The curren issue and full ex archive of his journal is available a www.emeraldinsigh.com/0960-0035.hm Analysis of he bullwhip effec wih order baching in muli-echelon supply chains Maloub Hussain College of Business Adminisraion, Abu Dhabi Universiy, Abu Dhabi, Unied Arab Emiraes, and Paul R. Drake Managemen School, Universiy of Liverpool, Liverpool, UK The bullwhip effec 797 Absrac Purpose The purpose of his paper is o analyze he effec of baching on bullwhip effec in a model of muli-echelon supply chain wih informaion sharing. Design/mehodology/approach The model uses he sysem dynamics and conrol heoreic conceps of variables, flows, and feedback processes and is implemened using ithink w sofware. Findings I has been seen ha he relaionship beween bach size and demand amplificaion is non-monoonic. Large bach sizes, when combined in ineger muliples, can produce order raes ha are close o he acual demand and produce lile demand amplificaion, i.e. i is he size of he remainder of he quoien ha is he deerminan. I is furher noed ha he value of informaion sharing is greaes for smaller bach sizes, for which here is a much greaer improvemen in he amplificaion raio. Research limiaions/implicaions Baching is associaed wih he invenory holding and backlog cos. Therefore, fuure work should invesigae he cos implicaions of order baching in muli-echelon supply chains. Pracical implicaions This is a conribuion o he coninuing research ino he bullwhip effec, giving supply chain operaions managers and designers a pracical way ino conrolling he bullwhip produced by baching across muli-echelon supply chains. Economies of scale processes usually favor large bach sizes. Reducing bach size in order o reduce he demand amplificaion is no a good soluion. Originaliy/value Previous similar sudies have used conrol heoreic echniques and i has been poined ou ha conrol heoriss are unable o solve he lo sizing problem. Therefore, sysem dynamic simulaion is hen applied o invesigae he impac of various bach sizes on bullwhip effec. Keywords Bullwhip effec, Baching, Informaion sharing, Muli-echelon supply chain, Simulaion, Supply chain managemen, Invenory managemen Paper ype Research paper 1. Inroducion A poenially devasaing phenomenon seen in supply chains is he bullwhip effec, i.e. he amplificaion of demand variabiliy as i progresses up a supply chain. I was firs observed in indusry by Forreser (1961), who named he effec demand amplificaion, and here has since been much research published by many auhors who have sudied i. Forreser poined ou ha demand amplificaion is due o sysem dynamics and can be ackled by reducing delays in he supply chain. Serman (1989) hrough he Beer Game inerpres he phenomenon as a consequence of players irraional behaviors or mispercepions of feedback. Towill (1996) confirmed he findings of Forreser ha reducing delays and collapsing all cycle imes reduce he bullwhip effec. Lee e al. (1997) found ha he bullwhip effec is caused by demand signal processing, order baching, Inernaional Journal of Physical Disribuion & Logisics Managemen Vol. 41 No. 8, 2011 pp. 797-814 q Emerald Group Publishing Limied 0960-0035 DOI 10.1108/09600031111166438
IJPDLM 41,8 798 price variaions, and raioning and gaming, and can be reduced hrough informaion sharing. Slack and Lewis (2002) give a exbook inroducion o hese causes wih some remedies. Wangphanich e al. (2010) also menion lae deliveries and incomplee shipmens, i.e. poor and unreliable service, as causes. In general, hey characerize facors ha conribue o uncerainy in demand as causes. However, hey remind us ha some indusries wih reliable demand paerns can sill experience he bullwhip effec due o a lack of synchronizaion in ordering up he supply chain: The bullwhip effec indicaes ha he socking level variabiliy in supply chains ends o be higher upsream han downsream, e.g. i is caused by facors such as deficien informaion sharing, insufficien marke daa, deficien forecass or oher uncerainies (Sevenson, 2005). Is effecs include inaccurae forecasing leading o periods of low capaciy uilizaion alernaing wih periods of having no enough capaciy, i.e. periods of excessive invenory caused by over producion alernaing wih periods of sock-ou caused by under producion, leading o inadequae cusomer service and high invenory coss. Since he bullwhip effec is very cosly o upsream echelons of he supply chain, here is a real and subsanial cos benefi associaed wih is reducion. Recenly, some sophisicaed echniques have been applied o his reducion, such as geneic algorihms o deermine opimal ordering a each echelon (O Donnell e al., 2006), fuzzy invenory conrollers (Xiong and Helo, 2006), and disribued inelligence (De La Fuene and Lozano, 2007). Alhough many remedies o he bullwhip effec have been published, i is sill a concern in he real world, so research ino undersanding and conrolling i coninues (Wangphanich e al., 2010). I is generally advocaed ha bach size should be reduced as much as possible (Burbridge, 1981), bu here has been limied deailed invesigaion ino he impac of bach size on demand amplificaion, which raises he quesion, Does findings of Burbridge (1981) hold oally rue in respec of minimizing demand amplificaion? This paper addresses his gap in he research by inroducing baching ino he four-ier supply chain model and hen conducing simulaion experimens o undersand: he impac of bach sizes on he bullwhip effec under deerminisic and sochasic demand processes and he impac of informaion sharing across wide ranges of bach sizes. The remainder of his paper is organized as follows. Secion 2 provides brief survey of he relaed lieraure. In Secion 3, he mehodology is inroduced and hen he supply chain simulaion model is presened in Secion 4. Afer ha, he impac of he baching on bullwhip effec under sep and sochasic demand process has been explored, and value of informaion sharing wih respec o bach size has been discussed in Secion 5. Sensiiviy analysis has been carried ou in Secion 6. Secion 7 concludes. 2. Baching and bullwhip effec Order baching is one of he key causes of he bullwhip effec idenified by Lee e al. (1997) and Riddalls and Benne (2001). I refers o he phenomenon of placing orders o upsream echelons in baches. Finding he opimal soluion o baching is no easy since i is direcly relaed o invenory holding and backlog coss. In many producion-disribuion sysems maerials move from one echelon o anoher in fixed lo sizes. For example, a reailer migh order a full ruck or conainer load from he wholesaler o qualify for a quaniy discoun and o opimize ranspor coss by fully uilizing he fixed-cos ruck or conainer. For a manufacurer, significan economies
of scale can be achieved by producing in large baches, bu he resulan large invenories will increase he sock holding coss. The invenory manager, however, always favors policies ha mee he forecased demand wih minimal invenory. The rapprochemen of hese conflicing objecives is a fundamenal aim of invenory managemen heory. Baching is a clusering of iems for purchasing, ransporaion, or manufacuring processes and is also known as lo sizing. I is a mechanism ha induces ime-phased producion ha is usually non-synchronized wih he acual demand. In his way, baching resuls in excessive invenory or backorders. The reasons for bach ordering include he economic order quaniy (EOQ), periodic invenory review, and ransporaion economies. Baching is also relaed o economic bach quaniy where i is beneficial economically for a company o produce large baches since i can reduce he number of faciliy se-ups and improve manufacuring efficiency. Companies prefer o order in baches o gain economies of scale. Long process se-up imes are a major cause of large producion baches wihin facories wih he corollary being ha rapid changeovers are required o reduce bach sizes. These large bach sizes can lead o large flucuaions in invenory levels as firs a large bach is produced, far in excess of curren demand, so ha he invenory levels rise o high levels only o be reduced unil hey reach a reorder poin, a which poin a new large bach eners he invenory. Furhermore, baching amplifies he demand as i passes up a supply chain as he real demand is rounded up o whole bach sizes for producion processes and ordering from suppliers, and his rounding-up sacks up along he supply chain when differen bach sizes are used. For example, demand for a produc may be en unis, he producion bach size may be 100, and an ousourced componen used in he produc (one componen per produc) may have an order bach size of 40. The iniial demand of en is amplified o 100 in he facory, which resuls in a furher amplified order for 3 40 ¼ 120 componens, assuming here are no componens in sock already. This amplificaion can coninue unabaed up he supply chain. For example, if he componen supplier ordered sub-componens in baches of 50, he demand signal would jump o 150. There is a clear and crucial need o fully undersand he impac of varying he bach size on demand amplificaion across muli-echelon supply chains in order o enable operaions managers o make beer decisions around baching. Burbridge (1981) emphasized he need o reduce he bach size as much as possible. Technical or economical problems may no allow he implemenaion of smaller bach sizes. Cachon (1999) has sudied he impac of order baching in a wo-level supply chain wih a single supplier and many reailers. The sudy suggess ha he bullwhip effec a he supplier s level can be reduced by balancing he orders of he reailers, a longer order inerval ime, and smaller bach sizes. Riddalls and Benne (2001) sudied he impac of bach producion cos on he bullwhip effec. They proposed measuring he magniude of he bullwhip effec in a wo-ier supply chain by observing he peak order rae of he upper level (he supplier). They found ha he relaionship beween bach size and demand amplificaion is non-linear and depends on he remainder of he quoien of average demand and bach size. The limiaion of heir findings is ha here is always an iniial increase (overshoo) in he order rae afer a sep change in demand. Hence, such assessmen of he peak of he order rae as a measure of he bullwhip effec is no an accurae, qualiaive measure of demand amplificaion. The bullwhip effec 799
IJPDLM 41,8 800 Holland and Sodhi (2004) sudied a wo-ier supply chain model in which he reailer is bound o order in ineger muliples of he bach size (e.g. for order quaniy of 50 unis, bach size should be eiher 1, 2, 5, 10, 25, or 50). Boh reailer and manufacurer follow a periodic review and order-up-o-level replenishmen policy. Simulaion was run for five differen bach sizes and saisical analysis was carried ou o quaniaively measure he impac on he bullwhip effec of bach size across each echelon. They found ha he bullwhip effec across each echelon of he supply chain was proporional o he square of he bach size. Hejazi and Himolla (2006) argue ha lo-sizing decisions of an upsream member may also cause order baching a he downsream level of he supply chain, and hus be a major source of he bullwhip effec. Therefore, he members of he supply chain seem no only o be locally opporunisic, bu also heir decisions are based on variables idenified in he supply chain level, and mos ofen decisions are made knowing he abiliies of upsream manufacuring. Mehra e al. (2006) used a simulaion, based on an acual process indusry, o invesigae he resuls of wo lo size (or bach size) reducions wihin coninuous processing firm. Resuls of he sudy indicae ha lo size reducion can be a valid performance improvemen mehod for acual firms uilizing a coninuous flow sysem. Poer and Disney (2007) coninued he work of Holland and Sodhi by considering he impac of a full range of bach sizes on demand amplificaion in a single echelon of Auomaic Pipeline Invenory and Order-Based Producion Conrol Sysem (APIOBPCS). They found ha he bullwhip effec from baching can be reduced if he average demand is an ineger muliple of he bach size. I has been recognized generally ha he bullwhip effec can be minimized by reducing he bach size as much as possible, bu here has been lile sudy of he impac of bach size across a muli-echelon supply chain. Riddalls and Benne (2001) poined ou ha conrol heoriss are unable o solve he lo sizing problem. Poer and Disney (2007) menioned ha he impac of order baching on bullwhip has no been clearly explored. They poined ou ha sudying he impac of bach size on he APIOBPCS, under a sochasic demand process, using he ransform echniques of conrol heory is exremely challenging. Sysem dynamics simulaion hen seems an appropriae mehodology o invesigae he impac of varying bach size on he bullwhip effec wih a sochasic demand process. The value of informaion sharing as a remedy o reduce he bullwhip effec has been widely recognized. However, whils some sudies have analyzed he value of informaion sharing in capaciy consrain supply chains, here has been lile research ino he value of informaion sharing when here is order baching; his paper addresses hese gaps. 2.1 Review of APIOBPCS One of he mos commonly sudied periodic review models in he supply chain lieraure is he Beer Game menioned above. This is a simplified bu sill realisic represenaion of a muli-echelon supply chain (Larsen e al., 1999), consising of a reailer, a wholesaler, a disribuor, and a brewer (facory). The model was developed a Massachuses Insiue of Technology in he 1960s, wih he earlies descripion of he game daing back o Forreser s (1961) work in indusrial dynamics. Coming from a conrol heory background, Towill (1982) inroduced a greaer level of deail ino his model by using he Invenory and Order-Based Producion Conrol Sysem (IOBPCS) o model each echelon in more deail, applying a basic periodic review algorihm for issuing orders ino
he supply pipeline, based on curren invenory defici and incoming demand from cusomers. As is name implies, IOBPCS combines make-o-sock and make-o-order producion conrol as seen in much indusrial pracice. Edghill and Towill (1989) exended he model by incorporaing variable desired invenory as a funcion of he demand. Laer, a work-in-progress (WIP) feedback loop was added o he IOBPCS: Le he producion arges be equal o he sum of an exponenially smoohed demand (over Ta unis of ime) plus a fracion (1/Ti) of he invenory error, plus a fracion (1/Tw) of he WIP error. This is he APIOBPCS (John e al., 1994), which is used in his paper o model he individual iers of a supply chain. Riddalls and Benne (2002) analyzed he impac of a pure ime delay o represen he producion lead-ime and explored he sabiliy boundaries of he APIOBPCS. Disney exended he model ino he vendor-managed invenory scenario. Dejonckheere e al. (2004) sudied he order-up-o-level invenory conrol model and is varians as an imporan subse of he APIOBPCS. Adjusing he gain of he invenory error (Ti) and he pipeline feedback (Tw) allows he APIOBPCS o mimic a range of make-o-sock and make-o-order producion conrol sraegies. The bullwhip effec 801 3. Mehodology Sysem dynamics is an approach o undersanding complex sysems, using modeling and simulaion echniques capable of modeling feedback loops explicily and evaluaing he dynamics of complex processes and sysems. If difference equaions are used o model a sysem, as in he model presened here, hen he model can be implemened in a spreadshee o simulae he sysem in operaion, for example (Shukla e al., 2009). One of he mos commonly applied mehodologies o sudy he various aspecs of he muli-echelon supply chain model is he conrol heoreic approach. The problem now a days ha faces conrol heoriss is ha, alhough hey are ofen able o wrie differenial equaions on he dynamic behavior of he model, in many cases hese differenial equaions canno be inegraed. Insead he conrol heoriss resor o numerical approach, usually wih he help of compuer simulaion (Pidd, 2004). Furher, mahemaical and conrol heoreic approaches can demand an academically advanced undersanding of mahemaics ha mos supply chain operaions managers do no have (Agaran e al., 2007). In conras, he use of sysem dynamic simulaion mehods can help praciioners o beer undersand he basic phenomenon and o examine he effecs of parameers. The paricular sysem dynamics sofware used in his research is ithink w. This requires a reasonably good knowledge of spreadshee modeling as well as difference equaions. I is also very ime consuming and prone o errors as he spreadshee can soon become quie inricae and ulimaely unwieldy. Proprieary sofware packages have been developed o be more user-friendly and funcionally powerful for he ask of sysems dynamics modeling and simulaion, especially in heir user-inerface. One package ha is used commonly for sysem dynamics modeling is MATLAB w (Coppini e al., 2010), which has is origins in he radiional conrol engineering communiy. The paricular sysem dynamics sofware used in his research is ithink w. This has been developed more for he business communiy raher han for conrol engineers, so i should be suiable for supply chain managers and designers.
IJPDLM 41,8 802 ithink w is a useful ool ha can help managemen o gain insigh in he dynamic complexiy of business sysems (Ashayeri e al., 1998). However, limiaion of sysem dynamics and ithink w sofware is ha sysem dynamics simulaion is a modeling ool. For opimizaion, sysem dynamics mus be coupled wih an opimizaion ool. Models are buil in ithink w using flows (e.g. of producs from a facory o an invenory), socks o model simple invenories or process delays such as a facory beween flows, connecors o provide informaion flows (e.g. feedback of acual invenory levels for comparison wih desired levels) and converers o apply gain facors or oher formulae o variables (Figure 1). 4. Muli-echelon supply chain model Figure 2 shows he simulaion model of he four-echelon supply chain produced in ithink w. A he maerial flow level, each echelon consiss of one invenory and one ime delay, i.e. facory or oher faciliy. Each echelon operaes independenly based on demand from downsream (owards he end-cusomer). A echelon-n, he inpu o he facory or oher faciliy a ime period is he order rae (ORATE n ), which is deermined by feeding forward he exponenially smoohed sales (SSALES n ), i.e. he demand forecas, and he acual end-cusomer demand, i.e. he smoohed sales from he reailer (SSALES 1 ), and feeding back he error in he invenory and he WIP, wih he aim of keeping he invenory a he desired level. The error in he invenory (EINV n ) is he difference beween he desired invenory level (DINV n ) and he acual invenory level (AINV n ). Here, DINV n is fixed and equal o original demand. The WIP (WIP n ) is he accumulaion of orders ha have been placed on he echelon bu no ye compleed and he desired WIP is DWIP n n. The error in he WIP (EWIP ) is he difference beween he desired DWIP n and he acual WIP n. Ti is a divisor applied o he invenory defici o conrol he rae of recovery and Tw similarly conrols he WIP replenishmen rae. The reailer shares is end-cusomer demand wih he oher iers, which hen base heir producion raes (ORATE n ) on he weighed sum of his end-cusomer demand and incoming orders from heir previous ier, i.e. heir immediae cusomer in he supply chain. Wih full informaion enrichmen (informaion enrichmen percenage (IEP) ¼ 100 percen) a ier bases is ORATE n solely on end-cusomer demand, whils wih no informaion enrichmen (IEP ¼ 0 percen) producion is based solely on he incoming orders from he previous ier. ORATE n can be based on a combinaion using IEP of end-cusomer demand plus (100 2 IEP) percen of he incoming orders from he previous ier; in he ithink w model hese percenages are referred o as IEP1 and IEP2, respecively. Demand needs o be forecas a each ier before applying i in scheduling and here are poenially many mehods o do his. Simple exponenial smoohing is used in he APIOBPCS model used here. This is jusified as i is he basis of much indusrial pracice and he approach used in oher published models, e.g. in Mason-Jones e al. (1997), Coppini e al. (2010), and Shukla e al. (2009). In ithink w he buil-in funcion SMTH1 calculaes he firs-order exponenially smoohed value, wih he smoohing consan (Ta) represening he ime o average sales and he average age of daa Figure 1. Building blocks of ithink Sock Flow Converer Connecor sofware
Ti 1 ORae1 Ta 1 Transpor delay SSALES 1 Acual invenory 1 Tier 1-reailer The bullwhip effec DInv 1 EInv 1 Bach size Tw 1 Tp 1 Com rae 1 EWIP 1 DWIP 1 Sales 1 803 Ta 2 Ti 2 ORae 2 Traspor delay 2 SSALES 2 Acual invenory 2 Tier 2- wholesaler IEP 1 IEP 2 EInv 2 Tw 2 Comrae 2 EWIP 2 Sales 2 Bach size DWIP 2 DInv 2 Tp 2 Ta 3 Ti 3 ORae 3 Traspor delay 3 SSALES 3 Acual invenory 3 Tier 3 - disribuor IEP 1 Comrae 3 Sales 3 IEP 2 Tw 3 EWIP 3 EInv 3 DInv 3 Bach size Tp 3 DWIP 3 Ti 4 Ta 4 Tier 4 - Facory ORae 4 Producion delay SSALES 4 Acual Invenory 4 IEP 2 DInv 4 IEP 1 EInv 4 Bach size Tw 4 Tp 4 DWIP 4 Comrae 4 EWIP 4 Sales 4 Figure 2. ithink model of muli-echelon supply chain wih informaion sharing and baching in he forecas. The value of Ta deermines he degree of smoohing applied o he demand and is subjec o 0 # 1/Ta #1. COMRATE n is he compleion (oupu) rae of he facory or faciliy a echelon-n. As a simple ime delay (Tp) is used o model he lead-ime, COMRATE n is simply equal o ORATE n 2Tp. The acual invenory AINVn is he accumulaion of sock deermined by COMRATE n 2 SALES n : In summary, a echelon-n: for n ¼ 1 : SALES 1 ¼ he acual end 2 cusomer demand daa ð1þ
IJPDLM 41,8 804 SSALES n for n. 1 : ORATE n for n. 1:SALES n ¼ ORATE n21 ¼ SSALES n 21 þ SALES n ¼ IEP n SSALES 1 þð100% 2 IEP n Þ SSALES n 2 SSALES n 21 Ta n þ EINV n Ti n þ EWIP n Tw n ð2þ ð3þ ð4þ for n ¼ 1 : ORATE 1 ¼ SSALES 1 þ EINV1 Ti 1 þ EWIP1 Tw 1 COMRATE n ¼ ORATE n 2Tp ð6þ AINV n ¼ AINV n 21 þ COMRATE n DINV n ¼ SALES n 0 EINV n ¼ DINV n 2 AINV n DWIP n EWIP n ¼ Tp n SSALES n ¼ DWIP n 2 WIP n 2 SALES n The supply chain model used in his paper is exended by inroducing bach ordering across each APIOBPCS echelon. Baching is inroduced by he ROUND funcion in he ithink w sofware package. The round funcion rounds values up o he nex ineger value. So o conver an ORATE o baches of size (BS), he following formula is used: Number of baches ¼ ROUND ORATE n ð12þ and he new ORATE is hen: Bached ORATE ¼ Number of baches BS n ð13þ Unless saed oherwise, he APIOBPCS parameer values applied in his paper are Ti ¼ Tw ¼ Tp ¼ 6, and Ta ¼ 2Tp ¼ 12, i.e. a good se of values in accord wih he findings of he Mason-Jones e al. (1997) and also used by Wilson (2007). When he four-echelon supply chain is simulaed, i is he fourh echelon ha experiences he greaes demand amplificaion as i is farhes from he end-cusomer (Coppini e al., 2010), he bullwhip effec experienced a his echelon is sudied here. To verify he ithink w model, he difference equaions (1)-(13) were also implemened in a spreadshee model. This produced resuls ha agreed wih he ithink w resuls. 4.1 Measuring he bullwhip effec Several approaches can be applied o measure he bullwhip effec. A commonly used approach based on he variance-o-mean raio is given in equaion (12) (Chen e al., 2000; Wangphanich e al., 2010), and here is a similar approach based on he sandard deviaion-o-mean raio (Fransoo and Wouers, 2000; Xiong and Helo, 2006): BS n ð5þ ð7þ ð8þ ð9þ ð10þ ð11þ
Bullwhip ¼ s2 ORATE =m ORATE s 2 SALES =m SALES s 2 ORATE and m ORATE are he uncondiional variance and mean, respecively, of ORATE a he ier of he supply chain being measured. s 2 SALES and m SALES are he uncondiional variance and mean of SALES a he firs ier, i.e. he end-cusomer demand. I is normally assumed ha he wo uncondiional means are idenical so ha hey cancel in equaion (12), i.e. average orders ¼ average end-cusomer demand, o give he simpler bullwhip measure in equaion (13), which is used here and by ohers (Muramasu e al., 1985; Disney and Towill, 2003; Boani and Monanari, 2010):! Bullwhip ¼ s2 ORATE s 2 SALES! ð14þ ð15þ The bullwhip effec 805 5. Impac of baching and informaion sharing on bullwhip effec 5.1 Sep change in demand Figure 3 shows he impac of he various bach sizes on he bullwhip effec a he reailer level, wih Tw ¼ Tp ¼ 6, Ta ¼ 2Tp ¼ 12, and IEP ¼ 0 percen, under a sep change in demand;, i.e. demand is changed from 2,000 o 2,400 and simulaion is run for 500 weeks. Similar resuls are observed for upsream echelons. Noe, in his graph some of he ploed oupu variances give he appearance of being zero. However, hey are no acually zero bu relaively very small values ha are difficul o depic on a scale ha is large enough o accommodae he oher much larger values. This is also rue of he oher oupu variance graphs ha appear laer. I can be seen ha he relaionship beween bach size and demand amplificaion is non-monoonic. In general, demand amplificaion canno be reduced by reducing he bach size as found by Riddalls and Benne (2001). 2,000 1,800 1,600 Oupu variance (in 1,000s) 1,400 1,200 1,000 800 600 400 200 0 0 400 800 1,200 1,600 2,000 2,400 2,800 3,200 Bach size Figure 3. Impac of bach size on bullwhip effec for sep demand
IJPDLM 41,8 806 Burbridge (1981) emphasized reducing he bach size as much as possible. However, when he quoien of he average demand and bach size (average demand/bach size) is ineger, demand amplificaion does no grow wih he increase of bach size in APIOBPCS as poined ou by Poer and Disney (2007). In oher words, large bach sizes, when combined in ineger muliples, can produce order raes ha are close o he acual demand, produce lile effec on he demand amplificaion, i.e. i is he size of he remainder of average demand divided by bach size ha is he deerminan here. Hence, unless he bach is made very small (in his case, 400) demand amplificaion is no suppressed simply by reducing he bach size as poined ou by Burbidge, raher i can be conrolled by a judicious mix of decreases in bach size and adjusing he bach size so ha he average demand is an ineger muliple of i, i.e. he remainder of demand/bach size is zero or close o zero. However, i is noed ha use of a large bach size placed a one of he local minima amplificaion poins has he danger ha changes in average demand can lead o large increases in amplificaion unless he bach size is adapive, i.e. here is high sensiiviy. 5.2 Sochasic demand process Poer and Disney (2007) repored ha sudying he impac of bach size under a sochasic demand process in APIOBPCS is exremely difficul using a conrol heoreic approach of Laplace and Z-ransforms. APIOBPCS is a periodic review sysem for issuing orders based on incoming demand signals and feedback loops of invenory and pipeline defici. These feed-forward and feedback loops are in urn affeced by conrol parameers and i is hard o undersand he naure of he ransformaion involved. Hence, conrol heoriss have been unable o sudy he impac of bach size under a sochasic demand process, so he sysem dynamics simulaion approach seems an appropriae mehodology for he invesigaion. To simulae a sochasic cusomer demand, SALES follows a normally disribued, saionary sochasic I.I.D. process wih a known mean, m, and variance s 2.Iis assumed ha s is significanly smaller han m, so ha he probabiliy of negaive demand is negligible (Lee e al., 1997). A normally disribued sochasic demand paern wih a known mean of 2,000/week and sandard deviaion of 400 is simulaed. Following Reddy and Rajendran (2005), replicaion is carried ou for 50 simulaion runs, each for 500 weeks, and averages of he resuls are aken. I can be seen from Figure 3 ha he paern, raher han he ampliude, of he impac of bach size on he demand amplificaion is he same as seen in Figure 4 for he sochasic change in SALES. Again i is found ha he oupu variance (bullwhip effec) decreases o a local minimum as he quoien of average demand and bach size approaches an ineger value. Clearly, reducing demand amplificaion due o baching is no jus abou geing as close as possible o a bach size of one, i is also abou how close demand is o an ineger muliple of he bach size. Figures 3 and 4 show ha when he quoien of bach size and average demand is no ineger, increasing he bach size increases he gap beween he minimum variance poins and he magniude of he peak demand amplificaion beween hese poins. Consequenly, fairly small changes in large bach sizes can cause big changes in demand amplificaion. If operaions managers wih large bach sizes monior rends in average demand, i may be possible o monior and anicipae movemen up he curve of he oupu variance, i.e. o forecas high amplificaion, and subsequenly plan
2,500 The bullwhip effec 2,000 Oupu variance (in 1,000s) 1,500 1,000 500 807 0 0 400 800 1,200 1,600 2,000 2,400 2,800 3,200 Bach size Figure 4. Impac of bach size on bullwhip effec for random demand o change he bach size o reduce his. If he bach size is changed so ha here is an ineger muliple of i ha maches demand, he bullwhip effec is minimized. If he bach size is increased beyond he average demand, hen he oupu variance, i.e. he bullwhip effec, increases rapidly and linearly. A corollary o his is ha if he demand sars o decrease below he bach size, hen he bullwhip effec will grow rapidly. Again, he operaions manager should monior for his condiion. Managerial implicaions of our work are followings; relaionship beween bach sizes and he bullwhip effec is no linear. I canno be guaraneed ha smaller bah size will effecively reduce he demand amplificaion. Economies of scale processes usually favor large bach sizes. Reducing bach size in order o reduce he demand amplificaion is no a good soluion. I depends how close average demand is o an ineger muliple of he correc bach size. There are cerain ranges in bach size, like when quoien of average demand and bach size is approaching o ineger value, a modes increase in bach sizes can lead o subsanial reducion in bullwhip effec. By monioring his rend, producion manager can forecas high amplificaion in advance and can beer plan o change he bach size o reduce his amplificaion. This is quie logical ha as bach size increases, he marginal cos of he producion reduces, so i is convenien o ake advanage of his emporary low producion cos and a small increase in producion can be accommodaed by increasing he bach size o ineger muliple of average demand wihou needing he whole new bach. By looking a he graph of he demand amplificaion due o bach size, operaions manager can subsanially reduce he invenory holding and backlog cos by carefully choosing he bach size wihou complex mahemaical calculaions. When he upsream echelons of he supply chain are no working wih baching consrains in heir order raes, changing he bach size of he only reailers does no have any impac on he demand amplificaion of he facory.
IJPDLM 41,8 808 5.3 Impac of informaion sharing wih respec o bach size The impac of informaion sharing on he bullwhip effec has been discussed by many auhors and hey have revealed he value of informaion sharing (Lee e al., 2000, 2004; Moinzadeh, 2002; Roman, 2009). Whils informaion sharing is frequenly cied as being he key o reducing demand amplificaion, here has been lile research o invesigae he value of informaion sharing in a bached model alhough baching is acknowledged as a major cause of amplificaion. The phenomenon of demand amplificaion across muli-echelon supply chain can be seen clearly in Figure 5, which shows he oupu variance of he sep response of 20 percen for Tier 1 and Tier 4 wih 0 and 100 percen IEP. Figure 5 shows ha in percenage erms he increase in demand amplificaion beween Tiers 1 and 4 is greaes wih he smaller bach sizes, i.e. a large bach size may cause a large oupu variance a Tier 1, bu hen his oupu variance does no increase so much in percenage erms, as i passes up he supply chain. So whils he drive in manufacuring migh be o reduce bach sizes, his will lead o greaer demand amplificaion in percenage erms a upsream of supply chain. I is furher noed ha he value of informaion sharing is greaes for he smaller bach sizes, as here is a much greaer improvemen in he amplificaion raio when IEP is changed from 0 o 100 percen, where amplificaion raio is he raio of he oupu variances of Tiers 4 and 1. In he lieraure, a ypical amplificaion raio observed beween wo echelons is 2:1 (Towill, 1992) and beween four echelons is 20:1 (Houlihan, 1987). In Figure 5, for bach sizes less han 400, an amplificaion raio of he order of 20:1 is indeed seen beween Tier 4 wih IEP ¼ 0 percen (no informaion sharing) and Tier 1. However, his raio is far less for he larger bach sizes. The amplificaion raio can be reduced o he order of 8:1 for he smaller bach sizes hrough full informaion sharing, i.e. IEP ¼ 100 percen and his agrees wih he findings of Chen e al. (2000) and Chafield e al. (2004). For he larger bach sizes, whils he amplificaion raio is less, making demand amplificaion arguably a less significan problem, he use of informaion sharing can almos eliminae any significan demand amplificaion. There is a dilemma here because Oupu variance (in 1,000s) 2,000 1,600 1,200 800 400 Oupu variance (in 1,000s) 250 200 150 100 50 0 0 300 600 900 Bach size Tier 1 Tier 4-IEP = 0% Tier 4 IEP-IEP = 100% Figure 5. Impac of informaion sharing on bach size 0 0 400 800 1,200 1,600 2,000 2,400 2,800 3,200 Bach size
informaion sharing will have a cos associaed wih is implemenaion, and whils i may deal wih he problem of demand amplificaion very well, he problem is primarily caused a Tier 1 wih very large bach sizes for he supply chain sudied here. In conras, informaion sharing is clearly of grea value when he bach size is smaller. So, wih he increasing drive o reduce bach sizes, here is an increasing jusificaion for adoping and invesing in informaion sharing. When bach size is larger han average demand, he bullwhip effec does no exis, or he variance of he order quaniy is smaller han he variance of demand resuling in an ani-bullwhip or de-whip effec. From he managerial poin of view, a de-whip effec means ha he producion planning phase a he manufacurer level becomes easier and more sable. The manufacurer prefers o smooh producion, hus he prefers a smooh ordering paern from he reailer. Bullwhip effec increases he variances in orders and desabilizes he producion planning phase a he manufacurer level. When he variance of he order quaniy is smaller han he variance of he demand (de-whip effec), he producion manager can sabilize he producion schedule and minimize he producion cos. The bullwhip effec 809 6. Sensiiviy analysis Sysem dynamics approaches ypically involve four sages: model idenificaion, verificaion, model esing, and policy design (Serman, 2000). The purpose of model esing is o increase confidence in he model, leading o he accepance of underlying dynamic resuls. Among he various model esing procedures, one commonly applied echnique in sysem dynamics simulaion is sensiiviy analysis, which invesigaes he robusness of he model and deermines he sabiliy boundaries of he sysem. The above simulaion resuls are based on a specific se of design parameers, i.e. Ti ¼ Tp ¼ Tw ¼ 6, Ta ¼ 2Tp ¼ 12. There is he possibiliy ha hese resuls are paricular o his combinaion of design parameers. Therefore, sensiiviy analysis is carried ou by changing he values of design parameers associaed wih he model in order o validae he above findings and o explore he sabiliy and criical sabiliy boundaries of he sysem. The simulaion resuls of he sensiiviy analysis are shown in Figures 6-9. Increasing he values of Ti and Ta slows down he response of he APIOBPCS and decreases he bullwhip effec as poined ou by Disney and Towill (2003). Wih he small values of Ti, he feedback of he error in he invenory has a greaer effec as EINV ¼ (DINV 2 AINV)/Ti is larger, i.e. here is an increased gain in he loop Oupu variance (in 1,000s) 800 700 600 500 400 300 200 100 Ti = 4 Ti = 5 Ti = 6 Ti = 7 Ti = 8 0 0 400 800 1,200 Bach size 1,600 2,000 2,400 Figure 6. Impac of Ti on bullwhip effec
IJPDLM 41,8 810 Figure 7. Impac of Tp on bullwhip effec Oupu variance (in 1,000s) 800 700 600 500 400 300 200 100 Tp = 4 Tp = 5 Tp = 6 Tp = 7 Tp = 8 0 0 400 800 1,200 1,600 2,000 2,400 Bach size Figure 8. Impac of Tw on bullwhip effec Oupu variance (in 1,000s) 800 Tw = 4 700 Tw = 5 600 Tw = 6 500 Tw = 7 400 Tw = 8 300 200 100 0 0 400 800 1,200 1,600 2,000 2,400 Bach size 800 Figure 9. Impac of Ta on bullwhip effec Oupu variance (in 1,000s) 700 Ta = 4 Ta = 8 600 Ta = 12 500 400 300 200 100 0 0 400 800 1,200 Bach size 1,600 2,000 2,400 and his provides an explanaion for he over-reacion and bullwhip effec. If one considers he exponenial smoohing, he noise or high-frequency componen of demand is increasingly filered ou by increasing Ta bu he smooher will be slower. If he smooher is made o respond faser by decreasing Ta, hen he noise will no be so heavily smoohed and will resul in bullwhip effec. This is quie logical because he noise and spikes in demand signals are smoohed ino he order calculaion and hence he oupu variance of he order rae decreases.
I is observed ha reducing Tp minimizes he bullwhip effec and his resul verifies he Time Compression Paradigm. However, when Tp # 2 he oupu of he farhes echelons sars decreasing. A possible explanaion for his is ha he sysem ouches he sabiliy boundaries. There is lile effec of he Tw. Smaller values of Tw damp he peaks in he response of he ORATE providing an opporuniy o reduce he demand amplificaion alhough he seling ime is increased. 7. Summary Baching is a clusering of iems for purchasing, packaging, ransporaion, or manufacuring processes. The reasons for bach ordering include he EOQ, periodic invenory review, and ransporaion economies. Bach ordering ofen resuls in bullwhip effec, which has serious implicaions for whole supply chain. Burbridge (1981) emphasized reducing he bach size; he resuls presened here show ha relaionship beween bach size and demand amplificaion is non-linear. When he quoien of he average demand and bach size is ineger, demand amplificaion does no grow wih increases in bach size. I has been proposed ha if operaions managers wih large bach sizes monior rends in average demand, hey could anicipae movemens up he curve of he oupu variance, i.e. high amplificaion, and subsequenly plan o adjus he bach size o reduce his. If he bach size is increased beyond he average demand, hen he oupu variance, i.e. he bullwhip effec, increases rapidly and linearly. A corollary o his is ha if he demand sars o decrease below he bach size, hen he bullwhip effec will grow rapidly. Again, operaions managers could monior for his condiion. I is furher noed ha he value of informaion sharing is greaes for smaller bach sizes, for which here is a much greaer improvemen in he amplificaion raio when IEP changes from 0 o 100 percen. Whils he amplificaion raio beyond Tier 1 is much less for large bach sizes, making i a less significan problem, informaion sharing can almos eliminae any significan demand amplificaion. There is a dilemma here because informaion sharing will have a cos associaed wih is implemenaion, and whils i may deal wih he problem of demand amplificaion very well, he problem is primarily caused a Tier 1 wih very large bach sizes. In conras, informaion sharing is clearly of grea value when he bach size is smaller. So, wih he increasing drive o reduce bach sizes, here is an increasing jusificaion for adoping and invesing in informaion sharing. Baching is associaed wih he invenory holding and backlog cos. Therefore, fuure work should invesigae he cos implicaions of order baching in muli-echelon supply chains. The bullwhip effec 811 References Agaran, M., Buchanan, W.W. and Yurseven, M.K. (2007), Regulaing bullwhip effec in supply chain hrough modern conrol heory, Proceedings of he PICMET, Porland, OR, USA, Augus, pp. 2391-8. Ashayeri, J., Keij, R. and Bröker, A. (1998), Global business process re-engineering: a sysem dynamics-based approach, Inernaional Journal of Operaions & Producion Managemen, Vol. 18 Nos 9/10, pp. 817-31. Boani, E. and Monanari, R. (2010), Supply chain design and cos analysis hrough simulaion, Inernaional Journal of Producion Research, Vol. 48 No. 10, pp. 2859-86.
IJPDLM 41,8 812 Burbridge, J.L. (1981), The new approach o producion, Producion Engineer, Vol. 40 No. 12, pp. 769-84. Cachon, G.P. (1999), Managing supply chain demand variabiliy wih scheduled ordering policies, Managemen Science, Vol. 45 No. 6, pp. 843-56. Chafield, D.C., Kim, J.G., Harrison, T.P. and Hayya, J.C. (2004), The bullwhip effec impac of sochasic lead ime, informaion qualiy, and informaion sharing: a simulaion sudy, Producion and Operaions Managemen, Vol. 13 No. 4, pp. 340-53. Chen, F., Drenzer, Z., Ryan, J.K. and Simchi-Levi, D. (2000), The impac of exponenial smoohing forecass on he bullwhip effec, Naval Research Logisics, Vol. 47 No. 4, pp. 269-86. Coppini, M., Rossignoli, C., Rossi, T. and Srozzi, F. (2010), Bullwhip effec and invenory oscillaions analysis using he beer game model, Inernaional Journal of Producion Research, Vol. 48 No. 13, pp. 3943-56. Dejonckheere, J., Disney, S.M., Lambrech, M.R. and Towill, D. (2004), The impac of informaion enrichmen on he bullwhip effec in supply chains: a conrol heoreic approach, European Journal of Operaional Research, Vol. 153 No. 3, pp. 727-50. De La Fuene, D. and Lozano, J. (2007), Applicaion of disribued inelligence o reduce he bullwhip effec, Inernaional Journal of Producion Research, Vol. 45 No. 8, pp. 1815-33. Disney, S.M. and Towill, D.R. (2003), On he bullwhip and invenory variances produced by an ordering policy, Omega, Vol. 31 No. 3, pp. 157-67. Edghill, J.S. and Towill, D.R. (1989), The use of sysem dynamics in manufacuring sysem, Transacion of Insiue of Measuremen and Conrol, Vol. 11 No. 4, pp. 208-16. Forreser, J.W. (1961), Indusrial Dynamics, Wiley, New York, NY. Fransoo, J.C. and Wouers, M.J.F. (2000), Measuring he bullwhip effec in supply chain, Supply Chain Managemen, Vol. 5 No. 2, pp. 78-89. Hejazi, A. and Himolla, O.P. (2006), Manufacuring lo sizing as a source of he bullwhip effec: a case sudy of elecronics and furniure supply chains, Inernaional Journal of Services and Operaions Managemen, Vol. 2 No. 3, pp. 237-55. Holland, W. and Sodhi, M.S. (2004), Quanifying he effec of bach size and order errors on bullwhip effec using simulaion, Inernaional Journal of Logisics: Research and Applicaions, Vol. 7 No. 3, pp. 251-61. Houlihan, J.B. (1987), Inernaional supply chain managemen, Inernaional Journal of Physical Disribuion & Maerials Managemen, Vol. 17 No. 2, pp. 51-66. John, S., Naim, M.M. and Towill, D.R. (1994), Dynamic analysis of a WIP compensaed decision suppor sysem, Inernaional Journal of Manufacuring Sysem Design, Vol. 1 No. 4, pp. 283-97. Larsen, E.R., Morecrof, J.D.W. and Thomsen, J.S. (1999), Complex behaviour in a producion-disribuion model, European Journal of Operaional Research, Vol. 119 No. 1, pp. 61-74. Lee, H.L., Padmanabhan, V. and Whang, S. (1997), Informaion disorion in he supply chain: he bullwhip effec, Managemen Science, Vol. 43 No. 4, pp. 546-59. Lee, H.L., Padmanabhan, V. and Whang, S. (2004), Informaion disorion in supply chain: he bullwhip effec, Managemen Science, Vol. 50 No. 12, pp. 1875-86. Lee, H.L., So, K.C. and Tang, C.S. (2000), The value of informaion sharing in a wo level supply chain, Managemen Science, Vol. 46 No. 5, pp. 626-43.
Mason-Jones, R., Naim, M.M. and Towill, D.R. (1997), The impac of pipeline conrol on supply chain dynamics, The Inernaional Journal of Logisics Managemen, Vol. 8 No. 2, pp. 47-61. Mehra, S., Inman, S.A. and Tuie, G. (2006), A simulaion-based comparison of bach sizes in a coninuous processing indusry, Producion Planning & Conrol, Vol. 17 No. 1, pp. 54-66. Moinzadeh, K. (2002), A muli-echelon sysem wih informaion exchange, Managemen Science, Vol. 48 No. 3, pp. 414-26. Muramasu, R., Ishi, K. and Takahashi, K. (1985), Some ways o increase flexibiliy in manufacuring sysems, Inernaional Journal of Producion Research, Vol. 23 No. 4, pp. 691-703. O Donnell, T., Maguire, L., McIvor, R. and Humphreys, P. (2006), Minimizing he bullwhip effec in a supply chain using geneic algorihms, Inernaional Journal of Producion Research, Vol. 44 No. 8, pp. 1523-43. Pidd, M. (2004), Compuer Simulaion in Managemen Science, 5h ed., Wiley, Hoboken, NJ. Poer, A. and Disney, S.M. (2007), Bullwhip and baching: an exploraion, Inernaional Journal of Producion Economics, Vol. 104 No. 2, pp. 408-18. Reddy, A.M. and Rajendran, C. (2005), A simulaion sudy of dynamic order-up-o policies in a supply chain wih non-saionary cusomer demand and informaion sharing, Inernaional Journal of Advanced Manufacuring Technology, Vol. 25 Nos 9/10, pp. 1029-45. Riddalls, C.E. and Benne, S. (2001), The opimal conrol of bached producion and is effec on demand amplificaion, Inernaional Journal of Producion Research, Vol. 72 No. 2, pp. 159-68. Riddalls, C.E. and Benne, S. (2002), The sabiliy of supply chains, Inernaional Journal of Producion Research, Vol. 40 No. 2, pp. 459-75. Roman, S. (2009), Informaion sharing versus order aggregaion sraegies in supply chains, Journal of Manufacuring Technology Managemen, Vol. 20 No. 6, pp. 804-16. Sevenson, G. (2005), The muliple faces of bullwhip effec: refined and refined, Inernaional Journal of Physical Disribuion & Logisics Managemen, Vol. 35 No. 10, pp. 762-77. Shukla, V., Naim, M.M. and Yaseen, E.A. (2009), Bullwhip and backlash in supply pipelines, Inernaional Journal of Producion Research, Vol. 47 No. 23, pp. 6477-97. Slack, N. and Lewis, M. (2002), Operaions Sraegy, Prenice-Hall, Harlow. Serman, J. (1989), Modeling managerial behavior: mispercepion of feedback in a dynamic decision making experimen, Managemen Science, Vol. 35 No. 3, pp. 321-39. Serman, J.D. (2000), Business Dynamics: Sysem Thinking and Modeling for a Complex World, McGraw Hill, Boson, MA. Towill, D.R. (1982), Dynamic analysis of an invenory and order based producion conrol sysem, Inernaional Journal of Producion Research, Vol. 20 No. 6, pp. 671-87. Towill, D.R. (1992), Supply chain dynamics he change engineering challenge of he mid 1990s, Proceedings of he Insiuion of Mechanical Engineers, Vol. 206, pp. 233-45. Towill, D.R. (1996), Time compression and supply chain managemen a guided our, Supply Chain Managemen, Vol. 1 No. 1, pp. 15-27. Wangphanich, P., Kara, S. and Kayis, B. (2010), Analysis of he bullwhip effec in muli-produc, muli-sage supply chain sysems a simulaion approach, Inernaional Journal of Producion Research, Vol. 48 No. 15, pp. 4501-17. The bullwhip effec 813
IJPDLM 41,8 814 Wilson, C.M. (2007), The impac of ransporaion disrupions on supply chain performance, Transporaion Research, Vol. 43 No. 4, pp. 295-320. Xiong, G. and Helo, P. (2006), An applicaion of cos-effecive fuzzy invenory conroller o counerac demand flucuaion caused by bullwhip effec, Inernaional Journal of Producion Research, Vol. 44 No. 24, pp. 5261-77. Furher reading ithink User s Manual (1997), High Performance Sysems, Inc., Hanover, NH. Poer, A., Towill, D., Böhme, T. and Disney, S.M. (2009), The influence of muli-produc producion sraegy on facory induced bullwhip, Inernaional Journal of Producion Research, Vol. 47 No. 20, pp. 5739-59. Corresponding auhor Maloub Hussain can be conaced a: maloub@gmail.com To purchase reprins of his aricle please e-mail: reprins@emeraldinsigh.com Or visi our web sie for furher deails: www.emeraldinsigh.com/reprins