ON THE BULLWHIP AVOIDANCE PHASE: SUPPLY CHAIN COLLABORATION AND ORDER SMOOTHING

Transcription

1 ON THE BULLWHIP AVOIDANCE PHASE: SUPPLY CHAIN COLLABORATION AND ORDER SMOOTHING Salvatore Cannella, Elena Cancmno To cte ths verson: Salvatore Cannella, Elena Cancmno. ON THE BULLWHIP AVOIDANCE PHASE: SUPPLY CHAIN COLLABORATION AND ORDER SMOOTHING. Internatonal Journal of Producton Research, Taylor Francs, 00, pp.. <0.00/0000>. <hal-00> HAL Id: hal-00 Submtted on Dec 00 HAL s a mult-dscplnary open access archve for the depost and dssemnaton of scentfc research documents, whether they are publshed or not. The documents may come from teachng and research nsttutons n France or abroad, or from publc or prvate research centers. L archve ouverte plurdscplnare HAL, est destnée au dépôt et à la dffuson de documents scentfques de nveau recherche, publés ou non, émanant des établssements d ensegnement et de recherche franças ou étrangers, des laboratores publcs ou prvés.

2 Internatonal Journal of Producton Research ON THE BULLWHIP AVOIDANCE PHASE: SUPPLY CHAIN COLLABORATION AND ORDER SMOOTHING Journal: Internatonal Journal of Producton Research Manuscrpt ID: TPRS-00-IJPR-0.R Manuscrpt Type: Orgnal Manuscrpt Date Submtted by the Author: 0-Jul-00 Complete Lst of Authors: Cannella, Salvatore; Unversty of Palermo, Faculty of Engneerng Cancmno, Elena; Unversty of Palermo, Faculty of Engneerng Keywords: BULLWIP EFFECT, PERFORMANCE MEASURES Keywords (user): BULLWIP EFFECT, PERFORMANCE MEASURES

3 Page of Internatonal Journal of Producton Research ON THE BULLWHIP AVOIDANCE PHASE: SUPPLY CHAIN COLLABORATION AND ORDER SMOOTHING ABSTRACT Salvatore Cannella, Elena Cancmno Unversty of Palermo, Faculty of Engneerng vale delle Scenze, Parco d Orleans, 0 Palermo, Italy cannella@unpa.t; ecancmno@unpa.t Ths paper provdes an assessment on the mpact of collaboraton and smoothng replenshment rules on supply chan operatonal performance and customer servce level. Three supply chan confguratons (.e. Tradtonal, Informaton Exchange and Synchronsed) n whch orders are generated by smoothng (S, R) nventory control polces, are studed for varatons of proportonal controller for dfferent proportonal controllers. A supply chan stress test s performed through a sudden and ntense change n demand. The man conclusons of ths paper are: () the mpact of Supply Chan Collaboraton on overall supply chan performance s hgher than that of order smoothng. Order smoothng mtgates bullwhp effect, but t may have negatve mpact on customer servce. Supply Chan Collaboraton mtgates the bullwhp effect, provdes nventory stablty, lmts lumpy orders and enhances customer servce level. () The negatve effect on customer servce level of order smoothng s almost elmnated n synchronsed supply chans. KEYWORDS: mult-echelon; nformaton sharng; supply chan performance metrcs; nventory management; order-up-to perodc revew; dfferental equaton modellng; cost reducton strateges PROBLEM SCOPE In 00, n Budapest, at the Euroma Internatonal Conference, Holweg and Dsney (00) dentfy sx dstnct developmental stages of the Bullwhp Effect research feld: - pre the producton and nventory control era - - the producton smoothng era - 0- the development of control theory - - the beer game phase the bullwhp redscovery phase - snce 000 the bullwhp avodance phase. Chen s et al. (000) conng of Order Rate Varance Rato as the quantfcaton metrc for demand amplfcaton along a supply chan and Cachon and Fsher s (000) research on the value of nformaton sharng could reasonably be consdered the startng pont of the current research perod devoted to one of the most fascnatng Supply Chan Rubk s cubes. One dstnctve feature of the Bullwhp Avodance Phase s the focus toward the effcacy of bullwhp solvng approaches. Operaton Management communty have focused ther efforts onto two dfferent approaches for avodng and/or lmtng the bullwhp effect: collaboraton n supply chan and smoothng replenshment rules. Collaboraton n supply chan conssts n transformng suboptmal ndvdual solutons of ndvdual lnks nto a comprehensve soluton through sharng customer and operatonal nformaton. In the bullwhp avodance phase several authors showed how supply chan collaboraton allows to decelerate the order varablty n upstream drecton (Chen et al. 000, Dsney and Towll 00, Chatfeld et al. 00, Km et al. 00), reduces nventory holdng costs (Shang et al. 00, Kelepours et al. 00, Byrne and Heavey 00) and mproves customer servce level (Hosoda et al. 00). A smoothng replenshment rule s a perodc revew (S, R) nventory control polcy where the order s smoothed va proportonal controllers. The ratonale for ths polcy s to lmt the ters overreacton/under-reacton upon changes n demand. Smoothng replenshment rules mtgate bullwhp effect (Dejonckheere et al. 00, Dsney et al. 00b, Warburton 00, Jakšč and Rusjan 00, Km and Sprnger 00) and lmt nventory costs (Chen and Dsney 00, Wrght and Yuan 00, Boute et al.

4 Internatonal Journal of Producton Research Page of ). However, dampenng order varablty may have negatve mpact on customer servce (Dejonckheere et al. 00, Dsney et al. 00, Dsney et al. 00, Dsney and Lambrecht 00), as excessve smoothng of order rate could mpede to fulfl the marketplace demand n tme. Ths sde effect on customer servce level was manly shown n supply chans wthout collaboraton mechansms. The paper attempts to provde a structured assessment on the mpact of collaboraton and smoothng replenshment rules on supply chan operatonal performance and customer servce level. The research objectves are () to contrast the mpact of collaboraton and the mpact of smoothng order rules, and () to show whether the negatve effect on customer servce of order smoothng rate perssts n collaboratve supply chan structures. To fulfl the research objectve, three supply chan confguratons:.e. Tradtonal, Informaton Exchange and Synchronsed (Holweg et al. 00) n whch orders are generated by smoothng (S, R) nventory control polces, are studed for dfferent values of proportonal controller. A supply chan stress test s performed va a sudden and ntense change n demand. The assessment system s based on two crtera: supply chan operatonal performance and customer servce level and takng nto account both local (sngle echelon) and systemc performance (supply chan) measures. Supply chans are modelled by dfferental equatons. The man results are: () the mpact of Supply Chan Collaboraton s hgher than that of order smoothng on the overall supply chan performance. Order smoothng mtgates bullwhp effect, lmts nventory varablty and lumpy orders, but, as showed n lterature and reasserted n ths work, t may have a negatve mpact on customer servce. Supply chan Collaboraton avods bullwhp effect, provdes nventory stablty and enhanced customer servce level. () The negatve effect on customer servce level of order smoothng s almost avoded n collaboratve supply chan. The paper s organsed as follows. In Secton supply chan collaboraton and smoothng replenshment rules are brefly dscussed. Secton presents the three studed supply chan archetypes. Secton reports the methodologcal approach and the mathematcal formalsm of the supply chan models. Secton s devoted to descrbe the measurement system. In Secton the expermental desgn s detaled. Techncal dscussons are presented n secton and results are reported n secton. Fnally, Secton provdes conclusons. BULLWHIP AVOIDANCE PRACTICES: SUPPLY CHAIN COLLABORATION AND SMOOTHING REPLENISHMENT RULES AT A GLANCE The nventory replenshment rule and Supply Chan Collaboraton as bullwhp avodance practces are presented n the followng sub-sectons.. Supply Chan Collaboraton The word collaboraton orgnates from the Latn cum-laborare: act of workng jontly. Supply Chan Collaboraton refers to the shared efforts made by members to acheve a common goal. The shared effort s to transform suboptmal ndvdual solutons of ndvdual lnks n the supply chan nto a comprehensve soluton (Sefert 00). The common goal of collaboraton s the elmnaton of neffcences, such as the bullwhp effect, whch occur through uncoordnated sequences n the supply chan. Vsblty of nformaton flow s the key enabler of members coordnaton: the Holy Gral of supply chan (Holweg et al. 00). Snce the 0s, when the Quck Response programme was ntroduced n apparel frms (Hunter 0), large-scale collaboraton projects have gradually modfed the modus operand n global supply chans. The mplementaton of collaboraton projects has reshaped materal and nformaton flows, ntensfed allances and transformed strateges, organsatons and corporate culture. These structural changes have In 00 Towll et al. presented a creatve classfcaton framework for bullwhp studes. They dentfed three observer s perspectves to analyse the bullwhp effect: Varance lens, Shock lens and Flter lens. Usng a mathematcal modellng, the bullwhp shock lens ams to nfer on the performance of supply chans for an unexpected change n marketplace demand. Ths approach can be vewed as a crash test or a stress test : studyng the system performance under an ntense and volent solctaton. Barlla (Hammond ), Campbell (Cachon and Fsher ), Procter & Gamble and Hewlett-Packard (Lee et al. ), Wal- Mart (Waller et al. ), -Eleven (Lee 00), Phlps (De Kok et al. 00) are outstandng examples of successful supply chan collaboraton mplementatons. Furthermore, several mathematcal models have showed the effcacy on supply chan collaboraton n terms of bullwhp dampenng, nventory varance reducton and customer servce level mprovement. Table reports a nonexhaustve lst of contrbutons to the topc n the bullwhp avodance phase. Large-scale projects are specfc ntatves of Supply Chan Collaboraton. Notorous large-scale projects are effcent consumer response (McKnsey & Co. ), vendor managed nventory (Cachon and Fsher, Dsney and Towll 00b), contnuous replenshment (Andrask ), collaboratve plannng, forecastng and replenshment (VICS, Holmström et al. 00), centralsed nventory management (Lee et al. ).

5 Page of Internatonal Journal of Producton Research nspred researchers to develop new theoretcal models of supply chan structures (Lee and Whang 00), n order to capture the dfferent dmensons of collaboraton and to clarfy ts ontologcal nature. In the elucdaton of supply chan collaboraton concept, the endeavour of Operaton Management has conssted n formalsng () how nformaton vsblty can be appled to nventory control polces, and () how collaboratve confguratons are dstngushed n terms of nventory control polces. A frst framework of collaboratve supply chans based on the degree of synchronsaton of members nventory control polces was provded by Holweg et al. (00). They dentfed four supply chan archetypes, each of them charactersed by a specfc combnaton of two dmensons: plannng collaboraton and nventory collaboraton. Plannng collaboraton refers to real-tme sharng of market demand data for the generaton of conjont forecastng. Inventory collaboraton refers to real-tme sharng of nformaton on nventory levels and n-transt tems for centralsed replenshment actvtes. The Supply Chan Confguratons dentfed by Holweg et al. (00) are:. Tradtonal Supply Chan (no collaboraton): each level n the supply chan ssues producton orders and replenshes stock wthout consderng the stuaton at ether up- or downstream ters of the supply chan. It s a decentralsed supply chan. Each member generates an ndependent producton-dstrbuton plan on the bass of ncomng orders from drect customers.. Informaton Exchange (plannng collaboraton): retaler and suppler order ndependently, yet exchange demand nformaton and acton plans n order to algn ther forecasts for capacty and longterm plannng. It s a decentralsed supply chan: each member generates an ndependent productondstrbuton plan on the bass of ncomng orders from drect customers and from market demand data.. Vendor Managed Replenshment (nventory collaboraton): the task of generatng the replenshment order s gven to the suppler, who takes responsblty for mantanng the retaler s nventory and subsequently the retalers servce levels. A centralsed producton-dstrbuton plan s generated by supplers on the bass of downstream partner vsblty of nventory levels and work n progress.. Synchronsed Supply (nventory and plannng collaboraton): the suppler takes charge of the customer s nventory replenshment on the operatonal level and uses ths vsblty n plannng ts own supply operatons. A centralsed producton-dstrbuton plan s jontly generated by supply chan members on the bass of complete vsblty of nventory levels, work n progress levels and market demand.. Smoothng Replenshment Rule In producton-nventory systems, order tmng and quantty are defned by a coordnated set of rules and procedures that allows for routng decson on when and how much to order for each tem needed n the manufacturng or procurement process to fll customer demand, whle mantanng nventores at the rght level (Hax and Candea ). These rules and procedures n nventory control systems are commonly known as replenshment polces. A standard classfcaton of order quantty control polces s based on the tmng of the nventory revew: Contnuous Revew Systems versus Perodc Revew Systems. If orderng costs are relatvely hgh when compared to the nventory revew costs and/or suppler accepts orders only wth a gven frequency (daly, weekly, monthly), the perodc revew system s essentally more desrable (see e.g. Hax and Candea, Dsney and Lambrecht 00). In practcal applcatons the most largely used perodc revew polcy s the (S, R) order rule (Hax and Candea ). Each revew perod R the nventory s revewed and a quantty O s ordered to brng the level of the avalable nventory up to a level S, known n the lterature as order-up-to level. The avalable nventory conssts of the nventory on hand plus the nventory on order but not yet arrved (ppelne nventory or work n progress) (Dsney and Lambrecht 00). The S level s dynamcally computed every perod R as the sum of the forecast on the customer demand, plus a target on-hand nventory, plus a target ppelne nventory. The quantty O s generated to satsfy the customer demand, and to fll entrely the gap between the target and the current levels of on-hand nventory, as well as the gap between the target and the current levels of the ppelne nventory. A smoothng replenshment rule s a (S, R) polcy n whch the entre defct between the S level and the avalable nventory s not recovered n a revew perod. For each revew perod R the quantty O s generated to recover only a fracton of the gap between the target on-hand nventory and the current level of on-hand nventory, and a fracton of the gap between the target ppelne nventory and the current level of ppelne nventory. The amount of the gaps to recover s regulated by decson parameters known as Supply chan collaboraton has been defned through a number of dmensons (Baley and Evans 00) such as nformaton ntegraton, synchronsed plannng, work flow coordnaton, new busness models (Lee and Whang 00); nformaton sharng, decson synchronsaton, ncentve algnment (Smatupang and Srdharan 00); cross functonalty, process algnment, jont decson makng, shared performance metrcs (Barratt 00). Smoothng replenshment rules are also known as Inventory and Order Based Producton Control System (IOBPCS) order polces (Coyle ). The features of smoothng replenshment rules were studed and popularsed by the Cardff Busness School (see Towll, John et al., Dsney and Towll 00). For an extensve dscusson on smoothng replenshment famly see Lalwan et al. (00) and Sarmves et al. (00).

6 Internatonal Journal of Producton Research Page of proportonal controllers. The nventory proportonal controller Ty modulates the recovery of the onhand nventory gap and the work n progress proportonal controller Tw determnes the recovery of the ppelne nventory gap. A partcular class of smoothng (S, R) s the matched controller case (Dsney and Towll 00, 00, Dsney et al. 00), known as Dezel and Elon settng (Dezel and Elon ). It refers to the case n whch the nventory proportonal controller Ty s equal to the work n progress proportonal controller Tw. The smoothng replenshment can be defntely consdered one of the major topcs n the Bullwhp Avodance Phase, as t s an effectve remedy to demand sgnal processng, a cause descrbed by Lee s et al. (), see Table. The ratonale for ths order polcy s to lmt the ters over-reacton/underreacton for changes n demand. In the lterature t s shown that properly tunng the value of the proportonal controllers n the smoothng (S, R) polcy offers an opportunty to reduce bullwhp (Dsney and Towll 00a, Dsney et al. 00) at a lower cost than holdng extra nventory (Chen and Dsney 00). In partcular, the Dezel and Elon confguraton was shown to be a partcularly stable settng for proportonal controllers (Dsney and Towll 00). However, smoothng replenshment rules may have negatve mpact on customer servce (Dejonckheere et al. 00, Dsney et al. 00, Dsney et al. 00, Dsney and Lambrecht 00), as excessve smoothng of the order rate could mpede to fulfl the marketplace demand n tme. Ths opposte trend between bullwhp reducton and customer servce level was manly shown n no collaboratve supply chans. In Appendx a hydraulc analogy s presented to clarfy the effect on performance of order smoothng. Table reports a non-exhaustve lst of authors that nferred on the mpact of collaboraton and order smoothng n the Bullwhp Avodance Phase. TABLE In the lterature, proportonal controllers have been defned wth dfferent appellatves, e.g. adjustment tme (Forrester, Sterman, Warburton 00), fracton of the nventory and wp dscrepancy (John et al. ), tme to adjust for wp and net stock errors (Dejonckheere et al. 00), proportonal nventory poston feedback gan (Dsney and Grubbström 00), fracton of the nventory defct (Boute et al. 00), smoothng parameter (Jakšč and Rusjan 00) or feedback gan (Dsney and Lambrecht 00). In the (S, R) polcy, proportonal controllers can be thought of amplfers or attenuators (Dsney et al. 00). The proportonal controllers of a smoothng replenshment rule are attenuators, as they are set to recover a fracton of the nventory defcts. In the mathematcal formalsaton of smoothng replenshment rules, proportonal controllers can be dvsors or multplers of the nventory gaps. When they are dvsors ther value s greater than. When they are multplers ther value s a postve number less than. When they are equal to order polcy turns to a classcal (S, R).

7 Page of Internatonal Journal of Producton Research SUPPLY CHAIN MODELS: INFORMATION FLOW AND REPLENISHMENT DECISION To nfer on the mpact of collaboraton and the mpact of smoothng replenshment rules, three levels of ncreasng collaboraton represented by three Holweg s et al. (00) supply chan archetypes, n whch orders are generated by smoothng (S, R), are modelled: I. Tradtonal Supply Chan II. Informaton Exchange III. Synchronsed Supply The presented models are unconstraned capacty K-stage sngle-product producton-dstrbuton seral systems wth a undrectonal flow of materal. The generc echelon s poston s represented by ndex. Echelon = stands for the manufacturer and =K+ for the fnal customer. Fgure shows the flow of materals for the three confguratons. Nomenclature for varables s reported n appendx A. Fgure. Flow of materals n the supply chans The confguratons dffer n the nformaton flow and n the use of nformaton to generate the smoothng replenshment rule. In the followng subsecton the shared data and the order polces are presented n detal.. Tradtonal Supply Chan In the tradtonal supply chan the nformaton flow conssts n the mere transmsson of members orders upstream. A generc echelon only receves nformaton about order quantty O + from the downstream adjacent echelon (Fgure ). Fgure. Tradtonal Supply Chan Each generc echelon generates the order quantty O on the bass of local data and parameters (Inventory level I, local Work n progress level W, safety stock factor, lead tme and proportonal controllers Ty and Tw) and on the ncomng orders from the downstream adjacent echelon O +. The order quantty O (equaton ) s the sum of the followng components: - forecast on the order from the subsequent echelon d ˆ - smoothed work n progress gap - smoothed nventory gap ˆ O ( t) = d ( t) + ( TW ( t) W ( t)) + ( TI ( t) I ( t)) () Tw Ty Echelon =K forecasts customer demand d ˆK on the bass of markets sales d, and the remanng echelons only take nto account downstream ncomng orders O + for ther forecast d ˆ.. Informaton Exchange In the nformaton exchange supply chan the nformaton flow conssts on the transmsson of members orders n up-stream drecton and on sharng the nformaton on market demand. A generc echelon receves nformaton on the order quantty O + from the downstream adjacent echelon and on the up-todate market demand d (Fgure ). Fgure. Informaton Exchange Supply Chan The sngle-product modellng assumpton s wdely used n bullwhp analyss. The applcaton of Laplace transform and Z transform to producton nventory control (Smon, Vassan ), the mono-step numercal method to analyse the demand amplfcaton phenomenon (Forrester ), the management games performed at Mt to nvestgate the human behavour n supply chan (Sterman ), the formalsaton of the wdely-known four causes of the bullwhp effect (Lee et al. ), the generaton of the Order Rate Varance Rato (Chen et al. 000), cornerstones n the nventory control feld, are based on the sngle-product assumpton. Specfcally, wthn the bullwhp avodance phase lterature, Dejonckheere et al. (00), Dsney and Towll (00a), Chandra and Grabs (00), Gonçalves et al. (00), Boute et al. (00), Hosoda and Dsney (00), Ouyang (00), Aggelogannak et al. (00), Agrawal et al. (00) can be cted.

8 Internatonal Journal of Producton Research Page of A generc echelon generates the order quantty O on the bass of local data and parameters, ncomng orders O + and market demand d. The order quantty O (equaton ) s the sum of the followng components: - forecast on market demand - smoothed work n progress gap - smoothed nventory gap ˆ O ( t) = d ( t) + ( TW ( t) W ( t)) + ( TI ( t) I ( t)) () K Tw Ty Unlke a tradtonal supply chan, all echelons receve nformaton on market demand d n the nformaton exchange. The customer s demand forecast d ˆK s drectly ncluded n the replenshment rule, whle, as n the tradtonal, the forecast on orders ncomng by echelon + d ˆ, s used to compute Target Work n Progress (equaton ) and Target Inventory (equaton ).. Synchronsed Supply In the synchronsed supply chan the nformaton flow conssts n the transmsson of members orders, Inventory levels, Work n progress levels, lead tmes and safety stock factors upstream and n sharng the nformaton on market demand. A generc echelon receves nformaton about order quantty O + from the downstream adjacent echelon, on the up-to-date market demand d and Safety stock factors Tc j, Lead Tmes Tp j, Inventory levels I j,, and Work n progress Levels W j from all downstream echelons j=+ K (Fgure ). Fgure. Synchronsed Supply Chan The order quantty O (equaton ) s the sum of the followng components: - forecast on market demand - smoothed Mult-echelon work n progress gap - smoothed Mult-echelon nventory gap ˆ O ( t) = d ( t) + ( TvW ( t) vw ( t)) + ( TvI ( t) vi ( t)) () K Tw Ty Unlke tradtonal and nformaton exchange, synchronsed supply chan s a centralsed structure n whch any echelon consders ts successors as part of ts nventory system for determnng replenshment quantty. Whle n the prevous confguratons Target Inventory and Target Work n progress are functons of the echelon local data, n the synchronsed supply chan both current and target levels of Inventory and Work n progress at echelon also take nto account data ncomng from all downstream echelons. Table summarses the dfferences n ncomng data and Table detals the components of the replenshment n the three supply chans, respectvely. Table. Incomng data for a generc echelon n the dfferent supply chan confguratons Table. Components of smoothng replenshment rules METHODOLOGICAL APPROACH AND MATHEMATICAL FORMALISM The operatons management lterature s rch n classfcatons of methodologes used to nvestgate supply chan performance and the bullwhp phenomenon (Rddalls, et al. 000, Klejnen and Smts 00, The ncluson of successors nventory levels nto the replenshment decson dates back to the s. Dsney and Towll (00c) report that the concept was ntally dscussed by Magee (), n a presentaton of a conceptual framework for desgnng a producton control system, ponted by the authors as the poneer model of Vendor Managed Inventory. Two years later, the publcaton of Clark and Scarf (0), recognsed as the semnal work n mult-echelon nventory analyss (Whang, Dong and Lee 00, Swamnathan and Tayur 00, DeCrox 00) could be reasonably consdered the frst mathematcal formalsaton for a fully coordnated decson-makng approach (Sahn and Robnson Jr. 00).

9 Page of Internatonal Journal of Producton Research Dejonckheere et al. 00, Dsney et al. 00a, Geary et al. 00, Towll et al. 00, Dsney and Lambrecht 00). A classfcaton of methodologcal approaches for supply chan analyss from the perspectve of decson makng herarchcal level was provded by Rddalls et al. (000). They dentfy two man approaches: OR technques and methodologes based on the dynamcs of system. Accordng to ther framework, OR technques have ther place at a local tactcal level n the desgn of supply chans and n day-by-day decson makng, whle the mplcaton of strategc desgn on supply chan performance and the global network functonng are better analysed by usng methodologes based on the dynamcs of system (contnuous tme dfferental equaton models, dscrete tme dfference equaton models, dscrete event smulaton systems). In the Bullwhp Avodance Phase Holweg and Dsney (00) clarfed the latter methodologcal approach for supply chan analyss. They recognsed three dstnct and methodologcally ndependent research domans: the dscrete tme approach, the contnuous tme approach and the control theory approach. The authors affrmed that Herbert Smon () and Jay Forrester () lad the foundatons to the contnuous tme doman approach towards the study of supply chan dynamcs. The Nobel Prze dscussed the applcaton of lnear determnstc control theory to producton control, by usng Laplace transform technques (Axsäter ), whle Forrester adopted soluton methods for the ntal-value problem of nonlnear repeated couplng of frst-order dfferental equaton systems. The numercal methods used to approxmate a soluton for the ntal-value problem are generally mono-step, such as Euler-Cauchy method (tangent or constant-slope), Kutta s method, trapezodal ntegraton method, and Heun method (three-term Taylor seres), or mult-step, such as Adams-Bashfort method, and Adams- Moulton method. Several mathematcal toolboxes desgned to solve a broad range of problems or ad-hoc applcatons (such as Vensm, thnk, DYNAMO and Powersm) can be used to approxmate the soluton of dfferental equatons. The methodologcal approach adopted n ths paper s based on the dynamcs of system, namely the contnuous tme approach. The supply chan confguratons are modelled through frst-order nonlnear dfferental equatons. The mathematcal formalsm of the supply chan confguratons studed n ths work s reported n Tables and. Table. Equatons Table. Supply Chan Confguratons and related Equaton System MEASUREMENT SYSTEM Performance measurements are used to determne the effcency and effectveness of an exstng system, or to compare alternatve systems (Neely et al. ). Performance measures are also used to desgn proposed systems, by determnng the values of the decson varables that yeld the most desrable level of performance (Beamon ). Supply chan performance metrcs have been classfed on the bass of several crtera: fnancal vs. non-fnancal (De Ton and Toncha 00), qualtatve vs. quanttatve (Gunasekaran et al. 00), strategc/tactcal/operatonal (Gunasekaran and Kobu 00), and functonbased vs. value-based (Bagch ). The bullwhp effect s a multfaceted and extremely complex phenomenon that mpacts on operatonal, tactcal and strategc aspects of performance: order-producton-dstrbuton effcacy, operatonal and customer responsveness, servce level, holdng nvestments and costs, flexblty. Due to the polyhedral mpact of bullwhp, the scentfc communty has recently advocated for multdmensonal analyses of supply chan and bullwhp phenomenon through the adopton and development of sutable performance measures and comprehensve metrcs systems (Towll et al. 00, Gunasekaran and Kobu 00). Accordng to the recent lterature, a structured and extended supply chan assessment framework s adopted to respond to the problem scope of ths work. It s based on two crtera: operatonal performance and customer servce level and t measures both local (sngle echelon) and systemc performance (supply chan). The operatonal performance s measured through a set of metrcs, whose reducton reflects mproved cost effectveness of members operatons. Customer servce level s assessed by the wdely adopted fll rate, whose ncrease expresses reduced backlog and decreased stock-out costs. In Table referenced and heren propounded metrcs are classfed and assocated to the related nformaton content and costs. Table Measurement System

10 Internatonal Journal of Producton Research Page of Order Rate Varance Rato Ths metrc was proposed by Chen et al. (000) and s so far the most common bullwhp measure n the lterature (Dsney and Lambrecht 00). Dsney and Towll (00a) noted that, for a statonary random sgnal, over long perods of tme the means cancel out as µ o =µ d. Order Rate Varance Rato s the quantfcaton of the nstablty of orders n the network (ndexes are reported n Table ). ORVrR σ / µ O O m, m, = () σ / µ m, d d Inventory Varance Rato Ths metrc was proposed by Dsney and Towll (00a) to measure net stock nstablty, as t quantfes the fluctuatons n nventory. An ncreased nventory varance results n hgher holdng and backlog costs 0, nflatng the average nventory cost per perod (Dsney and Lambrecht 00). IVrR m, σ / µ I I m, m, = () σ / µ d d Average Inventory Average nventory s the mean of a ter s Inventory values over the nterval T. The metrc s commonly used n producton-dstrbuton system analyss n order to provde concse nformaton on nventory nvestment, see e.g. holdng cost modelled as lnearly dependent from stock levels n Cachon and Fsher (000), Dsney and Grubbström (00), Shang et al. (00), Chen and Dsney (00), Rechhart et al. (00), Wrght and Yuan (00). T AI = I ( t) (0) m, m, T t = 0 Systemc Average Inventory Systemc Average Inventory (Cannella and Cancmno 00, Cancmno and Cannella 00) s the sum of the Average Inventory values of all ters n a gven supply chan confguraton. Summng nventory levels all along supply chan s a well-establshed ndustral practce. Compaq Computer and Procter & Gamble routnely measure both ther own nventory and downstream nventory at ther dstrbutors (Hausman 00). SAI K m = AI () m, = 0 Fll Rate Fll Rate s representatve of customer servce level (Zpkn 000). The Fll Rate s evaluated every sngle t and computed on the sales to the ultmate customer. Although the metrc s based on the nformaton of one level of the supply chan (echelon K), t captures the performance of all partners, snce the servce to the fnal customer s the end purpose of the entre supply chan (Hausman 00). C ( t) m, K FR ( t) = () m d ( t) Average Fll Rate The Average Fll Rate s the mean of a subset of Fll Rate values computed over a lmted tme nterval Γ T. The nterval Γ s selected by consderng, among all numercal smulatons Ω, the longest tme span [% τ '' % τ '] wth Fll Rate values lower than, that s: the maxmum duraton of shortage. Ths procedure permts to analyse the producton-dstrbuton network only durng stock-outs and to compare the magntude of backlog among the dfferent the supply chan structures and parameter settngs. The problem of quantfyng the stock-out costs s a dffcult and unsatsfactorly solved queston n nventory theory, especally because of the ntangble components (Hax and Candea ). The adopton of a lmted tme nterval Γ to compute the customer servce level s related to a wdely used assumpton to estmate the stock-out cost as proportonal to the product of the number of unts out of stock and the duraton of stock-outs, such as n Holt et al. (0). τ '' AFR = FR ( t ) m m Γ % () t=τ% ' '' ' '' ' Γ= max ( τ τ ) = % τ % τ () ω m m 0 Inventory varance rato s representatve of backlog cost f the modellng allows negatve nventory. In ths work the non-negatve condton of nventory s assumed and the Inventory Varance Rato reflects ncreased holdng cost per unt, mssng producton schedules costs, utlsaton of transport capacty costs. Backlog costs are dentfed by Fll Rate.

11 Page of Internatonal Journal of Producton Research Zero-Replenshment For (S, R) order polcy, the Zero-Replenshment Phenomenon s defned as the event n whch, n a revew perod R, a ter does not place any order (Cannella and Cancmno 00, Cancmno and Cannella 00). An order pattern charactersed by a sgnfcant number of Zero-Replenshment Phenomena s known n lterature as sporadc, ntermttent or lumpy (Slver 0, Croston, Schulz, Chatfeld and Hayya 00). In a gven tme horzon, f the demand s a postve and statonary sgnal and the parameters of the nventory replenshment rule reman unaltered, the occurrence of the Zero-Replenshment Phenomenon could be ndcatve of an erroneous excessve dmensonng of prevous orders. The Zero-Replenshment metrc s the total amount of the Zero-Replenshment Phenomenon occurrences n the observaton perod T. The metrc s used to measure tmely and pondered reactvty and scalablty of ter s operatons. Zero-Replenshment cannot be vewed as a stand-alone supply chan performance metrc and t shall be analysed together wth a customer servce level measure: apparently, null or low Zero-Replenshment values could be ndcatve of optmal operatons and lot szng, but ths s true only when at the same tme the system assures a hgh customer servce level. Otherwse, a poor customer servce level assocated to a null or low Zero- Replenshment reflects poor system responsveness. T ZR = x ( t) () x m, m, m, t= 0 O ( t) = 0 m, ( t) = 0 O ( t) 0 m, () Systemc Zero-Replenshment The Zero-Replenshment phenomenon can be evaluated at a systemc level referrng to a Systemc Zero- Replenshment, computed as the sum of the Zero-Replenshment of the sngle echelons n a gven supply chan confguraton. K SZR = ZR () m = m, Proportonal Controller Bullwhp Slope and Proportonal Controller Inventory Instablty Slope Dejonckheere et al. presented n 00 a study on the dynamc behavour of four-ter mult-echelon supply chans. They adopted the Order Rate Varance Rato to assess and compare dfferent bullwhp soluton approaches. In order to contrast varous supply chan confguratons, they plotted the obtaned values usng the echelon poston as an ndependent varable. They observed the nterpolated curve and nferred qualtatvely about the lnear or geometrc nature of the trend. The authors state that a geometrc ncrease of the Order Rate Varance Rato nterpolatng curve s representatve of strong bullwhp propagaton, more ntense than n a lnear trend. Dejonckheere s et al. curve s a smart representaton of bullwhp propagaton n a mult-echelon system and permts to concsely compare dfferent supply chan confguratons (Cannella et al. 00, Cannella and Cancmno 00). To extend Dejonckheere s et al. nferrng technque to a general case, a statstcal analyss of the curve could be performed for both Order Rate Varance Rato and Inventory Varance Rato. Adoptng an analogous approach, a smlar curve can be obtaned for a sngle echelon usng the matched proportonal controller as the ndependent varable. In ths case the curve s a compact representaton of the echelon s senstvty to bullwhp for proportonal controller varatons wthn a gven range. Under the assumpton of lnearty, a frst-order regresson can be performed n order to compare the echelon s senstvty for dfferent supply chan confguratons on the bass of the lnear regresson coeffcent, named Proportonal Controller Bullwhp Slope. To obtan a graphcal representaton of echelon s senstvty to the proportonal controller n a gven supply chan confguraton (n ths work Tradtonal, Informaton Exchange and Synchronsed), the slope values are reported n a radar dagram. Each axs of the radar represents an echelon, and the value on the axs s the respectve Proportonal Controller Bullwhp Slope. The larger the radar area, the greater the mpact of a proportonal controller varaton on the gven confguraton n terms of Order Rate Varance Rato. Ths procedure can be analogously performed for Inventory Varance Rato. In ths case the lnear regresson coeffcent s named Proportonal Controller Inventory Instablty Slope and the effect of parameter varatons on the net stock fluctuatons s the scope of the analyss. EXPERIMENTAL DESIGN Three levels of collaboraton and three levels of order smoothng are studed. The M levels of collaboraton are represented by the three supply chan confguratons detaled n the prevous sectons, the N levels of smoothng order depend on three settngs of the matched proportonal controller Ty=Tw (Dezel and Elon settng). The total number of experments Ω s the product of the number of levels for order smoothng N and the number of supply chan confguratons M (Table ). In order to solate the effect of collaboraton and order smoothng, the

12 Internatonal Journal of Producton Research Page 0 of parameters lead tme, safety stock factor and demand smoothng forecast are not vared throughout the Ω experments. Table. Indexes In ths work the numercal experments are performed under the followng settngs: - The seral systems are composed by K= echelons. - The M levels of collaboraton are represented by the three supply chan confguratons, Tradtonal, Informaton Exchange, Synchronsed. - The N levels of order smoothng are dentfed by the followng matched proportonal controller desgns, presented n ascendng order of smoothng: Ty=Tw=Tp () Ty=Tw=Tp+ () Ty=Tw=Tp (0) - The values of lead tme, safety stock factor and demand smoothng forecast factor are: [Tp, Tc, α ]= [,, 0.]. - The actual marketplace demand d s ntalsed at unts per tme unt, untl there s a pulse at t=, ncreasng the demand value up to unts per tme unt (Sterman ). The step demand pattern d(t) s assumed to perform a stress test accordng to Towll s et al. shock lens perspectve (00). - The values of the ntal state varable values are: [W (0), I (0), B (0)]=[ Tp d(0), Tc d(0), 0]. - The numercal experments Ω are performed for a tme length T=. - The solutons for the ntal-value problem are approxmated through Vensm PLE. The Euler-Cauchy method wth order of accuracy t = 0. s adopted. The numercal experment output s next presented. In Tables and Order Rate Varance Rato and Inventory Varance Rato are reported, respectvely. Results are reported by echelon (row), and by supply chan confguraton (column), grouped by matched proportonal controller level. Table. Order Rate Varance Rato Table. Inventory Varance Rato Proportonal Controller Bullwhp Slope and Proportonal Controller Inventory Instablty Slope are reported n Fgure. Each axs of the radar represents an echelon, and the value on the axs s the Proportonal Controller Slope for that echelon. These values are ndcatve of the echelon s senstvty to varatons n smoothng parameters wthn the studed range. The radar areas are representatve of the magntude of the mpact of a matched proportonal controller varaton on the gven confguraton n terms of Order Rate Varance Rato and Inventory Varance Rato. Fgure. Proportonal Controller Bullwhp Slope and Proportonal Controller Inventory Instablty Slope Average Inventory s reported accordng to Dejonckheere s et al. notaton (00) n Fgure. The output values are plotted usng the echelon poston as the ndependent varable. Each dagram groups supply chan confguraton for the three values of matched proportonal controller. Fgure. Average Inventory Zero-Replenshment values are reported n Fgure. Results are dsplayed by echelon, by supply chan confguraton and by matched proportonal controller. Fgure. Zero-Replenshment Average Fll Rate, Systemc Average Inventory, and Systemc Zero-Replenshment are presented n Fgure. The horzontal bar chart represents the Average Fll Rate; the hstogram stands for the Systemc Average Inventory, and the column wth cylndrcal shape represents the Systemc Zero-Replenshment. The numercal value for each metrc s reported next to the corresponded dagram. In the lterature several settngs of matched (Nam and Towll, Dsney et al. 00, Dsney et al. 00) and unmatched (Dsney et al., Hong Mng et al. 000, Wrght and Yuan 00) proportonal controller desgns have been tested. In ths work the proportonal controller expermental levels are related to lead tme. Equaton () and (0) are from proportonal controllers desgn of John et al. (), equaton () refers to Dsney and Towll (00). 0

13 Page of Internatonal Journal of Producton Research Fgure. Average Fll Rate, Systemc Average Inventory, Systemc Zero-Replenshment DISCUSSIONS Results are analysed by supply chan confguraton n the followng subsectons and then summarsed n Secton.. Tradtonal Supply Chan The results from the study ndcate that, n the Tradtonal confguraton, order smoothng strongly mpacts on performance. Tradtonal supply chan shows bullwhp effect for every desgn of proportonal controllers under an unexpected varaton n market demand. Ths result s n lne wth Chatfeld s et al. (00) and Dejonckheere s et al. (00) conclusons: tradtonal supply chan exhbts a geometrcal ncrease of order varance n up-stream drecton for the three studed levels of order smoothng. The dfference n the three order smoothng levels conssts of the magntude of bullwhp, strongly lowered for ncreasng smoothng. Results also reconfrm Dsney s et al. concluson (00): bullwhp magntude s monotoncally reduced for ncreasng order smoothng. Results show a reducton of order varablty for echelon = from to shftng from the low smoothng level (Ty=Tw=Tp desgn) to the hgh smoothng level (Ty=Tw=Tp desgn). Inventory Varance Rato and Average Inventory show the same trend that Order Rate Varance Rato: fluctuaton and average levels of nventory are hgh for all smoothng settngs, however the two related metrcs decrease for ncreasng order smoothng levels. Systemc Average Inventory decreases from % to % for ncreasng order smoothng values. Dfferences emerge n node-to-node ncrease of Inventory Varance Rato wth respect to the Order Rate Varance Rato trend. Echelon = (manufacturer) shows a lower value Inventory Varance Rato than ts subsequent =. Ths phenomenon s due to the unlmted raw materal supply assumpton. Zero-Replenshment ndcates sporadc order occurrence n the tradtonal supply chan for all smoothng levels. The metrc shows the same trend of all prevous measures, decreasng for ncreasng order smoothng; lumpy orders are not elmnated by proportonal controller n tradtonal supply chans. On the contrary, Fll Rate has an opposte trend wth respect to operatonal performance metrcs: a monotoncally decrease of customer servce level for ncreasng order smoothng. Shftng from a low smoothng to a hgh smoothng, Average Fll Rate decreases from.% to.%. Ths result confrms lterature conclusons for tradtonal supply chan on the relaton between order smoothng and customer servce level (Dejonckheere et al. 00, Dsney et al. 00, Dsney et al. 00, Dsney and Lambrecht 00). To sum up: I. Tradtonal supply chan exhbts a geometrcal ncrease of order varance n up-stream drecton, hgh nventory varablty and ntermttent order phenomenon. The magntude of the noxous phenomena s strongly related to the order smoothng levels. II. As order smoothng ncreases, the supply chan operatonal performance mproves (Inventory varance rato, Average Inventory, Zero-Replenshment) but the customer servce level worsens (Fll Rate). Smoothng the order rate notceably lmts the magntude of bullwhp effect but t can result n poor customer servce. III. The smoothng parameter varatons sgnfcantly mpact on performance of tradtonal supply chans. Informaton Exchange In Informaton exchange supply chan, the bullwhp effect decelerates upstream wth respect to the tradtonal structure. However, bullwhp effect s not completely elmnated even after sharng market nformaton as n Agrawal et al. (00). As n Chatfeld et al. (00) and Dejonckheere (00), nformaton exchange supply chan exhbts a lnear ncrease of order varance n up-stream drecton for the three studed levels of order smoothng. As n the Tradtonal supply chan, the dfference n the supply chan response to the three smoothng order levels s the magntude of bullwhp, strongly reduced for ncreasng smoothng parameters. More specfcally, a notceable reducton of bullwhp s showed for echelon = shftng from low smoothng (Ty=Tw=Tp desgn) to medum smoothng (Ty=Tw=Tp desgn), n whch the value of Order Rate Varance Rato goes from to. Inventory Varance Rato, Average Inventory and Zero-Replenshment show the same trend of Order Rate Varance Rato: as smoothng order ncrease, supply chan operatonal performance mproves. Systemc Average Inventory decreases from % to % for ncreasng smoothng values and lumpy orders are reduced. Although the operatonal performance n nformaton exchange has the same trend than n tradtonal supply chans for varatons of the order smoothng level, n ths case the gradent s less steep and the values of the metrcs reveal a better performance. The radar areas of Proportonal Controller Bullwhp Slope and Proportonal Controller Inventory Instablty Slope show that echelons senstvty to proportonal controller varaton s stll notceable, but the mpact s reduced wth respect to the Tradtonal confguraton.

14 Internatonal Journal of Producton Research Page of Ths has two man mplcatons: n ths type of supply chan, as n tradtonal supply chans, smoothng order stll mpact on supply chan performance; Informaton Exchange confguraton outperforms the Tradtonal supply chan. The two mplcatons are confrmed by the values of Fll Rate, whch are generally hgher (.%;.%; 0.%) and show the same opposte trend wth respect to operatonal performance, as n tradtonal supply chan. To sum up: IV. Informaton exchange supply chan exhbts a lnear ncrease of order varance upstream. Bullwhp, Inventory Instablty and Intermttent Orders are not completely elmnated but reduced wth respect to tradtonal supply chans. As n tradtonal supply chans, the magntude of ths noxous phenomenon s related to the order smoothng levels. V. The smoothng parameter varatons mpact the performance of the supply chan wth slghtly reduced magntude as compared to the Tradtonal confguraton. Customer servce level shows the same opposte trend wth respect to operatonal performance for ncreasng smoothng parameters, as n tradtonal supply chans, but wth weaker ntensty. VI. Informaton Exchange generally outperforms the Tradtonal confguraton. Ceters parbus, all performance measures are superor to tradtonal. VII. Proportonal controller tunng remans crucal for supply chan performance n nformaton exchange.. Synchronsed Supply Results ndcate that proportonal controller tunng n Synchronsed Supply confguraton weakly mpacts on supply chan performance. Synchronsed supply chan outperforms the prevous scenaros, both n terms of operatonal performance and customer servce level. A remarkable performance mprovement s observed, regardless the proportonal controller settng. The results reassert the emprcal studes of Holweg et al. (00) on synchronsed supply chan performance: bullwhp s generally elmnated, nventory s always stablsed and ntermttent demand s elmnated. Order Varance Rato values are sgnfcantly lower than n prevous supply chan confguratons. Ths metrc reveals the amplfcaton dampenng property of synchronsed supply chan: the shock n market demand causes a weak amplfcaton of orders at the echelons = and =, promptly smoothed at the hghest nodes of the chan. Synchronsed supply chan possesses the nventory stablty transmsson property: the Inventory Varance Rato measure reveals a monotonous node-to-node reducton n upstream drecton for all proportonal controller desgns. Furthermore, the Dejonckheere s et al. notaton shows dramatc mprovements n operatonal performance for all order smoothng desgns, as nventory levels are notceable reduced for all echelons. Systemc Zero-Replenshment for the desgn Ty=Tw=Tp and Ty=Tw=Tp+ s equal to the optmal theoretcal value and ndcates the maxmum operatonal responsveness. Only desgn Ty=Tw=Tp shows a Zero- Replenshment value equal to, correspondng to a reducton of lumpy orders of % and 0% wth respect to Tradtonal and Informaton Exchange. Besdes, Average Fll rate reveals the stablty property of Synchronsed for varatons of proportonal controllers n terms of customer servce level: the maxmum dfference n the three smoothng order levels s.%. Ceters parbus, Average fll rate mproves up to.% (Ty=Tw=Tp desgn). The radar areas of Proportonal Controller Bullwhp Slope and Proportonal Controller Inventory Instablty Slope confrm the nsenstvty of synchronsed supply chan echelons to varatons on smoothng levels. The opposte trend of process and customer servce metrcs perssts but the extent of the varaton s relatvely slght: the values of the metrcs reman almost unaltered through varatons of proportonal controllers. Ths ndcates the weak mpact of parameter settng on supply chan performance wth respect to the Informaton Exchange and Tradtonal Supply Chans, at least wthn the range studed. The Synchronsed Supply summares the benefts of hgh collaboraton: the Systemc Zero-Replenshment n two sets s equal to the optmal theoretcal value and ndcates the maxmum operatonal responsveness. Hgh values of Average Fll Rate, low nventory levels and varance, and low order varance for all settngs reflect the confguraton s stablty, robustness and scalablty. To sum up: VIII. Bullwhp s generally avoded, nventory s always stablsed, and ntermttent orders are elmnated for all order smoothng levels. IX. Synchronsed supply chan largely outperforms Tradtonal and Informaton Exchange supply chans. X. The values of the metrcs persst almost unaltered for dfferent proportonal controllers. The negatve effect of order smoothng rate on customer servce n almost absent. XI. The smoothng parameter varatons mpact very weakly on the synchronsed supply chan performance. RESULTS The man results of ths work are: () Supply Chan Collaboraton mpacts more than order smoothng on overall supply chan performance.

15 Page of Internatonal Journal of Producton Research Both Collaboraton and smoothng order have sgnfcantly mpact on supply chan performance. Order smoothng mtgates bullwhp effect and lmts nventory varablty and lumpy orders; however, as showed n lterature and reconfrmed n ths work, t may have negatve mpact on customer servce. As order smoothng ncreases, the supply chan operatonal performance mproves but the customer servce level worsens. Smoothng the order rate can be consdered a sedatve of bullwhp effect. Despte the potental loss of customer servce, both n tradtonal and nformaton exchange supply chans order smoothng s an effectve approach aganst bullwhp effect. Supply Chan Collaboraton elmnates bullwhp effect, provdes nventory stablty and enhanced customer servce level. For an ncreasng collaboraton degree (n tradtonal to synchronsed supply chans) the overall supply chan performance mproves. Partcularly, synchronsed supply chan allows the elmnaton of neffcences by lnkng the nventory and replenshment decson, and a reducton of nventory levels. It s lkely to consder Supply Chan Collaboraton the bullwhp avodance technque par excellence: vsblty s the soluton. ()The negatve effect on customer servce of smoothng order s almost elmnated n collaboratve supply chan. The sde effect on customer servce level, caused by ncreasng order smoothng n low collaboratve supply chans, s avoded n synchronsed supply chans. Furthermore, results support the former concluson of ths work on the mpact of collaboraton supply chan on operatonal performance and customer servce level. The outcomes of ths work are summarsed n Fgure. Fgure. Impact of Supply Chan Collaboraton and order smoothng on operatonal performance and customer servce level CONCLUSIONS The paper provded a structured assessment of the mpact of collaboraton and smoothng replenshment rules on supply chan operatonal performance and customer servce level. The research objectve were to assess the mpact of collaboraton and the smoothng order rules, and to show f the negatve effect on customer servce of smoothng order rate perssts n collaboratve supply chan structures. To fulfl the research objectves three supply chan confguratons, Tradtonal, Informaton Exchange and Synchronsed (Holweg et al. 00), n whch orders are generated by smoothng (S, R) polces are studed for dfferent proportonal controllers. A supply chan stress test was performed through a sudden and ntense change n demand. The assessment system was based on two crtera, operatonal performance and customer servce level and measured both local (sngle echelon) and systemc performance (supply chan). Supply chans were modelled through dfferental equatons. The man techncal consderatons on the three confguratons are: - Tradtonal supply chan I. Tradtonal supply chan exhbts a geometrcal ncrease of order varance n up-stream drecton, hgh nventory varablty and ntermttent order phenomenon. The magntude of these noxous phenomena s strongly related to the order smoothng levels. II. As order smoothng ncreases, the supply chan operatonal performance mproves (Inventory varance rato, Average Inventory, Zero-Replenshment) but the customer servce level worsens (Fll Rate). Smoothng the order rate notceably lmts the magntude of bullwhp effect but t can result n poor customer servce. III. The smoothng parameter varatons sgnfcantly mpact on performance of tradtonal supply chans - Informaton exchange supply chan. IV. Informaton exchange supply chan exhbts a lnear ncrease of order varance upstream. Bullwhp, Inventory Instablty and Intermttent Orders are not completely elmnated but reduced wth respect tradtonal supply chan. As n tradtonal supply chan, the magntude of ths noxous phenomenon s related to the order smoothng levels. V. The varaton on the smoothng parameter has a slght mpact on the supply chan performance as compared to the Tradtonal confguraton. Customer servce level shows the same opposte trend wth respect to operatonal performance for ncreasng smoothng parameters, as n tradtonal supply chan, but wth weaker ntensty. VI. Informaton Exchange supply chans generally outperform the Tradtonal confguraton. Ceters parbus, all performance measures are superor to tradtonal. VII. Proportonal controller tunng remans crucal for supply chan performance n nformaton exchange. - Synchronsed supply chan VIII. Bullwhp s generally elmnated, nventory s always stablsed, and ntermttent orders are elmnated for all order smoothng levels. IX. Synchronsed supply chans largely outperform Tradtonal and Informaton Exchange supply chans. X. The values of the metrcs persst almost unaltered through varatons of proportonal controllers. The negatve effect of order smoothng rate on customer servce n almost absent.

16 Internatonal Journal of Producton Research Page of XI. The smoothng parameter varatons mpact very weakly on the synchronsed supply chan performance. As a summary, the man conclusons of ths paper are: () Supply Chan Collaboraton affects overall supply chan performance more than order smoothng. () The negatve effect on customer servce of smoothng order s almost elmnated n collaboratve supply chans. The lmtatons of the present study also represent opportuntes for further research n the bullwhp feld. The mpact of mprecse nformaton, multproduct scenaros, varable manufacturng lead tme, capactated raw materal supply condton, and stochastc demand on synchronsed supply chan need addtonal research. ACKNOWLEDGMENT The authors wsh to thank professor José M. Framñán and the anonymous referees for nsghtful comments on earler versons of the paper. Ths research was accomplshed whle the authors were wth the Unversty of Sevlle (Span) and Cardff Unversty (UK) as vstng PhD students, funded by the Italan Mnstry of Unversty and Research. Appendx Nomenclature MODEL VARIABLES AND PARAMETERS W I B O C vw vi d ˆd α T p T c work n progress nventory of fnshed materals backlog of orders replenshment order quantty unts/orders fnally delvered mult-echelon work n progress mult-echelon nventory market demand market demand forecast forecast smoothng factor producton-dstrbuton lead tme safety stock factor T w wp proportonal controller T y TW TI TvW TvI STATISTICS σ d σ O σ I nventory proportonal controller target nventory target work n progress target mult-echelon work n progress target mult-echelon nventory varance of the market demand varance of the order quantty varance of the nventory µ steady state value of the order rate O µ steady state market demand d µ steady state value of the nventory level I TIME VARIABLES T Γ τ ' τ '' tme horzon lmted tme nterval startng tme of FR< (stock-out) n confguraton m fnshng tme of FR< (stock-out) n confguraton m

17 Page of Internatonal Journal of Producton Research τ% ' startng tme of FR< n the worst case τ% '' fnshng tme of FR< n the worst case INDEXES K n N m M ω Ω Appendx echelon s poston n the supply chan total number of echelons level of order smoothng total number of order smoothng levels supply chan confguraton total number of confguratons generc smulaton total number of smulatons The weght of Proportonal Controller tunng: water tank model and trade-off analyss. Suggested by Holweg et al. (00), the mpact of proportonal controller tunng s heren descrbed through a hydraulc smlarty. In the water tank analogy, water represents nventory, flows represent tem dstrbuton rates along the chan, valves represent the orderng decson. The regulaton of the valve depends from the decson parameters of the order rule and from demand and lead tmes. For a smoothng (S, R) polcy, these decson parameters are the safety stock factor, the demand forecastng coeffcent and the proportonal controller. For fxed safety stock factor and demand forecastng coeffcent, the proportonal controller tunng s the unque regulator of the valve. In a hydraulc system, an mmnent alteraton of the flow rate can generate a phenomenon known as water hammer (Allev 0), a threatenng shockwave propagatng n the ppelne. A water hammer can cause the condut to break f the pressure of the flud s hgh enough. The remedy to the water hammer conssts n reducng the flud pressure. One possblty s to nstall a shock absorber, a hydro-pneumatc devce desgned to smooth out or damp shock mpulses and dsspate knetc energy. Water pressure can also be reduced dmnshng the flow rate by tunng a valve. In the water tank analogy, the water hammer phenomenon can symbolse bullwhp, the shockwave symbolses the nformaton dstorton, the shock absorber symbolses the safety stock, and the regulaton of the valve represents proportonal controller tunng. In supply chan large safety stocks enable producton nventory system to absorb market-related shocks and assure a hgh customer servce level (Graves and Wllems 00, Dsney et al. 00), but mples massve holdng costs (Hax and Candea ). Large safety stock can only offer a costly ex post pseudo-remedy to ncreasng demand when bullwhp s already spreadng along the chan. On the contrary, proportonal controllers, lke the pressure regulatng valve for the water hammer phenomenon, prevent the phenomenon lmtng the potental propagaton of the bullwhp shockwave along the chan. As safety stock, proportonal controllers reveals has ts drawback. In a hydraulc system, reducng excessvely the flow rate can mpede to reach n tme the desred flud level; analogously, n a supply chan, an exaggerate order rate smoothng can cause the customer servce level to degenerate. The proportonal controller tunng has to be based on a robust and context-related trade-off analyss between operatonal cost savng and backlog costs, especally n no-collaboratve supply chans. The order-upto polcy can be tuned to sut a varety of objectves. The one that wll be the best n a gven stuaton wll depend on a number of factors (Dsney et al. 00). Appendx The dfferent decson level n adoptng bullwhp solvng approach: tactcal and strategc dmensons The adopton of a bullwhp technque s evdently concerned wth manageral decsons. Wthn Anthony s () plannng and control decson framework, proportonal controller tunng of the (S, R) can be consdered a tactcal decson, whle the adopton of a supply chan collaboraton practce falls under the category of strategc decsons. Paraphrasng Anthony, the proportonal controller tunng s embedded n the process by whch managers assure that resource are used effectvely and effcently n the accomplshment of the organsaton s objectve n a medum range tme horzon. On the other hand, the adopton of a supply chan collaboraton practce s part of the process of decdng on the objectves of the organsaton, on changes n these objectves, on the polces used to attan these objectves. In tradtonal and nformaton exchange supply chans, smoothng the order rate notceable lmts the magntude of bullwhp effect but can result n poor customer servce level. These result hghlght that, as showed n lterature (Dejonckheere et al. 00, Dsney et al. 00, Dsney et al. 00, Dsney and Lambrecht 00) n low collaboratve supply chans the proportonal controller tunng has to be based on a robust and context-related trade-off analyss between operatonal cost savng and backlog/lost sales costs. In tradtonal and nformaton

18 Internatonal Journal of Producton Research Page of exchange supply chans, the rsk related to tactcal decson makng on the degree of smoothng order s relevant. Ths rsk s undoubtedly lowered n synchronsed supply chan, where smoothng parameter varatons very weakly mpact on performance Synchronsed supply chan elmnates bullwhp, provdes nventory stablty and enhanced customer servce level: t avods every plague n Pandora s ndustral box (Holweg et al. 00). It would seem ntutve that all companes should mplement supply chan synchronsaton practces. In the real busness world, realsng supply chan collaboraton means adoptng a Large Scale Supply Chan collaboraton project. Ths knd of solutons, by ther very nature, mposes ts own logc on a company s strategy, organzaton and culture. It s recognsed that the enormous techncal challenge of mplementng collaboraton practces requres large nvestments of money, tme, and expertse (Davenport, ). 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22 Internatonal Journal of Producton Research Page 0 of Table. Concluson on proportonal controller and supply chan collaboraton n the bullwhp avodance phase Chen, Drezner, Ryan, Smch-Lev (000) Dsney, Towll (00) Dejonckheere, Dsney, Lambrecht, Towll (00) Chatfeld, Km, Harrson, Hayya (00) Dejonckheere, Dsney, Lambrecht, Towll (00) Dsney, Towll, Van de Velde (00b) Shang, L, Tadkamalla (00) Warburton (00) Byrne, Heavey (00) Dsney, Farasyn, Lambrecht, Towll, Van de Velde (00) METHODOLOGY ORDER POLICY PERFORMANCE METRICS MODEL STRUCTURES DEMAND PATTERN CONCLUSIONS ON ORDER SMOOTHING CONCLUSIONS ON COLLABORATION Statstcal Methods (S, R) Order Rate Varance Rato Dscrete Tme Dscrete Tme Optmsaton Methods Object-Orented Smulaton Spreadsheet Smulaton Dscrete Tme Dscrete Tme Optmsaton Methods Dscrete Event Smulaton Taguch Technque Contnuous Tme Dscrete Event Smulaton Dscrete Tme (S, R) Smoothng (S, R) Smoothng (S, R) (S, R) Smoothng (S, R) Smoothng (S, R) (S, R) Smoothng (s, S) (S, R) Smoothng Order Rate Two supply chans - Two-echelon Auto regressve Tradtonal - Mult-echelon Epos Two-echelon VMI supply chan Step Snusodal Tradtonal Order Rate Varance Real-lfe Producton-Inventory Rato System..d. Step Two four-echelon Order Rate Varance supply chans Rato - Tradtonal - Epos Two four-echelon Order Rate Varance supply chans Rato - Tradtonal - Epos..d...d. Order Rate Varance Rato Tradtonal Producton-Inventory..d. Inventory Varance System Rato Orderng, setup, backorder, and transportaton costs Inventory Level Order Rate Transportaton, orderng, producton, setup, nventory and backorder costs Order Rate Varance Rato Inventory Varance Rato Fll Rate Three three-layer supply chans - Tradtonal - Epos - VMI Tradtonal Producton-Inventory Step System Two three-layer supply chans - Tradtonal - Epos Tradtonal Producton-Inventory System Wth matched proportonal controllers (Dezel and Elon confguraton) the system s stable. The order smoothng parameter has a sgnfcant mpact on the bullwhp effect. (For step ncrease) for the smoothng polcy, there s less overshootng n orders compared to the order-up-to polcy. (For step ncrease) nventory related costs wll be larger for the smoothng polcy than for the order-up-to polcy. The selecton of forecast factors and proportonal controller mples a trade off between nventory holdng and shortage costs. The smoothng order-up-to polcy mtgates the geometrcal ncrease of Order rate varance rato along a tradtonal supply chan. Bullwhp s monotoncally ncreasng n the proportonal controllers n the Dezel and Elon Confguraton. It s possble to avod the bullwhp effect va the proper desgn of the producton and nventory control system. The dfference between the varablty n the centralsed and decentralsed supply chans ncreases n upstream drecton. Wth centralsed nformaton, the ncrease n varablty at each stage s an addtve functon of the lead tme and the lead tme squared, whle for supply chans wthout centralsed nformaton, the ncrease n varablty at each stage s at least multplcatve. Centralsng customer demand nformaton can sgnfcantly reduce the bullwhp effect. Informaton sharng decelerates the bullwhp effect n upstream drecton. Informaton sharng scenaros exhbts a lnear trend wth echelon, whereas non-nformaton sharng exhbts a quas-exponental ncrease of order varance amplfcaton. Informaton sharng reduces total order varance amplfcaton and node-tonode varance amplfcaton. Sharng nformaton dampens the bullwhp trend from geometrcal to lnear but does not elmnate t when orders are regulated by a (S, R). Informaton sharng and smoothng order-up-to dampen bullwhp n all echelons. S-shaped Integraton of supplers help cut cycle tmes and reduce nventores. Real-lfe data set..d. Auto regressve and movng average The WIP proportonal controller can dmnsh the nventory oscllatons. Fne tunng the orderng polcy can guarantee that the nventory wll return exponentally fast to the desred level, whle not generatng an overshoot. Bullwhp avodance, nventory reducton and customer servce level objectves can sometmes all be acheved smultaneously. Dampenng the bullwhp effect may have negatve mpact on customer servce. By tunng the order polcy t s possble to explot the The use of mproved nformaton sharng technques has a more sgnfcant mpact on the supply chan costs than the forecastng technque. 0

23 Page of Internatonal Journal of Producton Research Km, Chatfeld, Harrson, Hayya (00) Chen, Dsney (00) Hosoda, Nam, Dsney, Potter (00) Jakšč, Rusjan (00) Kelepours, Mlots, Pramatar (00) statstcal propertes of the demand process. Statstcal Methods (S, R) Order Rate Varance Rato Dscrete Tme Optmsaton Methods (S, R) Smoothng Statstcal Methods (S, R) Dscrete Tme Spreadsheet Smulaton (S, R) Smoothng (S, R) Two fve-layer supply chans - Tradtonal - Epos..d. Order Rate Varance Rato Tradtonal Inventory Varance Auto regressve and Producton-Inventory Rato movng average System Holdng and shortage costs Standard Devaton of the Predcton Errors Km, Sprnger (00) Contnuous Tme Smoothng Amplfcaton rato Wrght, Yuan (00) Contnuous Tme Smoothng Agrawal, Sengupta, Shaker (00) Boute, Dsney, Lambrecht, Van Houdt (00) Dscrete Tme (S, R) Dscrete Tme Optmsaton (S, R) Smoothng Two-echelon Epos supply chan Two-echelon Order Rate Varance Tradtonal supply Rato chans Order Rate Varance Two two-echelon Rato supply chans - Tradtonal Fll Rate - Epos Two-echelon Tradtonal supply chan Order Rate Varance Rato Four-echelon Root Mean Square Tradtonal supply Holdng, shortage chan and purchase costs Real-lfe data set Snusodal Real-lfe data set Step Two two-stage supply Order Rate Varance chans Auto regressve Inventory Varance - Tradtonal - Epos Order Rate Varance Two-echelon Rato Tradtonal supply Holdng, shortage chan and capacty costs It s possble to reduce costs by tunng the nventory proportonal controller to the demand pattern. The proportonal controller s able to reduce bullwhp by % and realse economc savngs of nearly 0%. Choosng low nventory proportonal controller value leads to bullwhp effect elmnaton. The lkelhood of strong cyclcalty may be reduced by ncreasng the wp proportonal controller, or lowerng nventory proportonal controller. A relatvely low nventory proportonal controller and a Local trends modfed by slghtly hgher wp proportonal controller provde stablty..d. dsturbances when combned wth ether Holt s or Brown s forecastng method...d. Dampenng the order varablty at the retaler may lead to lower total supply chan costs. Order varance amplfcaton ncreases total supply chan costs, both n the flexble and nflexble capacty scenaro. The bullwhp effect s attenuated from exponental to lnear when nformaton s shared. Sharng EPOS data reduces the second echelon s holdng and backlog costs by -%. Informaton sharng results n % order varablty reducton, on average, and n 0% mean cycle nventory reducton. Some part of bullwhp effect wll always reman even after sharng both nter as well as ntra echelon nformaton.

24 Internatonal Journal of Producton Research Page of Fgure. Flow of materals n the supply chans Fgure. Tradtonal Supply Chan Fgure. Informaton Exchange Supply Chan Fgure. Synchronsed Supply Chan Table. Incomng data for a generc echelon n the dfferent supply chan confguratons ncomng data Tradtonal Supply Chan - Order from subsequent echelon O+ Informaton Exchange - Order from subsequent echelon O+ - Market demand d Synchronsed Supply Chan - Order from subsequent echelon O + - Market demand d Table. Components of smoothng replenshment rules - Safety stock factors from all downstream echelons Tc +; Tc + Tc K - Lead tmes from all downstream echelons Tp +; Tp + Tp K - Inventory levels from all downstream echelons I +, I +; I K - Work n progress levels from all downstream echelons W +, W + W K smoothed nventory gap dfference between Target Inventory TI and Inventory level I, dvded by the Inventory proportonal controller Ty. The Target Inventory TI s the product of the forecast on the order from the subsequent echelon dˆ and the local safety stock factor Tc smoothed wok n progress gap dfference between Target Work n Progress TW and Work n Progress W, dvded by the Work n Progress proportonal controller Tw. The Target Work n progress TW s the product of the forecast on the order from the subsequent echelon d ˆ and the local lead tme Tp. smoothed Mult-echelon nventory gap dfference between Target Mult-echelon Inventory vti and Mult-echelon Inventory level vi, dvded by the Inventory proportonal controller Ty. The Mult-echelon Inventory level vi s the sum of the nventory levels I j from echelon to echelon K (nventory level at echelon plus nventores levels of all downstream echelons + K). The Target Mult-echelon Inventory vti s the forecast on market demand d ˆ multpled by the sum of lead tmes Tp j from echelon to the echelon K (sum of lead tmes Tp j from echelon to K echelon K, t s the tme perod needed to delver the fnshed product from the generc echelon to the fnal customer K+). smoothed Mult-echelon work n progress gap dfference between Target Mult-echelon Work n Progress vtw and Mult-echelon Work n Progress vw, dvded by the Work n Progress proportonal controller Tw. The Mult-echelon Work n progress vw s the sum of the Work n progress levels W j from echelon to echelon K (work n progress at echelon plus work n progress of all downstream echelons + K). The Target Multechelon Work n progress vwi s the forecast on market demand d ˆ multpled by the sum of safety stocks Tc j from echelon to echelon K (sum of safety stock factors Tc j from echelon to echelon K, t s the decson parameter set to cover the mult-echelon nventory at echelon ). K

25 Page of Internatonal Journal of Producton Research Table. Equatons Work n progress Inventory Backlog Orders fnally delvered. Demand forecast W ( t) = W ( t ) + C ( t) C ( t Tp ) () I ( t) = I ( t ) + C ( t Tp ) C ( t) () B ( t) = B ( t ) + O ( t) C ( t) () + C ( t) = mn{ O ( t) + B ( t ); I ( t ) + C ( t Tp )} () + dˆ ( t) = αo ( t ) + ( α ) dˆ ( t ) () + O ( t ) = d ( t ) () K+ Non-negatvty condton of order quantty O ( t) 0 (0) Uncapactated raw materal supply condton C ( t) = O ( t); = () Target Work n Progress Target Inventory TW ( t) = Tp dˆ ( t) () TI ( t) = Tc dˆ ( t) () Mult-echelon Work n progress K vw ( t) = W ( t) () Mult-echelon Inventory K vi ( t) = I ( t) () Target Mult-echelon Work n progress Target Mult-echelon Inventory Order quantty for Tradtonal Supply Chan Order quantty for Informaton Exchange Supply Chan Order quantty for Synchronsed Supply Chan j j = = j j K TvW ( t) = dˆ ( t) Tp () K j K j = TvI ( t) = dˆ ( t) Tc () K j Table. Supply Chan Confguratons and related Equaton System Confguraton Equaton Tradtonal Supply Chan (), (), (), (), (), (), (), (0), (), (), () Informaton Exchange (), (), (), (), (), (), (), (0), (), (), () Synchronsed Supply (), (), (), (), (), (), (), (0), (), (), (), (), () j = O ( t) = dˆ ( t) + ( TW ( t) W ( t)) + ( TI ( t) I ( t)) () Tw Ty O ( t) = dˆ ( t) + ( TW ( t) W ( t)) + ( TI ( t) I ( t)) () K Tw Ty O ( t) = dˆ ( t) + ( TvW ( t) vw ( t)) + ( TvI ( t) vi ( t)) () K Tw Ty Equaton () models two condtons: backlog allowng and non-negatve nventory. Orders no fulflled n tme are backlogged so that nventory remans a postve or null value. Demand s forecasted by smple exponental smoothng, a good choce for one-perod-ahead forecastng (Dsney and Lambrecht 00). Exponental smoothng resulted to be the preferred technque among several methods n the over-cted Makrdaks et al. () artcle. Infnte raw materal avalablty s assumed as n Beamon and Chen 00. Orders from echelon = are always entrely fulflled.

26 Internatonal Journal of Producton Research Page of Table Measurement System OPERATIONAL PERFORMANCE Customer Servce METRICS INPUT OUTPUT t Tme Level Parameter Set Level T Order Rate Varance Rato Inventory Varance Rato Average Inventory Systemc Average Inventory Γ Echelon Confguraton Sngle Multple Local Zero-Replenshment Systemc Zero-Replenshment Proportonal Controller Bullwhp Slope Proportonal Controller Inventory Instablty Slope Systemc Informaton content Magntude of bullwhp effect Stablty of orders Varatons of producton and dstrbuton lead tme Stablty of Inventory Probablty of stock-out Probablty of obsolescence Stock capacty utlsaton Inerta of the producton-dstrbuton system Operatonal scalablty and responsveness Impact of proportonal controller tunng on order stablty Robustness of the order rule Impact of proportonal controller tunng on nventory stablty Fll Rate Customer servce level tme seres Average Fll Rate Average customer servce level Related Manageral Implcaton: Costs Procurement Ordered tems Orderng (admnstratve, transportaton, handlng, nspecton) Overtme Subcontractng Increased holdng cost per unt Mssng producton schedules Job sequencng Resource re-allocaton, Use of transport capacty Holdng Handlng Spolage and obsolescence Salvage Slack capacty Overtme Subcontractng Decson makng Stock-out Mssed sales and loss of customer s goodwll Penaltes Backlog Prorty specal order Job sequencng Resource re-allocaton

27 Page of Internatonal Journal of Producton Research Table. Indexes Supply Chan Confguraton Echelon m =,... M =, K The ndex m stands for the supply chan confguraton The ndex s representatve of the echelon s poston n the network. The echelon = stands for the manufacturer and =K+ for the fnal customer Set n =,... N The ndex n dentfes the level of order smoothng Smulaton ω =, Ω The ndex ω dentfes the generc smulaton. The total number of smulatons s Ω=M*N Table. Order Rate Varance Rato Order Rate Varance Rato Ty=Tw= Ty=Tw = Ty=Tw = Ech Trad Info Sync Trad Info Sync Trad Info Sync Table. Inventory Varance Rato Inventory Varance Rato Ty=Tw = Ty=Tw = Ty=Tw = Ech Trad Inf Sync Trad Inf Sync Trad Inf Sync Fgure. Proportonal Controller Bullwhp Slope and Proportonal Controller Inventory Instablty Slope Bullwhp Slope Inventory Slope = = Tradtonal Informaton Synchronsed = = = = = = 00 = = 0 = = 0 00 = = = 0 = = 0 = = = = = = =

28 Internatonal Journal of Producton Research Page of Fgure. Average Inventory Average Tradtonal Informaton Synchronsed echelon Fgure. Zero-Replenshment Zero echelon echelon Tradtonal Informaton Synchronsed Ty=Tw= Ty=Tw= Ty=Tw= Ech. Ech. Ech. Ech Ty=Tw= Ty=Tw= Ty=Tw= Fgure. Average Fll Rate, Systemc Average Inventory, Systemc Zero-Replenshment Ty=Tw Tradtonal Informaton Synchronsed.% 0.%.%.%.%.%.% 0.%.% Average Fll Rate Ech. 0 0 Ech. Ech. Ech Ty=Tw= Ty=Tw= Ty=Tw= Ech. Ech. Ech Ech.