Adolfo Crespo Márquez

Transcription

1 In. J. Smulaon and Process Modellng, Vol. 4, No. 2, Capacy consraned supply chans: a smulaon sudy Salvaore Cannella* and Elena Cancmno Faculy of Engneerng, Unversy of Palermo, vale delle Scenze, Parco d Orleans, Palermo, Ialy E-mal: cannella@unpa. E-mal: ecancmno@unpa. *Correspondng auhor Adolfo Crespo Márquez School of Engneerng, Deparmen of Indusral Managemen, Unversy of Sevlle, Camno de los Descubrmenos s/n., Sevlle, Span E-mal: adolfo.crespo@es.us.es Absrac: hs paper explores he relaonshp beween consraned capacy and supply chan performance. Sx capacy consran levels are suded under dfferen nvenory polces and nformaon sharng sraeges. he resuls sugges ha an ncremen of producon capacy, used n ndusry as local approach o manage ncreasng ncomng orders, does no necessarly mply an mprovemen n cusomer servce. In presence of nformaon dsorons, he sraegy of augmenng producon capacy can lead o sasfy a a hgher cos an over-esmaed marke demand. he collaborave pracces provde bullwhp effec dampenng and nvenory sably, and ncrease he ably of he srucure o avod hs rsk. Keywords: mul-echelon; cenralsed supply chan; supply chan managemen; lmed capacy; bullwhp effec; demand amplfcaon; order polcy; perodc revew; order-up-o; APIOBPCS; smoohng replenshmen; EPOS; supply chan mercs; cusomer servce level; connuous me dfferenal equaon. Reference o hs paper should be made as follows: Cannella, S., Cancmno, E. and Márquez, A.C. (2008) Capacy consraned supply chans: a smulaon sudy, In. J. Smulaon and Process Modellng, Vol. 4, No. 2, pp Bographcal noes: Salvaore Cannella s PhD suden a he Deparmen of Manufacurng, Indusral and Managemen Engneerng of he Unversy of Palermo, Ialy, and vsng a he Deparmen of Indusral Managemen, Hgh School of Engneerng, Unversy of Sevlle, Span. Elena Cancmno s PhD suden a he Deparmen of Manufacurng, Indusral and Managemen Engneerng of he Unversy of Palermo, Ialy, and vsng a he Deparmen of Indusral Managemen, Hgh School of Engneerng, Unversy of Sevlle, Span. Adolfo Crespo Márquez s currenly Assocae Professor a he School of Engneerng of he Unversy of Sevlle, n he Deparmen of Indusral Managemen. He holds a PhD n Indusral Engneerng from he same unversy. Hs works have been publshed n several nernaonal journals. Whn he area of manenance he has exensvely parcpaed n many engneerng and consulng projecs for dfferen companes and for he Spansh Mnsres of Defence and Scence and Educaon. He s he Presden of INGEMAN (a Naonal Assocaon for he Developmen of Manenance Engneerng) n Span. 1 Problem saemen In he las decades many researchers have explored he relaon beween supply chan performance and capacy consran. OR mehods have beng used o suppor day-by-day decsons for bach szng and job sequencng problems, whle wha-f analyss has beng adoped as a decson suppor sysem n he feld of supply chan reengneerng as enables o explore he mpac of consraned capacy on he global performance of he whole srucure. In he feld of mehods based on he sysem, he semnal work from Evans and Nam (1994) nvesgaed he relaon beween capacy consran and supply chan performance Copyrgh 2008 Inderscence Enerprses Ld.

2 140 S. Cannella e al. n erms of demand amplfcaon for a sep ncrease n sales. hey hghlghed ha n a radonal supply chan capacy consrans provde dampenng of demand amplfcaon, bu n he meanme do no mprove cusomer servce levels wh respec o he unconsraned case. Curously, her work has no been recognsed n he mansream operaon managemen leraure, and her challengng resuls have no been furher explored. he am of hs work s o conrbue o he supply chan reengneerng research feld, by answerng o he followng research quesons: How dfferen capacy levels are relaed o he magnude of demand amplfcaon and cusomer servce level? How lmed capacy mpacs on supply chans characersed by dfferen nformaon sharng sraeges? he paper s organsed as follows. In Secon 2, a revew on recen supply chan modellng leraure s presened. Secon 3 repors he nvenory conrol polcy modelled n he smulaon sudy, he descrpon of he adoped mehodology and he mahemacal formalsm of he supply chan models. Performance mercs, expermenal ses, daa analyss and dscusson are repored n Secon 4. Secon 5 provdes conclusons and suggesons for fuure research. 2 Consraned supply chan modellng leraure revew In he feld of supply chan modellng and analyss Rddalls e al. (2000) denfy four man caegores of mehodologes, namely: connuous me dfferenal equaon models, dscree me dfference equaon models, dscree even smulaon sysems and classcal Operaonal Research (OR) mehods. hey sae ha OR echnques have her place a a local accal level n he desgn of supply chans, whle he mplcaon of sraegc desgn on supply chan performance s analysed by usng he former mehodologes. In he consraned capacy supply chan analyss, opmsaon approaches are ypcally used o solve bach szng and job sequencng problems (Vlachos and agaras, 2000; Bcheno e al., 2001; Smch-Lev and Zhao, 2003; Q, 2007), whle he mpac of lmed capacy on he global performance of he whole supply chan s generally assessed usng conrol heory and wha-f analyss, such as connuous smulaon and dscree even smulaon (Evans and Nam, 1994; Gavrnen e al., 1999; Helo, 2000; Dsney and Gubbsröm, 2004; Wkner e al., 2007). Vlachos and agaras (2000) presen an opmsaon procedure of a perodc revew nvenory sysem wh regular and emergency replenshmens. In her model he capacy of he emergency order quany s consraned. Resuls show ha he consran on he capacy has a sgnfcan effec on he sysem performance under emergency orderng polces, especally when he revew perod and he regular replenshmen lead me are long. Bcheno e al. (2001) presen an algorhm o mnmse nvenory levels under consraned oal capacy, deermnng opmal produc-ndvdual bach szes and replenshmen cycles under he consran of lmed avalable changeover me n an auomove seel supply nework. he opmal bach szes are found o be a funcon of all lead mes, all demand volumes, all coss per un, and he oal avalable changeover me. he auhors conclude ha a change n he bach szng polcy combned wh lead me reducon could provde savngs n nvenory of abou 60% compared o he orgnal suaon. Smch-Lev and Zhao (2003) develop a dynamc programmng model o analyse a sngle produc, perodc revew, wo-sage producon-nvenory sysem wh a sngle capacaed manufacurer and a sngle realer facng..d. demand, under hree dfferen nformaon sraeges. he mpac of nformaon sharng on he manufacurer s suded as a funcon of he producon capacy. hey conclude ha for he model wh nfne producon capacy he nformaon sharng sraegy has he same fll rae as he no nformaon sharng sraegy. When he producon capacy s ghly consraned, he savngs provded by nformaon sharng wh he opmal polcy s relavely hgh. Q (2007) develops a dynamc programmng algorhm o sudy an negraed decson makng model for a supply chan sysem where a manufacurer faces a prce-sensve demand and mulple capacaed supplers. he goal s o maxmse oal prof by deermnng an opmal sellng prce and a he same me acqurng enough supplyng capacy. He concludes ha, when he sourcng nformaon s no avalable, s beer o make a conservave producon plan, and when he marke demand nformaon s unknown, s beer o make an aggressve producon plan. Evans and Nam (1994) develop a connuous me dfferenal equaon model of a hree-er Forreser (1961) supply chan. Egh combnaons of hree capacy levels are used o sudy he response of consraned radonal serally-lnked srucures for a sep npu n cusomer demand. her mos noable resul s ha he unconsraned case s no he hghes ranked sysem n he smulaons performed, as s characersed by he presence of demand amplfcaon, commonly know as bullwhp effec (Lee e al., 1997; Chen e al., 2000; Dsney and owll, 2003a, 2003b; Chafeld e al., 2004; Holweg and Dsney, 2005; Geary e al., 2006; Mragloa, 2006). On he conrary, hey hghlgh ha consraned supply chans may produce mproved sysem performance a echelon level n erms of demand amplfcaon, bu hs does no mean mproved cusomer levels. Gavrnen e al. (1999) perform an nfnesmal perurbaon analyss o address a perodc revew nvenory conrol problem n hree wo-echelon supply chans, n order o explore he rade-offs beween nvenores, capaces, and nformaon. One of her conclusons s ha nformaon s more benefcal f he suppler s capacy s hgh as compared o when s low.

3 Capacy consraned supply chans: a smulaon sudy 141 Helo (2000) dscusses, by usng a sysem dynamcs (Serman, 2000) smulaon, he rade-off beween capacy ulsaon and lead mes. he analyss recommends smaller order szes, echelon synchronsaon and capacy analyss as mehods of mprovng he responsveness of a supply chan. Dsney and Gubbsröm (2004) use z-ransforms and probably densy funcons o analyse he economc mpac of order and nvenory-relaed cash flows resulng from a generalsed order-up-o polcy, consderng coss assocaed wh he producon order rae whn and above a capacy consran. hey conclude ha he classcal order-up-o polcy s no longer opmal when a broader range of coss s consdered n he objecve funcon. I s shown ha ncorporang proporonal conrollers n he wo feedback loops s economcally desrable for a parcular scenaro and a parcular se of cos funcons. Wkner e al. (2007) sudy va a sysem dynamcs ool he properes of he make-o-order envronmen wh fne capacy under he Auomac Ppelne Invenory and Order Based Producon Conrol Sysem archeype, commonly known as APIOBPCS replenshmen rule (John e al., 1994). I s shown ha, under capacy consrans, exsng producon plannng and conrol sysems should accommodae a comparaor o ulse he dfference n he arge and acual backorders n he orderng rule. he auhors hghlgh ha by developng an orderng polcy ha accouns for capacy flexbly, plus he feedback monorng of he backlog sae, s possble o ensure lead me expecaons. hs paper presens a connuous me dfferenal equaon model, amed a nvesgang on he performance of mul-er supply chan srucures, analysed under dfferen nformaon sharng sraeges and capacy consran condons. 3 Modellng he consraned supply chans 3.1 Invenory conrol polcy models here are several classfcaons for he polces ha regulae he flow of maerals whn he supply chan. Swamnahan e al. (1998) dsngush wo man ypes of nvenory conrol: he cenralsed and he decenralsed. he cenralsed polcy akes no accoun he nvenory levels n he supply chan as a whole. he ably o access nformaon on nvenory levels a oher radng parners n he supply chan s a fundamenal requremen for mplemenng he cenralsed managemen. A ypcal cenralsed supply chan s he Vendor Managed Invenory (Waller e al., 1999; Dsney and owll, 2002; Kuk, 2004; Sar, 2007; Vgl, 2007). On he conrary, n he decenralsed nvenory conrol he replenshmen rule akes no accoun only he nformaon on local nvenory saus. A furher classfcaon of nvenory conrol polces s based on he replenshmen rule: he perodc revew/order-up-o/base-sock polcy, and he connuous revew/reorder pon/order quany model (Boue e al., 2007). In a base-sock polcy he revew perod s fxed, and he sze of he order s such ha he nvenory poson s rased up o a arge level. A modfcaon o he classcal order-up-o polcy s obaned by nroducng a proporonal conroller n he nvenory poson feedback loop (Chen and Dsney, 2007). hs knd of nvenory conrol polcy s called smoohng replenshmen rule. In hs work he capacy consran condon s nvesgaed n wo decenralsed and one cenralsed four-er serally-lnked supply chan, under perodc revew/ smoohng order-up-o/base-sock polcy. 3.2 Mehodology, smulaon ool and model nomenclaure he supply chan models are nonlnear repeaed couplng of frs-order dfferenal equaon sysems (Rddalls e al., 2000), solved hrough a dgal compuer soluon of connuous me sysem. he numercal mehods used o approxmae a soluon for he nal-value problem are mono-sep, such as Euler-Cauchy mehod (angen or consan-slope), Kua s mehod, rapezodal negraon mehod, and Heun mehod (hree-erm aylor seres), or mul-sep, such as Adams-Bashfor mehod, and Adams-Moulon mehod. Several mahemacal oolboxes desgned o solve a broad range of problems or ad-hoc applcaons, such as Vensm, hnk, DYNAMO and Powersm, can be adoped o approxmae he soluon of he dfferenal equaons. he connuous me nonlnear dfferenal equaons are expressed n he angen mehod recurson dfference equaon formula: X = X + ( X ) (1), ( X ) = f( X, U, C) (2), X represens a sae varable of he sysem, s he sep sze or order of accuracy, (X, ) s he varaon of he sae varable n, U s a generc exogenous varable, and C represens parameers or consans. able 1 repors he operaons managemen varables and parameers of hs model. able 1 Maeral varables Wp Inv S F Model nomenclaure Work n progress (ncludes ncomng rans uns) a echelon a me Invenory of fnshed maerals a echelon a me uns/orders fnally shpped from echelon a me hroughpu a echelon a me Informaon varables d ˆ Demand forecas a echelon a me ˆcus d Cusomer demand forecas a me cus d Cusomer demand a me

4 142 S. Cannella e al. able 1 Informaon varables R Rcc 1 Model nomenclaure (connued) Replenshmen order quany a echelon a me (amoun of ems ha would be requred under no capacy consran condon) Acual replenshmen order quany a echelon a me (amoun of ems requred under capacy consran condon) B Exsng backlog of orders a echelon a me Inv Wp VrInv VrWp VrInv VrWp 2 Rcc arge nvenory a echelon a me arge work n progress a echelon a me Vrual nvenory a echelon a me Vrual work n progress a echelon a me arge vrual nvenory a echelon a me arge vrual work n progress a echelon a me σ Order quany varance a echelon, µ Order quany mean value a echelon, Rcc σ Cusomer demand varance 2 cus d µ Cusomer demand mean value cus d Parameers α δ cf p c y w Forecas smoohng facor Fnal seady-sae demand Capacy facor Physcal producon/dsrbuon lead me a echelon (ncomng rans me from suppler plus he producon lead me) Cover me for he nvenory conrol a echelon Smoohng nvenory parameer a echelon Smoohng work n progress parameer a echelon he supply chans modelled n hs work are sngle produc models wh no bll of maeral beween echelons. In Fgure 1 he em flow s represened. Fgure 1 Supply chan em flow 3.3 Decenralsed model he decenralsed base-sock supply chan (model A) presened n hs work s a serally-lnked four-echelon supply chan, n whch radng parners use a smoohng replenshmen rule. Each echelon only receves nformaon on local sock, local work n progress levels, and local sales. he realer forecass cusomer demand on he bass of marke me seres, and he remanng echelons only ake no accoun for her replenshmen downsream ncomng orders. Equaons (3) (5) represen he sae varables of he model. Wp = Wp + S F (3) 1 1 Inv = Inv + F S (4) 1. Work n progress (3) and Invenory (4) descrbe he physcal flow of ems n downsream drecon. Noe ha a every 1 echelon he shpmens sen by he suppler S mmedaely become work n progress. B = B + Rcc S (5) Backlog (5) s represenave of servce level for each er. Backloggng s allowed as a consequence of sockholdng; n each echelon he backlog wll be fulflled as soon as on-hand nvenory becomes avalable. S = Rcc + B Inv + F (6) + 1 mn( 1; 1 ). Equaon (6) expresses he dynamc of delvered orders. F = (7) S 1. p Equaon (7) models he producon/delvery lead me delay, represened by he parameer p. dˆ = αrcc + (1 α) dˆ ; 0 < α 1, 4 (8) dˆ = αd + (1 α) dˆ ; 0 < α 1 (9) cus cus cus 1 1 ˆ ˆcus 4. d = d = (10) Equaons (8) and (9) represen he exponenal smoohng formula o forecas demand (Makrdaks e al., 1998). he forecas smoohng facor α represens he weghng facor of he exponenal smoohng rule. he value of α s beween 0 and 1. he hgher he value of α, he greaer s he wegh placed on he more recen demand levels. he lower he α value he greaer s he wegh gven o demand hsory n forecasng fuure demand. wo equaons are adoped o ˆcus ake no accoun he forecas on cusomer orders d and he forecas on orders placed by ers ˆ d. Equaon (10) shows ha only he er nex o he fnal cusomer carres ou a forecas based on marke demand, whle a he upsream sages he npu demand daa s gven by equaon (8). he adoped perodc revew/smoohng order-up-o/ base-sock replenshmen rule (11) s he APIOBPCS. hs order polcy s expressed as le he producon arges be equal o he sum of a forecas of perceved demand, plus a fracon (1/ y ) of he nvenory dscrepancy beween acual and arge levels of fnshed goods, plus a fracon (1/ w ) of he dscrepancy beween arge WIP and acual WIP. (John e al., 1994)

5 Capacy consraned supply chans: a smulaon sudy 143 ˆ 1 1 R = d + ( Wp Wp) ( Inv Inv). + (11) w Equaon (12) models he non-negavy condon for he replenshmen order quany. R 0,. (12) here are several ways for mplemenng a capacy consran condon whn a supply chan model; a lmaon could be placed on he order rae or n he order accepance channel. Evans and Nam (1994) sugges ha consranng he order quany appears o be he realsc placemen whn he supply chan. Equaon (13) expresses he acual replenshmen order quany, whch s he amoun of ems requred under capacy consran condon. Rcc = mn( R ; cf ). (13) he order quany of every er canno exceed he capacy facor cf, whch s compued as a mulple of δ, he acual markeplace demand afer he sep-shaped ncrease. arge nvenory (14) s updaed every perod accordng o he coverng me and he new demand forecas. ˆ Inv = d. (14) c arge orders are placed n he ppelne on he bass of he demand forecas and producon/delvery lead me (15). ˆ Wp = d. (15) p 3.4 POS decenralsed model In he POS decenralsed base-sock supply chan (model B) all echelons base her nvenory polcy on local sock, local work n progress levels, local sales, downsream ncomng orders and he acual markeplace demand. hs srucure s modelled hrough equaons (3) (10), (12) (16). he order decson rule mplemened n he POS decenralsed base-sock (16) akes no accoun he conjon use of he marke demand forecas (9), based on he end consumer order rae, and he demand forecas a echelon (8), based on he orders placed by he subsequen sage. he cusomer demand forecas s drecly ncluded no he replenshmen rule, whle he forecas on he order ncomng by echelon + 1 s used o compue arge Work n Progress (15) and arge Invenory (14), as n he decenralsed model. ˆ cus 1 1 R = d + ( Wp Wp) ( Inv Inv). + (16) 3.5 Cenralsed model w he nvenory polcy for he cenralsed base-sock supply chan (model C) s based on local sock, local work n progress levels, local sales, downsream ncomng orders, acual markeplace demand, nvenory nformaon and work n progress daa ncomng from he downsream radng parner. he model s descrbed by y y equaons (3) (7), (9), (12), (13), (17), (18) (21). Equaon (17) represens he perodc revew order quany for he cenralsed base-sock supply chan. R dˆ ( VrWp VrWp ) cus 1 = + w 1 ( + VrInv VrInv ). y (17) he varable Vrual Invenory for an ndvdual echelon s he sum of he local Invenory plus all Invenores of subsequen echelons (18). 4 j VrInv = Inv. (18) j= he varable Vrual Work In Progress for echelon s gven by orders-n-he-ppelne a sage plus he sum of work n progress of all downsream echelons (19). 4 j VrWp = Wp. (19) j= arge Vrual Invenory (20) n echelon depends from he forecased markeplace demand and from he sum of he local and subsequen ers cover mes for he nvenory conrol. 4 ˆ cus j c. j= VrInv = d (20) arge Vrual Work In Progress (21) n echelon depends from he forecased markeplace demand and from he sum of he local and subsequen sages physcal producon dsrbuon lead me. 4 ˆ cus j p. j= VrWp = d (21) 4 Performance mercs, expermenal ses, daa analyss and dscusson 4.1 Supply chan performance mercs In hs sudy, he supply chan performance s evaluaed hrough he followng mercs: Order Rae Varance Rao (ORVrRao), also known as Bullwhp Magnude, Average Invenory, and Backlog. he ORVrRao (22) was proposed by Chen e al. (2000) o quanfy he bullwhp effec. ORVrRao σ µ = (22) 2 Rcc Rcc. 2 σ cus µ cus d d Formula (22) s a smar and concse quanfcaon of he order rae nsably. One value of ORVrRao s compued for each echelon n he chan. A geomerc or exponenal ncrease of ORVrRaon upsream drecon n he supply chan s represenave of he ransmsson of bullwhp effec (Dejonckheere e al., 2004). he values of ORVrRao are

6 144 S. Cannella e al. nerpolaed along each chan and he curve slopes are calculaed. he slope of ORVrRao s a sngle value, whch s ndcave of he exen of bullwhp effec propagaon and nvenory nsably along a gven supply chan srucure. A complemenary measure of supply chan performance s he AverageInvenory (23), compued as he mean value of Invenory a echelon over he smulaon me span. 1 AverageInvenory = Inv. (23) = 0 A concse measure of mul-echelons sysem performance relaed o sock levels s he Global Average Invenory (GAI), compued as he sum of Average Invenory values over he four ers. As cusomer servce level measure, Backlog (5) s adoped o quanfy he accumulaon of unflled orders. he Backlog s evaluaed every sngle and he me seres reproduce he supply chan cusomer servce level hsory. o assocae a cusomer servce level ndcaor o each supply chan and concsely compare dfferen scenaros, an addonal measure s used: he AverageBacklog (24). 1 AverageBacklog = B. (24) = Expermenal ses: assumpon and parameer vecors For each base-sock model sx capacy consran levels are suded. he capacy facor cf s modelled as a funcon of he fnal markeplace seady sae demand δ. hs relaon beween capacy consrans and cusomer demand s assumed also n Evans and Nam (1994) and Smch-Lev and Zhao (2003). In hs work he sx seleced levels of capacy facor are [δ; 1.5δ; 2δ; 3δ; 4δ; ]. he expermenal ses are characersed by: he smulaon runs are for a oal of 52 me uns, wh order of accuracy o = Markeplace demand s assumed o be 4 uns per me un, unl here s a pulse a = 5, ncreasng he demand value up o 8 uns per me un. he values of he parameer vecor [α; cf; p ; c ; y ; w ] elemens are: forecas smoohng facor α = 0.5; physcal producon/dsrbuon lead me p = 2; cover me for he nvenory conrol c = 3; smoohng nvenory parameer y = 3; smoohng work n progress parameer w = 3. he smoohng nvenory parameer y and he smoohng work n progress parameer w are chosen on he bass of he emprcal formula y = w = 1 + p, (Dsney and owll, 2006). Noe ha he Dezel and Elon (1967) smoohng parameer confguraon s used. he sae value vecor a = 0 [ Wp0; Inv0; B 0] s as Serman s (1989) confguraon. For echelon 1 (manufacurer) no replenshmen lead me s consdered. he nex sub-secon repors daa analyss for he expermenal ses. 4.3 Daa analyss For he decenralsed base-sock supply chan (model A), he POS decenralsed base-sock supply chan (model B), and he cenralsed base-sock supply chan (model C) all he performance measures are grouped for capacy facor cf. he values of ORVrRao, measured n ndvdual echelons, are repored n able 2. he slopes of he nerpolaons are shown n alc n he las row of each daa se. Echelon 1 s excluded from he slope compuaon, due o he fac ha srucurally dffers from he ohers as s replenshmen lead me s null. able 2 Order Rae Varance Rao Order Rae Varance Rao slope cf δ cf 1.5δ slope cf 2δ Cf 3δ slope cf 4δ cf slope For each echelon he values of Average Invenory are repored n able 3. he GAI s shown n alc. able 3 Average nvenory Average nvenory cf δ Cf 1.5δ GAI

7 Capacy consraned supply chans: a smulaon sudy 145 able 3 Average nvenory (connued) cf 2δ Average nvenory cf 3δ GAI cf 4δ cf GAI he values of Backlog measured n ndvdual echelons are ploed over he enre me horzon n Fgure 2. he Average Backlog measures for models A, B, and C are shown n able 4. Fgure 2 able 4 Backlog Average backlog Average backlog cf δ cf 1.5δ cf 2δ cf 3δ cf 4δ cf A B C Dscusson he frs research queson addressed by hs work was o explore how dfferen capacy levels are relaed o he magnude of demand amplfcaon and cusomer servce level. Usng acual nvenory levels as cusomer servce level, Evans and Nam provde a qualave nsgh no he relaonshp beween cusomer care and capacy consran. A lmaon of hs merc s ha does no provde a drec lnk beween levels of capacy consran and exen of cusomer servce level. In hs work hs lmaon s overcome hrough he use of Backlog. Monorng hs varable conrbues o answer he frs research queson. When he capacy facor s equal o he fnal seady demand, a sep ncrease n demand causes a dmnuon of servce level, and capacy sauraon mpedes o recover he accumulaon of prevous unfulflled orders. Backlog values do no mprove sgnfcanly for ncreasng values of cf, ncluded he unconsraned capacy case. hs resul suggess ha n a decenralsed supply chan an ncremen of producon capacy does no necessarly cause an mprovemen n cusomer servce. In he aforemenoned sudy, Evans and Nam sae ha he radonal supply chan under unconsraned capacy s no he hghes ranked sysem n erms of demand amplfcaon dampenng. In he frs supply chan analysed n hs work (model A) he slope values of ORVrRao monoonously ncrease as he capacy facor seps up. he same performance rend s showed by he GAI. hese resuls confrm Evans and Nam s conclusons for a decenralsed srucure: he capacy consran provdes a general mprovemen of process performance whn he mul-echelon sysem for a sep npu n demand, n erms of demand amplfcaon and supply chan sably. he relaon beween supply chan performance mprovemen and capacy lmaons s due o he fac ha he capacy consran lms he overesmaed forecas on he real sep-shaped markeplace demand along he chan, as dampens he order quanes. Noe ha he bullwhp reducon assocaed o he consraned capacy s an apparen mprovemen of he performance of he supply chan. In hs sudy, s assumed ha one produc s processed wh no bll of maeral, ha s a one o one rao of raw maeral, and n parcular he parnershp beween ers s based on srucured and exclusve conracs. However, n he real busness world, when producon capacy s sauraed (fully ulsed) a radng parner would search for addonal capacy by enlargng s porfolo wh unsrucured conracs. hs s a double rsk, as can lead o sasfy a a hgher cos a demand ha s amplfed by nformaon dsoron. he radonal supply chan s more nclne o exreme demand amplfcaon along he whole supply chan (Dsney e al., 2004), and a drec consequence of bullwhp effec s

8 146 S. Cannella e al. a remarkable ncremen n ers order raes ha corresponds o a greaer producon capacy need, and ncreases he chance o ncur he aforemenoned double rsk. In he presence of demand amplfcaon, he capacy consran can lead o sasfy a a hgher cos, n parcular n a supply chan wh unsrucured conracs, an over-esmaed marke demand. he second research queson was o undersand how lmed capacy mpacs on supply chans characersed by dfferen nformaon sharng sraeges. A general resul s ha he POS decenralsed (model B) and he cenralsed supply chan (model C) ouperform he decenralsed srucure, boh n erms of process mercs and cusomer servce. As n model A, for models B and C he slope of ORVrRao and he value of GAI ncrease as cf grows, bu he magnude of hs ncremen s no sgnfcan. In parcular hs s evden n he decenralsed supply chan. he sde effec of demand amplfcaon dampenng, provded by he capacy consraned condon, has a lower mpac on supply chans characersed by nformaon sharng sraeges. hs effec s due o he fac ha he redesgn of nformaon paerns s one of he mos effecve solvng approaches o demand amplfcaon phenomenon and supply chan nsably. Informaon sharng pracces overshadow he capacy lmaon smoohng effec on demand amplfcaon. Analysng he case of capacy facory equal o he fnal seady-sae demand, s shown ha capacy sauraon mpedes o recover he accumulaon of backlogged unfulflled orders, also n he nformaon sharng supply chans. Regardless he perssence of unfulflled orders, he average backlog decreases as he level of nformaon sharng ncreases. hs reducon rend s showed n all he expermenal ses. he resuls sugges ha he effec of lmed capacy on nformaon sharng supply chans s sgnfcanly reduced wh respec o classcal decenralsed base-sock mul-echelons n erms of demand amplfcaon dampenng and cusomer servce level. Under collaborave pracces, bullwhp dampenng and nvenory sably provded by nformaon sharng ncrease he ably of he srucure o avod he rsk of sasfyng a a hgher cos a demand ha s amplfed by nformaon dsoron. In he supply chan re-engneerng feld, expandng he producon capacy s a local approach commonly used n ndusry o manage ncreasng ncomng orders. When he ncreased demand s due o he presence of nformaon dsoron along he chan, hs soluon convers no an amplfer of bullwhp effec. In he sraegc capacy managemen, one prory s o elmnae he nformaon dsoron n he supply chan, n order o dmenson he producon/dsrbuon channel capacy wh relaon o he acual markeplace demand. 5 Conclusons he am of hs paper was o explore he relaonshp beween consraned capacy and supply chan performance. he effec of sx capacy consran levels was suded n wo decenralsed and one cenralsed four-er serally-lnked supply chan, under perodc revew/smoohng order-up-o/base-sock polcy. he supply chan performance mercs used n hs work were ORVrRao, Average Invenory, and Backlog. Connuous me dfferenal equaon mehodology was adoped for he mahemacal formalsaon of he models, and Vensm sofware was used as solvng negraon ool. he man resuls of hs sudy are: In a decenralsed supply chan an ncremen of producon capacy does no necessarly cause an mprovemen n cusomer servce. In he presence of demand amplfcaon, he capacy consran can lead o a double rsk: sasfyng a a hgher cos an over-esmaed marke demand. A supply chan wh unsrucured conracs s more mpaced by hs negave phenomenon. Under collaborave pracces, bullwhp dampenng and nvenory sably provded by nformaon sharng ncrease he ably of he srucure o avod he double rsk. In he sraegc capacy managemen, one prory s o elmnae he nformaon dsoron n he supply chan, n order o dmenson he producon/dsrbuon channel capacy wh relaon o he acual markeplace demand. Fuure research wll nvolve sudes on he lmed capacy producon/dsrbuon under several real supply chan condons, hrough he use of complemenary mehodologcal approaches, such as dscree even smulaon. Acknowledgemens he auhors hank he anonymous referees for her commens and suggesons. hs work was suppored by he CoRI Program and he PhD Course of Unversy of Palermo, and he projec DPI funded by he Spansh Mnsry of Scence and Educaon. References Bcheno, J., Holweg, M. and Nessman, J. (2001) Consran bach szng n a lean envronmen, Inernaonal Journal of Producon Economcs, Vol. 73, No. 1, pp Boue, R.N., Dsney, S.M., Lambrech, M.R. and van Houd, B. (2007) An negraed producon and nvenory model o dampen upsream demand varably n he supply chan, European Journal of Operaonal Research, Vol. 178, No. 1, pp

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