Effects of vendor-managed inventory on the bullwhip effect

Transcription

1 Effecs of vendor-managed invenory on he bullwhip effec Dr. Susanne Hohmann received her maser s degree from he Ruhr Universiy of Bochum. From 2001 o 2004 she wored as a research assisan a he Insiue of Producion and Indusrial Informaion managemen a he Universiy Duisburg-Essen, Essen Campus. Since 2006 she has been woring as Projec Manager a HAVI Global Soluions. Her main research ineress lie in Supply Chain Managemen, Operaions Research, Producion Planning and Conrol Sysems. She was awarded several prizes for her disseraion on he bullwhip effec. Prof. Dr. Sephan Zelewsi eaches business managemen wih a focus on producion Managemen a he Universiy of Duisburg-Essen. He holds a chair for Producion and Indusrial Informaion Managemen a he faculy of Economics a he campus of Essen. He also is a member of he Insiue of Business and Economic Sudies (IBES), he Insiue for Compuer Science and Business Informaion Sysems (ICB), as well as he Cenre for Logisics & Traffic (ZLV). His wor scope and main research ineress include producion managemen, especially logisics and supply chain managemen, he use of modern compuer echnologies in he area of producion managemen, operaions research and game heory, nowledge managemen and arificial inelligence and heir operaional applicaions (especially nowledge-based sysems and muli-agen sysems), producion heory as well as philosophy of science (especially consrucions of economic heories from he perspecive of he non saemen view). For furher informaion please visi: hp:// Dr. Susanne Hohmann, née Keller * Veroniasrasse 53d Essen Germany phone: / uni.hohmann@googl .com Prof. Dr. Sephan Zelewsi Universiy of Duisburg-Essen, Campus Essen Insiue for Producion and Indusrial Informaion Managemen Universiaessrasse Essen Germany phone: / (secreary s office) fax: / [email protected] * Corresponding Auhor

2 Effecs of vendor-managed invenory on he bullwhip effec Susanne Hohmann, HAVI Global Soluions, Germany Sephan Zelewsi, Universiy of Duisburg-Essen, Germany ABSTRACT The bullwhip effec means ha demand variabiliy increases as one moves up he supply chain. In he following aricle he bullwhip effec is quanified for each par of he supply chain which is presupposed o consis of a producer, a wholesaler, a reailer and a consumer. Afer considering he causes of he bullwhip effec, i will be shown wih he help of a nonlinear opimizaion model o wha exen he bullwhip effec can be reduced using vendor-managed invenory (VMI) as one concep of Collaboraive Planning, Forecasing and Replenishmen (CPFR). In conras o oher sudies in his field he reducion of he bullwhip effec will be accuraely quanified for each par of he supply chain. Keywords: bullwhip effec, demand disorion, simulaion models, supply chain managemen, quaniaive analysis, vendor-managed invenory, CPFR MOTIVATION The bullwhip effec in supply chains represens a long recognised phenomenon in he area of logisics. The maerial flows of he supply chain s paricipans do no correspond o he consumer demand, which, nown as demand pull, is he decisive facor in he supply chain. The chance of a smooh running of he supply chain in view of he maerial and informaion flow is missed on a regular basis as soon as he bullwhip effec occurs. The occurrence of he bullwhip effec leads o raised coss in he supply chain (McCullen & Towill, 2002, p. 169; Reddy, 2001, p. 59). The reducion of he bullwhip effec and herefore he reducion of raised coss in he supply chain lead o an increased profiabiliy of business. Esimaions sugges he increase of profiabiliy of business may be up o % (McCullen & Towill, 2002, p. 169) or up o % (Meers, 1997, p. 89). The use of vendor-managed invenory (VMI) is based on a close cooperaion beween he producer and he paricipan ha has poin of sales daa a heir disposal. Wih his coalescence of supply chain pars he appearance of some causes ha lead o he bullwhip effec can be prevened (Richardson, 2004, p. 19; Waller, Johnson, & Davis, 1999, p. 183). This aricle provides a muli-dimensional analysis of he differen causes of he bullwhip effec, is impac on he differen supply chain pars and is couneracions. I will, herefore, be exacly shown wha impac he bullwhip effec has on he supply chain and o wha exen he bullwhip effec can be reduced in each par of he supply chain by using vendor-managed invenory. This deailed approach adds a holisic, quaniaive analysis o he exising lieraure and enables he predicion and reducion of he bullwhip effec. Vendor-managed invenory is chosen as he concep of CPFR which implies he closes collaboraion beween producer and reailer. The appearance of he bullwhip effec can be aribued o five reasons in oal: Demand disorion, mispercepions of feedbac, bach ordering, price flucuaions, and sraegic behavior. Keller, In his paper, we concenrae on wo of heses causes, demand disorion and mispercepions of feedbac, because hey are especially relaed o he examined opic of VMI. The analysis of heses wo causes provides he bes approach o VMI s efficiency evaluaion. Firs, however, he concepual principles will be explained. CONCEPTUAL PRINCIPLES THE BULLWHIP EFFECT The phenomenon bullwhip effec means ha goods and informaion do no pass hrough he supply chain in he required quaniy and o he required poin in ime. Thus, he supply chain managemen does no resul in a cos-opimised and jus-in-ime coordinaed supply. The firs academic descripion of he bullwhip effec is usually ascribed o Forreser (Forreser, 1972, p. 21). Forreser assumes lead imes o be an immanen par of dynamic sysems. Lead imes occur beween differen pars of a sysem due o handling of maerial and informaion. Forreser analyses differen variables lie soc, producion and lead imes and demonsraes he effecs of changes in he sysem. He saes ha i is common in pracice, and validaed by empirical

3 daa, for variance of orders o far exceed he variance of consumer demand. This effec is amplified a each sage in he supply chain (Forreser, 1972, p. 22). These variaions had up o his poin been regarded as ineviable, as hey were said o be caused by exernal influences (Forreser, 1972, p. 22). Forreser conradics his by showing ha he variaions are caused by lead imes. In pracice he bullwhip effec is simulaed by he well-nown beer game. The resul of his game is ha he simulaed coss are en imes higher han he benchmar coss (Serman, 1989, p. 328). The disribuion of orders in he beer game is characerized by hree facors which are graphically shown in figure 1. Oscillaion: Order and invenory quaniies are dominaed by large ampliude flucuaions. Amplificaion: The ampliude and variance of order quaniies increase seadily from cusomer o producer. Phase lag: The order rae peas laer as one moves from he reailer o he producer. Figure 1. Characerisaion of he bullwhip effec The shores arrows represen he bullwhip effec and he phase lag of he reailer respecively. The longes arrows represen he bullwhip effec and he phase lag of he producer respecively. This increasing ampliude of order quaniies is also well-nown in pracice. The mos popular case is ha of Procer & Gamble, who faced his ampliude wih heir brand Pampers despie he consan demand of diapers (Lee, Padmanabhan, & Whang, 1997a, p. 546; Lee, Padmanabhan, & Whang, 1997b, p. 93). The orders do no coincide wih he acual consumer demand. The variabiliy increases as one moves up he supply chain: he bullwhip effec occurs (Dejoncheere, Disney, Lambrech, & Towill, 2003, p. 567). The bullwhip effec can be defined as he increase of variabiliy (measured by variances) of orders relaed o he variabiliy of consumer demand. Maerial and informaion do no flow seadily hrough he supply chain. The orders seem o be hi by a whiplash. Thus, he quaniy of soc is oo high (Lee e al., 1997b, p. 93). Moreover, he rapid ( jus in ime ) saisfacion of consumer needs canno be guaraneed any more. The rapid, cos-minimised and flexible saisfacion of consumer needs wih high-qualiy goods is he objecive of supply chain managemen. This objecive is in jeopardy as soon as he bullwhip effec occurs. The members of he supply chain run he ris of losing he consumer o compeiors (McCullen & Towill, 2002, p. 169). VENDOR MANAGED INVENTORY (VMI) Measures aen agains he merely locally spread informaion in he supply chain, leading among oher hings o he bullwhip effec, include he diffusion of informaion. Basically, his means o ae ino accoun which informaion is shared in which manner wih whom. Each member of he cooperaion has o benefi from he sharing of informaion. The degree of informaion sharing increases wih he amoun of members and informaion (Schönsleben, 2000, p. 33; Lau, Huang, & Ma, 2004, p. 23). The coordinaion beween firms can eiher only include he sharing of informaion or i can also include he delegaing of cerain aciviies o he parner (Yu, Yan, & Cheng, 2001, p. 116; Dong & Xu, 2002, p. 75), for insance VMI. Using VMI means o share informaion concerning planning and forecasing, and furhermore o collaborae wih a view o he replenishmen of soc (Karolefsi, 2002, p. 19). The soc is replenished based on curren sales daa insead of forecasing mehods wih huge safey soc (Sabah, Aury, & Daughery, 2001, p. 91). The vendor accouns for he quaniy of soc and he mehod of replenishmen. For example, each morning he is informed of he quaniy of soc and he poin of sales daa and delivers he required goods in he afernoon (Fisher, 1997, p. 112; Raghunahan & Yeh, 2001, p. 406). The reailer shifs he responsibiliy for he soc o he vendor. In reurn, he reailer provides poin of sales daa (for he opic of one producer wih several VMI-cusomers see Robins, 1995, p. 42). VMI sees o reduce adminisraive complexiy and coss of soc in increased service level (Holmsröm, 1998, p. 1; Waller e al., 1999, p. 184). The reailer benefis from VMI due o he decreasing uncerainy regarding heir being supplied wih goods. The vendor may benefi from VMI by being able o place a larger assormen of his goods a he reailer s. Moreover, he vendor does no rely on his forecass of consumer demand any longer as he now nows he acual consumer demand (for his and for furher informaion abou a decision suppor sysem for VMI see Achabal, McInyre, Smih, & Kalyanam, 2000, p. 433; for sudies ino he impac of VMI on he bullwhip effec see Disney & Towill, 2003a, p. 625; Disney & Towill, 2003b, p. 199). RELEVANT LITERATURE This paper provides an exensive and exac quanificaion of he bullwhip effec for each par of he supply chain which canno be found in supply chain

4 lieraure so far. From our poin of view i is however essenial o quanify he bullwhip effec separaely for each member of he supply chain because only in his way effecs of supply chain improvemens can be horoughly evaluaed. This is due o wo reasons: Firs, he analysis for each supply chain member allows a deailed analysis which member benefis mos from measures agains he bullwhip effec. This could be of imporance for furher invesigaions such as opimal allocaion of efficiency gains in supply chains. Second, i allows an evaluaion of he supply chain srucure, e.g. if each member is really necessary for he supply chain or if i may lead o inefficiencies such as he wholesaler in our example for VMI. The success of measures aen agains he bullwhip effec will be quanified in he same way. This quanificaion is represened separaely for each cause leading o he bullwhip effec. Our model reflecs 40 periods raher han only 2 or 3 periods lie models used in he relevan lieraure because we waned o prove our resuls wih a model based on mid-erm condiions. In he following, he relevan lieraure, which all presen imporan conribuions o he quaniaive analysis of he bullwhip effec, is briefly reviewed and differences o his paper are highlighed. QUANTIFICATION OF THE CAUSES OF THE BULLWHIP EFFECT Meers (Meers, 1997) assumes he necessiy o forecas demand. The purpose of his paper is o demonsrae he significance of he bullwhip effec esimaed in he increase of demand variance on he one hand and in he effecs on overall business profiabiliy on he oher hand. He uses a dynamic programming model o compare he coss of various producion policies. He minimises coss, consising of he sum of producion, expeced holding and excess demand penaly coss and discouned fuure coss, minus he effec of revenue. He hen esimaes he excess coss of he bullwhip effec by comparing he opimal soluion coss under differen parameer seings. Profis can be gained by eliminaing he bullwhip effec (Meers, 1997, p. 98). The saring poin of Meers is he same as in his paper: he coss minimizaion. In conras o his paper, he does no quanify he bullwhip effec for each par of he supply chain bu only for he supply chain as a whole and only concenraes on one cause of he bullwhip effec, he demand disorion. This paper deduces he bullwhip effec o wo specific causes o analyze he effecs of vendormanaged invenory properly. Lee and colleagues (Lee e al., 1997a) reduce he bullwhip effec o four causes (of he wo causes examined in his paper, Lee and colleagues only menion demand disorion ). They focus on he reailer of he supply chain whose analysis is, according o he auhors, applicable for each oher member of he supply chain as well. The reailer s demand is serially correlaed. Lee and colleagues formulae a coss minimizaion problem including he discouned holding and shorfall coss. They, herefore, esablish a heorem saing ha under cerain condiions he variance of reail orders is sricly larger han he variance of reail sales. Furhermore, i says ha he variance of reail orders sricly increases wih he replenishmen lead ime. Lee and colleagues choose coss minimizaion as iniial saring poin, which is he same as his paper. Ye hey imply he exisence of a normally disribued demand model unlie he forecas model in his paper. The bullwhip effec is no defined as he raio of he variance of consumer demand o he variance of he members orders. Lee and colleagues only see o show he inequaliy of he variance of orders o he variance of he previous demand. They only consider wo periods in order o define he bullwhip effec. The auhors owe he proof of he bullwhip effec for furher periods. As already menioned, Lee and colleagues do no differeniae he bullwhip effec for each member of he supply chain. This paper chooses a broader approach. A par of his paper is relaed o he paper of Zäpfel and Wasner (Zäpfel & Wasner, 1999) and presens enhancemens o heir approach. They provide equaions o define he relaion of he supply chain members and heir behavior. This disincion of equaions leads o a modelling in which he various reasons of he bullwhip effec and he measures aen agains i can be described by behavior equaions. Zäpfel and Wasner derive a model from hese equaions which, however, is no presened in heir paper. Wih he aid of sofware hey find soluions o he model under differen parameer seings for α, β and γ. Compared o he aforemenioned paper of Lee and colleagues hey do no provide a general mahemaical proof for he exisence of he bullwhip effec. Insead, he bullwhip effec is presened graphically in form of mahemaical insances. Zäpfel and Wasner do no analyse he developmen of he bullwhip effec for each member of he supply chain eiher. In conras o he paper of Zäpfel and Wasner, we disinguish hree componens of lead ime: ime for producion, ranspor lead ime, and informaion lead ime. Moreover, he objecive includes he coss of over delivery, i.e. ardiness. Chen and colleagues (Chen, Ryan, & Simchi-Levi, 2000) see o show he impacs of differen forecasing mehods and differen disribued demands on he forecas of demand. They begin wih a posiively correlaed demand which is parly esimaed by exponenial smoohing. Chen and colleagues esimae he variance qex of reail orders (Chen e al., 2000, p. 273) and relae i o he variance of demand. An increase of his raio, and hus an in-

5 crease of he bullwhip effec, may be ascribed o hree facors of influence: (1) he lead ime (L), (2) he smoohing parameer α and (3) he correlaion parameer ρ. The larger he lead ime and he larger he smoohing parameer, he larger he bullwhip effec is. Thus, a reailer facing long lead imes mus choose a small smoohing parameer in order o reduce he bullwhip effec. The impac of correlaion parameer ρ depends on he correlaion of demand: negaively correlaed demands lead o higher variabiliy han posiively correlaed demands. To coninue, Chen and colleagues analyse he impacs of demand disorion on demands wih linear rend. The rend parameer is esimaed wih exponenial smoohing including a second smoohing parameer α2. The bullwhip effec increases wih he use of α2, a fac ha is lined o he need o esimae an addiional parameer and herefore, o cope wih addiional uncerainy concerning he forecas of demand. Nex, Chen and colleagues compare he increase in variabiliy for wo forecasing mehods, moving average (MA) and exponenial smoohing (EX). They consider he impac of he forecasing mehods on correlaed demand and on demand wih linear rend. The comparison of moving average for correlaed demand (MA) and demand wih linear rend (MAT) leads o he resul: MAT MA var q var q Chen and colleagues conclude from he comparison of boh forecasing mehods, wih EXT for exponenial smoohing and demand wih linear rend: EX MA EXT MAT var q var q and var q var q Conrary o his paper and he previously quoed lieraure, he saring poin of Chen and colleagues for quanifying he bullwhip effec is no coss minimizaion. They raher quanify reail orders, esimae heir variances and relae hem o he variance of consumer demand. The bullwhip effec is represened as his raio. I is imporan o noe ha he bullwhip effec is no shown for more han one period of ime. Converse o Chen and colleagues, we use in addiion o he correlaion parameer ρ and he lead ime L, he smoohing parameer α and he parameer β and γ. The parameer β and γ which give he raio of how he already ordered bu no ye delivered quaniies are aen ino accoun for soc evaluaion. I is o be emphasised ha Chen and colleagues, oo, only prove he bullwhip effec for jus one par of he supply chain. The beer game of Serman (Serman, 1989) is he saring poin for he analysis of he mispercepions of feedbac. He conducs empirical ess in he form of he game. The resuls show ha mos subjecs fail o accoun adequaely for he supply line. I is probable ha only a fracion of he supply line is aen ino accoun. This leads o over ordering and insabiliy. Serman does no show a mahemaical model o prove he exisence of mispercepions of feedbac. He provides only empirical resuls for he parameers. Serman shows he resuls of he beer game for each par of he supply chain. QUANTIFICATION OF MEASURES AGAINST THE BULLWHIP EFFECT Measures agains he bullwhip effec are mosly only verbally described in he relevan lieraure bu no quanified (e.g. Lee e al., 1997b, p. 98). Very few researchers have aemped a quanificaion of measures, in paricular VMI, as can be seen in he following lieraure review. Disney and Towill (Disney & Towill, 2003a; Disney & Towill, 2003b) examine he impac of VMI on he producer. They disinguish various reasons for he bullwhip effec. The bullwhip effec caused by he reason demand disorion is, lie in his paper, defined as he raio beween variances of orders and variances of consumer demand. The radiional supply chain managemen and VMI are compared wih difference equaions. Disney and Towill conclude ha he bullwhip effec can be reduced by half. The bullwhip effec is only esimaed for he producer and again no for each member of he supply chain as in his paper. Jašič and Rusjan (Jašič & Rusjan, 2008) invesigae he effec of replenishmen policies on he bullwhip effec wih he help of a ransfer funcion analysis used in conrol engineering. They show ha for a simple supply chain consising of a manufacurer and a reailer here is no bullwhip effec for cerain replenishmen policies. They do no specifically refer o VMI. Wrigh and Yuan (Wrigh & Yuan, 2008) quanify he miigaion of he bullwhip effec by ordering policies and forecasing mehods for a four-sage supply chain. They do no analyse he effecs of VMI. THE BULLWHIP EFFECT AS A RESULT OF DEMAND DISTORTION AND MIS- PERCEPTIONS OF FEEDBACK DESCRIPTION OF CAUSES This analysis is based on a simple supply chain consising of a producer, a wholesaler, a reailer and a consumer. The consumer sars he flow of maerial and informaion wih his demand. Each sage of he supply chain has o forecas demand regularly as he consumer demand is no consan over ime. The members of he supply chain assume posiively correlaed demand o forecas he de-

6 mand of he nex period. The members of he supply chain are only in he possession of local informaion. They are no in he possession of global informaion concerning acual consumer demand. Consequenly, each member is only in he possession of local informaion concerning he demand of heir immediae cosumer. The informaion of consumer demand is only available for he reailer (Lee e al., 1997b, p. 95, for furher sudies on coordinaion wih demand simulaion see Xiao & Luo & Jin, 2009 or Huang & Gangopadhyay, 2004, for he impac of coordinaed decisions in supply chains see Núñez-Muñoz & Monoya-Torres, 2009). The firms need o inerpre orders of heir cusomers in order o derive consumer demand wih he aid of forecasing. Based on forecasing, each firm releases an order o he upsream firm in he supply chain. The firms use exponenial smoohing as a forecas mehod. The forecas is updaed each period afer nowing he acual order quaniy of he downsream firm. The orders consis of hree pars, i.e. (1) maerial o replace expeced loss from soc as a resul of he curren demand, (2) maerial o reduce he discrepancy beween he desired and he acual soc, and (3) maerial o mainain an adequae supply line of unfilled orders. Obviously, he orders are no only based on acual demand bu also on safey socs. The exen o which he orders reflec demand is no eviden for he upsream firm ha uses his order o deduce consumer demand. Hence, he upsream firm has o deal wih uninerpreable informaion. As a consequence of safey soc and he resuling mispercepions, he order is higher han consumer demand. The upsream firm hen ends o augmen is own orders on is own accoun, as i is no willing o run he ris of no being able o saisfy he apparenly increased cosumer demand. Consequenly, he quaniy of orders increases as one moves up he supply chain due o added safey socs a each sage. The quaniy of orders of upsream firms is much higher han consumer demand. The heigh of consumer demand, however, is only nown by he reailer (Fransoo & Wouers, 2000, p. 78; Lee e al., 1997b, p. 95; Posey & Bari, 2009). Neverheless, i is imporan o noe ha his eeping of safey socs is a consequence of raional behavior of each supply chain member. The opic of raional behavior was inroduced by Lee and colleagues (Lee e al., 1997a, p. 552). The raional behavior of individuals, hough, leads o increasing variances of orders, as only pars of he supply chain are opimised. The supply chain as a whole is no opimised. Thus, he bullwhip effec occurs. Mispercepions of feedbac, leading o he bullwhip effec, are closely relaed o demand disorion as here are idenical reasons leading o heir respecive occurrence. The cause mispercepions of feedbac is based on wo reasons: (1) Locally spread informaion resuls in he use of forecas mehods and (2) he hree-parie srucure of orders, as menioned above, hampers he derivaion of consumer demand. When analysing demand disorion we focus on he demand forecas N of firm in period, whereas when analysing mispercepions of feedbac he emphasis is pu on maerial ΔL of firm in period o reduce he discrepancies of desired and acual soc as well as he maerial ΔM of firm in period o mainain an adequae supply line of unfilled orders...,. QUANTIFICATION OF CAUSES A firs, relaions beween supply chain members are presened in form of definiion equaions. I is shown how informaion and maerial flow hrough he sysem, how hese flows connec supply chain members and where hese flows lead o changes in soc and demand. The relaions beween supply chain members assume premises (Zäpfel & Wasner, 1999, p. 297) which are valuable for all following analyses: Each member has a soc a his disposal (we suppose here are no capaciy resricions; for he opic of capaciy resricions see Cachon & Lariviere, 1999). There are lead imes for informaion and maerial. Each order has o be compleed as quicly as possible. Orders remain unil hey are compleed (for he impac of his assumpion on he bullwhip effec see Chen e al., 2000, pp. 272, 277, where i is demonsraed ha his assumpion does no influence he bullwhip effec). The objecive is o minimise coss, consising of coss for soc, coss for shorfall and coss for over delivery (coss for over delivery is ofen added o coss of soc) (Zäpfel & Wasner, 1999, p. 306). In his paper, coss for over delivery are separaed from coss of soc. The definiion equaions of each member of he supply chain are represened in figure 2 (following Zäpfel & Wasner, 1999, p. 299 and Keller, 2004, p. 25). I can be seen ha he producer has inpu of maerial. The inflow in period presens he quaniy of produced goods in period -m. Each member has a soc consising of safey soc plus changes in soc in he curren period. Because of he lead ime members include he quaniy of orders which has already been released bu has no ye arrived. The quaniy of ousanding orders is esimaed o mainain an adequae supply line. Thus, his quaniy may no be oo large in order o mae sure ha he incoming goods are sill required. The symbols used are:

7 m n i 1 x x Z A L index for members index for periods ime of producion lead ime of maerial because of picing, pacaging and ranspor lead ime of informaion quaniy of producion of he producer in period ( = 1) quaniy of orders of member in period for = 2,3 inflow in soc of member in period ouflow of soc of member in period amoun of soc of member a he end of period * L safey soc of member L gap beween desired and acual soc of member in period M amoun of ousanding goods of member in period * M desired level of ousanding goods of member M gap beween desired and acual amoun of ousanding orders of member in period F H shorfall quaniy of member in period over delivery quaniy of member in period

8 m producer ( = 1) 1 2 n A n Z wholesaler ( = 2) x 1 1 m Z 1 1* 1 L max 0,L L j j j1 L Z A i i i A F H ix 2 Z 2 1 A n i 2 2* 2 L max 0,L L j j j1 L Z A 2 2* 2 M max 0,M M 1 1* 1 M max 0,M M M xj Zj j j j1 M x Z j1 F max 0, x A ji j j1 H max 0, A x j j i j1 F max 0, x A H max0, A x j ji j j1 j j i 2 3 n A n Z reailer ( = 3) i i i A F H ix 3 consumer ( = 4) Z 3 2 A n i 3 3* 3 L max 0,L L j j j1 L Z A F max 0, x A j j j1 H max 0, A x 3 3* 3 M max 0,M M j j j j j j1 M x Z A A F H x 3 4 Z no lead ime 4 Z 4 3 A Figure 2. Definiion equaions of supply chain members.

9 The causes for he occurrence of he bullwhip effec are considered using several behavior equaions. They are composed of wo facors: he order of he downsream member and he own demand of he previous period. The curren demand is derived from hese wo facors excep for he exogenous consumer demand. The behavior equaions are demonsraed in figure 3 wih he following used symbols: N demand forecas of member for period α, β, γ parameers, where 0 α, β, γ 1 and γ β (he parameers are explained below) The behavior equaions of he members reflec he characerisics of he demand disorion. Each member is forced o forecas consumer demand wih he help of incoming orders of downsream members. The members use exponenial smoohing (for he common use of exponenial smoohing as forecas mehod compare Hyndman, Koehler, Snyder, & Grose, 2002) wih he wo parameers: orders of downsream members arriving wih phase lag and own demand of he previous period. The choice of parameer α indicaes he smoohing of ampliudes in order quaniy N of member for period. A large α implies a greaer consideraion of orders of downsream members x i han 1 of own demand N 1in he previous period -1. On he one hand, his resuls in he opporuniy of quic alignmens, on he oher hand, in he ris of overesimaing non-represenaive orders (Zäpfel & Wasner, 1999, p. 301). Based on he forecas of he curren period each member releases an order o he upsream member consising of hree componens: saisfacion of curren demand forecas N, adjusmen of changes in soc L and mainaining he supply line wih consideraion of he ousanding orders M. In order o deermine he quaniy of orders x of member ( = 2 or 3) in period or he quaniy of 1 producion x of he producer ( = 1) in period, i is necessary o reduce he demand forecas N in he respecive behavior equaion of member by changes in soc L and by mainaining he supply line concerning ousanding orders M. These reducing influences are weighed by he parameers β and γ o demonsrae he percepions of changes in soc and of ousanding orders, respecively. A large β means quic alignmen o changes in safey soc as changes in soc increase he quaniy of orders in he curren period. A large β may lead o excessive adjusmens in soc alhough his is no jusified by increased orders of he downsream member. A soliary adjusmen of soc due o soc changes would mean ha members release orders wihou regard for he ousanding orders. Ye he ousanding orders are already par of soc changes. Orders would be released wice or even more ofen. To preven his double ordering he ousanding orders have o be aen ino accoun by inroducion of parameer γ. Parameer γ is closely relaed o parameer β as he ousanding orders are a par of soc changes. The raio of γ o β represens he par of ousanding orders which is consciously perceived by he members. γ = β means ha here is no mispercepion of feedbac, he ousanding orders are weighed lie he soc changes so ha double ordering does no occur (Moseilde, Larsen, & Serman, 1991, p. 209). A closer consideraion of hese wo parameers follows. Regarding demand disorion, we assume ha hese parameers are fixed, based on empirical average values (Moseilde e al., 1991, p. 212).

10 producer ( = 1) i 1 N x 1 N x max0,n Zj Ajxj Zj j1 j1 L M wholesaler ( = 2) 2 x, i > i 1 N x 1 N x max 0,N Z A x Z j j j j j1 j1 reailer ( = 3) N x 1 N x max 0,N Z A x Z j j j j j1 j1 3 x, i > 0 consumer ( = 4) no lead ime 4 x, i = 0 N 4 4 x Figure 3. Behavior equaions for he demand disorion The definiion and behavior equaions are combined ino one model. The objecive is o minimise relevan coss K: K l L f F h H min! This formula is based on he following assumpions and parameers (following Zäpfel & Wasner, 1999, p. 301) which are also uilised when considering he furher causes of he bullwhip effec: The planning horizon is fixed o 40 periods o show he run of order and soc quaniies. One period corresponds o 1 ime uni.

11 The order quaniies x0 m n io x 0 are 4 unis per period, so ha each member has an iniial ouflow A0 of 4 unis. Per uni coss l of soc and per uni coss h of over delivery are boh fixed a 1 moneary uni / (maerial uni ime uni [period]), coss f of shorfall per uni are assumed o equal 3 moneary unis / (maerial uni ime uni [period]). Time of producion m amouns o 3 periods, lead ime of maerial n amouns o 2 periods and lead ime of informaion i amouns o 1 period. Consumer demand increases in period 1 from 4 unis per period o 5 unis per period and hen remains consan: x 5 for 2,..., wihou he wholesaler. The wholesaler is no needed due o he concep of VMI. Measure: VMI wih wholesaler and forecas of producer (α = 0.36, β = 0.26, γ = 0.09): In addiion o consumer demand, he producer, in his measure, also uses his own demand forecas from he previous period o esimae he curren demand (see behavior equaions in he following figure 4). The producer s bullwhip effec is sill high due o coordinaion of soc. The wholesaler s bullwhip effec has been reduced. VMI inegraes he producer ino he flow of informaion. Thus, he producer does no have o cope wih uncerainy concerning he supply any more. Safey soc * L and he desired level of ousanding goods in he supply line * M of he members each amouns o 6 unis respecively. Parameer α = 0.36, parameer β = 0.26 and parameer γ = 0.09 (he choice of his parameers follows empirical average amouns, Moseilde e al., 1991, p. 212). The model is solved wih he opimizaion sofware ool Lingo. The following model will be furher used as a reference model for reducing he bullwhip effec. Model: α = 0.36, β = 0.26, γ = 0.09: The order quaniies (also including he quaniy of producion) reflec he ypical oscillaing ampliude of he bullwhip effec he more one moves up he supply chain (see figure 1 above). Besides he oscillaion of order quaniies and he phase lag in ampliudes, we observe ha order quaniies increase in he supply chain. The bullwhip effec is calculaed as he quoien of variance of order quaniies of members o variance of consumer demand. The producer s bullwhip effec is he highes one in he supply chain, whereas he reailer s bullwhip effec is he lowes one. For exac figures please see able below. USE OF VMI We now analyse wheher he bullwhip effec caused by demand disorion and mispercepions of feedbac can be reduced hrough he use of VMI. Furhermore, we analyse he exen of he reducion. We inroduce wo measures agains he bullwhip effec. In one measure he wholesaler is included in he supply chain, in he oher one he is no. Addiionally, he mispercepion of feedbac is prevened from aing place in he second measure

12 producer ( = 1) i 1 N x (1 ) N x max 0,N Z A x Z j j j j j1 j1 4 x, i > 0 wholesaler ( = 2) i N x x reailer ( = 3) N x x 4 x, i > 0 consumer ( = 4) 4 no lead ime x, i = 0 N 4 4 x Figure 4. Behavior equaion for measure VMI wih wholesaler and forecas of producer

13 The progress of order quaniies is represened in he following figure 5. The order quaniies for Figure 5. Progress of order quaniies wih he measure VMI wih wholesaler and forecas of producer (α = 0.36, β = 0.26, γ = 0.09) wholesaler and reailer are mosly idenical. Measure: VMI wihou wholesaler and wih forecas of producer (α = 0.36, β = γ = 0.26): The use of forecas mehods and he righ percepion of ousanding orders (β = γ) leads o a decreased bullwhip effec in he supply chain. The producer s bullwhip effec is reduced, he reailer s bullwhip effec does no occur anymore. The wholesaler is hus no needed in VMI, hey even lead o increased inefficiency in he supply chain. The orders per period converge o he fixed order quaniy of 5 unis per period as can be seen in he following figure 6. Figure 6. Progress of order quaniies wih he measure VMI wihou wholesaler and wih forecas of producer (α = 0.36, β = γ = 0.26) The accurae resuls concerning he bullwhip effec, he quaniies of orders and soc as well as coss of he model wihou measure VMI and coss of he models wih measure VMI are represened in he following able. model/ measure model wihou measure VMI (α = 0.36, β = 0.26, γ = 0.09) model wih measure VMI (α = 0.36, β = 0.26, γ = 0.09) model wih measure VMI and wihou wholesaler (α = 0.36, β = γ = 0.26) bullwhip effec cumulaed order quaniies cumulaed soc coss producer oal wholesaler soc reailer shorfall consumer over delivery producer oal wholesaler soc reailer shorfall consumer over delivery producer oal wholesaler soc reailer shorfall consumer over delivery 4.17 Table 1. Quanified resuls of model and measures.

14 IMPLICATIONS We were able o demonsrae ha he use of VMI leads o dramaic reducion of he bullwhip effec in supply chains. The oal coss, he quaniies of orders, and soc decrease as well. We provided simulaion resuls showing ha he exen of reducion increases wih he eliminaion of he wholesaler in he supply chain and wih he prevenion of mispercepions of feedbac. The use of VMI solves problems concerning coordinaion wihin he supply chain. This leads o a significan reducion of he bullwhip effec and hus o an increase in profiabiliy. Wih he presened model, he exen of he bullwhip effec can be prediced. A managerial implicaion could be o use his abiliy o analyze he efficiency of he supply chain. The modelling and quanificaion of he couneracion of he bullwhip effec allows he opimizaion of he supply chain wih regards o he described causes of he bullwhip effec. However, he provided model is resriced o a small supply chain consising of 3 o 4 pars. A globalized supply chain wih more pars being locaed in differen pars of he world will lead o a more complex supply chain and also o a more complex informaion model due o e.g. lead ime aspecs of differen ime zones (for supply chain design see Charu & Grabis, 2009). Anoher aspec of furher invesigaion could be o srenghen he VMI producer-reailer-relaionship wih buybac conracs (see e.g. Shi & Xiao, 2008, p. 7). These enhancemens migh be a saring poin for furher invesigaion on he bullwhip effec. REFERENCES Achabal, D. D., McInyre, S. H., Smih, S. A., & Kalyanam, K. (2000). A decision suppor sysem for vendor managed invenory. Journal of Reailing, 76, Cachon, G. P., & Lariviere, M. A. (1999). Capaciy Choice and Allocaion: Sraegic behavior and supply chain performance. Managemen Science, 45, Charu, C., & Grabis, J. (2009). A goal modeldriven supply chain design. Inernaional Journal of Daa Analysis Techniques and Sraegies, 1(3), Chen, F., Ryan, J. K., & Simchi-Levi, D. (2000). The impac of exponenial smoohing forecass on he bullwhip effec. Naval Research Logisics, 47, Dejoncheere, J., Disney, S. M., Lambrech, M. R., & Towill, D. R. (2003). Measuring and avoiding he bullwhip effec: A conrol heoreic approach. European Journal of Operaional Research, 147, Disney, S. M., & Towill, D. R. (2003a). Vendormanaged invenory and bullwhip reducion in a wo-level supply chain. Inernaional Journal of Operaions & Producion Managemen, 23, Disney, S. M., & Towill, D. R. (2003b). The effec of vendor managed invenory (VMI) dynamics on he bullwhip effec in supply chains. Inernaional Journal of Producion Economics, 85, Dong, Y., & Xu, K. (2002). A supply chain model of vendor managed invenory. Transporaion Research, 34, Fisher, M. L. (1997). Wha is he righ supply chain for your produc? Harvard Business Review, 75, Forreser, J. W. (1972). Indusrial Dynamics. 7 h ediion, Cambridge, MA: The MIT Press. Fransoo, J. C., & Wouers, M. J. F. (2000). Measuring he bullwhip effec in he supply chain. Supply Chain Managemen, 5, Holmsröm, J. (1998). Implemening vendormanaged invenory he efficien way: A case sudy of parnership in he supply chain. Producion and Invenory Managemen Journal, 59, 1-5. Huang, Z., & Gangopadhyay, A. (2004). A simulaion sudy of supply chain managemen o measure he impac of informaion sharing. Informaion Resources Managemen Journal, 17(3), Hyndman, A., Koehler, A.B., Snyder, R.D., & Grose, S. (2002). A sae space framewor for auomaic forecasing using exponenial smoohing mehods. Inernaional Journal of Forecasing, 18 (3), Jašič, M., & Rusjan, B. (2008). The effec of replenishmen policies on he bullwhip effec: A ransfer funcion approach. European Journal of Operaional Research, 184, Karloefsi, J. (2002). Moving ino producion, special repor: CPFR. Food Logisics, 15, and Keller, S. (2004). The reducion of he bullwhip effec a quaniaive approach from he business managemen perspecive (in German). Docoral disseraion, Universiy of Duisburg-Essen. Wiesbaden: Gabler. Lau, J. S. K., Huang, G. Q., & Ma, K. L. (2004). Impac of informaion sharing on invenory replen-

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16 7,0 6,5 6,0 orders 5,5 5,0 4,5 4,0 3, ime producer wholesaler reailer consumer bullwhip effec Figure 1

17 Figure 5 Figure 6