show i Table 2. Step 4 (easure supplier perforace ad idetify supplier priority). After obtaiig the priority weight of each criterio ad subcriterio, the third structured iterview is desiged ad odified. This iterview collects the weights of alteratives to idetify the best suppliers. The priority weight is deteried for alteratives i this step. The copetitive rivals that are supposed to be suppliers for aufacturers are copared by each subcriteria stadard.afterfidigthelocalweightofeachalterative i subcriteria, the global weight of each alterative i each criterio ca be calculated. The evaluatio of the global weight of each alterative ca be obtaied by ultiplyig the global weights of subcriteria ad the local weight of each alterative. Based o the global priority, the weight of each alterative ca be evaluated ad suarized. A exaple of FEAHP-based supplier rakig is described i Sectio Dyaic Prograig. As purchasig price is tievaryig i the odel, the cost objective is judiciously captured by the followig dyaic value fuctio: V 1,t = i { 0 x it c it p it x it +V 1,t+1 (D t x it )}, (15) where stage is decisio dates i tie periods, t = 1,2,...,T. The decisio variable is the quatities ordered fro supplier i, x it =0,1,...,c it. To accout for both objectives, a distace-to-ideal fraework is eployed to itegrate the risk ad cost objective fuctios, usig the optial values of idividual objectives obtaied earlier. To icorporate the ideal values of risk ad cost, the su (weights) of deviatios fro such ideal values is iiized. Hece, a dyaic value fuctio is derived as follows: V 2,t = i 0 x it c it {w c1 p it x it +w c3 +V 2,t+1 (D t x it w i x it )}, (16) where V 2,t is the iiu total weighted deviatio. w c1 is the cost weight defied by decisio-akers usig the FEAHP. w c3 is the risk weight defied by decisio-akers usig the FEAHP. 4. Nuerical Experiets To validate the effectiveess of the proposed SSOA odel, a series of experiets are coducted to obtai idustrial data fro a apparel aufacturer. The aufacturer eeds to purchase a specified aout of raw fabric fro 3 appropriate aterial suppliers for the productio of its custoers orders.

6 6 Matheatical Probles i Egieerig Table 2: The fuzzy evaluatio of criteria of the overall objective. C 1 C 2 C 3 C 4 C 5 Weights C 1 (1, 1, 1) (2, 3, 4) (3, 4, 5) (5, 6, 7) (2, 3, 4) 0.43 C 2 (0.25, 0.33, 0.5) (1, 1, 1) (3, 4, 5) (2, 3, 4) (4, 5, 6) 0.33 C 3 (0.2, 0.25, 0.33) (0.2, 0.25, 0.33) (1, 1, 1) (3, 4, 5) (2, 3, 4) 0.13 C 4 (0.14, 0.17, 0.2) (0.25, 0.33, 0.5) (0.2, 0.25, 0.33) (1, 1, 1) (2, 3, 4) 0.02 C 5 (0.25, 0.33, 0.5) (0.17, 0.2, 0.25) (0.25, 0.33, 0.5) (0.25, 0.33, 0.5) (1, 1, 1) 0.09 Level 1. Overall objective Supplier selectio Level 2. Criteria Level 3. Subcriteria Cost (C 1 ) Quality (C 2 ) Risk (C 3 ) Profile (C 4 ) Service (C 5 ) Level 4. Subcriteria Level 5. Decisio alteratives Supplier 1 (S1) Supplier 2 (S2) Supplier (S) Figure 4: Geeral hierarchy for supplier selectio. The 3 suppliers have bee selected fro its N collaborative suppliers. The aufacturer seeks to deterie how uch should be purchased fro the 3 key suppliers i order to iiize its overall cost ad axiize its utility over a ultiperiod plaig horizo Experiet for FEAHP-Based Supplier Rakig. The FEAHP starts fro the pairwise copariso atrices of five criteria (Table 2).Based o these atrices,the weights of suppliers ad criteria are calculated ad preseted i Table 3. The supplier s iforatio ad aufacturer s deads are show i Tables 4 ad 5,respectively.Thesolutiostosigle objectives are show i Table 6, where cost is iiu. Table 7 shows the order allocatio based o iiu risk. This paper presets the results of 6 experiets. The criteria for selectio of global suppliers are as follows: (i) overall cost of products (C 1 ):productprice(a 1 ), freight cost (A 2 ), pealty for delayed payet (A 3 ), ad tariff ad custo duties (A 4 ); (ii) product quality (C 2 ):rejectiorate(a 5 ), respose to chages (A 6 ),adrateofwarratyclais(a 7 ); (iii) risk factors (C 3 ):leadtie(a 8 ), political stability (A 9 ), geographical locatio (A 10 ), ad iability to eet further requireets (A 11 ); (iv) supplier s profile (C 4 ):fiacialstatus(a 12 ), perforace history (A 13 ), ad productio capacity (A 14 ); (v) service perforace of suppliers (C 5 ):reedyfor quality probles (A 15 ) ad delivery schedule (A 16 ). These criteria ca be foud i the hierarchical structure show i Figure Deteriatio of Criteria ad Subcriteria Weights. The exaple of the pairwise copariso atrices shows that the fifthrowadcoluattachiportacetotherow scriterio relative to the colu s criterio (Table 2). Due to a good cost perforace, the criterio for the first row is slightly preferred to the oe o product quality, risk

7 Matheatical Probles i Egieerig 7 Level 1. Overall objective Supplier selectio Level 2. Criteria Cost (C 1 ) Quality (C 2 ) Risk (C 3 ) Profile (C 4 ) Service (C 5 ) Level 3. Subcriteria A 1 A 2 A 5 A 6 A 8 A 9 A 12 A 13 A 15 Level 4. Decisio alteratives Supplier 1 (S1) Supplier 2 (S2) Supplier 3 (S3) Figure 5: Hierarchy for supplier selectio. Table 3: The fuzzy evaluatio of the attributes of criterio C 1. A 1 A 2 A 3 A 4 Weights A 1 (1, 1, 1) (2, 3, 4) (3, 4, 5) (3, 4, 5) 0.49 A 2 (0.25, 0.33, 0.5) (1, 1, 1) (3, 4, 5) (2, 3, 4) 0.31 A 3 (0.2, 0.25, 0.33) (0.2, 0.25, 0.33) (1, 1, 1) (3, 4, 5) 0.09 A 4 (0.2, 0.25, 0.33) (0.25, 0.33, 0.5) (0.2, 0.25, 0.33) (1, 1, 1) 0.11 Table 4: The fuzzy evaluatio of the attributes of criterio C 2. A 5 A 6 A 7 Weights A 5 (1, 1, 1) (4, 5, 6) (2, 3, 4) 0.55 A 6 (0.17, 0.2, 0.25) (1, 1, 1) (3, 4, 5) 0.19 A 7 (0.25, 0.33, 0.5) (0.2, 0.25, 0.33) (1, 1, 1) 0.26 factors, ad service perforace of suppliers (the fuzzy values of (2, 3, 4), (3, 4, 5), ad(2,3,4), resp.), which is strogly preferred to the supplier s profile (the value of (5, 6, 7)). Due to a good quality perforace, the criterio for the secod row ad colu is oderately ore iportat tha the service perforace of suppliers (the value of (4, 5, 6)). Havig fewer risk factors, the third row s criterio is slightly preferred to a good profile (value of (3, 4, 5)). Decisio akers oly eed tofillitheupperhalfofthecoparisoatrixbyassuig that the pairwise copariso of cost ad service perforace is (2, 3, 4),followigthepairwisecoparisoofservice perforace ad cost (0.25, 0.33, 0.5).Thevalueof(1, 1, 1) is assiged to diagoal eleets. Calculate various decisio alteratives of fuzzy ubers basedo Sectio3 as follows: S c1 = (13, 17, 21) ( , , ) = (0.23, 0.37, 0.60), S c2 = (10.25, 13.33, 16.5) ( , , ) = (0.18, 0.29, 0.47), S c3 = (6.40, 8.50, 10.67) ( , , ) = (0.11, 0.19, 0.30), S c4 = (3.59, 4.75, 6.03) ( , , ) = (0.06, 0.10, 0.17), S c5 = (1.92, 2.20, 2.75) ( , , ) = (0.03, 0.05, 0.08). Copare the followig decisio alteratives: V(S c1 S c2 )=1, V(S c1 S c3 )=1, V(S c1 S c4 )=1, V(S c1 S c5 )=1, V(S c2 S c1 ) = 0.75, V (S c2 S c3 )=1, (17)

8 8 Matheatical Probles i Egieerig Table 5: The fuzzy evaluatio of the attributes of criterio C 3. A 8 A 9 A 10 A 11 Weights A 8 (1, 1, 1) (4, 5, 6) (4, 5, 6) (1, 1, 2) 0.59 A 9 (0.17, 0.2, 0.25) (1, 1, 1) (4, 5, 6) (2, 3, 4) 0.39 A 10 (0.17, 0.2, 0.25) (0.17, 0.2, 0.25) (1, 1, 1) (3, 4, 5) 0.01 A 11 (0.5, 1, 1) (0.25, 0.33, 0.5) (0.2, 0.25, 0.33) (1, 1, 1) 0.01 Table 6: The fuzzy evaluatio of the attributes of criterio C 4. A 12 A 13 A 14 Weights A 12 (1, 1, 1) (3, 4, 5) (3, 4, 5) 0.51 A 13 (0.2, 0.25, 0.33) (1, 1, 1) (3, 4, 5) 0.18 A 14 (0.2, 0.25, 0.33) (0.2, 0.25, 0.33) (1, 1, 1) 0.31 Table 7: The fuzzy evaluatio of the attributes of criterio C 5. A 15 A 16 Weights A 15 (1, 1, 1) (3, 4, 5) 0.52 A 16 (0.2, 0.25, 0.33) (1, 1, 1) 0.48 V(S c2 S c4 )=1, V(S c2 S c5 )=1, V(S c3 S c1 ) = 0.29, V (S c3 S c2 ) = 0.54, V(S c3 S c4 )=1, V(S c3 S c5 )=1, V(S c4 S c1 ) = 0.27, V (S c4 S c2 ) = 0.05, V(S c4 S c3 ) = 0.42, V (S c4 S c5 )=1, V(S c5 S c1 ) = 0.87, V (S c5 S c2 ) = 0.72, V(S c5 S c3 ) = 0.33, V (S c5 S c4 ) = Calculate the followig decisio alteratives weights: d (c 1 )=i (1, 1, 1, 1) =1, d (c 2 )=i (0.75, 1, 1, 1) = 0.75, d (c 3 )=i (0.29, 0.54, 1, 1) = 0.29, d (c 4 )=i (0.27, 0.05, 0.42, 1) = 0.05, d (c 5 )=i (0.87, 0.72, 0.33, 0.21) = (18) (19) Priority weights for W = (1, 0.75, 0.29, 0.05, 0.21) vector. Noralizig the W vector: w 1 = w 2 = = 0.43, = 0.33, 0.29 w 3 = = 0.13, 0.05 w 4 = = 0.02, 0.21 w 5 = = (20) After oralizatio of the values, priority weights of the ai goal are calculated as (0.43, 0.33, 0.13, 0.02, 0.09). The results (pricipal vectors) show that the criteria have the followig approxiate priority weights: cost (0.43), quality (0.33),risk(0.13),supplier s profile(0.02) ad service perforace of suppliers (0.09). Differet attributes are copared by each criterio separatelywiththesaeprocedureasdiscussedabove.thefuzzy evaluatio atrices of attributes ad the weight vectors of subcriteria are show i Tables 3, 4, 5, 6,ad Calculate the Suppliers Weights. Siilarly, the fuzzy evaluatio atrices of decisio alteratives ad the correspodig weight vector of each alterative with respect to the correspodig attributes are deteried. The priority weights of suppliers with respect to each criterio are give by addig each supplier s weight to each correspodig attribute s weight. The results are show i Tables 8, 9, 10, 11, ad 12. Fially,thepriorityweightofeachsuppliercabecalculated by ultiplyig the weight of each correspodig criterio.theresultsareshowitable 13.Thesuaryofthe overall attributes is show i Table 13.It should be oted that aog the three give suppliers, S1 has the highest weight ad therefore is selected as the best supplier to satisfy the goals ad objectives of the aufacturig copay. Table 13 also shows the fial score of each supplier s results ad rakigs. As ca be see, S1 (0.5) scores higher tha S2 (0.23) ad S3 (0.23). The iportat results are show i Figures 6 ad Experiet for Dyaic Order Allocatio. Arealapparel aufacturer purchasig eviroet usually has the followig four scearios. (1) A aufacturer s dead for coo aterial is the sae i all plaig periods; i order to obtai orders steadily, suppliers reserve a certai capacity ad offer a reasoable price. (2) Deads for coo aterial are steady, but suppliers do ot reserve a certai capacity; so,priceadcapacityfluctuateidifferetplaigperiods. (3) Suppliers prices are differet throughout the plaig

9 Matheatical Probles i Egieerig 9 Table 8: The fuzzy evaluatio of the subcriteria of criterio C 1. A 1 A 2 A 3 A 4 Alterative priority Weight weight Alteratives S S S Table 9: The fuzzy evaluatio of the subcriteria of criterio C 2. A 5 A 6 A 7 Alterative priority Weight weight Alteratives S S S Table 10: The fuzzy evaluatio of the subcriteria of criterio C 3. A 8 A 9 A 10 A 11 Alterative priority Weight weight Alteratives S S S Table 11: The fuzzy evaluatio of the subcriteria of criterio C 4. A 12 A 13 A 14 Alterative priority Weight weight Alteratives S S S C 1 C 2 C 3 C 4 C 5 S1 S2 S3 Figure 6: The suppliers based o the criteria. Priority scores Table 12: The fuzzy evaluatio of the subcriteria of criterio C 5. A 15 A 16 Alterative priority Weight weight Alteratives S S S period. (4) Suppliers capacities ad prices are differet throughout the plaig periods Sceario 1: Suppliers Ca Reserve a Certai Capacity ad Offer a Reasoable Price i All Plaig Periods. After gettig the weight score of each supplier ad criterio i the first stage, w c1 = 0.43 ad w c2 = I additio to havig the capacity ad price iforatio o each supplier, the S1 S2 S3 Priority scores Figure 7: Fial priority weights of the suppliers. dyaic approach etioed i Sectio 3.2 ca be rewritte as follows: V 2,t = i {0.43 p it x it x it c it +V 2,t+1 (D t x it w i x it )}. (21) If the aufacturer etirely just focuses o iiizig cost aloe, the risk will icrease substatially by 215%

10 10 Matheatical Probles i Egieerig Table 13: Dead iforatio. Period Dead Table 14: Price ad capacity iforatio. Supplier Orderig price (per uit) Period 1 Period 2 Period 3 Capacity S S S Table 15: Optial order quatities with respect to iiu risk. S S2 S3 Table 16: Optial order quatities with respect to iiu cost. S S S3 Table 17: Optial order quatity with respect to iiu cost ad risk. S S2 1 1 S tha etirely focusig o iiizig risk. O the opposite extree, if the aufacturer just etirely focuses o iiizig risk, this would raise its cost by 20% tha just etirely focuses o iiizig cost oly. By applyig the bi-objective dyaic fuctio, the tradeoff solutio icurs at 13.9% ad 94% higher tha the objective of iiizig cost ad iiizig risk respectively. These experietal results show that the proposed dyaic prograig approach ca geerate a better trade-off solutio tha etirely focusig o iiizig cost ad iiizig risk aloe. (Tables 13, 14, 15, 16, ad 17) Sceario 2: Suppliers Have Differet Capacities ad Offer Differet Prices i Differet Plaig Periods. After gettig the weight score of each supplier ad criterio i the first stage, w c1 = 0.43 ad w c2 = I additio to havig the capacity ad price iforatio o each supplier, the Table 18: Dead iforatio. Period Dead Table 19: Price ad capacity iforatio. Supplier Orderig price (per uit) Period 1 Period 2 Period 3 Capacity S S S Table 20: Optial order quatities with respect to iiu risk. S S2 S3 Table 21: Optial order quatities with respect to iiu cost. S S2 2 2 S dyaic approach etioed i Sectio 3.2 ca be rewritte as follows: V 2,t = i {0.43 p it x it x it c it +V 2,t+1 (D t x it w i x it )}. (22) If the aufacturer etirely just focuses o iiizig cost aloe, the risk will icrease substatially by 141% tha etirely focusig o iiizig risk. O the opposite extree, if the aufacturer just etirely focuses o iiizig risk, this would raise its cost by 20.7% tha just etirely focuses o iiizig cost oly. By applyig the bi-objective dyaic fuctio, the tradeoff solutio icurs at 9.2% ad 77% higher tha the objective of iiizig cost ad iiizig risk respectively. These experietal results show that the proposed dyaic prograig approach ca geerate a better trade-off solutio tha etirely focusig o iiizig cost ad iiizig risk aloe. (Tables 18, 19, 20, 21,ad22). If the aufacturer etirely just focuses o iiizig cost aloe, the risk will icrease substatially by 61.1% tha etirely focusig o iiizig risk. O the opposite extree, if the aufacturer just etirely focuses o iiizig risk, this would raise its cost by 12.2% tha just etirely focuses o iiizig cost oly. By applyig the bi-objective dyaic fuctio, the tradeoff solutio icurs at 4.1% ad 17.8% higher tha the objective of iiizig cost ad iiizig risk respectively. These

11 Matheatical Probles i Egieerig 11 Table 22: Optial order quatity with respect to iiu cost ad risk. S S2 3 S3 3 1 Table 23: Dead iforatio. Period Dead Supplier Table 24: Price ad capacity iforatio. Orderig price (per uit) period Capacity S S S Table 25: Optial order quatities with respect to iiu risk. Period Total risk Total cost S S2 S Table 26: Optial order quatities with respect to iiu cost. Period Total risk Total cost S S2 6 6 S3 6 1 Table 27: Optial order quatity with respect to iiu cost ad risk. Period Total risk Total cost S S2 2 S experietal results show that the proposed dyaic prograig approach ca geerate a better trade-off solutio tha etirely focusig o iiizig cost ad iiizig risk aloe. (Tables 23, 24, 25, 26,ad27) Sceario 3: The Maufacturer s Deads ad the Supplier s Prices Are Differet throughout the Plaig Periods. After gettig the weight score of each supplier ad criterio i the first stage, w c1 = 0.43 ad w c2 = I additio to havig the capacity ad price iforatio o each supplier, the Table 28: Dead iforatio. Period Dead Table 29: Price ad capacity iforatio. Supplier Orderig price (per uit) Period 1 Period 2 Period 3 Capacity S S S Table 30: Optial order quatities with respect to iiu risk. S S2 1 S dyaic approach etioed i Sectio 3.2 ca be rewritte as follows: V 2,t = i {0.43 p it x it x it c it +V 2,t+1 (D t x it w i x it )}. (23) If the aufacturer etirely just focuses o iiizig cost aloe, the risk will icrease substatially by 28% tha etirely focusig o iiizig risk. O the opposite extree, if the aufacturer just etirely focuses o iiizig risk, this would raise its cost by 4% tha just etirely focuses o iiizig cost oly. By applyig the bi-objective dyaic fuctio, the tradeoff solutio icurs at 1% ad 16% higher tha the objective of iiizig cost ad iiizig risk respectively. These experietal results show that the proposed dyaic prograig approach ca geerate a better trade-off solutio tha etirely focusig o iiizig cost ad iiizig risk aloe. (Tables 28, 29, 30, 31,ad32). If the aufacturer etirely just focuses o iiizig cost aloe, the risk will icrease substatially by 32% tha etirely focusig o iiizig risk. O the opposite extree, if the aufacturer just etirely focuses o iiizig risk, this would raise its cost by 4% tha just etirely focuses o iiizig cost oly. By applyig the bi-objective dyaic fuctio, the tradeoff solutio icurs at 1% ad 15.7% higher tha the objective of iiizig cost ad iiizig risk respectively. These experietal results show that the proposed dyaic prograig approach ca geerate a better trade-off solutio tha etirely focusig o iiizig cost ad iiizig risk aloe. (Tables 33, 34, 35, 36,ad37) Sceario 4: Deads, Price, ad Capacity Are Differet throughout the Plaig Periods. After gettig the weight

12 12 Matheatical Probles i Egieerig Table 31: Optial order quatities with respect to iiu cost. S S S Table 32: Optial order quatity with respect to iiu cost ad risk. S S S Table 33: Dead iforatio. Period Dead Supplier Table 34: Price ad capacity iforatio. Orderig price (per uit) period Capacity S S S Table 35: Optial order quatities with respect to iiu risk. Period Total risk Total cost S S2 1 S Table 36: Optial order quatities with respect to iiu cost. Period Total risk Total cost S S S Table 37: Optial order quatity with respect to iiu cost ad risk. Period Total risk Total cost S S S score of each supplier ad criterio i the first stage, w c1 = 0.43 ad w c2 = I additio to havig the capacity ad Table 38: Dead iforatio. Period Dead Table 39: Price ad capacity iforatio. Supplier Orderig price (per uit) Capacity period S S S Table 40: Optial order quatities with respect to iiu risk. S S2 1 S price iforatio o each supplier, the dyaic approach etioed i Sectio 3.2 ca be rewritte as follows: V 2,t = i {0.43 p it x it x it c it +V 2,t+1 (D t x it w i x it )}. (24) If the aufacturer etirely just focuses o iiizig cost aloe, the risk will icrease substatially by 20% tha etirely focusig o iiizig risk. O the opposite extree, if the aufacturer just etirely focuses o iiizig risk, this would raise its cost by 5% tha just etirely focuses o iiizig cost oly. By applyig the bi-objective dyaic fuctio, the tradeoff solutio icurs at 1% ad 9% higher tha the objective of iiizig cost ad iiizig risk respectively. These experietal results show that the proposed dyaic prograig approach ca geerate a better trade-off solutio tha etirely focusig o iiizig cost ad iiizig risk aloe. (Tables 38, 39, 40, 41,ad42). 5. Coclusios This paper ivestigates the topic of ultiobjective order allocatio based o supplier selectio i the purchasig stage with sigle aterial ad ultiple suppliers take ito cosideratio. A atheatical odel for ivestigatio is established, which cosiders iiizig the total cost ad risk i all purchasig processes. These objectives are particularly useful for aufacturig copaies to survive i a ake-toorder eviroet ad iprove the perforace of supply chai aageet. The SSOA odel coprises two processes, aely, a FEAHP-based supplier/criteria rakig process ad a DPbased order allocatio process. I the FEAHP process, the weight of each criterio ad supplier is obtaied. Based

13 Matheatical Probles i Egieerig 13 Table 41: Optial order quatities with respect to iiu cost. S S S Table 42: Optial order quatity with respect to iiu cost ad risk. S S S3 3 6 o their weights, the optial order allocatio solutio is obtaied usig the DP techique. The effectiveess of the proposed optiizatio odel is validated by usig real data fro a aufacturig copay. The experietal results show that the proposed odel ca hadle order allocatio effectively. The proposed optiizatio odel ca hadle order allocatiobasedosupplierselectio.furtherresearchwillcosider the effects of various ucertaities o supply chai aageet, such as ucertai custoers orders ad possible aterial shortages. Ackowledget The authors would like to ackowledge the fiacial support of The Hog Kog Polytechic Uiversity uder the RPUG project. Refereces [1] L. de Boer, E. Labro, ad P. Morlacchi, A review of ethods supportig supplier selectio, Europea Joural of Purchasig ad Supply Maageet,vol.7,o.2,pp.75 89,2001. [2] A. Aaodt ad E. Plaza, Case-based reasoig: foudatioal issues, ethodological variatios, ad syste approaches, AI Couicatios,vol.7,o.1,pp.39 59,1994. [3] Z. Degraeve, E. Labro, ad F. Roodhooft, Evaluatio of vedor selectio odels fro a total cost of owership perspective, Europea Joural of Operatioal Research,vol.125,o.1,pp.34 58, [4] H.Deg,C.H.Yeh,adR.J.Willis, Iter-copaycopariso usig odified TOPSIS with objective weights, Coputers ad Operatios Research,vol.27,o.10,pp ,2000. [5] T. L. Saaty, How to ake a decisio: the aalytic hierarchy process, Europea Joural of Operatioal Research, vol. 48, o. 1, pp. 9 26, [6] R. E. Steuer ad P. Na, Multiple criteria decisio akig cobied with fiace: a categorized bibliographic study, Europea Joural of Operatioal Research, vol.150,o.3,pp , [7] B. Srdjevic ad Z. Srdjevic, Bi-criteria evolutio strategy i estiatig weights fro the ahp ratio-scale atrices, Applied Matheatics ad Coputatio, vol.218,o.4,pp , [8] A. Ishizaka, D. Balkeborg, ad T. Kapla, Does AHP help us ake a choice? A experietal evaluatio, Joural of the Operatioal Research Society,vol.62,o.10,pp ,2011. [9] P. J. M. va Laarhove ad W. Pedrycz, A fuzzy extesio of Saaty s priority theory, Fuzzy Sets ad Systes, vol. 11, o. 1 3, pp ,1983. [10] J. J. Buckley, Fuzzy hierarchical aalysis, Fuzzy Sets ad Systes,vol.17,o.3,pp ,1985. [11] F. T. S. Cha ad N. Kuar, Global supplier developet cosiderig risk factors usig fuzzy exteded AHP-based approach, Oega,vol.35,o.4,pp ,2007. [12] Y. M. Wag, Y. Luo, ad Z. Hua, O the extet aalysis ethod for fuzzy AHP ad its applicatios, Europea Joural of Operatioal Research,vol.186,o.2,pp ,2008. [13] M. Dagdevire ad I. Yuksel, Developig a fuzzy aalytic hierarchy process (ahp) odel for behavior-based safety aageet, Iforatio Scieces, vol. 178, o. 6, pp , [14] S. H. Ghodsypour ad C. O Brie, A decisio support syste for supplier selectio usig a itegrated aalytic hierarchy process ad liear prograig, Iteratioal Joural of Productio Ecooics, vol , pp , [15]H.Fazlollahtabar,I.Mahdavi,M.T.Ashoori,S.Kaviai,ad N. Mahdavi-Airi, A ulti-objective decisio-akig process of supplier selectio ad order allocatio for ulti-period schedulig i a electroic arket, Iteratioal Joural of Advaced Maufacturig Techology,vol.52,o.9 12,pp , [16] Y. Tag, Z. Wag, ad J. A. Fag, Cotroller desig for sychroizatio of a array of delayed eural etworks usig a cotrollable probabilistic PSO, Iforatio Scieces, vol. 181, o. 20, pp , [17] S. H. Ghodsypour ad C. O Brie, The total cost of logistics i supplier selectio, uder coditios of ultiple sourcig, ultiple criteria ad capacity costrait, Iteratioal Joural of Productio Ecooics,vol.73,o.1,pp.15 27,2001. [18] Z. Guo, W. Wog, S. Leug, ad M. Li, Applicatios of artificial itelligece i the apparel idustry: a review, Textile Research Joural,vol.81,o.18,pp ,2011. [19] Y. Tag, H. Gao, J. Kurths, ad J. Fag, Evolutioary piig cotrol ad its applicatio i uav coordiatio, IEEE Trasactios o Idustrial Iforatics,vol.8,o.4,pp ,2012. [20] Y. Tag, Z. Wag, W. Wog, J. Kurths, ad J. Fag, Feedback learig particle swar optiizatio, Applied Soft Coputig, vol. 11, o. 8, pp , [21] W.Zhu,Y.Tag,J.Fag,adW.Zhag, Adaptivepopulatio tuig schee for differetial evolutio, Iforatio Scieces, vol. 223, pp , [22] W. Zhu, J. Fag, Y. Tag, W. Zhag, ad Y. Xu, Idetificatio of fractioal-order systes via a switchig differetial evolutio subject to oise perturbatios, Physics Letters A, vol. 376, o. 45,pp ,2012. [23] W. Zhu, J. Fag, Y. Tag, W. Zhag, ad W. Du, Digital IIR filters desig usig differetial evolutio algorith with a cotrollable probabilistic populatio size, PLoS Oe, vol. 7, Article ID e40549, [24] E. A. Deirtas ad Ö. Üstü, A itegrated ultiobjective decisio akig process for supplier selectio ad order allocatio, Oega,vol.36,o.1,pp.76 90,2008.

14 14 Matheatical Probles i Egieerig [25] B. Soylu ad S. Kapa Ulusoy, A preferece ordered classificatio for a ulti-objective axi redudacy allocatio proble, Coputers ad Operatios Research, vol. 38, o. 12, pp , [26] Y.Tag,Z.Wag,W.K.Wog,J.Kurths,adJ.Fag, Multiobjective sychroizatio of coupled systes, Chaos, vol.21, o.2,article025114,2011. [27] N. Xu ad L. Nozick, Modelig supplier selectio ad the use of optio cotracts for global supply chai desig, Coputers ad Operatios Research, vol. 36, o. 10, pp , [28] H. M. Wager ad T. M. Whiti, Dyaic versio of the ecooic lot size odel, Maageet Sciece, vol. 5, pp , [29] C. Baset ad J. M. Y. Leug, Ivetory lot-sizig with supplier selectio, Coputers & Operatios Research, vol.32,o.1,pp. 1 14, [30] B. Alidaee ad G. A. Kocheberger, A ote o a siple dyaic prograig approach to the sigle-sik, fixedcharge trasportatio proble, Trasportatio Sciece, vol. 39, o. 1, pp , [31] S. Li, A. Murat, ad W. Huag, Selectio of cotract suppliers uder price ad dead ucertaity i a dyaic arket, Europea Joural of Operatioal Research, vol.198,o.3,pp , [32] T. Sawik, Selectio of a dyaic supply portfolio i aketo-order eviroet with risks, Coputers & Operatios Research,vol.38,o.4,pp ,2011. [33] R. H. Li, A itegrated FANP-MOLP for supplier evaluatio ad order allocatio, Applied Matheatical Modellig, vol.33, o. 6, pp , [34] F. Mafakheri, M. Breto, ad A. Ghoie, Supplier selectioorder allocatio: a two-stage ultiple criteria dyaic prograig approach, Iteratioal Joural of Productio Ecooics,vol.132,o.1,pp.52 57,2011. [35] L. A. Zadeh, Fuzzy sets, Iforatio ad Coputatio, vol. 8, pp , [36] N. K. Kasabov ad Q. Sog, Defis: dyaic evolvig euralfuzzy iferece syste ad its applicatio for tie-series predictio, IEEE Trasactios o Fuzzy Systes,vol.10,o.2,pp , 2002.

15 Advaces i Operatios Research Hidawi Publishig Corporatio Advaces i Decisio Scieces Hidawi Publishig Corporatio Joural of Applied Matheatics Algebra Hidawi Publishig Corporatio Hidawi Publishig Corporatio Joural of Probability ad Statistics The Scietific World Joural Hidawi Publishig Corporatio Hidawi Publishig Corporatio Iteratioal Joural of Differetial Equatios Hidawi Publishig Corporatio Subit your auscripts at Iteratioal Joural of Advaces i Cobiatorics Hidawi Publishig Corporatio Matheatical Physics Hidawi Publishig Corporatio Joural of Coplex Aalysis Hidawi Publishig Corporatio Iteratioal Joural of Matheatics ad Matheatical Scieces Matheatical Probles i Egieerig Joural of Matheatics Hidawi Publishig Corporatio Hidawi Publishig Corporatio Hidawi Publishig Corporatio Discrete Matheatics Joural of Hidawi Publishig Corporatio Discrete Dyaics i Nature ad Society Joural of Fuctio Spaces Hidawi Publishig Corporatio Abstract ad Applied Aalysis Hidawi Publishig Corporatio Hidawi Publishig Corporatio Iteratioal Joural of Joural of Stochastic Aalysis Optiizatio Hidawi Publishig Corporatio Hidawi Publishig Corporatio