The Aalysis of Bullwhip Effect i Supply Chai Based o Strategic Alliace Rui Xu, Xiaoli Li, Xiaomi Sog, Gag Liu School of Busiess, Hubei Uiversy, Wuha, 430062, P. R. Chia, wdxj826@126.com Abstract. Bullwhip effect is a widespread ad serious problem i supply chai maagemet, both domestic ad foreig scholars studied ad came to a coclusio cosistetly: That the mai fuctios that cause bullwhip effect are eed forecasts, batches orderig, ad fluctuatios i price, ratioal decisiomakig, ad time defermet ad i coordiatio, supply chai structure. May scholars have doe quatifyig study o bullwhip effect, but o oe has thik of the elemet that the orderig eterprises may magify their demad ad calculated the effect i the whole supply chai. This paper leads o the magifyig rate of market demad based o the research of Lee ad Che ad others, quatifyig the overstock caused by bullwhip effect i the whole supply chai, ad cotrast the codio uder strategic alliace patter ad the codio uder o-strategic alliace patter, the testified the first patter ca brig beefs to eterprises ad is useful for savig resources, which ca serve as good apocalypse for maagers ad etrepreeurs i supply chai. 1 Itroductio Supply chai maagemet has beig paid close attetio to both by the theory boudary ad the busiess circles. As the most importat fuctio idex sig i supply chai structure ad the most importat performace idex sig i the operatio of supply chai bullwhip effect becomes the hot to be studied. It refers to the pheomeo that ultimate marketplace demad is elarged icreasigly i the process of trasferrig alog supply chai toward the upper eterprises from the retail dealer. It was first brig about by Forrester(1958 [1] i idustrial dyamics, he listed a series of bullwhip effect examples i oe book, i his opiio, bullwhip effect is caused by the costat chage of orgaizatio behavior. Bullwhip effect leads to a maufacture makig a productio pla wrogly, elargig stock ivestmet, cuttig dow profs, reducig the stadard of service, thereby brigs catastrophic cosequece to eterprises, may domestic ad foreig scholars have doe large amout of research o the cause ad how to removes bullwhip effect. The
454 Rui Xu, Xiaoli Li, Xiaomi Sog, Gag Liu maily studyig cocetrates o the existece, the quatifyig, the weakeig, ad the cotrol of bullwhip effect. For the weakeig ad cotrollig of bullwhip effect, the first step is to fid out the cause ad the secod step is to quatify bullwhip effect. For the first step, domestic ad foreig scholars foud out seve fuctios such as demad forecastig, batches orderig, fluctuatios of price, ratioal decisio -makig, time defermet ad icoordiatio, ad supply chai structure. For the secod step, there are may aalysis. Wa(2002 [2] discussed the impacts of suppliers' assigmet over bullwhip effect. Lu(2002 [3] certificated that the fluctuatios i price or suppliers' shortsighted makig price would lead to bullwhip effect. Che adopted differet forecastig techologies. At the same time, Che(2000 [4] certificated that iformatio share ca dimiish bullwhip effect efficietly, but ca ot elimiate bullwhip effect completely. Ad Che(2000 [5] adopted the expoet level ad smooth law to calculate, aalysis the bullwhip effect i the two kids of demadig patters, ad cotrasted the results. Graves, Alwa ad Li used time series aalysis for bullwhip effect studyig. Graves(1999 [6] had doe this: calculated bullwhip effect whe usig a expoetial smoothig forecast ad adaptive base-stock, uder the ARIMA(0, 1, 1 patter which meas usteady demadig. Alwa(2003 [7] proved that uder the AR(1 demadig patter, usig optimum forecastig method ad (s, S strategy, bullwhip effect will ot happe whe the eighbor term demad are egatively related. Li(2004 [8] expaded the research from peculiar time series two stage model to geeral ARIMA(0, 1, 1 time series may stage models, brought forward ad proved that ati-bullwhip effect exists. Their study maily cocetrates o three methods, such as system dyamics model takig Forrester(1958 [1] as a represetative, autoregressive model takig Che(2000 [4] as a represetative, ad Kalma filter model [9]. These study all cocetrates bullwhip effect o suppliers, ad have ot thik about the factor of demad ad supply whe models. For these disadvatages, this article builds a ew model whe leadig o a market demad exaggerate rate ad basig o Lee s (1997 [10] model ad hypothesis. Besides, this article quatifies ad cotrasts the bullwhip effect uder strategic alliace model ad o-strategic alliace model from the whole supply chai. As a result, proves that strategic alliace model ca brig beefs to all the eterprises i supply chai. 2 The Quatifyig Aalysis of Lee et al (1 Assumes i a two stage supply chai there is oe supplier ad i retail dealers (i= 1, 2,,, retail dealers demads area AR(1 models follow: D d D 1 (1 Amog the express d represets a costat, d>0; expresses the relevace modulus, -1<<1; D expresses the forecastig demad of retail dealer i at the stage t; expresses a radom variable obeyig (0, 2 logormal distributio. (2 Assumes that the retail dealers ad supplier do ot share iformatio, i the codio, all the eterprises forecast their market demad idepedetly ad retail dealers adopt (s, S orderig tactics which meas that whe the stock is lower tha
The Aalysis of Bullwhip Effect i Supply Chai Based o Strategic Alliace 455 the value s, makes stock icrease to S level by orderig goods. s meas the orderig po, S meas the maximal stock. Assume agai that the retail dealers do ot have fixed cost whe orderig goods from the maufacturer, the s=s. Each retail dealer's target orderig level S expresses as follow: S m k v (2 Amog the express, m idicates the codio mea umber, idicates the codio variace, ad p idicates cost of beig out of stock; h idicates stock cost; l idicates lead time, the: l l d 1 1 j (1 m ( l 1 D 1 p j1 1 (3 l 1 1 j 2 (1 2 j1 v (1 (4 p k 1( p h (5 Accordig to hypothesis (1, suppliers' demad forecastig is: Y D ( S S 1 (6 Put expressio (2 o expressio (6 to get: Y D ( m m 1 (7 Put expressio (3 o expressio (7 to get: l1 (1 Y D ( D D 1 1 (8 Put expressio (1 o expressio (8 to get: l2 l2 (1 d l2 (1 Y D 1 1 1 (9 3 The Model of this article (1 Assumes that the factual demad durig t+1 term is A t+1 ; (2 Assume that at the ed of t+1 term the backlog of excess demad is B t+1. 3.1 The Market Backlog of Excess Demad i Supply Chai uder Nostrategic Alliace Model Uder this model, there is o iformatio share, every retail dealer forecasts demad ad sed out their orders to the supplier idepedetly. Sice the ucertay of marketplace, sometimes demad is greater tha supplies i the whole market, ad the a ratioal supplier ofte distributes a fixed rate of the each retail dealer s order. Assume retail dealer i forecasts that the supplyig rate accordig to his order is i (which is a costat, the he will exaggerate his order by 1/ i times. Assumes that
456 Rui Xu, Xiaoli Li, Xiaomi Sog, Gag Liu every retail dealer wat to get the full amout of their forecastig demad, the they order will be: D D i ( 0 i 1 (10 Because of the isharig of iformatio, each supplier has to predicts the demads of every retailer accordig to their orders durig the last term. So revise (9 wh (10 to get supplier s demad forecastig for each retail dealer durig term t is: l2 l2 (1 d l2 D 1 (1 Y 1 i 1 (11 The supplier s overall demad forecastig for every retail dealer durig term t +1 is the total of supplier s demad forecastig for each retail dealer durig term t+1 just as follow: Y Y t1 1 i1 Put expressio (11 o expressio (12 to get: l2 l2 (1 d l2 D (1 Yt 1 1 1 1 i1 i i1 (13 At the ed of term t+1, the total backlog of excess demad i the supply chai is the total demad forecastig Subtract the actual demad durig the term just as follow: B Y A t1 t1 t1 Put expressio (13 o expressio (14 to get: l2 l2 (1 d l2 D (1 Bt At 1 1 1 1 1 i1 i 3.2 The Market Backlog of Excess Demad i Supply Chai uder Strategic Alliace Model Uder this patter, all retail dealers ad suppliers form a strategic alliace, sharig iformatio, trustig each other, ad wieldig Third-party logistics eterprises such as the distributio ceter for ued tock ad distributio. I this codio, oly supplier has to forecast the whole market demad accordig to the actual market iformatio from the retail dealers. Assume that the forecastig is a AR(1 model, which has bee proved right by expressio (9, ad the forecastig model is: Yt 1 d Dt t (16 D t D i1 (17 Amog the express, d is a costat, d >0; is the relevace modulus, -1< <1; is a radom variable obeyig (0, 2 logormal distributio. (12 (14 (15
The Aalysis of Bullwhip Effect i Supply Chai Based o Strategic Alliace 457 Put expressio (17 o expressio (16 to get: Y d D t1 t i1 (18 For both express (9 ad express (18 are supplier s total demad forecastig for all retail dealers, ad they are both AR(1 models, we ca assume that they have equal relevace modulus, this meas: l 2 (19 Sice the marketplace facig the supplier uder strategic alliace patter is just the whole marketplace facig the retail dealers, ca be assumed that: t i1 (20 The uder this model, at the ed of term t+1, the total backlog of excess demad i the supply chai is: B t1 Y t1at1 (21 Cotrastig (12 ad (15 to get: C B B (22 t1 t1 t1 (C t+1 is the cuttig dow amouts of backlog of excess demad or stock i supply chai because of strategic alliaces. Put expressio (14 ad (20 o expressio (22 to get: C Y Y (23 t1 t1 t1 Put expressio (13, (18, (19 ad (20 o expressio (23 to get: l2 l2 1 1 1 C ( d d ( 1 D ( 1 1 1 t i 1 i1 i i1 (24 (1- l+2 d/(1- ad d ca be uderstood as safety stock uder strategic alliace suatio, ca be uderstood as that supplier oly have oe retail dealer or he ca use ay retail dealer s safety stock to meet other retail dealer s access demad, the syergy effect of strategic alliace model happes, ad the total safety stock must be reduced, which meas: d d (25 For: l2 1 2 l1 1 (26 1 So: l2 1 d 1 > d d > (27 The we ca get: l2 1 d d 1 >0 (28
458 Rui Xu, Xiaoli Li, Xiaomi Sog, Gag Liu For 0< i 1, so: 1 ( 1 D 0 i1 i (29 For: l2 1 2 l1 1 1 (30 So: l2 1 ( 1 1 1 i1 >0 (31 Accordig to (28, (29, (31, C t+1 0 4 Coclusios 4.1 The Advatages of This Article s Model (1 Differet idustries are cofroted wh differet market supply ad demad suatios; eve the same idustry is cofroted wh differet market supply ad demad suatios at differet terms. The mai reaso of bullwhip effect is the dissymmetry of iformatio, ad the most obvious actio for retails dealer is to magify their demads. But the past scholars did t thik of this elemet. For this, this article s model leads o a marketplace exaggerate rate 1/ i (0< i 1, whe 0< i <1 idicates that the market demad is greater tha supplies, dow-stream eterprises exaggerates their order whe sedig out order to the supplier; whe i =1, idicates a ormal buyer s market. So this article s model perfects Lee (1997 [10] ad Che(2000 [5] ad others model ad is represetive, ca be broadly used i differet idustries ad eterprises, ca be used i differet market codios ad has better adaptabily i today s chagig market. (2 The former models all cocetrates bullwhip effect o suppliers, i fact, the reduce of bullwhip effect ca save the resource of the whole society, the get beefs for every eterprise i supply chai, from this po, bullwhip effect has bad effects to all eterprises i supply chai, ad the past models themselves are ot easy for further studies of bullwhip effect i multi-level supply chai. This article s model stadig i the po of the whole supply chai, calculate the backlog of excess demad i supply chai directly, ad calculate the ecoomic beefs (resource savigs from strategic alliace model, givig the maagers of supply chai a direct express ad servig as a basic basis for further distributio of the beefs amog all the eterprises i supply chai. (3The article has discussed the improvemet of backlog of excess demad i supply chai by the strategic alliaces model, at the same time, i the model of this article, as log as that the forecastig demads of both the most dow-stream eterprise ad most upstream eterprise are kow, the the backlog of excess demad i the whole supply chai is able to be got. Because of these, this article s
The Aalysis of Bullwhip Effect i Supply Chai Based o Strategic Alliace 459 model is more simplified ad easy to carry out studies of bullwhip effect i multilevel supply chai. 4.2 The Disadvatages of This Article s Model The deficiecy of this article s model is that does ot thik about the effect o orders from the backlog of excess demad durig, ad oly cocetrates o the disproportio of supply ad demad durig a give term. Cotrastig the advatages ad the disadvatage, is obvious that this article s model is better tha the farmer s models. It breaks up the limatio that oly cocetrates the effect o supplier, addig the magifyig elemet, perfects the past models, is iovatio, makes the model have a wider use, ad supplies a ew agle of view to study bullwhip effect for the later scholars, serves good apocalypse for maagers ad etrepreeurs i supply chai. Ackowledgmets This research has bee supported by the key projects of bureau of sciece ad techology of Wuha uder Grat 20064003113-31 ad educatio departmet of Hubei Provice uder Grat 2006y073. Refereces 73. 1. J.W. Forrester, Idustrial Dyamics, Harvard Busiess Review 36(4, 37-66 (1958. 74. 2. J. Wa, M.Q. Li, J.S. Kou, Impact of Capacy Allocatio o Bullwhip Effect i Supply Chai, Joural of Systems Egieerig 17(4, 340-348 (2002. (i Chiese 75. 3. G.B. Lu, Q.Y. Hu, X.B. Ga, Research o Combied Pricig ad Ivetory Strategy, Joural of Systems Egieerig 17(6, 531-536 (2002. (i Chiese 76. 4. F. Che, Z. Drezer, J.K. Rya, D. Simchi-Levi, Quatifyig the Bullwhip Effect i a Simple Supply Chai: The Impact of Forecastig, Lead Times, ad Iformatio, Maagemet Sciece 46(3, 436-443 (2000. 77. 5. F. Che, J.K. Rya, D. Simchi-Levi, the Impact of Expoetial Smoothig Forecasts o the Bullwhip Effect, Naval Research Logistics 47(4, 269-286 (2000. 78. 6. Graves, C. Stephe, A Sigle-em Ivetory Model for a No-statioary Demad Process, Maufacturig & Service Operatios Maagemet 1(1, 50-61 (1999. 79. 7. Alwa, C. Layth, Liu, J. Joh, D.Q. Yao, Stochastic Characterizatio of Upstream Demad Processes i a Supply Chai, IIE Trasactios 35(3, 207-219 (2003. 80. 8. G. Li, S.Y. Wag, G. Yu, H. Ya, Bullwhip Effect ad Validy of Productio-smoothig Model, Joural of Maagemet Scieces i Chia 7(1, 1-18 (2004. (I Chiese 81. 9. X. Li, Y.S. Che, How to Cotrol the Bullwhip Effect Based o Systematic Structure Improvemet, Logistics Techology (10, 58-60 (2006. (I Chiese 82. 10. H.L. Lee, V. Padmaabha, Iformatio Distortio i a Supply Chai: The Bullwhip Effect, Maagemet Sciece 43(4, 546-558 (1997.