Information Sharing on the Bullwhip Effect in a Four-Level Supply Chain

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1 Informaion Sharing on he Bullwhip Effec in a Four-evel Supply Chain Wu-in Chen eparmen of Compuer Science Informaion Managemen Providence Univeriy Taichung Taiwan wlchen@pu.edu.w Wan-Qiao ai Pou Chen Group Taiwan ujm5693@homail.com Chin-Yin Huang eparmen of Indurial Engineering Enerprie Informaion Tunghai Univeriy Taichung Taiwan Tel: ( huangcy@hu.edu.w Abrac. In a global upply chain rucure marke dem change dynamically. To conquer he dynamic informaion haring ha been applied in enerprie o reduce invenory co. Thu he enerprie compeiivene can be mainained. To inveigae he iue of informaion haring mo cholar build a wolevel upply chain model o implify he analyi. However he wo-level model do no fi wih he upply chain in he real world which coni of more han hree level. By mahemaical derivaion hi udy propoe he analyic model o analye he four-level upply chain verifie he value of informaion haring for each ier enerprie of he upply chain. Thi udy aume ha he marke dem follow AR (1 model which wa alo ued in many udie of he lieraure he lead ime of each ier i alo conidered. A fir he bullwhip effec of each ier i verified in a four-level upply chain. Then by analying oal invenory of each ier he benefi of informaion haring for each ier i quanified. The reul of hi udy how ha he bullwhip effec ill exi in he upplier he raw maerial upplier even hough dem informaion i hared. Invenory variaion raie rapidly a elf-correlaion coefficien ρ increae ard deviaion (volailiy σ increae. The effec of lead ime on invenory among enerprie inerac wih one anoher. Informaion haring bring much more ignifican benefi for he upplier for he raw maerial upplier. Under he condiion of he volaile marke dynamic he condiion ha he downream manufacurer i highly aociaed wih he marke dem he raw maerial upplier can reduce up o 35% of invenory by informaion haring. Keyword: Informaion Sharing Supply Chain Bullwhip effec Invenory Model Order-Up-To policy 1. INTROUCTION In he pa mo udie concerning analying he ben efi of informaion haring are he wo-level upply ch ain in he lieraure; however he upply chain of alm o each real-world indury ha more han level. B aed on he derivaion of ee e al. (000 where he wo level upply chain wa alo conidered hi udy analye he bullwhip effec for he four-level upply chain by deriving he variance of invenory for each ier. Our objecive i o quanify he benefi of each ire by informaion haring. The goal of hi udy are lied below: 1. Summarie he relaed udie regarding he bullwhip effec informaion haring in he lieraure o under he gap in he reearch field.. Baed on he AR(1 model for he dem marke derive he bullwhip effec for each ier in he four-level upple chain.

2 3. eermine he invenory deducion of each ier wih infor maion haring. The re of hi paper i organied a follow. Se cion ouline he relaed udie in he lieraure. Th e deailed upply chain model i provided in Secion 3; hi ecion alo analye he model wihou informaio n. Secion derive he bullwhip effec quanifie he benefi of each ier enerprie wih informaion haring. Finally he ummary concluion are preened in Secion 5.. ITERATURE REVIEW.1 EMAN MOE AN INVENTORY OF SUPPY CHAIN Each enerprie develop i own model o foreca ei her marke dem or he dem of i downream enerprie o balance dem upply. Box Jen kin developed he well-known forecaing model ARI MA (Auoregreive Inegraed-Moving Average Model in There are 3 parameer in ARIMA(p d q where p i he number of erm for auoregreion d i he number of ime of compuing difference in ime erie q i he number of erm of moving average. The fundamenal condiion of uing ARIMA i aionary which mean ha he value hould be rom wihou any rend (eiher increaing or decreaing. In cae here exi an eviden rend he moohing proce of aking he difference hould be applied. There are wo ype of invenory planning dependen planning independen planning. Independen planning i for finihed produc or for mainenance par (Hillier & ieberman 1995 dependen planning i for he re of maerial i according o independen planning of finihed produc by MRP. To implify he analyi hi udy only conider independen planning. Silver e al. (1998 claified he invenory policy ino yem: he coninuou review yem he periodic yem. The popular yem ued in he lieraure he Order-Poin Order-Up-To-evel yem belong o he coninuou review yem.. BUWHIP EFFECT Bayrakar e al. (008 propoed he following meaure o evaluae he performance of he upply chain: 1. oal co. ervice level 3. average invenory level. bullwhip effec. Thi udy focue on he bullwhip effec of he upply chain which i he key o he managemen of he upply chain. The bullwhip effec i he phenomenon of enlarging variance of dem along he upream enerprie of he upply chain. The bullwhip effec can be ignificanly oberved in he developing marke where he marke dem increae dramaically. Thee indurie include elecommunicaion manufacuring compuer par manufacuring food reailer car clohe (Hugo 011. The bullwhip effec influence he upply chain in many way reul in he following problem: 1. exceive invenory of he upply chain. defici or exceive produciviy 3. produc unavailabiliy. increaing he oal co of he upply chain 5. ale lo 6. incorrec producion planning (Sun & Ren 005. Therefore he bullwhip effec lead o he bad effec for many enerprie..3 INFORMATION SHARING ee e al. (000 uilied AR(1 dem model o analye he -level upply chain wihou informaion haring wih informaion haring which conain one manu facure one reailer. For he manufacurer boh he invenory he co wih informaion haring were reduced compared hoe wihou informaion haring. Yu e al. (00 ued dem model AR(1 o analy e hree ype of informaion haring: diribued conr ol collaboraive conrol cenral conrol. The reul demonraed ha informaion haring helped he man ufacurer reduce invenory. Zhang (00 propoed ha marke dem model ARMA could be ranferred in he upply chain; bei de for he manufacurer he lead ime invenory poli cy marke dem hiorical order have o be h ared o foreca i fuure dem. Baed on marke dem model AR(1 iu e al. (013 propoed o analye he 3-level upply chain. In addiion informaion i hared o ier 1 ier enerprie he reul howed ha i would bring benefi o ier enerprie wih informaion haring when he value of auocorrelaion coefficien ρ i from -1 o 1. Ganeh e al. (01 propoed o analye he muliplelevel upply chain bu lead ime wa no conidered in heir udy. Huang e al. (015 conidered he -ier upply chain wih muliple upplier. efici of informaion ranparence of coordinaion lead o he bullwhip effec he parner among he upply chain are hor of muual undering o one anoher. Tha reul in miundering in curren marke dem (Bhaacharya & Byopadhyay 011. Hence hi udy propoe he key facor o olve he bullwhip effec i hrough informaion haring in he upply chain. Tha i i can reduce exceive invenory ignificanly. Beide unlike mo udie which only conidered -level hi udy propoe o analye he muliple-level upply chain which i more pracical in he real world. The poiive lead ime i alo conidered in hi udy. The main goal of hi udy i o verify informaion

3 haring can alleviae he bullwhip effec reduce he invenory in he four-level upply chain. 3. ANAYZING THE FOUR-EVE SUPPY CHAIN WITHOUT INFORMATION SHARIN G 3.1 MOE ESCRIPTIONS AN ASSUMPTIONS Baed on ee e al. (000 hi udy exend o derive he dem he invenory for each ier enerprie in he fourlevel upply chain wihou informaion haring. Wih he derivaion provided in hi ecion he bullwhip effec he benefi of each ier enerprie can be furher derived in he nex ecion. Thi udy conider he four-level upply chain which coni of one reailer one manufacurer one upplier one raw maerial upplier. The rucure of he upply chain in hi udy i depiced in Fig. 1. The deailed upply chain model conidered in hi udy i decribed below. Only one produc i conidered. Afer he reailer receive marke dem a each planning period i will place he purchae order o he manufacurer. The imilar iuaion applie o he manufacurer he upplier he raw maerial upplier. Backorder i allowed for each ier enerprie. Fig. 1 The rucure of he four-level upply chain The following noaion are ued o decribe analye he model: d = average marke dem for each planning period ρ = auocorrelaion coefficien of he marke dem N (0 diribuion = error erm a planning period ha i.i.d. = dem of ier i enerprie a planning period ; i=1 3 = (purchaing order quaniy of ier i enerprie a planning period ; i=1 3 = he expeced value of he oal dem in he lead ime for ier i enerprie a planning period ; i=1 3 ( i v = he variance of he oal dem in he lead ime for ier i enerprie a planning period ; i=1 3 ( i T = he arge invenory level for ier i enerprie a planning period ; i=1 3 l = lead ime of purchaing for he reailer ( i ( i Y ( i m = lead ime of purchaing for he manufacurer S = lead ime of purchaing for he upplier Z = lead ime of procuremen for he raw maerial upplier 3. ANAYZING THE SUPPY CHAIN WITHOUT INFORMATION SHARING Following mo udie in he lieraure he ime erie model i uilied o repreen real marke dem. Thi udy follow Kahn (1987 o ue AR(1 model o foreca fuure marke dem below (1 (1 d 1. (1 The above AR(1 i alo he dem for he reailer. Thi udy aume ha each ier enerprie adop order-up-o level invenory policy. Afer each enerprie receive he curren dem i will hen deermine i arge invenory level below ( ( ( T i m i k v i ( ee e al. (000 had derived he purchaing order quaniy arge invenory level for ier 1 en erprie. Thi udy exploi imilar reaoning o derive he deciion for ier 3 enerprie. For ier 3 e nerprie (upplier can be derived a f ollow: (3 d (3 (3 T l (3 (1 (1 1 (1 1 l l1 (1 [ 1] (1 (1 1 (1 1 l1 (1 (1 (1 d (3 (1 T ( 1 1 (1 1 (3 l 1 {(1 [ (1 1 ]} (1 l 1 1 -i {(1 [ (1 1 ]} (1 (1 i1 ( i (1 (1 i1 k 1 l l1 { (1 [ 1]} { (1 (1 } (1 1 l i (1 (1 (1 (1 i1 (1 1 1 l1 (1 (1 (1 (1 (1 ( Similarly for ier enerprie (raw upplier T can be derived below: ( (3 (

4 l ( ( [ 1] [ ] 3 d (1 1 (1 1 [ l 1] (1 l1 (1 l (1 (1 (1 (1 (1 (1 { [ 1 (1 - ] (1 1 l l1 (1 [ 1] (1 (1 } (1 1 1 l1 (1 (1 (1 { [ 1 (1 (1 (1 1 [ l 1] (1 l1 (1 ] 1 l1 (1 (1 } ( l1 (1 (1 (1 [- ] 3 (1 3 1 d (1 (1 T ( ( ( 1 -i h [ (1 h] 1 i i -i k [ (1 e] [ (1 f ] 1 i1 1 i i (1 [ (1 g] [ g] 1 i1 1 (6 where l (1 (1 a (1 1 l l1 (1 [ 1] (1 (1 b (1 1 l1 (1 (1 c (1 h l (1 (1 (1 (1 3 (5 1 (1 e { 1 [ (1 1 l l1 (1 [ 1] (1 (1 l (1 (1 - ] (1 (1 1 l l1 (1 [ 1] (1 (1 } 1 1 l1 (1 (1 (1 f { [ 1 (1 1 l l1 (1 [ 1] (1 (1 ] (1 1 l1 (1 (1 } ( l1 (1 (1 (1 g -. 3 (1 The above equaion (3-6 can be validaed by Ganeh e al. (01 wih lead ime e o 0.. ANAYZING THE EFFECT ON BUWHIP AN THE BENEFIT OF INFORMATION SHARING.1 EFFECT ON BUWHIP Baed on he derivaion in he previou ecion each ier enerprie foreca fuure dem hen decide he invenory deciion. Therefore he invenory deci ion i affeced by he forecaing dem. The excei ve forecaing dem lead o increaing he invenor y co; on he conrary he inufficien forecaing de m reul in lo ale. The incorrec forecaing de m i enlarged wih he bullwhip effec. Therefore hi udy propoe ha informaion h aring i exploied o alleviae he bullwhip effec. A fi r he bullwhip effec of he upply chain wihou inf ormaion haring i meaured a each ier enerprie. T he bullwhip of ier 1 enerprie he reailer i verified below:

5 Var Y (1 ( l1 (1 (1 (1 (1 Var( ( Var( 1 1 l1. (7 (1 (1 (1 (1 cov( 1 1 Var( (1 (1 (1 (1 l1 l (1 Var P Var (1 (1 ( ( A for ier - enerprie he reul are ju oo mey o preen o he implified preenaion are g iven a follow: ( ( ( Var( Y Var( Q Var( (8 Var Y Var R Var (9 (3 (3 (3 ( ( ( Var Y Var S Var (10 ( ( ( ( ( ( where Q R S are funcion of ρ. I can be hown ha Q R S are alway poiive; henc e he bullwhip effec a ier o enerprie can al o be verified. Equaion (7-10 wih lead ime = 0 an d wih ρ = 0.1 are ploed in Fig. 3 repeciv ely. The effec of each facor ρ l on he bullwhip effec can be oberved in hee wo figure. Noe ha l = = = i aumed in F ig. 3. The bullwhip effec i pronounced a ρ i cloe o 1 i increaed. A for he lead ime of ea ch ier enerprie when he lead ime i no long he longer lead ime i he ronger bullwhip effec i. Ho wever a he lead ime i bigger han ome hrehold value lead ime will no affec he bullwhip effec any more. Baed on Equaion (7-10 he invenory level a each ier enerprie can be deermined bu he reul are no provided o implify he preenaion. Z. BENEFIT OF INFORMATION SHARING The bullwhip effec i verified a each ier enerprie i n he previou ubecion i more pronounced wi h higher ier enerprie. I will lead o inaccurae dema nd forecaed poor deciion on invenory. Thi re earch ugge informaion haring i adoped in he upply chain o alleviae he bullwhip effec. The inven ory level of ier - enerprie can be derived below: S 1 ( d (1 T full ( ( l1 (1 ( (1 (1 1 (1 l (1 1 k (1 (1 (1 i1 l3i d (1 (1 T ( (1 (1 1 1 (3 (3 full 1 l l1 { (1 [ 1]} { (1 (1 } (1 1 l1 1 (1 (1 (1 (1 (1 1 1 (1 (1 (1 (1 (1 l1 l 1 {(1 [ (1 1 ]} (1 l 1 1 -i {(1 [ (1 1 ]} (1 (1 i1 ( i k (1 (1 (1 i 1 l l1 { (1 [ 1]} { (1 (1 } (1 1 l i (1 (1 (1 (1 i (1 1 1 ( ( full 1 d (1 (1 T ( (1 (1 fi i e i i (1 (1 gi- g i i -i h [ (1 h] [ (1 ] e 1 i1 1 i i 1-i k [ (1 f] [ (1 g] 1 i3 1 i3 1 (1 [ g] 1. (1 Invenory reducion of ier - enerprie beween wihou informaion haring (in Subecion.1 wih informaion haring (Equaion 10-1 can be compued. Thi udy ue invenory reducion compued o quanify he value of

6 informaion haring a each ier enerprie. The invenory reducion a ier - enerprie are ploed in Fig. 5. From Fig. 5 imporan reul can be oberved below: 1. Informaion haring help upream enerprie reduce holding invenory. Invenory reducion increae a he ier of he enerprie increae.. The value of informaion haring increae a he ard deviaion of error erm in he marke dem model increae. 3. The value of informaion haring increae a he auocorrelaion coefficien increae.. When lead ime i poiive auocorrelaion coefficien he ard deviaion have ineracion o affec invenory 5. SUMMARY AN CONCUSIONS Thi udy fir propoe he rucure of he -level upply chain hen quanifie he bullwhip effec a each ier enerprie. Baed on he derived reul he criical facor o affec he bullwhip effec can be de ermined. Thi reearch furher propoe informaion ha ring i adoped o alleviae he bullwhip effec de ermine wheher informaion haring can reduce inveno ry level a each ier enerprie or no. Our reul how ha bullwhip effec ignificanl y influence higher ier enerprie. Furhermore i can be oberved ha he facor o ignificanly affec he bullwhip effec are auocorrelaion coefficien ρ ard deviaion σ he lead ime of each ier enerp rie l. Informaion haring indeed help red uce invenion level hi wa alo verified in ome udie in he lieraure. However he new impor an finding in hi udy i ha he higher ier of he enerprie i he more value of informaion haring will obain. When he marke dem i very volaile he invenory reducion can be up o 35% for he ra w maerial upplier. Pa udie on informaion haring of he upply chain almo dicued -level rucure. Thi udy h ow ha informaion haring benefi he upream ene rprie mo (upplier raw maerial upplier in hi udy. Hence hi udy ugge ha he manufacur e hould develop a he OM (Original eign Manuf acurer o he number of ier a well a he oal co in he upply chain can be reduced. I can herefore hare more profi o he reailer ha furher moi vae he reailer o hare he dem o he manufacu re. In um he win-win iuaion can be obained in he upply chain. ACKNOWEGMENTS REFERENCES Bayrakar E. Koh S.. Gunaekaran A. Sari K. & Taoglu E. (008. The role of forecaing on bullwhip effec for E-SCM applicaion. Inernaional Journal of Producion Economic 113( Bhaacharya R. & Byopadhyay S. (011. A review of he caue of bullwhip effec in a upply chain. The Inernaional Journal of Advanced Manufacuring Technology 5( Box G.E.P. & Jenkin G.M. (1970. Time erie analyi forecaing conrol. San Francico: Holden-ay. Ganeh M. Raghunahan S. & Rajendran C. (01. The value of informaion haring in a muli-produc mulilevel upply chain: Impac of produc ubiuion dem correlaion parial informaion haring. eciion Suppor Syem Hillier F.S. & iberman G.J. (1995. Inroducion o operaion reearch: Taa McGraw-Hill Educaion Huang Y. Ho R. & Fang C. (015 Quaniy dicoun coordinaion for allocaion of purchae order in upply chain wih muliple upplier Inernaional Journal of Producion Reearch 53( Hugo M. H. (011. Eenial of upply chain managemen (Vol. 6: John Wiley & Son. Kahn J. A. & Maachue Iniue of T. (1987. Inven orie he Volailiy of Producion: Maachue In iue of Technology eparmen of Economic. ee H.. So K. C. & Tang C. S. (000. The value of informaion haring in a wo-level upply chain. Managemen cience 6( iu Z. Zhao Q. Wang S. & Shi J. (013. Modeling The Impac Of Parial Informaion Sharing In A Three-Echelon Supply Chain. Aia-Pacific Journal of Operaional Reearch 30( Silver E. Pyke. F. & Peeron R. (1998. Invenory managemen producion planning cheduling. Yu Z. Yan H. & Cheng T. (00. Modelling he benefi of informaion haring-baed parnerhip in a wo-level upply chain. Journal of he Operaional Reearch Sociey 53( Zhang X. (00. Evoluion of ARMA dem in upply chain. Manufacuring & Service Operaion Managemen 6(

7 Fig. ifference on variance of each ier enerprie wih lead ime = 0 Fig. 3 ifference on variance of each ier enerprie wih ρ = 0.1 Fig. Illuraion of informaion haring of he upply chain

8 Fig. 5 Invenory reducion of ier - enerprie when informaion haring i applie