INVENTORY COST CONSEQUENCES OF VARIABILITY DEMAND PROCESS WITHIN A MULTI-ECHELON SUPPLY CHAIN Francisco Campuzano Bolarín Technical Universiy of Caragena Deparameno de Economía de la Empresa Campus Muralla del Mar 3001 Caragena Spain E-mail: francisco.campuzano@upc.es Andrej Lisec Univesiy of Maribor Faculy of Logisics Hočevarjev rg 1 871 Krško Slovenia E-mail: andrej.lisec@uni-mb.si Francisco Cruz Lario Eseban Technical Universiy of Valencia Deparameno de Organización de Empresas Economía financiera y conabilidad Camino de Vera s/n 460 Valencia Spain E-mail: fclario@omp.upv.es Absrac The bullwhip effec (Lee e al, 1997a) is a known supply chain phenomenon where small variaions in end iem demand creae oscillaions ha amplify hroughou he chain. Differen price elasiciy of demand influence differen changes of demand when prices of iems are changing on he ime horizon. The variance of he orders a he end user placed on suppliers or on manufacurer increases wih he orders flow upsream in he logisics chain. This creaes harmful consequences in invenory levels and all kind of invenory coss ha may affec added value of aciviies along he logisics chain and finally affec Ne Presen Value of all aciviies in he chain. Tradiional model of dynamic supply chain srucures is used for his paricular sudy, based on he seminal work of Forreser Diagrams (Forreser 1961). Simulaion plaform for supply chain managemen a sochasic demand developed by Campuzano (006) has been used. VENSIM Simulaion Sofware was previously used for developing hese supply chain dynamic models. In he developmen plaform generalised supply chain models are consruced graphically and also analyically. Our sudy here is o ge a dipper insigh ino he processes in a logisics chain, measuring he invenory cos consequences due o variabiliy demand amplificaion. Keywords: Bullwhip effec, Demand amplificaion, Logisic chain, Sysem Dynamics.
1. Inroducion A supply chain is he se of srucures and processes an organizaion uses o deliver an oupu o a cusomer. The oupu can be a physical produc such as an auomobile, he provision of a key resource such as skilled labor, or an inangible oupu such as a service or produc design (Serman, 000). A supply chain consiss of he sock and flow srucures for he acquisiion of he inpus o he process and he managemen policies governing he various flows. Each of hese processes feaures a number of clearly defined characerisics, which represen a wide range of opics o be invesigaed. Research on supply chains makes an aracive field of sudy, offering numerous approach roads o organisaional inegraion processes. Some of he problems regarded as mos imporan, which canalise any research projec in he area of supply chains, are hose relaed o demand variabiliy and demand disorion hroughou he Supply Chain. Forreser (1958) analysed Supply Chain and he differen levels exising in i, as well as he paricipan companies and he role played by each of hem inside he chain as a global group, and observed ha a small flucuaion in a cusomer s demand was magnified as i flowed hrough he processes of disribuion, producion and provisioning. This effec was idenified and also sudied by Burbidge (1991) and i is known as he Forreser Effec. Tha amplificaion owed iself, according o Forreser, o he problems derived from he exisence of delivery imes ("non zero lead imes"), and he inaccuracy of forecass carried ou by he differen members of he chain in he face of he variabiliy of he demand received. Mos of he research on he demand amplificaion has focused on demonsraing is exisence, idenifying is possible causes, and developing mehods for reducing i. Lee e al. (1997a) idenified five main causes of amplificaion: wrong mehods of demand forecasing, supply shorage anicipaion, bach ordering and price variaion. Demand amplificaion occurs mosly because of finie perurbaions in final demand and in lead ime all along he supply chain, which is always anicipaed and in ineracion wih oher causes. By his seminal work Indusrial Dynamics, A Major Breakhrough for Decision Makers in 1958, Jay Forreser is viewed as he pioneer of he modern-day supply chain managemen. His work on he demand amplificaion as sudied via sysems dynamics simulaion has explored hese supply chain phenomena from many viewpoins. How he indusry is facing his phenomenon is broadly sudied by Lee e all (1997a), where some consideraions of he bullwhip effec in supply chains are presened in deails, oo. Our sudy has also been moivaed by many oher producion-disribuion consideraions abou bullwhip effec in he supply chain perurbaions, such as hose given by Lee e al (1997a), and especially he resuls of Disney (001, 00, 003a, 003b) and oher researchers of his phenomenon from Cardiff Business School. The objecive of his work is o sudy he long erm cos consequences of he Bullwhip effec wihin a generic muli echelon supply chain. The behaviour of he generic sysem under sudy is analyzed hrough a simulaion model based on he principles of he sysem dynamics mehodology. The simulaion model proposed by Campuzano (006) provides an experimenal ool, which can be used o evaluae alernaive long erm decisions such as replenishmen orders, capaciy planning policies, or even iner-organizaional sraegies ( wha-if analysis), as his mehodology allows sudying he inerdependences among every echelon modelled.
. Measuring he bullwhip effec An inegraed supply chain includes he purchasing of raw maerials, he manufacuring wih assembly or someimes also disassembly, and he disribuion and repackaging of produced goods sen o he final cliens. Various operaing sages in he logisic chain (nodes of he chain) can be represened by a simple model of some maerial-ransformaions or locaionransformaions processing cells (and arcs). In each processing cell, a value is added and some coss are incurred. A each processing cell here is a supply and a demand and ofen boh are sochasic by naure. Price variaions or he Promoion Effec and many oher acions in a supply chain refer o he pracice of offering producs a reduced prices o simulae demand. Assuming an elasic demand, his creaes emporary increases in demand raes where cusomers ake advanage of his opporuniy and forward buy or sock up. However his has serious impacs on he dynamics of he supply chain and added value especially when a cerain securiy level of supply is prescribed. Invenories are insurance agains he risk of shorage of goods in each cell of he logisic chain. They are limied by he capaciy of each processing node of he chain and ransporaion capabiliy of inpu and oupu flows. Ordering goods (inpu flow) in disribuion cenres can be sudied as a muli-period dynamic problem. The demand (oupu flow) during each period has o be considered as a sochasic variable. The disribuion of his variable is ofen described wih a cerain probabiliy funcion which is here normal. The inensiy variaion of flows of iems in supply chains influence ransporaion coss and coss of aciviies in logisic nodes and consequenly he ne presen value (NPV) of all aciviies ha have o be performed in such logisic neworks. As menioned above, bullwhip effec refers o he scenario where he orders o he supplier end o have larger flucuaions han sales o he buyer and he disorion propagaes up a supply chain in an amplified form. As disorion creaes addiional coss, he indicaors or measures of bullwhip are supposed o be in correlaion wih coss or added value. Our sudy was based on he producion and invenory conrol resuls, especially on he variabiliy rade off sudy, presened by Dejonckheere e al. (003), a conrol heoreic approach o measuring and avoiding he bullwhip effec, presened by hese auhors, and he sudy of he impac of informaion enrichmen on he bullwhip effec in supply chains - a conrol engineering perspecive by Dejonckheere e al. (004), where some measures have been inroduced. The amplificaion upsream he supply chain can be measured hrough he variance of demand along he supply chain. The variance of a se of daa is defined as he square of he sandard deviaion and is hus given by s for esimaion of populaion varianceσ. Lee a al.(1997b) suggesed he changes of variance in demand σ upsream as he measure of bullwhip effec. I is a good measure only when he unis of flow are no changing along he chain, which is no he case in many logisics cases. In he recen lieraure by Chen e al. (000), i is suggesed ha o avoid his problem bullwhip effec should be measured by changing he raio of σ µ upsream of supply chain, bu again i does no help o avoid he effec of changing uni measure. Chen e
al. (000) suggesed ha is measure could be he raio of hese parameers beween inpu and oupu flows a each aciviy cell in a supply chain, when only one sage is considered, or he raio of hese parameers beween final demand and firs sage of manufacuring when oal supply chain is o be evaluaed (Equaion 1). σo / µ O Bullwhip = σ / µ O: Orders D: Demand D D σ O = σ D (1) On he oher hand Disney and Towill (003b) propose ha he las variance raio measure can easily be applied o quanify flucuaions in ne invenory as shown in Equaion. σ / µ NS NSAmp= () σ / µ NS: Ne Sock D: Demand NS D D 3. Mehodological approach The Sysem Dynamics mehodology (SD) is a modelling and simulaion echnique specifically designed for long-erm, dynamic managemen problems. I focuses on undersanding how he physical processes, informaion flows and managerial policies inerac so as o creae he dynamics of he variables of ineres. The oaliy of he relaionships beween hese componens defines he srucure of he sysem. Hence, i is said ha he srucure of he sysem, operaing over ime, generaes is dynamic behaviour paerns. I is mos crucial in Sysem Dynamics ha he model srucure provides a valid descripion of he real processes. The ypical purpose of a Sysem Dynamics sudy is o undersand how and why he dynamics of concern are generaed and hen search for policies o furher improve he sysem performance. Policies refer o he long-erm, macro-level decision rules used by upper managemen. Sysem Dynamics differs significanly from a radiional simulaion mehod, such as discree-even simulaion where he mos imporan modelling issue is a poin-by-poin mach beween he model behaviour and he real behaviour, i.e. an accurae forecas. Raher, for a Sysem Dynamics SD model i is imporan o produce he major dynamic paerns of concern (such as exponenial growh, collapse, asympoic growh, S-shaped growh, damping or expanding oscillaions) (Vlachos e al. 007). Therefore, he purpose of our model would no be o predic wha he oal supply chain profi level would be each week for he years o come, bu o reveal under wha condiions he oal profi would be higher, if and when i would be negaive, if and how i can be conrolled (Serman 000). The srucure of a sysem in SD mehodology is exhibied by causal loop (influence) diagrams; a causal loop diagram capures he major feedback mechanisms he negaive feedback loops (balancing) or he posiive feedback (reinforcing) loops. While a negaive feedback loop exhibis a goal-seeking behaviour, i.e., afer a disurbance, he sysem seeks o reurn o an equilibrium siuaion, in a posiive feedback loop, an iniial disurbance leads o furher change, suggesing he presence of an unsable equilibrium. Causal loop diagrams play wo imporan roles in SD.
Firs, hey serve as preliminary skeches of causal hypoheses during model developmen, and second, hey can simplify he represenaion of a model. The srucure of a dynamic sysem model conains he sock (sae) and flow (rae) variables. Sock variables are he accumulaions (i.e., invenories) wihin he sysem, while flow variables represen he flows in he sysem (i.e., order rae), which are he by-producs of he decision-making process. Sock-flow diagrams represen he model srucure and he inerrelaionships among he variables. The mahemaical mapping of a SD sock-flow diagram occurs hrough a sysem of differenial equaions, which is numerically solved wih he help of a simulaion. Nowadays, high-level graphical simulaion programs such as Powersim, Sella, Vensim and i-hink suppor he analysis and sudy of hese sysems. 4. Problem and model consrucion The main characerisics of he model used for his research are summarized in he nex poins: - We have considered a four sage supply chain sysem consising of idenical agens, where each agen orders producs only from is upper sage. These are Cusomer, Reailer, Wholesaler and Manufacurer. - An agen ships goods immediaely upon receiving he order if here is sufficien amoun of on hand invenory. - Orders may be parially fulfilled (every order o be delivered includes acual demand and backlogged orders- if here exis), and unfulfilled orders are backlogged. - Shipped goods arrive wih a ransi lead-ime of goods and hey are also rearded because of informaion lead ime. - Las sage (manufacurer) receives raw maerials from an infinie source and manufacure finished goods under capaciy consrains. The firs sep for developing he model was he creaion of he causal loops which inegrae he key facors of he sysem and pu he relaions on he links beween pair of hem. I is expeced ha he differences beween bullwhip indicaors are he highes in he case of he radiional supply chain. Oher srucures are given o reduce bullwhip effec. Figure 1: The radiional 4 sage supply chain
Figure : The causal loop frequenly occurring in real cases a disribuion par of he radiional supply chain. Ofen, is producion par has varied MRP assembly or arbores cen srucures. Source: Campuzano (006) UPCT RPI 08/007/39 Figure presens he sock and flow srucure for a muli-echelon supply chain sysem in is corresponding causal loop diagram. The arrows represen he relaions among variables. The direcion of he influence lines displays he direcion of he effec. Signs + or a he upper end of he influence lines indicae he ype of effec. When he sign is +, he variables change in he same direcion; oherwise hey change in he opposie one. 5. The decision rule The ordering policy we have chosen for our analysis is a generalized Order-Up-To policy. In any order-up-o policy, ordering decisions are as follows: O = S invenoryposiion (3) The order quaniy is equal o S, reduced for invenory sae as: Invenory posiion= Invenory on hand-backlogged orders+orders placed bu no ye received. where O is he ordering decision made a he end of period,s is he order-up-o level used in period and he invenory sae equals ne sock plus on order (orders placed bu no ye
received), and ne sock equals invenory on hand minus backlog. The order-up-o level is updaed every period according o: S = Dˆ + kσˆ (4) L L Where S is equal o he esimae mean of demandd L over L periods ( L D = D L ) increased for L prescribed service level wih buffer socks, σ is an esimaion of he sandard deviaion over L periods, and k is fill rae facor which depend on demand disribuion (here i is supposed o be Normally disribued). The policy is needed where ne presen value of all aciviies in he value chain is opimal. The ordering policy depends on demand, which is sochasic and reac on price policy. 6. Numerical Invesigaion In his secion i is demonsraed he applicaion of he developed mehodology using a numerical example and discuss few ineres insighs ha are obained. We will considerae a Tradiional supply chain wih four echelons, ha is cusomer, reailer, wholesaler and manufacurer. The iniial values for he main parameers of ha supply chain were randomly seleced: - The demand paern follows a normal disribuion - The iniial invenory for every echelon is 100 unis - Manufacurer capaciy : 160 unis/per day - Lead ime for wholesaler is 3 days and for he manufacurer is days. Lead imes are supposed o be consan excep in case of sock ou - Manufacuring process akes days - Fill rae facor for every echelon is wo days - Exponenial smoohing forecasing process (α=) - The invenory cos were fixed as follows: o Holding cos : 0,5 euros uni/period o Sock ou cos: 1 Euro/per sock-ou o Order cos : 0,5 euros/order 365 periods were simulaed. I is observed enough as he sysem reached a sable sae. 6.1 Simulaion resuls Nex Figure shows (illusraion 3) he variabiliy of he orders sen a every echelon regarding o Demand signal.
UNITS 80 60 40 Demand Reailer Wholesaler Manufacurer 0 0 0 5 10 15 0 5 30 35 40 45 50 55 60 65 70 Time (Day) Figure 3: Variabiliy of he orders sen a every echelon regarding o Demand signal Nex Figure shows he bullwhip effec a every echelon. 60 45 Reailer Wholesaler Manufacurer 30 15 0 0 73 146 19 9 365 Time (Day) Figure 4: Bullwhip effec a every echelon Nex illusraion (illusraion 5) shows NSAmp a every echelon.
60 45 Reailer Wholesaler Manufacurer 30 15 0 1 7 53 79 105 131 157 183 09 35 61 87 313 339 365 Time (Day) Figure 5: NSAmp a every echelon Las Figures are showing how he demand variabiliy increases upsream he supply chain. This variabiliy arises some problems caused by he inerdependences of every echelon wihin he supply chain. The incremen in he demand variabiliy will produce replenishmen orders wih high variable sizes, wha will affec he forecas process accuracy a every echelon. Therefore he invenory levels a every echelon will have a high variabiliy oo, and someimes will no be able o face demand peaks, wha will produce sock ou periods. Tha variabiliy will be refleced in high holding cos (invenory excess) and high sock ou cos (no invenory available o saisfy replenishmen orders). Nex Figure shows he fill raes reached a every level. The reailer has he lower fill rae as suffers he variable lead imes a he upsream members (wholesaler and manufacurer) caused by sock-ou periods a hese levels. 100 % 75 50 5 Reailer Wholesaler Manufacurer 0 1 53 105 157 09 61 313 365 Time (Day) Figure 6: Fill raes a every echelon
Lower fill raes reached a reailer level will be refleced in higher sock ou cos han wholesaler and manufacurer. Tha is showed in he nex Figure. 40 30 Reailer Wholesaler Manufacurer 0 10 0 1 7 53 79 105 131 157 183 09 35 61 87 313 339 365 Time (Day) Figure 7: Coss per sock ou a every echelon Las illusraion shows he periods wih sock-ou. When a sock ou period occur he cos raise (oherwise cos will keep consan). Therefore holding cos a wholesaler and manufacurer will be higher han hose obained by reailer. As we saw above Bullwhip and NSAmp reached he highes values a manufacurer level wha will be refleced in he highes holding cos (Figure 8). 0,000 15,000 10,000 Reailer Wholesaler Manufacurer 5,000 0 1 53 105 157 09 61 313 365 Time (Day) Figure 8: Holding cos a every echelon As he reader may observe in Figures 4 and 5, i is remarkable how easily sock-ou coss per period may be conneced o significan increases in Bullwhip Effec or NSAmp. Obviously, significan increases in NSAmp enail sock-ou coss, bu also relevan holding coss, since invenory mus grow o respond o backlogged orders. The correlaion beween invenory cos
and hese demand and ne invenory variaion measures wihin he supply chain have been also sudied by Campuzano e al. (006). 7. Conclusions The dynamic model used for he simple sudy abou invenory cos carried ou in his paper demonsraed is uiliy for sudying he inerdependences among differen members of he same supply chain. Moreover he model developed may be regarded as a very useful ool for he acic level of an organisaion or company. Afer validaing is performance, he achieved ool offers he essenial parameers (auxiliary variables) and elemens (level variables and flow variables) for Demand Managemen. By simply changing he values which define hese parameers, he model is capable of giving resuls which, once analysed, ease he decisionmaking process. I is worh menioning ha he resuls obained canno be generalised o all cases. The usefulness of his model is he fac ha i may generae differen scenarios hanks o join aleraion of several parameers, in such a way ha researchers may decide which case bes adaps o he goals se; i is no abou obaining opimum resuls for he problem addressed. Holweg and Bicheno (00) show how useful simulaion may be o carry ou managemen models, given he difficulies which some companies find o hink beyond facory gaes. The simulaion model brings beer undersanding of he effecs which operaional decision-making may have for an enerprise and is associaes in he Supply Chain where he business process is developed. The conribuion made o Supply Chain design mehodology by he use of Sysem Dynamics bears an imporan formaive componen. Consrucion and simulaion of diverse supply chains may help explain he influence of key facors in Demand Managemen along each level. In his way and i is proposed as he aim of fuure research, Bullwhip Effec may be reduced, along he differen levels of he Supply Chain no only by modifying differen parameers in i bu also using new collaboraive supply chain srucures as Vendor Managed Invenory or Elecronic Poin of Sales. The use of a dynamic model simulaing hese srucures may show no only he Bullwhip reducion a every echelon, bu also oher consequences concerning invenory cos, ranspor cos or even how affec he accuracy of he forecas on he order policy used. References 1. Burbidge, J. L. (1991) Period Bach Conrol (PBC) wih GT The way forward from MRP, BPCIS Annual Conference, Birmingham.. Campuzano Bolarín, F., (006) Variable Demand Managemen Model for Supply Chains. Bullwhip effec Analysis Ph. D. Thesis, Technical Universiy of Valencia, Spain. Awarded by he Spanish Logisics Cener (CEL). Bes Naional Logisics Thesis 007. 3. Campuzano Bolarín, Francisco, Bogaaj Marija, Ros McDonnell Lorenzo (006). The Correlaion beween Invenory Coss and Some Bullwhip Measures in Logisic Neworks. Suvremeni Prome (Conemporary Traffic). Vol 6 nº 1-6, 91-96 ISSN 0351-1898 4. Chen, F., Drezner, Z., Ryan, J. K., Simchi-Levi, D. (000) Quanifying he bullwhip effec in a simple supply chain: The impac of forecasing, lead-imes and informaion, Managemen Science, Vol. 46, no. 3, 436 443
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