Research Article Improving the Performance of Modular Production in the Apparel Assembly: A Mathematical Programming Approach

Transcription

1 Mahemaical Problems i Egieerig, Aricle ID , 7 pages hp://dx.doi.org/1.1155/214/ Research Aricle Improvig he Performace of Modular Producio i he Apparel Assembly: A Mahemaical Programmig Approach Xiaoqig Wag, 1 Chu-Hug Chiu, 2 ad Wei Guo 3 1 Liga (Uiversiy) College, Su Ya-Se Uiversiy, Guagzhou 51275, Chia 2 Su Ya-Se Busiess School, Su Ya-Se Uiversiy, Guagzhou 51275, Chia 3 Guagdog Hydropower Plaig & Desig Isiue, Guagzhou 51635, Chia Correspodece should be addressed o Xiaoqig Wag; xqwag2@gmail.com Received 5 April 214; Revised 1 Jue 214; Acceped 17 Jue 214; Published 3 July 214 Academic Edior: sa-mig Choi Copyrigh 214 Xiaoqig Wag e al. his is a ope access aricle disribued uder he Creaive Commos Aribuio Licese, which permis uresriced use, disribuio, ad reproducio i ay medium, provided he origial wors properly cied. We cosruc he mahemaical models o fid he opimal allocaio of he module s capaciy (module members) o differe assembly operaios i a module for give garme assembly asks i a modular producio sysem. he objecives of he models are miimizig he holdig cos for wor process (WIP) iveories i he module ad he oal deviaio of he WIP iveories from heir correspodig arge values i he module durig a specific ime ierval. he soluios of he models ca be used as referece o achieve beer allocaio of he module members o differe operaios i a module o fulfill he give garme assembly asks. 1. Iroducio I he apparel marke, here are remedous differe ypes of producs, he correspodig demad for each ype of produc is volaile ad upredicable, ad he life cycle of he producs is very shor. he apparel reailers eed o respod quickly o he chagig marke i order o keep heir survivals [1, 2]. Cosequely, he reailers require heir suppliers o repleish he producs quickly wih he exac amou hey wa [3 8]. O he oher had, he apparel assembly i he radiioal apparel maufacurig is very ime-cosumig [9, 1]. he producio sysem used for apparel assembly is he progressive budle sysem (PBS). I PBS, each operaio is doe by a sigle worker who operaes a saioary machie. he worker receives he ufiished garmes i budles; he (or she) he performs he sigle operaio o each garme. he garmes he move o he ex worker for he ex operaio i budles. he mai philosophy behid PBS is maximizig he uilizaio of each worker s workig capaciy. Due o he differe ad ucerai operaig ime eeded for differe operaios i give assembly asks [11 13], PBS has o deped heavily o he buffers bewee operaios o avoid he sarvaio of garmes a some operaios. hus, i PBS,hehroughpuime(fromhecuigpiecesofiished garmes) is log ad wor process (WIP) iveory is high [3, 9]. o mee he reailers requiremes ad, a he same ime, keep heir ow iveory as low as possible, he apparel maufacurers eed o employ he more flexible producio sysems for he apparel assembly [14]. Alhoughhe assembly process i PBS ca be modified o achieve some degree of flexibiliy [15, 16], employig modular producio sysem (MPS) [3, 17 21] wih some performace improveme sraegy [5] is more promisig o achieve hese goals. I MPS, he module, which cosiss of a group of workers, is i charge of a par of, someimes a whole, garme. I mos of he ime, each module member performs a sigle assembly ask, jus like i PBS. Bu if WIP iveory is buildig up a some operaios, he module members a oher operaios will move o hose operaios o help, hus icreasig he work capaciy ad decreasig he iveory a hose operaios. So, i MPS, he hroughpu ime is shor ad WIP iveory is

2 2 Mahemaical Problems i Egieerig small [22, 23]. I seems ha MPS is he perfec soluio for he apparel maufacurer o respod o he quick repleishme requireme by he reailers. Alhough MPS ca provide obvious beefis for he apparel maufacures, he diffusio of MPS i he apparel idusry is slow. he possible reasos for his pheomeo are sudied by he researchers, mos from he perspecive of huma resource pracices [2, 21]. I his paper, we focus o he implemeaio of MPS oheoperaioallevel.basedoaovelmahemaical programmig model called separaed coiuous liear programmig (SCLP) ad is exesio, separaed coiuous coic programmig (SCCP), we cosruc wo mahemaical models o fid he opimal allocaio of he module s capaciy (module members) o differe operaios for give assembly asks. he objecives of he models are miimizig he holdig cos for WIP iveories i he module ad he oal deviaio of he WIP iveories from heir correspodig arge values i he module durig a specific ime ierval. he soluios of he models ca be used as referece o achieve beer allocaio of he module members o operaios i he module so ha he buildig-up of boleec he apparel assembly ca be avoided ad he flow balace ca be achieved. o our kowledge, our wors he firs oe o faciliae he adopio of MPS by addressig he opimal allocaio of module members o operaios for give assembly asks. he paper is orgaized as follows. I he ex secio, he lieraure o he adopio ad performace of MPS i he apparel idusry is reviewed. We also give a brief iroducio osclpadsccpowhichourmodelsarebased.i Secio 3, we prese wo models for opimal allocaio of he module members o differe operaios for give assembly asks i a module o achieve he miimizaio of he holdig cos of WIP iveories ad he oal deviaio of he WIP iveories from heir correspodig arge values durig a specific ime ierval. I Secio 4 we summarize wha we ge ad poi ou some fuure research direcio. 2. Lieraure Review 2.1. Lieraure o he Adopio ad Performace of MPS i he Apparel Maufacurig. As we said before, MPS allows apparel maufacurers o respod quickly o he repleishme requireme of he reailers ad, a he same ime, reduce heir ow eed o hold large WIP iveory. Eve more, here is also research showig ha he workers i he MPS ear more ha heir couerpars i he PBS [24]. Bu sillheadopiolevelofmpsiapparelmaufacurigis low [2, 21]. Research shows ha here are several key facors affecig he performace of MPS i a specific apparel maufacurer ad, cosequely, affecig he adopio level of MPS i ha apparel maufacurer. he mos impora facor is he huma resource pracices. By usig he empirical sudy, [2, 21] show ha he proper modificaio of huma resources pracices from PBS o MPS is crucial for he smooh rasiio from PBS o MPS i may apparel maufacurers. I PBS, he objecive is maximizig he idividual worker s oupu. he sewig process is highly fragmeed ad each worker uderakes oe operaio i isolaio. he commuicaio bewee workers is miimized. O he corary, i MPS, he objecive is maximizig he oupu of each module. Each module member uderakes oe or more operaios. he operaios each module member performs as well as he order i which hey perform hose operaios are differe for differe assembly asks. he ieracio amog module members is very impora o achieve he coiuous balace of he flow of producio ad he module s goal. he modificaio of huma resource pracices is ecessary o reflec hese differeces. For example, he iceive sysem i MPS should focusogroupiceiveiorderoecouragehemodule members o commuicae, coordiae, ad cooperae o maximize he module s oupu. he raiig arrageme should be also modified o ecourage module members o lear more operaios from raiig ad from oher module members. he supervisio should be modified oo. he supervisors should cosider he fucios each module member plays ad how hey become ivolved i he module work. he imporace of he modificaio of huma resource pracice is also observed i a case sudy by usig simulaio mehod [25]. he modificaios of huma resource pracices pose a huge work for he apparel maufacurers who wa o adop o MPS, ad he resuls of hose modificaios affec a lo he hroughpu ad repleishme speed he maufacurer could achieve. Apar from he huma resource pracices, research also ideifies oher facors affecig he adopio ad performace of MPS i he apparel maufacurig, icludig he imig of adopio, he relaioship bewee he apparel maufacurer ad is reailers, he iformaio sysem used i he apparel maufacurer ad reailers, he level of cooperaio wihi he apparel maufacurer, ad he compleeess ofheadopiopla. Xu e al. [26] showed ha whe marke is quie volaile, i is opimal for he maufacurer o pospoe adopio of MPS. Forza ad Vielli [27] showed ha he close collaboraio bewee reailers ad maufacures is criical for MPS adopio due o he fac ha he availabiliy of curre sales daa i real ime allows he apparel maufacurer o kow which produc is sellig beer ad herefore o udersad marke reds i a more comprehesive way. Of course, he iformaio sysem i he maufacurer should be able o process hese daa so ha more accurae demad iformaio ca be obaied. Also, he shor hroughpu ime provided by MPSmakesoseseifheapparelmaufacurerscaoship heir producs efficiely o where he reailers require [2]. he adopio pla should cosider all he facors meioed above before sarig he adopio process. here is sill oher research o he adopio of MPS from differe perspecive. For example, Li e al. [28] poi ou ha he producio sysems used by apparel maufacurers should be sigificaly relaed o heir maufacurig sraegy. he adopio of MPS is proper oly whe MPS maches he maufacurig sraegy of he apparel maufacurers.

3 Mahemaical Problems i Egieerig 3 Moreover, besides MPS, here are oher sudies ad models o he producio i fashio apparel. For example, omasik e al. [29] develop a accurae ad low-order ieger programmig model which iegraes schedulig ad resource allocaio for garmes producio; Rose ad Shier [3] apply a exac eumeraive approach for he cloh cu schedulig problem; Hsu e al. [31] formulae a mixed ieger programmig model for he schedulig problem for yar-dyed exile maufacurig ad propose a geeic algorihm o solve he problem; Yeug e al. [32, 33] sudy he supply chai coordiaio ad schedulig problem uder differe seigs, ad fas algorihms are developed o solve he complex problem; ad Choi e al. [34] ivesigaehescheduligad coordiaio problem of a mulisuppliers, sigle-warehouseoperaor sigle maufacurer supply chai. hey formulae he problem as a wo-machie commo-due-widow flow shop problem ad develop wo algorihms o solve he opimal schedulig ad coordiaio problems. I his paper, we focus o he implemeaio of MPS i he operaioal level. Specifically, we address he opimal allocaio of he module members o differe operaios for give assembly asks so ha he specific performace of ieresedcabeimproved. We are uaware of ay paper focusig o he implemeaio of MPS i he operaioal level. he oly relaed paper we foud is ha of Guo e al. [1]. I ha paper, a mahemaical model of he job shop schedulig (JSS) problem for PBS is proposed. he objecive is miimizig he oal pealies of earliess ad ardiess of order fulfillme by decidig whe o sar each order s producio ad how o assigheoperaiosomodulemembers. Iheexsubsecio,wewillgiveabriefiroducioo SCLPadSCCP,basedowhichourmodelsarebuil Brief Iroducio o SCLP ad SCCP. Liear programmig (LP) is a mahemaical model which has exremely wide rageofidusrialapplicaios.icabesolvedfasevewih very large size [35]. For his reaso, LP has bee pushed ad exeded o a ever-broadeig froier. SCLP is oe of such froier exesios which was firs iroduced by Aderso [36] who used i o model he job shop schedulig problem. here are several forms of SCLP. he followig is due o Weiss [37]: (SCLP) max [(γ + ( ) c) u () +d x ()]d s.. Gu (s) ds + Fx () α+a, Hu () b, u (), x(), [, ], where u(), x() are decisio variables ad are assumed o be bouded measurable fucios wih he measure of he break-poi se beig. γ, c, d, α, a, adb are vecors; G, F, ad H are marices. deoes he raspose operaio. he word separaed refers o he fac ha here are wo kids (1) of cosrais i SCLP: he cosrais ivolvig iegraio ad he isaaeous cosrais [38]. here exiss a rich lieraure o dualiy heory ad algorihms for SCLP. Ieresed reader may refer o [39] for he deailed review o he research resuls o SCLP. Specifically, Wag e al. [4] suggesed a polyomial approximaio algorihm for SCLP which produces a soluio wih ay predefied precisio. he resuled corol u() is a piecewise cosa fucio of ime (bag-bag corol) which ca be implemeed coveiely i pracice. I ha paper, hey furher exed SCLP o SCCP which has he followig form: (SCCP) max [(γ + ( ) c) u () +d x ()]d s.. α+a Gu (s) ds Fx () K 1, b Hu() K 2, u () K 3, x() K 4, [, ], (2) where K i, i = 1, 2, 3, 4, are closed covex coes i he Euclidea space wih appropriae dimesios. Remark. SCCP (2) ca also be regarded as a exesio for coic programmig (CP) which has he followig form: (CP) mi c x s.. Ax b K, where A is a m marix, b R m, c R,adK is a closed covex coe i R m. Ieresed reader ca refer o Neserov ad Nemirovskii [41] for he deailed iformaio o CP. Wag e al. [4] also proposed a polyomial approximaio algorihm for SCCP which produces a soluio wih ay predefiedprecisio.heresuledsoluioisalsobag-bag. Because of hese resuls, SCLP ad SCCP are paricularly useful o model large-size problems, usually he case i pracice, which has he ime cosrais o he compuig ime. 3. Problem Formulaios We have described he operaioal process i MPS i he firs secio of his paper. he garme assembly work which eeds o be processed by he module is asks. Differe asks require differe operaios o hem. he asks ca be classified io differe classes. he asks havig he same assembly requiremes belog o he same class. Figure 1 illusraes a ypical operaioal process for a specific class of asks i a module i MPS. I his figure, he recagle represes he module ad he circles represe he module members a differe operaios. he module members are servers. Each server performs oe specific operaio o he asks. here is a buffer before each server. Whe a class i ask proceeds o Server j, iwillge (3)

4 4 Mahemaical Problems i Egieerig λ i Server i 1 Server i 2 Server i k 3.1. SCLP Model. We cosider he opimal allocaio of he module s capaciy wihi a ime ierval [, ].heobjecive is miimizig he holdig cos of he WIP iveory i he module durig [, ]. hefollowigishemodelwe cosruc. Model 1: Figure 1: A ypical operaioal process for a specific class of asks i amoduleimps. mi ( c iij x iij ())d (4) service (processed) immediaely if he buffer before Server j is empy ad he Server j is free; oherwise, i has o joi he queue of class i asks i he buffer uil all he class i asks before i i he queue ge processed ad Server j chooses o work o a class i ask ex. Oly he, ha class i ask begis processig. Afer geig processed by Server j, ha class i ask moves o he buffer before he server which will perform he ex operaio o i ad wais for geig processed. his process coiues uil all eeded operaios are doe; he ha class i ask exiss he module. From he queueig heory perspecive, he module i which he asks ge processed is a queueig sysem wih muliple classes of asks ad muliple servers. he arrival rae ad he processig ime for each class of asks are sochasic. he roue of each ass predeermied. Assume ha each module member ca perform all operaios he ask eeded, ad he performace of every module member o ay operaio is he same. he capaciy of each server cabedyamicallyadjused.howodyamicallyallocae he module s capaciy o each server so ha he specific performaces of ieresed are opimized is a opimal schedulig problem i his queueig sysem. I he ex wo subsecios, wo mahemaical models are cosrucedoachieveheopimalallocaioofhemodule s capaciy o each server. hese models ca be show o be SCLP ad SCCP ad ca be solved efficiely by usig he mehods we meioed i Secio 2.2. Before we proceed, we eed o defie some oaios which we will use i he remaiig of his paper. Noaios (i) For asks i class i, he umber of he operaios eeded is deoed as. (ii) We use {i 1,...,i ki } o deoe he order of operaios for processig a class i asf i is processed by Server i 1 firsly ad he Sever i 2 uil Sever i ki. (iii) λ i () deoes he arrival rae of class i asks o he module a ime, i=1,...,. (iv) μ iij deoes he processig ime of class i asks o Server i j, i=1,...,, j=1,...,. (v) c iij deoes he rae of holdig cos of class i asks i he buffer before Server i j, i=1,...,, j=1,...,. (vi) a iij deoes he amou of class i asks i he buffer before Server i j a ime ; here i = 1,...,, j = 1,...,. s.. x ii1 () =a ii1 + x iij () =a iij + (μ iij u iij ()) 1, u iij (),x iij (), λ i (s) ds u ii1 (s) ds, i=1,..., u iij 1 (s) ds u iij (s) ds, i=1,...,; j=1,..., ; i=1,...,, j=1,2,...,, [, ], where x iij () is he sae variable ad represes he amou of class i asks i he buffer before Server i j a ime ad u iij () ishecorolvariableadrepresesheprocessigraefor class i asks o Server i j a ime, i=1,...,, j=1,2,...,. he objecive (4) is miimizig he oal holdig cos of WIPiveoryihemodulewihiheimeierval[, ]. he cosrais (5) ad (6) describe he dyamic of he assembly process i he module, ha is, how he sae variables x iij () are chagig wih he chagig of he corol variables u iij (). he cosrai (5) saeshaheamouofclassi asks i he buffer before Server i 1 a ay ime is equal o he summaio of he amou of class i asks i he buffer before Server i 1 a ime ad he amou of class i asks arrived from ouside durig [, ] lesseig he amou of class i asks processed by Server i 1 durig [, ]. he cosrai (6)saeshaheamouofclassi asks i he buffer before Server i j a ime is equal o he summaio of he amou of class i asksihebufferbeforeserveri j a ime ad he amou of class i asks processed by Server i j 1 durig [, ] lesseig he amou of class i asks processed by Server i j durig [, ], j=2,...,. he cosrai (7) is he processig capaciy cosrais. I saes ha he oal capaciy cosumed by he asks o all he servers cao exceed he module s capaciy, which is 1, a ay ime. Alhough he arrival rae of class i ask, λ i (), isimevaryig parameers i pracice, he variaio of i wihi a sufficie shor ime ierval, for example, wihi oe day, is small. hus we ca choose a sufficie small ad replace λ i () wih λ i,whe [,]. Wih his simplificaio, Model 1 reduces o he followig SCLP problem. (5) (6) (7)

5 Mahemaical Problems i Egieerig 5 Model 1 : mi s.. ( c iij x iij ())d u ii1 (s) ds + x ii1 () =a ii1 +λ i, [u iij (s) u iij 1 (s)]ds x iij () =a iij, i=1,...,; j=1,..., ; (μ iij u iij ()) 1, u iij (),x iij (), i=1,...,, j=1,2,...,, [, ]. i=1,..., We ca use algorihm described i Secio 2.2 o solve Model 1 efficiely SCCP Model. Suppose every buffer has is arge iveory level for WIP iveory. For he buffer before Server i j, he arge level is deoed as d iij.hefollowigmodelcabe used o fid he opimal allocaio of he module s capaciy wih he objecive of miimizig he oal deviaio of he WIP iveories from heir correspodig arge levels i he module durig [, ]. Model 2: mi s. (8) [(x iij () d ij ) 2 ]d (9) x ii1 () =a ii1 + x iij () =a iij + (μ iij u iij ()) 1, λ i (s) ds u ii1 (s) ds, i=1,..., u iij 1 (s) ds u iij (s) ds, i=1,...,; j=1,..., ; u iij (),x iij (), i=1,...,, j=i 1,i 2,...,, [, ]. (1) he objecive (9) is miimizig he oal deviaio of he WIP iveories from heir correspodig arge levels i all he buffers. he remaiig cosrais i Model 2 are he same as hose i Model 1. Model 2 ca be wrie io he SCCP form (2) byusig he variables rasformaio. We omi he deails of he variables rasformaio ad ieresed reader ca refer o secio 5.2 i [4]. WecausehealgorihmmeioediSecio 2.2 o solve Model 2 efficiely Implemeaio of he Soluios for Models 1 ad 2. I heabovewosubsecios,weproposehemodelsofid he opimal allocaio of a module s capaciy o differe operaios for give assembly asks so ha he holdig cos of he WIP iveory ad he oal deviaio of he WIP iveories from heir correspodig arge levels i he module durig [, ] are miimized. Afer we solve he wo models, we ge u iij () which represes he processig rae for class i asks o Server i j, where i=1,...,, j=i 1,i 2,...,, [,].Wecaallocae he module members o differe operaios accordig o he value of u iij (). heumberofmodulemembersia specific operaio, for example, he i j h operaio, is u iij he oal umber of module members i he module. If every module member oly ca perform several (o all) operaios ad/or he efficiecy for performig he same operaio is differe for differe module members, he capaciy of each module member ca be represeed by a vecor ad each compoe of he vecor represes he capaciyofhemodulememberoperformigaspecific operaio. Each server s capaciy is he summaio of capaciy of each module member o performig he operaio he server represes. he module s capaciy cosrai i Models 1ad2heshouldbereplacedbycapaciycosraisfor each server ad each module member. Whe he values of some capaciies chage, for example, if oe module member becomes ill ad cao perform ay operaios, he oal capaciy of he module also chages. he models ca be recompued ad he ew allocaio soluios ca be go quickly. 4. Coclusio ad Fuure Work I his paper, we cosruc wo mahemaical models o fid he opimal allocaio of he module s capaciy o he operaios for give asks, uder he assumpio ha each module member ca perform all operaios he ask eeded, ad he performace of every module member o ay operaioishesame.heobjecivesaremiimizighe holdigcosforwipiveoryihemoduleadheoal deviaio of he WIP iveories from heir correspodig arge values durig a specific ime ierval. he soluios of he models ca be used as referece o achieve beer allocaio of he module members o operaios for give asks. We also discuss he modificaios of he models whe each module member oly ca perform several (o all) operaios, ad/or he efficiecy for performig he same operaio is differe for differe module members. o our kowledge, his is he oly paper i he lieraure focusig o he implemeaio of MPS o he operaioal level by addressig he opimal allocaio of module members o operaios i a module.

6 6 Mahemaical Problems i Egieerig here are some research direcios eedig o be pursued i he fuure. For example, how o use he resul of his paper o derive he raiig pla for he module member so ha he oal capaciy of a module ca be icreased grealy i he shor ad/or log erm is a impora issue for faciliaig he adopio of MPS. Coflic of Ieress he auhors declare ha here is o coflic of ieress regardig he publicaio of his paper. Ackowledgmes his wors suppored i par by he Naural Sciece Foudaio of Chia uder Gra ad he 985 ProjecofSuYa-SeUiversiy. Refereces [1] M. Chrisopher, he agile supply chai: compeig i volaile markes, Idusrial Markeig Maageme, vol. 29, o. 1, pp , 2. [2].-M. Choi ad S. Sehi, Iovaive quick respose programs: a review, Ieraioal Producio Ecoomics,vol.127, o.1,pp.1 12,21. [3] A. Şe, he US fashio idusry: a supply chai review, Ieraioal Producio Ecoomics,vol.114,o.2,pp , 28. [4]M.Bruce,L.Daly,adN.owers, Leaoragile:asoluio for supply chai maageme i he exiles ad clohig idusry? Ieraioal Operaios & Producio Maageme,vol.24,o.1-2,pp ,24. [5]G.L.Hodge,K.GoforhRoss,J.A.Joies,adK.hoey, Adapig lea maufacurig priciples o he exile idusry, Producio Plaig ad Corol, vol.22,o.3,pp , 211. [6] M. Bruce ad L. Daly, Addig value: challeges for UK apparel supply chai maageme a review, Producio Plaig ad Corol,vol.22,o.3,pp.21 22,211. [7] F. Caro ad J. Gallie, Iveory maageme of a fas-fashio reail ework, Operaios Research, vol. 58, o. 2, pp , 21. [8] Z. L. Che, Iegraed producio ad ouboud disribuio schedulig: review ad exesios, Operaios Research, vol. 58,o.1,pp ,21. [9] I. M. apli, Backwards io he fuure: ew echologies ad old work orgaizaio i he US clohig idusry, i Rehikig Global Producio, I.M.apliadJ.Wiero, Eds.,Ashgae,Brookfield,V,USA,1997. [1] Z.X.Guo,W.K.Wog,S.Y.S.Leug,J..Fa,adS.F.Cha, Mahemaical model ad geeic opimizaio for he job shop schedulig problem i a mixed- ad muli-produc assembly evirome: a case sudy based o he apparel idusry, Compuers ad Idusrial Egieerig, vol.5,o.3,pp , 26. [11].-M. Choi, N. Liu, S. Re, ad C. Hui, No refud or full refud: whe should a fashio brad offer full refud cosumer reur service for mass cusomizaio producs? Mahemaical Problems i Egieerig,vol.213,AricleID561846,14pages, 213. [12] Y. He ad J. Zhag, Radom yield risk sharig i a wo-level supply chai, Ieraioal Producio Ecoomics, vol. 112, o. 2, pp , 28. [13] H. Peg ad M. Zhou, Quaiy discou supply chai models wih fashio producs ad ucerai yields, Mahemaical Problems i Egieerig, vol.213,aricleid895784,11pages, 213. [14] B.Dog,H.Jia,Z.Li,adK.Dog, Implemeigmasscusomizaio i garme idusry, Sysems Egieerig Procedia, vol. 3, pp , 212. [15] R. Huag ad S. Yu, Clarifyig cuig ad sewig processes wih due widows usig a effecive a coloy opimizaio, Mahemaical Problems i Egieerig, vol.213,aricleid , 12 pages, 213. [16] M. C. Gomes, A. P. Barbosa-Póvoa,adA.Q.Novais, Opimal schedulig for flexible job shop operaio, Ieraioal Joural of Producio Research, vol. 43, o. 11, pp , 25. [17] C. Y. Baldwi ad K. B. Clark, Maagig i a age of modulariy, Harvard Busiess Review,vol.75,o.5,pp.84 93, [18] A. J. Chuer, Iroducio o Clohig Producio Maageme, BSP Professioal Books, Oxford, UK, [19] E. Hill, Flexible Work Groups, Clemso Apparel Research,Clemso Uiversiy, Clemso, SC, USA, [2] J.. Dulop ad D. Weil, Diffusio ad performace of modular producio i he U.S. apparel idusry, Idusrial Relaios,vol.35,o.3,pp ,1996. [21] P. Berg, E. Appelbaum,. Bailey, ad A. L. Kalleberg, he performace effecs of modular producio i he apparel idusry, Idusrial Relaios,vol.35,o.3,pp , [22]F.H.Aberahy,J..Dulop,J.H.Hammod,adD.Weil, he iformaio iegraed chael: a sudy of he US apparel idusry i rasiio, i Brookigs Papers o Ecoomic Aciviy: Microecoomics,pp ,1995. [23] J. D. Blackbur, he quick respose moveme i he apparel idusry: a case sudy i ime-compressig supply chais, i ime-based Compeiio, J. D. Blackbur, Ed., Busiess Oe/Irwi,Homewood,Ill,USA,1991. [24]. Bailey, P. Berg, ad C. Sady, he effec of high-performace work pracices o employee earigs i he seel, apparel, ad medical elecroics ad imagig idusries, Idusrial ad Labor Relaios Review,vol.54,o.2A,pp ,21. [25] W. A. S. Casro, R. C. Casro, S. I. Miró, ad P. U. Aloso Maríez, Modular maufacurig: a aleraive o improve he compeiiveess i he clohig idusry, Ieraioal JouralofClohigScieceadechology,vol.16,o.3-4,pp , 24. [26] S. X. Xu, Q. Lu, ad Z. Li, Opimal modular producio sraegies uder marke uceraiy: a real opios perspecive, Ieraioal Producio Ecoomics,vol.139,o.1,pp , 212. [27] C. Forza ad A. Vielli, ime compressio i producio ad disribuio wihi he exile-apparel chai, Iegraed Maufacurig Sysems,vol.11,o.2,pp ,2. [28] S. Li, M. A. Moore, D. H. Kicade, ad C. Avery, Dimesios of apparel maufacurig sraegy ad producio maageme, Ieraioal Clohig Sciece ad echology, vol.14,o.1,pp.46 6,22. [29] R.N.omasik,P.B.Luh,adG.Liu, Scheduligflexiblemaufacurig sysems for apparel producio, IEEE rasacios o Roboics ad Auomaio,vol.12,o.5,pp ,1996.

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8 Advaces i Operaios Research Advaces i Decisio Scieces Applied Mahemaics Algebra Probabiliy ad Saisics he Scieific World Joural Ieraioal Differeial Equaios Submi your mauscrips a Ieraioal Advaces i Combiaorics Mahemaical Physics Complex Aalysis Ieraioal Mahemaics ad Mahemaical Scieces Mahemaical Problems i Egieerig Mahemaics Discree Mahemaics Discree Dyamics i Naure ad Sociey Fucio Spaces Absrac ad Applied Aalysis Ieraioal Sochasic Aalysis Opimizaio