This is an Open Access documen downloaded from ORCA, Cardiff Universiy's insiuional reposiory: hp://orca.cf.ac.uk/3849/ This is he auhor s version of a work ha was submied o / acceped for publicaion. Ciaion for final published version: Disney, Sephen Michael and Towill, Denis Royson 2003. The effec of vendor managed invenory (VMI) dynamics on he Bullwhip Effec in supply chains. Inernaional Journal of Producion Economics 85 (2), pp. 99-25. 0.06/S0925-5273(03)000-5 file Publishers page: hp://dx.doi.org/0.06/s0925-5273(03)000-5 <hp://dx.doi.org/0.06/s0925-5273(03)000-5> Please noe: Changes made as a resul of publishing processes such as copy-ediing, formaing and page numbers may no be refleced in his version. For he definiive version of his publicaion, please refer o he published source. You are advised o consul he publisher s version if you wish o cie his paper. This version is being made available in accordance wih publisher policies. See hp://orca.cf.ac.uk/policies.hml for usage policies. Copyrigh and moral righs for publicaions made available in ORCA are reained by he copyrigh holders.
Disney, S.M. and Towill, D.R., (2003) The effec of VMI dynamics on he bullwhip effec in supply chains, Inernaional Journal of Producion Economics, Vol. 85, No. 2, pp99-25. DOI: 0.06/S0925-5273(03)000-5. The Effec of Vendor Managed Invenory (VMI) Dynamics on he Bullwhip Effec in Supply Chains S.M. Disney and D.R. Towill Logisics Sysems Dynamics Group, Cardiff Business School, Cardiff Universiy, Aberconway Building, Colum Drive, Cardiff. CF0 3EU, UK. E-mail: DisneySM@Cardiff.ac.uk, Tel: +33 (0)29 2087 6083, Fax: +44(0)29 2087430 Absrac The paper compares he expeced performance of a Vendor Managed Invenory (VMI) supply chain wih a radiional serially-linked supply chain. The emphasis of his invesigaion is he impac hese wo alernaive srucures have on he Bullwhip Effec generaed in he supply chain. We pay paricular aenion o he manufacurer s producion ordering aciviies via a simulaion model based on difference equaions. VMI is hereby shown o be significanly beer a responding o volaile changes in demand such as hose due o discouned ordering or price variaions. Invenory recovery as measured by he Inegral of Time * Absolue Error (ITAE) performance meric is also subsanially improved via VMI. Noise bandwidh, ha is a measure of capaciy requiremens, is hen used o esimae he order rae variance in response o random cusomer demand. Finally, he paper simulaes he VMI and radiional supply chain response o a represenaive reail sales paern. The resuls are in accordance wih rich picure performance predicions made from deerminisic inpus. Key Words: Bullwhip, Forreser Effec, VMI, Supply Chains, Invenory Conrol. Word Coun: Toal 7744, Main body 562. Inroducion This paper is concerned wih he comparison of a Vendor Managed Invenory (VMI) supply chain o a radiional serially-linked supply chain. The paricular emphasis of his paper is he impac he wo supply chain srucures have on he Bullwhip Effec, (Lee, Padmanabhan and Whang, [,2]) generaed wihin he supply chain. The performance is invesigaed using difference equaions forming a simulaion model. Focusing on a one supplier, one cusomer relaionship special aenion is given o he manufacurer s producion scheduling aciviies. The laer is known o
Disney, S.M. and Towill, D.R., (2003) The effec of VMI dynamics on he bullwhip effec in supply chains, Inernaional Journal of Producion Economics, Vol. 85, No. 2, pp99-25. DOI: 0.06/S0925-5273(03)000-5. 2 be one well-esablished source of bullwhip (which we erm he Forreser effec afer he seminal work of Jay Forreser, [3]). A number of sandard ways of reducing bullwhip have been examined by Wikner e al [4], van Ackere e al [5], and summarised by Towill [6]. Furhermore hese mehods acually work in he realworld, as demonsraed by Towill and McCullen [7]. They found ha, for a global mechanical precision produc supply chain, bullwhip was ypically reduced via an appropriae BPR Programme by 50% and simulaneously sock urn improvemens of 2: were observed. Vendor Managed Invenory (VMI) is of paricular ineres in he bullwhip conex. Poenially VMI offers wo possible sources of bullwhip reducion. Firsly here is he eliminaion of one layer of decision-making. Secondly we have he eliminaion of some informaion flow ime delays. Since removing boh facors reduces disorion hey can be uilised o damp down bullwhip. Hence herein we provide an overview boh VMI and he radiional supply chain in which he laer is used as our performance benchmark. We also describe how bullwhip, and paricularly he Forreser effec, can arise in he real world. The difference equaions used o model he VMI and he radiional supply chains are described in deail. Opimum parameer seings from previous analyic and field research are also reviewed as possible saring poins for he simulaion sudies. The rich picure resuling from using sep response ess are conclusive in indicaing bullwhip reducion via VMI. As we have shown previously (Mason-Jones e al, [8]) his rich picure gives considerable insigh ino sysem response under a wide range of condiions. This includes he well-known supply chain phenomenon of rogue ordering. For example a large posiive spike of advance orders may appear, only o be followed by an equally large drop some ime in he fuure, i.e. a ne change of zero. Simulaing he uni sep inpu is also very useful as i is a very simple non-saionary inpu, from which many qualiaive and quaniaive performance aspecs may be inferred. Many of hese insighs are difficul o achieve in an analyical approach only where saionary characerisics are ypically sudied. Such a waveform emulaes price discouning, as illusraed by Fisher [9]. Invenory recovery is assessed via he use of he Inegral of Time x Absolue Error (ITAE) performance meric. VMI is shown o be subsanially beer in reducing ITAE following a sep
Disney, S.M. and Towill, D.R., (2003) The effec of VMI dynamics on he bullwhip effec in supply chains, Inernaional Journal of Producion Economics, Vol. 85, No. 2, pp99-25. DOI: 0.06/S0925-5273(03)000-5. 3 demand by he cusomer. A sep response is simply he inegral of he impulse (or he spike induced by rogue ordering due o promoions). Thus, in a linear sysem he impulse response is direcly relaed o he sep. However, he sep inpu has he advanage ha i is accumulaive and sligh differences ha off-se responses may be readily idenified. I is hus our demand signal of choice. Order rae variance is convenienly esimaed via he calculaion of noise bandwidh. I is shown ha he performance benefis prediced from he rich picure and order rae variance analysis are confirmed via simulaion of he supply chain responses o a ypical reail sales paern. 2. Overview of a radiional supply chain A supply chain is a sysem consising of maerial suppliers, producion faciliies, disribuion services, and cusomers who are all linked ogeher via he downsream feed-forward flow of maerials (deliveries) and he upsream feedback flow of informaion (orders), as shown in Figure (Sevens, [0]). In a radiional supply chain each player is responsible for his own invenory conrol and producion or disribuion ordering aciviies. One fundamenal characerisic and problem ha all players in a radiional supply chain (such as reailers, disribuors, manufacurers, raw maerial suppliers) mus solve is jus how much o order he producion sysem o make (or he suppliers o supply) o enable a supply chain echelon o saisfy is cusomers demands. This is he classic producion/ invenory conrol problem. According o Axsäer [], he purpose of a producion/ invenory conrol sysem (he mehod used o conrol invenory levels and producion raes) is o ransform incomplee informaion abou he marke place ino co-ordinaed plans for producion and replenishmen of raw maerials. Praciioners ackle he producion/invenory conrol problem by inspecing daa relaing o demands, invenory levels and orders in he pipeline and eiher, in a srucured, mahemaical way (for example, by using a decision suppor sysem wih a well (or poorly!) designed replenishmen rule), or in a less formal way (by using heir own experience and judgemen), place orders up he supply chain. In he real world, he ordering process is frequenly biased according o who is perceived as he mos imporan cusomer, or simply in favour of hose found o be mos roublesome.
Disney, S.M. and Towill, D.R., (2003) The effec of VMI dynamics on he bullwhip effec in supply chains, Inernaional Journal of Producion Economics, Vol. 85, No. 2, pp99-25. DOI: 0.06/S0925-5273(03)000-5. 4 Figure. Schemaic of a Tradiional Supply Chain The srucure of he radiional supply chain has developed parly as a resul of he need for a company o be in conrol of is own asses and parly because, unil recenly, i has been uneconomic o pass vas amouns of informaion around. The radiional supply chain is characerised by each player in he supply chain basing his producion orders or delivery orders solely on his sales o his cusomer, on his invenory levels and, someimes, on WIP arges. Each echelon in he supply chain only has informaion abou wha heir immediae cusomers wan and no on wha he end cusomer wans. This does no allow suppliers o gain any insigh ino wha heir cusomers are ordering o cover heir own invenory based Cusomer Service Level (CSL) and cos requiremens and wha he cusomers are ordering o saisfy immediae cusomer demand (Kaipia e al [2]). This lack of visibiliy of real demand can and does cause a number of problems in a supply chain if i is no properly designed and even hen flucuaions canno be compleely eliminaed. 3. Overview of a VMI supply chain In reacing o his scenario, many companies have been compelled o improve heir supply chain operaions by sharing demand and invenory informaion wih heir suppliers and cusomers. Differen indusries and marke secors have coined differen erms for VMI, bu mos are based essenially on he same idea. VMI is a supply chain sraegy where he vendor or supplier is given he responsibiliy of managing he cusomer s sock. For clariy he erms disribuor for he cusomer in he VMI relaionship and manufacurer for he supplier or vendor in he VMI relaionship will be used. VMI has become more popular in he grocery secor in he las 5 years due o he success of reailers such as Wal-Mar, Andel [3] and Salk, Evans and Shulman [4]. Addiionally, i is only relaively recenly ha he necessary informaion and communicaion echnology has become economically available o enable he sraegy,
Disney, S.M. and Towill, D.R., (2003) The effec of VMI dynamics on he bullwhip effec in supply chains, Inernaional Journal of Producion Economics, Vol. 85, No. 2, pp99-25. DOI: 0.06/S0925-5273(03)000-5. 5 alhough Holmsröm [5] has shown ha i can be enabled via fax or emails and spreadshees. Disney, Holmsröm, Kaipia and Towill [6] have implemened VMI in a supply chain using daa available from a popular ERP sysem and a spreadshee based decision suppor sysem. Moreover, VMI is no a new sraegy; i was eloquenly discussed by Magee ([7], pp298) in a presenaion of a concepual framework for designing a producion conrol sysem. Quoing direcly from he ex (as i very concisely porrays wha VMI acually is): Frequenly here is argumen as o who should conrol invenories. For example, should i be he sales organisaion or (some) oher uni ha draws on he socks and wans o be sure hey are here, or he operaion ha supplies he sock poin and wans o feed i economically? There is probably no resoluion o his quesion as saed; he difficuly is ha boh have a legiimae ineres. I is possible o resae he quesion slighly and reach a soluion. The user has o be sure he maerial ha he requires will be here. He has corresponding responsibiliy o sae wha his maximum and minimum requiremens will be. Once hese limis are acceped as reasonable, he supplier has he responsibiliy of meeing demand wihin hese limis, making whaever use he can of he flexibiliy he invenory provides. Thus boh have a share in he responsibiliy for and conrol over a sock uni. One specifies wha he maximum and minimum demands on he sock uni will be; he oher has he responsibiliy of keeping he sock uni replenished bu no overloaded as long as demand says wihin he specified limis, Magee [7]. VMI comes in many differen forms. Familiar names are Quick Response (QR), (Lee, So and Tang [8]), Synchronized Consumer Response (SCR), Coninuous Replenishmen (CR), Efficien Consumer Response (ECR), (Cachon and Fisher, [9]), Rapid Replenishmen (RR), Collaboraive Planning, Forecasing and Replenishmen (CPFR), (Holmsröm e al [20]) and Cenralised Invenory Managemen (CIM), (Lee, Padmanabhan and Whang, []), depending on secor applicaion, ownership issues and scope of implemenaion. However, in essence, hey are all specific as applicaions of VMI as summarised concepually in Figure 2.
Disney, S.M. and Towill, D.R., (2003) The effec of VMI dynamics on he bullwhip effec in supply chains, Inernaional Journal of Producion Economics, Vol. 85, No. 2, pp99-25. DOI: 0.06/S0925-5273(03)000-5. 6 Business Targes VMI Conrols Service Levels Sales (CONS) Infinie Maerial Socks Facory Order Rae (ORATE) (COMRATE) Facory Compleions Despach This Number Se Targe Sock (TINV) Finished Goods Socks (FINV) Se GIT Sock GIT Se Targe Sock, R Vending Socks(DINV) Facory Producion Orders Compleions Despaches Deliveries Toal Sysem Sock (SINV) Producion lead-ime Disribuion lead-ime Maerial flow Informaion defined by VMI ordering decision Informaion used by VMI ordering decision Figure 2. Overview of he VMI Scenario 4. Bullwhip Effec in Supply Chains The Bullwhip Effec is a new erm coined by Lee, Padmanabhan and Whang [,2]. I refers o he scenario where he orders o he supplier end o have larger flucuaions han sales o he buyer and he disorion propagaes upsream in an amplified form. Lee e al [,2] sae ha here are five fundamenal causes of Bullwhip; demand signalling processing, non-zero lead-imes, price variaions, raioning and gaming, and order baching. As we have said previously he Bullwhip Effec is no a new supply chain phenomenon, Schmenner [2] provides an hisorical overview of he problem, including a discussion on how Procer and Gamble have been concerned wih bullwhip since a leas 99. Furhermore we consider demand signal processing and non zero lead-imes o be encompassed by o he Demand Amplificaion or he Forreser Effec afer Jay Forreser [3] who encounered he problem in many real-world supply chains and demonsraed i via DYNAMO simulaion. The Forreser Effec is also encompassed by Serman s bounded raionaliy, (Serman, [22]), erminology ha is common in he field of psychology when used o describe players sub-opimal bu seemingly raional decision making
Disney, S.M. and Towill, D.R., (2003) The effec of VMI dynamics on he bullwhip effec in supply chains, Inernaional Journal of Producion Economics, Vol. 85, No. 2, pp99-25. DOI: 0.06/S0925-5273(03)000-5. 7 behaviour. I is he impac of VMI conrol on he Forreser induced Bullwhip Effec ha is he subjec of his paper. The effec ha he oher sources of bullwhip, as described by Lee e al [,2] have on he dynamics of he orders in VMI supply chains has been discussed elsewhere in Disney and Towill [23]. Tradiional supply chains are exremely prone o bullwhip. Salk and Hau [24], provide a deailed descripion of he Bullwhip Effec found in a clohing supply chain, and his was has been summarised by Towill and McCullen [7] as shown in Figure 3. This paricular supply chain suffered from he Forreser Effec, wih he demand variaion ypically increasing by an order of 2 o a each level of he supply chain. There is significan evidence ha he Bullwhip Effec is prevalen in many real world supply chains. I is no jus a phenomenon of ineres o academics, bu also a source of money haemorrhaging ou of supply chains via sock holding charges, producion ramp up/ramp down coss ec (McCullen and Towill, [25]). Yarn maker Order flucuaions are ypically +/-40% (hence amplificaion here+2x2x2=8 imes greaer hen markeplace variabiliy) Direcion of demand amplificaion and increasing variabiliy and uncerainy as he waveform moves upsream Fabric maker Order flucuaions are ypically +/-20% Garmen maker Order flucuaions are ypically +/-0% High sree reailer Flow of orders upsream Order flucuaions are ypically +/-5% Flow of maerials downsream Cusomers Figure 3. The Bullwhip Effec in a Tradiional Reail Supply Chain (Taken from Towill and McCullen 999)
Disney, S.M. and Towill, D.R., (2003) The effec of VMI dynamics on he bullwhip effec in supply chains, Inernaional Journal of Producion Economics, Vol. 85, No. 2, pp99-25. DOI: 0.06/S0925-5273(03)000-5. 8 I is, however, much harder o quanify he impac of Bullwhip on he profiabiliy of a company, alhough Meers [26] has sudied he problem wih a linear programming approach. He repors ha eliminaion of he Bullwhip Effec can resul in a 5% increase in profiabiliy using managerially relevan parameer seings and ha his saving can be even higher in a capaciy limied supply chain. Salk and Hau [24] also repor ha he producion on-coss (he coss associaed wih ramping up and down he producion level) is proporional o he cube of he deviaion abou he mean of he producion order rae. So variaions wihin he facory are reckoned o be exremely expensive. The Forreser Effec is noiceable in radiional supply chains as a paricular player over-orders in response o genuine changes in demand o accoun for invenory deviaions ha resul from he producion / disribuion lead-ime. This over-ordering is hen amplified up he supply chain, creaing wide flucuaions in he demand signal as i passes hrough he supply chain. This effec can be very concisely porrayed via Propagaion curves and has been used in previous conribuions (Mason-Jones, e al, [8] and Van Aken [27]) o clearly show how order variance amplifies up he supply chain. The propagaion curves in Figure 4, aken from Mason-Jones e al [8], show how demand is amplified (measured as peak value) as i is passed up he supply chain, agains he response ime of supply chain players ake o reach heir peak value (peak ime delay). The figure shows five radiional supply chain designs, wih a range of parameer seings ha reflec good soluions for a radiional supply chain; wihou pipeline conrol (Design ) based on hardware analogues, wih pipeline conrol (Design 2) based on hardware analogues, Serman s design (Design 4) wih pipeline conrols based on resuls from his analysis of he Beer Game (Serman [22]), and wo alernaive soluions wih pipeline conrols (Designs 3 and 5). Clearly much damping of he bullwhip effec can be obained via careful selecion of an appropriae Decision Suppor Sysem. However, oher advances o move owards he Seamless Supply Chain concep (Towill, [6]) may be even more profiable
Disney, S.M. and Towill, D.R., (2003) The effec of VMI dynamics on he bullwhip effec in supply chains, Inernaional Journal of Producion Economics, Vol. 85, No. 2, pp99-25. DOI: 0.06/S0925-5273(03)000-5. 9 (Wikner e al, [4]; van Ackere e al, [5]). We shall see laer in he paper where VMI sis wihin he performance improvemen porfolio. Waveform Peak Value 7 6 5 4 3 2 R 4 W/H D D R F F 3 W/H R R R D Design Design 2 Design 3 Design 4 Design 5 W/H D D W/H W/H F 2 F 5 F 0 0 2 3 4 Waveform peak ime delay (As a raio of lead-ime) Waveform Peak Time Delay Key: R= Reailer, D=Disribuor, W/H=Warehouse, F=Facory Figure 4. Propagaion Curves, Illusraing he Forreser Effec in Differen Supply Chain Designs (Mason-Jones, Naim and Towill, 997) 5. Descripion of he VMI Supply Chain Simulaion Model The difference equaions required o model our version of he VMI scenario are shown in Appendix. These difference equaions can quickly be urned ino a mahemaical model of he VMI supply chain by using z-ransforms. The formulaion and exploiaion of such a mahemaical model is no presened in his conribuion due o space resricions bu can be found in Disney [28] and Disney and Towill [29,
Disney, S.M. and Towill, D.R., (2003) The effec of VMI dynamics on he bullwhip effec in supply chains, Inernaional Journal of Producion Economics, Vol. 85, No. 2, pp99-25. DOI: 0.06/S0925-5273(03)000-5. 0 30]. Reference [29] is a comprehensive analysis of he sabiliy of a VMI supply chain and a single echelon of a radiional supply chain. In [30] he VMI model is sudied o deermine good parameer values for a range of circumsances. Thus we are able o compare one VMI sysem o anoher. Wha his paper uniquely conribues is o ake a selecion of hese VMI sysems and compares hem wih a radiional wosage supply chain as a benchmark. Hence we invesigae he benefis or oherwise of moving from he radiional supply chain wih all is real world fauls) o a VMI scenario. We know he VMI sysem is represenaive of a real world applicaion, Disney, Holmsröm, Kaipia and Towill [6], however his comparison is resriced o simulaion of hese models. Herein, he difference equaion represenaion will be exploied. The difference equaions may be quickly realised hrough spreadshee applicaions such as Microsof Excel. Difference equaions can also be implemened in sandard compuer languages wih relaive ease, as shown in Table. The equaions in Appendix describe he VMI supply chain when individual sock holding poins and ransporaion despaches are modelled explicily, whereas for simpliciy he pseudo code in Table models invenory and ransporaion as based on virual consumpion. Of course, he wo sysems are exacly he same when focusing on he producion order rae, (ORATE). A fixed producion lead-ime of 4 ime-unis will be used hroughou his paper. The specific flavour of VMI ha he difference equaions represen in Appendix is ermed VMI-APIOBPCS, or Vendor Managed Invenory, Auomaic Pipeline, Invenory and Order Based Producion Conrol Sysem. The VMI erm in VMI- APIOBPCS reflecs he mos significan fac abou a VMI supply chain, i.e. ha he disribuor (he cusomer in he VMI relaionship) passes invenory informaion and Poin of Sales (POS) daa o heir suppliers raher han placing replenishmen orders, (Kaipia e al [2], Corill [3]). The acual invenory a he cusomer is hen compared o a re-order poin ha has been agreed on by boh paries. This re-order poin is se o ensure adequae availabiliy wihou building up excessive socks. I riggers a replenishmen order ha is delivered o he cusomer if he acual invenory is below he re-order poin every planning period. Each pary also agrees he orderup-o poin, O. The dispaches beween he wo echelons are equal o he order-up o level, O, minus he re-order poin, R, and wihin his framework he dispaches can be of a consan or varying size.
Disney, S.M. and Towill, D.R., (2003) The effec of VMI dynamics on he bullwhip effec in supply chains, Inernaional Journal of Producion Economics, Vol. 85, No. 2, pp99-25. DOI: 0.06/S0925-5273(03)000-5. The re-order poin is se dynamically o reflec changes in demand. This is done by exponenially smoohing (over Tq ime unis) he sales signal and muliplying i by a consan (G) ha ensures appropriae cusomer service levels a he disribuor, aking ino accoun he ransporaion lead-ime beween he wo paries in he supply chain. Exponenial smoohing was chosen as he forecasing mechanism because i is; simple o implemen in compuer sysems (requiring less daa sorage), readily undersood and he mos favoured echnique by boh indusrialiss and academics. I should be noed ha he ne change in he re-order poin from one ime period o anoher is added o he sales signal and he vendor reas his as a demand. So, when demand is increasing and he disribuors re-order poin grows, he supplier or vendor reas he sock (re-order poin) requiremens a he disribuor as demand and incorporaes ha ino his forecass and sock levels, as he clearly should do. Obviously, he negaive argumen also applies, i.e. when he re-order poin is reducing in size over ime, demand signals o he manufacure and he sysem invenory levels reflec his. Pseudo Code Descripion Se all variables o zero; Se all variables o zero GET Ta, Ti, Tq, Tw and G; Ge inpu from user WHILE[<60, Do while ime incremen is less hen 60.. CONS=IF[>2,.,0.]; Demand is 0 unil ime equals 2, when i hen equals R=R+((/(+Tq))*((G*CONS)-R)); Calculae he re-order poin R DR=R-PR; Calculae he ne change in he re-order poin R PR=R; Sore curren R as previous R VCON=DR+CONS; Virual consumpion = acual consumpion plus ne change in R AVCON=AVCON+((/(+Ta))*(VCON- Se manufacurers forecas, AVCON AVCON)); COMRATE=CR4;CR4=CR3; CR3=CR2;CR2=CR; CR=ORATE; Se manufacurers compleion rae as a delayed funcion of he order rae (producion delay = 4 ime unis, he exra uni delay is o ensure he proper order of evens is obeyed) AINV=AINV-VCON+COMRATE; Calculae invenory levels EINV=((0-AINV)/Ti); Se invenory conribuion o ORATE DWIP=AVCON*4; Se arge Work In Progress (WIP) WIP=WIP+ORATE-COMRATE; Calculae acual WIP EWIP=((DWIP-WIP)/Tw); Se WIP conribuion o ORATE ORATE=AVCON+EINV+EWIP; Calculae he producion order rae, ORATE ++]; Incremen ime and reurn o sar of loop Table. Pseudo Code Represenaion of VMI-APIOBPCS in Response o a Sep Inpu
Disney, S.M. and Towill, D.R., (2003) The effec of VMI dynamics on he bullwhip effec in supply chains, Inernaional Journal of Producion Economics, Vol. 85, No. 2, pp99-25. DOI: 0.06/S0925-5273(03)000-5. 2 The erm APIOBPCS in VMI-APIOBPCS (John, Naim and Towill, [32]) refers o he srucure of he ordering decision used by he supplier or vendor in he VMI relaionship o schedule producion (or disribuion if ha is he suppliers business). APIOBPCS can be expressed in words as Le he producion arges be equal o he sum of a forecas (average consumpion smoohed over Ta ime unis) of perceived demand (ha is acually in VMI he sum of he sock adjusmens a he disribuor and he acual sales), plus a fracion (/Ti) of he invenory discrepancy beween acual and arge levels of finished goods, plus a fracion (/Tw) of he discrepancy beween arge WIP and acual WIP. This is a well-known producion-scheduling rule ha can be uned o reflec a wide range of scheduling sraegies. The APIOBPCS sysem has been sudied before by a number of auhors, John, Naim and Towill [32], Mason-Jones e al [8], Towill, Cheema and Evans [33] ec. I also has exacly he same srucure as Serman s Anchoring and Adjusmen heurisic used by him o model his Beer Game daa (Naim and Towill, [34]). 6. Descripion of he Tradiional Supply Chain Simulaion Model The APIOBPCS model, John, Naim and Towill [32], was chosen o represen a radiional supply chain. This was due o a number of reasons. Firsly i was fel imporan ha i is desirable ha like (APIOBPCS) is compared o like as much as possible (VMI-APIOBPCS) in order o gain as much undersanding as possible on he fundamenal srucure of VMI. Secondly, APIOBPCS was chosen for VMI and he radiional supply chain, as i is recognised as good pracice, Edghill, Olsmas and Towill [35] incorporaes all commonly available forms of informaion, represens human behaviour (Serman, [22] and Naim and Towill [34]) and is a well-undersood member of he IOBPCS (Towill, [36]) family. The APIOBPCS model can be expressed in words as oulined in he previous secion. I incorporaes hree variables; Ta, a parameer ha describes how quickly demand is racked in he forecasing mechanism, Ti, a parameer ha describes of much of he discrepancy beween acual invenory and arge invenory levels should be added o he producion/ disribuion order rae and
Disney, S.M. and Towill, D.R., (2003) The effec of VMI dynamics on he bullwhip effec in supply chains, Inernaional Journal of Producion Economics, Vol. 85, No. 2, pp99-25. DOI: 0.06/S0925-5273(03)000-5. 3 Tw, a parameer ha describes how much of he discrepancy beween acual WIP and arge WIP levels should be added o he producion/ disribuion order rae. Individual echelons, or APIOBPCS models, can be linked ogeher o form a supply chain, by coupling he ORATE signal of he consuming echelon o he CONS signal of he supplying echelon, as recognised by Burns and Sivazlian [37] and furher exploied by Towill and del Vecchio [38]. The difference equaions required for modelling a wo-level APIOBPCS supply chain (for example in a spreadshee) are shown in Appendix 2. Table 2 shows how he sysem can be implemened in a compuer language such as C++ or Visual Basic. Like he VMI model he producion and disribuion delays are assumed o be of four ime unis. Pseudo Code Se all variables o zero; GET TaS, TiS, TwS, Ta, Ti, Tw; WHILE[<60, CONS=IF[>2,.,0.]; AVCONS=AVCONS+((/(+TaS))*(CONSS- AVCONS)); COMRATES=CR4S;CR4S=CR3S; CR3S=CR2S;CR2S=CRS;CRS=ORATES; AINVS=AINVS-CONSS+COMRATES; EINVS=((0-AINVS)/TiS); DWIPS=AVCONS*4; WIPS=WIPS+ORATES-COMRATES; EWIPS=((DWIPS-WIPS)/TwS); ORATES=AVCONS+EINVS+EWIPS; AVCON=AVCON+((/(+Ta))*(ORATES- AVCON)); COMRATE=CR4; CR4=CR3; CR3=CR2; CR2=CR; CR=ORATE; AINV=AINV-ORATES+COMRATE; EINV=((0-AINV)/Ti); DWIP=AVCON*4; WIP=WIP+ORATE-COMRATE; EWIP=((DWIP-WIP)/Tw); ORATE=AVCON+EINV+EWIP; ++]; Descripion Se all variables o zero Ge inpu from user Do while ime incremen is less hen 60.. Demand is 0 unil ime equals 2, when i hen equals Se disribuors forecas, AVCON Se disribuors compleion rae as a delayed funcion of he disribuors order rae (producion delay = 4 ime unis, he exra uni delay is o ensure he proper order of evens is obeyed) Calculae disribuors invenory levels Se disribuors invenory conribuion o ORATE Se disribuors arge Work In Progress (WIP) Calculae disribuors acual WIP Se disribuors WIP conribuion o ORATE Calculae he disribuors order rae, ORATE Se manufacurers forecas, AVCON Se manufacurers compleion rae as a delayed funcion of he order rae (producion delay = 4 ime unis, he exra uni delay is o ensure he proper order of evens is obeyed) Calculae manufacurers invenory levels Se manufacurers invenory conribuion o ORATE Se manufacurers arge Work In Progress (WIP) Calculae manufacurers acual WIP Se manufacurers WIP conribuion o ORATE Calculae he manufacurers order rae, ORATE Incremen ime and reurn o sar of loop Table 2. Pseudo Code Represenaion of a Two Level APIOBPCS Supply Chain in Response o a Sep Inpu
Disney, S.M. and Towill, D.R., (2003) The effec of VMI dynamics on he bullwhip effec in supply chains, Inernaional Journal of Producion Economics, Vol. 85, No. 2, pp99-25. DOI: 0.06/S0925-5273(03)000-5. 4 7. Sep Response Comparison of he Forreser Effec To invesigae he Bullwhip Effec, he Facory Order Rae response of he wo supply chain srucures o a sep inpu will be used. Undersanding he dynamic response o a sep inpu will yield insigh ino how he sysem will be affeced by promoions. As here are an infinie number of designs for VMI and radiional supply chains ha migh be compared, previous bes pracise designs will be used o compare he wo supply chains via he sep response. The following designs were chosen o represen good designs of a radiional supply chain wih a producion lead-ime of 4 ime periods; John e al [32] recommended seings (Ta=8, Ti=4, Tw=8). This was derived using classical conrol heory and simulaion. I can be regarded as a very conservaive design relaing back o bes pracice in hardware conrol sysems. Disney e al [39] recommended seings (Ta=8, Ti=4, Tw=5). This was based on a Geneic Algorihms search, using Laplace ransforms, simulaion wih he aim of minimising he Forreser Effec, invenory holding, seleciviy, whils maximising robusness o errors in esimaion of WIP levels and producion lead-imes. Naim and Towill [34] values of (Ta=8, Ti=4, Tw=4). These were derived from improving Serman s [22] Beer Game derived opimum seings. Disney [28] recommended seings (Ta=4, Ti=7, Tw=28). This was based on he full soluion based search using z-ransforms and simulaion aimed a minimising he Forreser Effec, invenory holding, whils maximising Cusomer Service Levels. Operaional Seing Parameers of Opimum VMI Sysem G ~ W # Ta Ti Tq Tw 0.0 3 3 6 7 6 42 00 8 23 6 63 4 0.0 4 4 4 4 4 4 63 4 00 22 27 6 63 ~ G = Gain on exponenial forecass used o calculae he re-order poin level # W = Weighing funcion o rade-off producion capaciy requiremens agains sock requiremens Table 3. Sample Opimum Parameer Values for VMI Sysem
Disney, S.M. and Towill, D.R., (2003) The effec of VMI dynamics on he bullwhip effec in supply chains, Inernaional Journal of Producion Economics, Vol. 85, No. 2, pp99-25. DOI: 0.06/S0925-5273(03)000-5. 5 As oulined earlier, he VMI sraegy has 5 key parameers (Tq, G, Ta, Ti, Tw) ha deermine he dynamic response of he sysem. The erms Ta, Ti, Tq and Tw depend on he parameer G ha is independenly se o reflec he desired CSL given he ransporaion lead-ime beween he manufacurer and he disribuor, via he re-order poin equaion. A full-scale opimisaion procedure (Disney [28]) has been applied o hese parameers for a range of raios of producion adapaion coss (due o he Forreser Effec) o he associaed invenory holding coss and for differen values of he re-order poin G. The resuling opimal parameer seings for Ta, Ti, Tq and Tw for he case when G= and 4 are shown in Table 3. In his Secion i is sufficien o illusrae he VMI sysem sep response for he case where producion adapaion and invenory holding coss were given equal imporance for he wo designs chosen o represen good soluions for a VMI supply chain. Hence he good seings for he VMI supply chain used were; The opimum parameer seing when he disribuor has a re-order poin level se a planning periods average demand, (i.e. G=, Ta=6, Ti=7, Tq=6, Tw=42) The opimum parameer seing when he disribuor has a re-order poin level se a 4 planning periods average demand, (i.e. G=4, Ta=4, Ti =4, Tq=4, Tw=63) I can be seen from inspecion of Figure 5 ha he VMI design ouperforms he radiional supply chain, wih less peak overshoo, faser seling ime and a generally quicker response. We will now invesigae he comparison furher.
Disney, S.M. and Towill, D.R., (2003) The effec of VMI dynamics on he bullwhip effec in supply chains, Inernaional Journal of Producion Economics, Vol. 85, No. 2, pp99-25. DOI: 0.06/S0925-5273(03)000-5. 6 ORATE 3.5 3 2.5 2.5 0.5 0 VMI, Ta=6, Ti=7, Tq=6, Tw=42, G= VMI, Ta=4, Ti=4, Tq=4, Tw=63, G=4 APIOBPCS, Ta=8, Ti=4, Tw=8 APIOBPCS, Ta=8, Ti=4, Tw=5 APIOBPCS, Ta=8, Ti=4, Tw=4 APIOBPCS, Ta=4, Ti=7, Tw=28-0 0 0 20 30 40 Time Figure 5. Sep Response For VMI And Tradiional Supply Chains 8. General Dynamic Comparison of VMI and Tradiional Supply Chains In Table 4 we have compared VMI and radiional supply chains across a range of performance merics. The peak ORATE overshoo is he simple measure of bullwhip and has already been me in Fig. 5. Noe ha for compleeness Table 4 includes hree opimal soluions for each of he wo values of G (.0 and 4.0). These are for raios of producion adapaion/invenory holding coss W = 0.0; W =.0; and W = 00. The reason for his is ha W = 0.0 approximaes an agile sysem; W = 00 approximaes a lean (level scheduling) sysem; whils W =.0 is a compromise soluion. As noed by Chrisopher and Towill [40] here are occasions where agile is he bes business soluion, and where lean is he bes business soluion, and where some mix is required. Table 4. Bullwhip and Sock Performance Trade-Offs can be found a he end of he documen For he opimal VMI supply chains, he bullwhip is reasonably unaffeced by varying W for a given value of G. This is because he opimisaion programme (Disney, [27]) drives he VMI parameers o yield he bes possible response, (as we have seen in Table 3, he parameer seings o achieve his goal are subsanially differen). If he
Disney, S.M. and Towill, D.R., (2003) The effec of VMI dynamics on he bullwhip effec in supply chains, Inernaional Journal of Producion Economics, Vol. 85, No. 2, pp99-25. DOI: 0.06/S0925-5273(03)000-5. 7 peak ORATE overshoo is 2.5, hen X is a bullwhip effec of 50% and so on. So comparing he opimal VMI sysem wih he neares equivalen radiional supply chain i.e. G =, W =.0, and wih VMI opimal parameer seing, we see VMI reduces he bullwhip effec from 44% o 69%. Some auhors (for example Chen, Ryan and Simchi-Levi, [4]) use he raio of order and sales variance as a bullwhip measure ohers (for example Fransoo and Wouers [42]) have been using raios involving he sandard deviaion. Whils boh are concepually similar, he variance raio is preferred as his can be calculaed direcly from a sysem ransfer funcion, Disney and Towill [43] or efficienly enumeraed via he difference equaions. Hence in Table 4 we have included an esimae of variance obained via evaluaion of sysem noise bandwidh (Towill, [36]). This bullwhip measure has been reduced from 0.93 (Tradiional supply chain) o 0.46 (VMI sysem), almos a facor of 2 o. So he effec on boh bullwhip measures using VMI is a grea improvemen. We use he composie measure of Inegral of Time * Absolue Error (ITAE) o compare dynamic invenory performance. ITAE is much used as a means of ranking comparaive performance of compeiive hardware conrol sysems (Towill, [44]). The reasoning is ha large insananeous errors are unavoidable and should no be penalised. On he oher hand persisen errors occurring afer a long ime are o be avoided so should be heavily penalised, hence he ime weighing o achieve his effec. Alhough ITAE may be regarded as an inuiive performance measure is minimisaion does normally resul in a good sysem design [44]. Figure 6 shows how ITAE is compued and hus how a ransien waveform may be convered ino a single number. The firs observaion o make on ITAE in Table 4 is ha he values for he VMI sysems are very much dependen on he re-order poin G. For he like-for-like comparison beween VMI (G =, W = ) and he radiional supply chain he ITAE is always subsanially lower for he VMI sysem. Hence he invenory recovery dynamics are much improved by adoping VMI.
Disney, S.M. and Towill, D.R., (2003) The effec of VMI dynamics on he bullwhip effec in supply chains, Inernaional Journal of Producion Economics, Vol. 85, No. 2, pp99-25. DOI: 0.06/S0925-5273(03)000-5. 8.2.0 0.8 0.6 0.4 0.2 0.0 0 0 20 30 40 50 60 70 80 90 00 0 (a) Sep in Demand 2.0.0 0.0 -.0-2.0-3.0-4.0-5.0-6.0-7.0-8.0-9.0 0 0 20 30 40 50 60 70 80 90 00 0 (b) Corresponding Invenory Behaviour 40 20 00 80 60 40 20 0 0 0 20 30 40 50 60 70 80 90 00 0 (c) Produc of Time Absolue Error in invenory levels Figure 6. Compuaion of ITAE as a Measure of Invenory Response We are deermining he availabiliy resuling from seing he arge invenory o 0, in response o an i.i.d. normally disribued demand paern. In he VMI scenario his arge invenory refers o he sysem invenory (ha is he disribuors sock plus he goods in ransi and he manufacurers sock level minus he reorder poin) and for radiional supply chain his refers o he manufacurers arge sock posiion. The
Disney, S.M. and Towill, D.R., (2003) The effec of VMI dynamics on he bullwhip effec in supply chains, Inernaional Journal of Producion Economics, Vol. 85, No. 2, pp99-25. DOI: 0.06/S0925-5273(03)000-5. 9 demand signal was chosen o be a sandard normal disribuion wih a mean of 0 and a sandard deviaion / variance of. This scenario can be efficienly enumeraed via difference equaions in a spreadshee environmen. The availabiliy measure specifically refers o he probabiliy ha invenory levels are above zero (ha is he chance sock is available o be shipped o he disribuor). 9. Simulaed Responses o Typical Reail Sales Time Series To give some idea of he differences in behaviour in response o real-world disurbances, we have simulaed responses o a ypical reail sales paern. The corresponding ORATE variances have already been lised in Table 4 ( 2 calculaed from he ime series), bu we also include o enable a visual comparison. Noe ha if he reail sales paern had been random whie noise (or an independenly and idenically disribued normal disribuion), hen his 2 would be exacly equal o ha evaluaed via noise bandwidh. So he ORATE variances would lead us o expec significanly differen responses for he various sysems. This is indeed he case, as is quie obvious from Fig. 7 which shows ORATE and he associaed sock movemens abou he arge invenory level. The firs noeworhy poin is ha varying he weighing funcion W does produce an agile response, a lean response, and a compromise response. Also noe ha his family of responses is generaed for boh values of he re-order poin G. However, all of he radiional supply chains simulaed have excessive swings in ORATE. Furhermore, hese designs exhibi resonances ha are clearly a propery of he sysem design, and no of he exciaion caused by he sales ime series (Towill, [36]). In fac he business manager can be wrongfooed and assume ha here is seasonaliy presen in he demand. This i is he well-known second Forreser Effec of rogue seasonaliy (Berry and Towill, [45]). We have sudied he responses furher and summarized he resuls in Table 5 below.
Disney, S.M. and Towill, D.R., (2003) The effec of VMI dynamics on he bullwhip effec in supply chains, Inernaional Journal of Producion Economics, Vol. 85, No. 2, pp99-25. DOI: 0.06/S0925-5273(03)000-5. 20 ORATE 3000 2500 2000 500 000 500 0 W=0.0 W= W=00 0 0 20 30 40 50 60 70 80 90 00 0 Time Sysem Invenory 4000 3000 2000 000 0-000 -2000-3000 W=0.0 W= W=00 0 0 20 30 40 50 60 70 80 90 00 0 Time Opimal VMI designs when G= 3000 2500 W=0.0 W= W=00 4000 3000 W=0.0 W= W=00 ORATE 2000 500 000 500 0 0 0 20 30 40 50 60 70 80 90 00 0 Time Sysem Invenory 2000 000 0-000 -2000-3000 0 0 20 30 40 50 60 70 80 90 00 0 Time Opimal VMI designs when G=4 ORATE 3000 2500 2000 500 000 500 Design Design 2 Design 3 Manufacurers Invenory 4000 3000 2000 000 0-000 -2000 Design Design 2 Design 3 0 0 0 20 30 40 50 60 70 80 90 00 0 Time -3000 0 0 20 30 40 50 60 70 80 90 00 0 Time Tradiional supply chain designs Figure 7. Simulaed Responses of Sample Opimal VMI and Tradiional Supply Chains o a Typical Reail Sales Paern
Disney, S.M. and Towill, D.R., (2003) The effec of VMI dynamics on he bullwhip effec in supply chains, Inernaional Journal of Producion Economics, Vol. 85, No. 2, pp99-25. DOI: 0.06/S0925-5273(03)000-5. 2 Sysem Invenory Orders Supply chain ype Seings No. of direcion changes Range of he swings Variance Raio No. of direcion changes Range of he swings Variance Raio VMI Tradiional G= G=4 Design W=0.0 62 3553 6.89 76 692 5.634 W= 49 2730.53 70 560 0.502 W=00 63 2463 0.99 62 29 0.08 W=0.0 66 4708 29.87 76 604 5.07 W= 59 3300 7.84 72 68 0.62 W=00 63 3074 6.44 68 23 0. 2 3567 23.39 24 737.0 2 23 3898 24.77 28 937.3 3 7 5243 53.07 22 35 3.8 Table 5. Summary of he simulaed responses As expeced, he rogue seasonaliy is visible in he manufacurers invenory records. The swings in invenory are clearly due o sysem-induced exciaion; here are less changes in direcion in he invenory levels and large swings have occurred as is eviden in he range and variance of hose swings. Indeed, if we look a he auocorrelaion funcion of invenory and orders, he VMI supply chains ypically have a negaive correlaion a one periods delay, and hen sligh posiive and negaive correlaion hereafer, whereas he radiional supply chain has significan auocorrelaion across many periods. In he agile sysem boh invenory and ORATE behaviour are disincly sharp-edged. However, i mus be poined ou ha he G = VMI supply chain is relaively smooh in behaviour. I also has subsanially smaller swings in boh ORATE and invenory compared o any of he radiional supply chains. The superioriy of he VMI design is herefore boh widespread and considerable. 0. Conclusions VMI is a well-esablished supply sraegy ha has found favour in a number of marke secors. In many cases his has occurred in response o a feeling by he reailer ha i would be a good hing o delegae furher responsibiliy o he vendor. As a concep i
Disney, S.M. and Towill, D.R., (2003) The effec of VMI dynamics on he bullwhip effec in supply chains, Inernaional Journal of Producion Economics, Vol. 85, No. 2, pp99-25. DOI: 0.06/S0925-5273(03)000-5. 22 can be daed back o he classical conribuion of Magee [7]. He firs raised he issue of which player should conrol he supply pipeline. I is inuiively obvious ha beer sigh and hence undersanding of boh informaion flow and maerial flow should lead o beer business performance. In paricular i is possible o condense he pipeline so ha is behaviour approaches ha of a single echelon. This is achieved by using a consan (ha is one ha does no change over ime) re-order poin a he disribuor. As we have demonsraed via a VMI simulaion model his is indeed he case. We have compared he bullwhip performance of a number of VMI supply chains wih wo-level supply chains. In all cases here is subsanial reducion in bullwhip (ypically halving he effec). This is rue irrespecive of he bullwhip measure used. In he paper we have concenraed on he wo measures of peak order rae o a sep inpu (a rich picure approach) and order rae variance. The laer is widely used in indusry. From our perspecive i also has he advanage of being predicable from sysem noise bandwidh. Under cerain circumsances his is amenable o an analyic soluion, which we have developed bu no exploied here. In oher cases i is possible o ake subsanial compuaional shor cus o calculae variance and availabiliy. ITAE has been used as a composie measure of invenory dynamics. Here VMI also offers a subsanial improvemen in performance. Finally, as Berry and Towill [45] have shown, managers need o be aware ha in pracice here are poenially wo Forreser effecs. The firs (demand amplificaion) is universally known. Bu he second (rogue seasonaliy) can equally likely be induced by he sysem dynamics. Hence a periodiciy may appear in he ordering waveforms ha is no presen in he markeplace demand. Our simulaions have shown ha paricularly in he sock records rogue seasonaliy is induced by he radiional supply chain in response o ypical reail demand waveforms. In conras his is observed o be less of a problem wih he VMI sysem.
Disney, S.M. and Towill, D.R., (2003) The effec of VMI dynamics on he bullwhip effec in supply chains, Inernaional Journal of Producion Economics, Vol. 85, No. 2, pp99-25. DOI: 0.06/S0925-5273(03)000-5. 23 References [] Lee, H.L., Padmanabhan, P. and Whang, S., "Informaion disorion in a supply chain: he Bullwhip Effec", Managemen Science, Vol. 43, 997, pp543-558. [2] Lee, H.L., Padmanabhan, V., Whang, S., The Bullwhip Effec in supply chains, Sloan Managemen Review, Spring, 997, pp. 93-02. [3] Forreser, J., Indusrial dynamics, Cambridge MA, MIT Press, 96. [4] Wikner, J., Naim, M.M. and Towill, D.R., "The sysem simplificaion approach in undersanding he dynamic behaviour of a manufacuring supply chain", Journal of Sysem Engineering, Vol. 2, 992, pp64-78. [5] Van Ackere, A., Larsen, E.R. and Morecrof, J.D.W., Sysems hinking and business process redesign: An applicaion o he Beer Game", European Managemen Journal, Vol., No. 4, 993, pp42-423. [6] Towill, D.R., "Forridge - Principles of good maerial flow", Producion Planning and Conrol, Vol. 8, No. 7, 997, pp622-632. [7] Towill D.R. and McCullen, P., The impac of an agile manufacuring programme on supply chain dynamics, Inernaional Journal Logisics Managemen, December, Vol. 0, No., 999, pp83-96. [8] Mason-Jones R., Naim, M.M. and Towill, D.R., The impac of pipeline conrol on supply chain dynamics, Inernaional Journal of Logisics Managemen, Vol. 8, No. 2, 997, pp47-62. [9] Fisher, M., Hammond, J., Obermeyer, W. and Raman, A., "Configuring a supply chain o reduce he cos of demand uncerainy", Producion and Operaions Managemen, Vol. 6, No. 3, 997, pp2-225. [0] Sevens, G., Inegraing he supply chain, Inernaional Journal of Physical Disribuion and Logisics Managemen, Vol. 9, No. 8, 989, pp3-8. [] Axsäer, S., "Conrol heory conceps in producion and invenory conrol", Inernaional Journal of Sysems Science, Vol. 6, No. 2., 985, pp6-69. [2] Kaipia, R., Holmsröm, J. and Tanskanen, K., "VMI: wha are you losing if you le your cusomer place orders", Working Paper, Dep of Indusrial Managemen, Helsinki Universiy of Technology, Finland, 2000. [3] Andel, T., "Manage invenory, own informaion", Transpor and Disribuion, Vol. 37, Issue 5,996, pp54-58. [4] Salk, G., Evans, P. and Shulman, L.E., Compeing on capabiliies: The new rules of corporae sraegy, Harvard Business Review, March-April, 992, pp57-69. [5] Holmsröm, J., "Business process innovaion in he supply chain: a case sudy of implemening Vendor Managed Invenory", European Journal of Purchasing and Supply Managemen, Vol. 4, 998, pp27-3. [6] Disney, S.M., Holmsröm, J., Kaipia, R., Towill, D.R., "Implemenaion of a VMI producion and disribuion conrol sysem", Inernaional Symposium of Logisics, Salsburg, Ausria, July 200. [7] Magee, J.F., Producion planning and invenory conrol, McGraw-Hill Book Company, New York, 958, pp80-83. [8] Lee, H.L., So, K.C. and Tang, C.S., "The value of informaion sharing in a wolevel supply chain", Managemen Science, Vol. 46, No. 5, 2000, pp626-643. [9] Cachon, G. and Fisher, M., "Campbell soup's coninuous replenishmen program: evaluaion and enhanced invenory decision rules", Producions and Operaions Managemen, Vol. 6, No.3, 997, pp266-276. [20] Holmsröm, J., Framling, K., Kaipia, R. and Saranen, J., "Collaboraive Planning Forecasing and Replenishmen: New soluions needed for mass
Disney, S.M. and Towill, D.R., (2003) The effec of VMI dynamics on he bullwhip effec in supply chains, Inernaional Journal of Producion Economics, Vol. 85, No. 2, pp99-25. DOI: 0.06/S0925-5273(03)000-5. 24 collaboraion", Working Paper, Dep. of Indusrial Managemen, Helsinki Universiy of Technology, Finland, 2000. [2] Schmenner, R.W., Looking ahead by looking back: Swif, even flow in he hisory of manufacuring, Producion and Operaions Managemen, Vol. 0, No., Spring 200, pp87-96. [22] Serman, J., Modelling managerial behaviour: Mispercepions of feedback in a dynamic decision making experimen, Managemen Science, Vol. 35, No. 3, 989, pp32-339. [23] Disney, S.M. and Towill, D.R., "The effec of VMI on he Bullwhip Effec", Inernaional Conference on Producion Research, July 30- Augus 2, Prague, Czech Republic, 200. [24] Salk, G. and Hou, T.M., Compeing agains ime: How ime-based compeiion is reshaping global markes, The Free Press, New York, 990. [25] McCullen, P. and Towill, D.R., "Pracical ways of reducing bullwhip: The case of he Glosuch supply chain", Conrol, Dec/Jan 200, pp24-30. [26] Meers, R., Quanifying he Bullwhip Effec in supply chains, Journal of Operaions Managemen, Vol. 5, 997, pp89-00. [27] Van Aken, J.E., On he conrol of complex indusrial organizaions, London, Marinus Nijhoff Social Sciences Division, 978. [28] Disney, S.M., The producion and invenory conrol problem in Vendor Managed Invenory supply chains, PhD Thesis, Cardiff Business School, Cardiff Universiy, UK, 200. [29] Disney, S.M. and Towill, D.R., A discree linear conrol heory model o deermine he dynamic sabiliy of Vendor Managed Invenory, Inernaional Journal of Producion Research, Vol. 40, No., pp79-204 [30] Disney, S.M. and Towill, D.R., Opimisaion of he Dynamic Response of Vendor Managed Invenory, Compuers and Indusrial Engineering, Vol. 43, No. -2, pp27-58. [3] Corill, K., "Reforging he supply chain", Journal of Business Sraegy, November/ December 997, pp35-39. [32] John, S., Naim, M.M., Towill, D.R., Dynamic analysis of a WIP compensaed decision suppor sysem, Inernaional Journal of Manufacuring Sysems Design, Vol., No. 4, 994, pp283-297. [33] Towill, D.R., Evans, G.N. and Cheema, P., "Analysis and Design of an Adapive Minimum Reasonable Invenory Conrol Sysem", Producion Planning and Conrol, Vol. 8, No. 6, 997, pp545-557. [34] Naim, M.M. and Towill, D.R., 995, Wha s in he Pipeline?, 2nd Inernaional Symposium on Logisics -2, July, pp35-42. [35] Edghill, J., Olsmas, C. and Towill, D., "Indusrial case-sudy on he dynamics and sensiiviy of a close-coupled producion-disribuion sysem", Inernaional Journal of Producion Research, Vol. 26, No. 0, pp68-693. [36] Towill, D.R., Opimisaion of an invenory and order based producion conrol sysem, Proceedings of he Second Inernaional Symposium on Invenories, Budapes, Hungary, 982. [37] Burns, J.F. and Sivazlian, B.D., Dynamic analysis of muli-echelon supply sysems, Compuer and Indusrial Engineering, Vol. 2, 978, pp8-93. [38] Towill, D.R. and del Vecchio, A., "Applicaion of filer heory o he sudy of supply chain dynamics", Producion Planning and Conrol, Vol. 5, No., 994, pp82-96.