Bullwhip Effect Measure When Supply Chain Demand is Forecasting

Transcription

1 J. Basic. Appl. Sci. Res., (4)47-43, 01 01, TexRoad Publicaio ISSN Joural of Basic ad Applied Scieific Research Bullwhip Effec Measure Whe Supply Chai emad is Forecasig Ayub Rahimzadeh 1, Alireza Haji, ad Ahmad Makui 3 1 eparme of Idusrial Egieerig, Sciece ad Research Brach, Islamic Azad Uiversiy, Tehra, Ira eparme of Idusrial Egieerig, Sharif Uiversiy of Techology, Tehra, Ira 3 eparme of Idusrial Egieerig, Ira Uiversiy of Sciece ad Techology, Tehra, Ira ABSTRACT emad flucuaios i he supply chai lead o uceraiy i iveory policy ad hereupo he iveory coss icrease. This paper cosiders he impac of forecasig o he demad variaio i a serial hree-sage supply chai icludig a reailer, a maufacurer ad a supplier. Four forecasig mehods are cosidered ad demad variaios evaluaed as bullwhip effec measure. We use aalyical mehod o derive bullwhip effec o measure demad variaios i secod ad hird sage. Resuls show demad flucuaios icreases as oe move up supply chai. Ad he differe forecasig mehods lead o icreasig he variaios ad he more previous daa usig leads o more precisio. KEY WORS: Supply chai, Forecasig, Bullwhip Effec. 1. INTROUCTION A supply chai cosiss of all paries ivolved i fulfillig a cusomer reques. A supply chai usually icludes he maufacurer, suppliers, rasporers, warehouses, reailers ad cusomers. Wihi each orgaizaio such as maufacurer, he supply chai icludes all fucios ivolved i receivig ad fillig a cusomer reques.[1] I is becomig icreasigly difficul o igore he demad variaios i a supply chai. The demad variaios usually saed as bullwhip effec ha measured as each sage of supply chai demad variace divided by cusomers demad variace. I fac, as oe move up he supply chai from reailer o suppliers, observe more variabiliy i demad. Firsly he bullwhip effec has bee sudied by Forreser[],[3]. He sudied some evideces of bullwhip effec ad discussed he causes lead o his pheomeo. Oher papers demosraed he bullwhip effec ad foud some evideces of iveory volailiy [4], [5], [6], [7]. The Beer Game, which developed ad used i eachig iveory maageme i MIT, repored by Serma[8]. Lee e al. [9],[10] propose five mai causes of bullwhip effec, demad forecasig, o-zero lead ime, order bachig, shorages ad price flucuaios. To avoid he bullwhip effec, all causes should be elimiaed. They cosidered AR(1) demad process i a simple wo sage supply chai. Meers[11] ideify he bullwhip effec usig a lower boud o he profiabiliy of bullwhip effec. He measured he impac of bullwhip effec by comparig i wo cases: high demad variabiliy versus low demad variabiliy wih seasoaliy effec. Graves [1] * Correspodig auhor: Ayub Rahimzadeh, eparme of Idusrial Egieerig, Sciece ad Research Brach, Islamic Azad Uiversiy, Tehra, Ira. [email protected] 47

2 Rahimzadeh e al., 01 measures he bullwhip effec for a supply chai i which demad process follows a iegraed movig average. Che e al.[1] measure he bullwhip effec i a supply chai icludig wo sages wih AR(1) demad process observed by he reailer. The reailer forecass fuure demad by movig-average forecasig mehod. They ve derived a lower boud for he bullwhip effec. Che e al.[13] exed heir resuls for expoeial smoohig mehod. They quaified he bullwhip effec ad foud ha i depeds o boh he aure of cusomers demad process ad he used forecasig mehod. They cocluded he bullwhip effec would icreases whe he lead ime icreases. Xiaolog Zhag [14] cosiders a simple supply chai wih order-up-o repleishme sysem. He miimizes he mea-squared forecasig error for he demad process ad cocludes ha differe forecasig echiques lead o differe bullwhip effec accordig o lead ime ad demad process parameers. Previous sudies usually quaified bullwhip effec i wo sage supply chai icludig a reailer ad a maufacurer. So far, however, here has bee lile discussio abou hree sage supply chai. I his paper we exed demad forecasig o a hree sage serial supply chai, icludig a reailer, a maufacurer ad a supplier. The reailer observed cusomer demads, ad places a order based o los demads of cusomers. The maufacurer observed he reailer orders ad places he order o he supplier. I secio we describe he supply chai model. I secios 3 o 6 differe forecasig mehods preseed for measurig demad variabiliy. We evaluae bullwhip effec i secio 5, coclude i secio 6 ad Fuure sudies are herefore recommeded.. Problem efiiio To evaluae demad flucuaios, usually bullwhip effec is used. I his paper, a hree sage supply chai wih oe reailer, oe maufacurer ad oe supplier is cosidered. (figure1) Figure1. Supply chai model I his serial supply chai, i each period, he reailer faced o demad ad places order o he maufacurer, ad hereby he maufacurer places order o supplier. The demad i marke place ha is reailer s demad, has mea ad sadard deviaio.we are abou o evaluae he impac of forecasig o demad variaios deoed by bullwhip effec. We assume four forecasig echiques: las period, las period wih red correcio, movig average ad expoeial smoohig. I each case, he maufacurer predics fuure demad base o reailer orders, ad i a like maer he supplier forecass base o maufacure orders. 3. Las Period emad I his mehod, ad i easies case, each sage of supply chai use oly he laes period demad ad igore ay red of variaios. The reailer ad maufacurer forecas heir demads as: 48

3 J. Basic. Appl. Sci. Res., (4)47-43, 01 1 (1) Ad 1 () Ad he: I his mehod, here is o amplifyig i demad variace. Var ( ) Var( ) Var( ) (3) 4. Las period demad wih red correc I Las period mehod, here is o moivaio i predicio. A iellige mehod is usig laes red i predicio process. We cosider a coefficie, of las red, o miimize bullwhip effec. 1 ( 1 ) ( 1) 1 (4) Ad: 1 ( 1 ) ( 1) ( 1) 3 (5) B. E. Var( ) / Var( ) (6) The miimum of bullwhip effec occurs whe So, he bullwhip effec is 3/8 ad he forecas fucio is: ( ) / 1 (7) A movig average of las wo demads, ha reduce demad variaios. We exed he movig average o more previous daa i ex secio. 5. Movig Average Mehod I his mehod, we exed previous daa o las demads ad use movig average mehod sage. The reailer esimaes fuure demad by:... 1 (8) The maufacurer esimaes is fuure demad by: 1... (9) Because of s correlaios, we rewrie i i erms of ha are idepede. The we have: 3... ( 1) 1... (10) The variace of his relaio is: ( 1) Var( ) (11) 3 3 I case of = i became like las mehod ad whe > he variaios will decreased. Icreasig leads o lower flucuaios. 6. Expoeial Smoohig Mehod I his secio, expoeial smoohig mehod is used o forecas demad. 49

4 Rahimzadeh e al., 01 Ad he: k 1 ( 1 ) k (1) E( ) [1 (1 ) ] (13) Var ( ) [1 (1 ) ] /( ) (14) (6) The supplier demads forecased as: " ( 1 k (15) Because of correlaio bewee s, for derivig is mea ad variace we develop i i erms of. " (1 (1 3 3 (1 The i ca be wrie as: " Var( )/ 3 (1 (1 (1 4 k... (1... ( (1 1 1 (1 ( 1)(1 /( 4 ( 1) (1 ) (1 (1 ( 1)(1 /( 7. RESULTS Forecasig he fuure demads is impora i a supply chai. I his paper, we ivesigae he demad variaios deoed as bullwhip effec measure. The bullwhip effec calculaed as raio of he Supplier demad variace o he reailer demad variace. We evaluae four measure of bullwhip effec. I movig average mehod, whe las demads are used i predicio process, his raio is: ( 1) / 3 3 (18) The bullwhip effec ca be reduced by icreasig of. The demad variaio is demosraed i figure. (17) (16) (9) (4) Figure. Bullwhip Effec i case of movig average forecasig As icreases, i.e. more demad iformaio is used he demad variaio decreases. The bullwhip effec i case of expoeial smoohig mehod is: 430

5 J. Basic. Appl. Sci. Res., (4)47-43, 01 (1 ) ( 3)(1 ) ( 1)(1 ) ( ) [ The demad variaios showed i figure3. 1] ] (19) Figure 3. Bullwhip effec whe expoeial smoohig is used As icreases, demad variaio icreases ad decreasig lead o decreasig he demad variaios. Whe 0. 8 demad variaios has maximum level. 8. Coclusio The purpose of he curre sudy was o measure he demad variabiliy i a simple hree- sage supply chai. We used las demad, las demad wih red correcio, movig average ad expoeial smoohig mehod for forecasig he fuure demad i a serial supply chai. We use aalyical mehod o exed he model o hird sage. The mos obvious fidig o emerge from his sudy is amplifyig demad variabiliy as oe move up he supply chai. I was also show ha he more demad iformaio used o forecasig he demad, he smaller he icrease i variabiliy. The demad variaio is a icreasig fucio of he smoohig parameer. Moreover variabiliy for movig average mehod is decreasig fucio of umber of used daa. I ay case, supply chai sages mus use more demad iformaio o reduce demad variabiliy. However, his paper does o capure of some complexiies ivolved i real world. Muliple reailers ad maufacurers, i form of ework, ca be cosidered. Furhermore, i ca exed o muliple sages ad usig various forecasig mehods i various sages. REFERENCES [1] Chopra S. & Meidl P., 007. Supply Chai Maageme:Sraegy, Plaig, & Operaio, Preice Hall, 3rd Ediio. [] Forreser, J.W., Idusrial dyamics-a major breakhrough for decisio makig, Harvard Busiess Review, 36 (4), [3] Forreser, J.W., Idusrial dyamics. MIT Press,Combridge, MA.. [4] Blachard, O.J., The producio ad iveory behavior of he america auomobile idusry, Joural of Poliical Ecoomy, 91, [5] Blider, A. S., 198. Iveories ad sicky prices, America Ecoomic Review, 7,

6 Rahimzadeh e al., 01 [6] Blider, A. S., Ca he producio smoohig model of iveory behavior be saved?, Quarerly Joural of Ecoomics, 101, [7] Kha, J., Iveories ad he volailiy of producio, America Ecoomic Review, 77, [8] Serma, J.., Modelig maagerial behavior: Mispercepios of feedback i a dyamic decisio makig experime,, Maageme Sciece, 35(3), [9] Lee, H.L., Padmaabha, P.,Whag, S., 1997a. Iformaio disorio i a supply chai:the bullwhip effec. Maageme Sciece, 43(4), [10] Lee, H.L., Padmaabha, P.,Whag, S., 1997b. Bullwhip effec i a supply chai. Sloa Maageme Review, 38(3), [11] Meers, R., Quaifyig he bullwhip effec i supply chais, Joural of Operaios Maageme, 15, [11] Garaves, S.C., A sigle-iem iveory model for a o-saioary demed process, Maufacurig ad Service Operaios Maageme, 1(1), [1] Che, F., rezer, Z., Rya, J., Simchi-Levi,., 000a. Quaifyig he bullwhip effec i a simple supply chai. Maageme Sciece, 46(3), [13] Che, F., rezer, Z., Rya, J., Simchi-Levi,., 000b. The impac of expoeial smoohig forecass o he bullwhip effec. Naval Research Logisics, 47, [14] Zhag, X., 004. The impac of forecaig mehods o he bullwhip effec. I. J. of Produ Ecoomics, 88,