The Impact of Forecasting Methods on Bullwhip Effect in Supply Chain Management

Transcription

1 The Imact of Forecasting Methos on Bullwhi Effect in Suly Chain Management HX Sun, YT Ren Deartment of Inustrial an Systems Engineering, National University of Singaore, Singaore Schoo of Mechanical an Aerosace Engineering, Nanyang Technological University, Singaore Abstract Recently there has been a surge of interest an research on a henomenon oularly calle the bullwhi effect in suly chain management. The focus of this aer is the imact of eman forecasting on the bullwhi effect. Base on a thorough literature review, we classify existing researches into ifferent categories in terms of moeling methos. Then we show quantification results of the bullwhi effect for simle, two-stage, suly chains consisting of a single retailer an a single manufacturer. Orer-u-to inventory olicy is assume. The moeling results of three imortant forecasting methos (moving average, exonential smoothing, an minimum mean square error) are stuie. A comarison is mae between these forecasting methos, an some ractical guielines are eveloe to hel managers to select a forecasting metho that yiels the greatest esire benefit. Finally, ossible future research irections in this area are roose. Keywors Bullwhi effect, forecasting metho, suly chain management I. INTRODUCTION Suly chain management (SCM) has become a hot toic over the ast few years, as innovative an valuable SCM solutions have emerge. The awareness of real an otential imrovements in SCM has reache the highest levels of business an government. In SCM research, a henomenon known as the bullwhi effect has rawn much attention. The bullwhi effect reresents a market athology in which information about eman becomes increasingly istorte as it moves ustream in the suly-chain. Such a istortion can lea to excessive inventory throughout the suly-chain system, insufficient or excessive caacities, rouct unavailability, an higher costs in general. The earliest recognition of the bullwhi effect can be trace back to Forrester []. Other earlier aers incluing Blanchar [], Bliner [3], an Kahn [4] also foun evience of inventory volatility similar to the bullwhi effect. The beer game [5] that has been use in teaching suly chain management exhibite the same henomenon. Most of the revious research on the bullwhi effect has focuse on emonstrating its existence, ientifying its ossible causes, an roviing methos to reuce its imact. In articular, ee et al. [6,7] establishe five ossible sources that may lea to bullwhi effect: the use of eman forecasting, non-zero lea time, batche orer, rationing game uner shortage an rice fluctuations an romotions. However the quantification of the change in the magnitue of these causes is rarely foun. It is only recently that some authors begin to stuy the magnitue of the bullwhi effect given some stochastic eman attern, a forecasting metho, an an orering olicy [8,9,0,]. Forecasting methos lay an imortant role in suly chain management. This focus of this aer is the imact of ifferent forecasting methos, such as moving average (MA), exonential smoothing (ES), an minimum mean square error (MMSE) metho, on the bullwhi effect. This aer is organize as following: first we conuct a through literature review in Section, an then in Section 3 we show quantification results of the bullwhi effect using ifferent forecasting methos. In Section 4, we comare the avantages an isavantages of several most imortant forecasting methos. In Section 5, the guielines of choosing these methos are eveloe, an ossible future research irections are roose. II. ITERATURE REVIEW There are some early works on the quantification of the bullwhi effect. Calin [] consiers the imact of batch orering on the bullwhi effect. Kahn [4] emonstrates the existence of the bullwhi effect when the retailer follows an otimal inventory olicy an either eman in each erio is ositively serially correlate or the backlogging of excess eman is ermitte. Metters [3] attemts to estimate the imact of the bullwhi effect on suly chain erformance an conclues that the erformance eteriorates ue to increasing bullwhi effect. Baganha an Cohen [4] construct an analytical moel which emonstrates that inventories can sometimes have a stabilizing (i.e., variance reucing) effect on the suly chain an that the bullwhi effect is not always resent throughout the suly chain. It is imortant to mention that Graves [8] stuie the bullwhi effect resulting from a myoic base-stock olicy in conjunction with the use of an otimal forecasting scheme for a articular non-stationary eman rocess, namely, a first-orer integrate moving average rocess or ARIMA(0,,) rocess. Recently, Chen et al. [9,0] mae imortant contributions in this area. In one of their aers [9], they focus on quantifying the imact of eman forecasting on the bullwhi effect for a simle, two-stage suly chain consisting of a single retailer an a single manufacturer. The retailer uses a simle moving average forecast to estimate the mean an variance of eman. The retailer uses these estimates to form a simle orer-u-to inventory olicy. They fin a simle lower boun on the variance of the orers lace by the retailer relative to the X/05/$ IEEE. 5

2 variance of customer eman. They then exten these results to general multistage suly chains, in the case of both centralize an ecentralize customer eman information. The secon aer [0] assumes that the retailer alies an exonential smoothing forecasting technique. They consier not only correlate emans, but also emans with a linear tren. They quantify the bullwhi effect by roviing a lower boun on the variance of the orers lace by the retailer. Most imortantly, they fin that the magnitue of the increase in variability eens on both the nature of the customer eman rocess an on the forecasting technique use by the retailer. Alwan et al. [5] stuy the variability of the bullwhi effect in an orer-u-to suly chain system when MMSE otimal forecasting is emloye as oose to some commonly use simlistic forecasting methos. They fin that eening on the correlative structure of the eman rocess it is ossible to reuce, or even eliminate the bullwhi effect in such a system by using an MMSE forecasting scheme. Zhang [] makes a comrehensive comarison on the imact of forecasting methos on the bullwhi effect for a simle relenishment system in which a first-orer autoregressive rocess escribes the customer eman an an orer-u-to inventory olicy characterizes the relenishment ecision. Bullwhi effect measures are erive for the MMSE otimal forecasting roceure, MA an ES methos. The finings inicate that ifferent forecasting methos lea to bullwhi effect measures with istinct roerties in relation to lea time an unerlying arameters of the eman rocess. Moreover, a simle rule is establishe to hel managers select a forecasting metho that yiels the lowest inventory cost. Hosoa an Disney [6] analyze a three echelon suly chain moel. First-orer autoregressive en consumer eman is assume. They obtain exact analytical exressions for bullwhi an net inventory variance at each echelon in the suly chain. Table summarizes the major authors an their forecasting methos in quantifying the bullwhi effect. Although these researchers mae imortant contributions in this area, most of them focus only on one or two forecasting methos. We can not get a holistic icture from each of these aers. The eveloment an iscussion of managerial imlications which the ractitioners are most concerne are not aequate. In this aer we will synthesis these research results an eveloe a comrehensive guieline on how to choose forecasting methos aroriately. TABE I MAJOR AUTHORS AND THEIR FORECASTING METHODS Forecasting methos Authors Moving average Chen et al. [9], Zhang et al. [] Exonential smoothing Chen et al. [0], Zhang et al. [] Minimal Mean Square Error Alwan et al. [5], Zhang et al.[], Hosoa an Disney [6] III. MODEING THE BUWHIP EFFECT A. A Simle Suly Moel an Inventory Policy Consier a simle suly chain in which in each erio, t, a single retailer observes his inventory level an laces an orer qt to a single manufacturer. After the orer is lace, the retailer observes an fills customer eman for that erio, enote by t. We assume that any unfille emans are backlogge. There is a fixe lea time between the time an orer is lace by the retailer an when it is receive at the retailer, such that an orer lace at the en of erio t is receive at the start of erio t+. The customer emans seen by the retailer are ranom variables of the form t = µ + ρdt + εt () where µ is a nonnegative constant, ρ is a correlation arameter that satisfies ρ <, εt is the error terms, H et t reresent the history of eman observe u to erio t: Ht = { t, t, t,... }. () Here we assume that the retailer follows a simle orer-uto inventory olicy in which the orer-u-to oint, y t, is estimate from the observe eman as yt = Dt H + zσ, t t Ht (3) D σ th where t is an estimate of the mean lea time eman, th t is an estimate of the stanar eviation of the erio forecast error, z is a constant chosen to meet a esire service level. B. Simle Moving Average (MA) Metho. Moeling results In this section, we assume that the retailer uses a simle moving average to estimate t σ an et base on the eman observations from the revious erios. The moeling rocess for the moving average forecasting scheme in this section is base on Chen et al. [9]. We can have, t i i= DtH t = ( ) (4) In orer to quantify the bullwhi effect, we must etermine q the variance of t relative to the variance of D t, which is enote by B. Finally, we have the following lower boun on the increase in variability from the retailer to the manufacturer: BMA ( ) = Vq ( t)/ σ + ( + )( ρ ) (5) The boun is tight when z = 0.. Interretation of the results It is shown that the way one treats excess inventory has little imact on the increase in variability for most values of an ρ [9]. From (5), we can see the variability function is a X/05/$ IEEE. 6

3 ecreasing function of, where is large the increase in the variability is negligible, but when is small, the increase in the variability is significant. This means that the smoother the eman forecasts, the smaller the increase in the variability. The function is an increasing function of, if the lea time arameter oubles, then we must use twice as much eman ata to maintain the same variability. If ρ>0, meaning that the emans are ositively correlate, the larger ρ, the smaller the increase in variability. C. Exonential Smoothing (ES) Metho. Moeling results Now we assume that the retailer uses the exonential smoothing forecasting technique. The moeling roceure is base on the work of Zhang []. et α enote the fraction use in this rocess, also calle the smoothing factor, then ES forecast can be written as t+ H = ( ) t t H + α t t t Ht (6) Performing recursive substations in the above equation, we arrive at an alternative exression for the one-erio-ahea forecast: i t+ H = ( ) t α α t i i= 0 (7) Finally, we come to the result that the bullwhi effect measure associate with the ES(α) metho is ( ) ( ) BES ( ) Vq ( t)/ ( ) ρ ρ (8) = σ = + α + ( α) ( α) ρ ( α)[ ( α) ρ] This result is the same as those obtaine by Chen et al [0] an Alwan et al. [5].. Interretation of results From (8), the lower boun shows that the increase in variability is a function of three arameters: () the lea time,, () the smoothing arameter α, an (3) the correlation arameter ρ. The imact of lea time an the smoothing arameter is quite obvious. It is clear that longer lea times lea to larger increases in variability. In aition, we can see that the larger the smoothing arameter, the larger the increase in variability. Since α is the weight lace on the most recent observation of eman in the exonential smoothing forecast, this imlies that the more weight the forecast laces on a single observation, the larger the increase in variability. Finally, this result also imlies that a retailer facing a longer lea time must use a smaller smoothing arameter α in orer to reuce the bullwhi effect. Note that (-ρ)/(-(-α)ρ) is a ecreasing function of ρ, so that the increase in variability is a ecreasing function of ρ. In aition, notice that if 0 ρ<, (- ρ)/(-(-α)ρ), an if - <ρ 0, (- ρ)/(-(-α) ρ). Therefore, we see that as the eman correlation ρ increases, the increase in variability ecreases. In aition, for ositively correlate emans, the increase in variability will be less than for i.i.. emans (ρ=0). On the other han, for negatively correlate emans, the increase in variability will be greater than for i.i. emans. C. MMSE Forecasting Metho. Moeling results Now we use MMSE forecasting metho to reict the leatime eman. The moeling roceure is mainly base on the work of Zhang []. Consier linear forecasting methos that combine ast eman observations linearly to reict a future τ eman. et t+ Ht, τ =,,, be the τ erio-ahea of eman t + τ mae in erio t when H t is available, an let t+ τ t = t+ τ t+ τ Ht enote the associate forecast error. t+ τ t t+ τ H an t are given by τ t+ τ Ht = µ + ρ ( t µ ), (9) τ j t+ τ H = t ρεt+ τ j. j= 0 (0) For an AR() rocess, the bullwhi effect B(MMSE) is given by + ρ( ρ )( ρ ) BMMSE ( ) = Vq ( t )/ σ = +. () ( ρ) The roof is given by Zhang [].. Interretation of results Fig.. eicts B(MMSE) as a function of for three lea times =,, 3 in comarison with the case of zero lea time when the bullwhi effect is absent. It shows the following roerties of B(MMSE): ) There is no bullwhi effect when ρ 0; ) For ρ>0, a longer lea time leas to a more significant bullwhi effect. Further more, for all >0, the bullwhi effect is most significant when ρ 0.5. These two roerties can also be verifie from the algebraic exression for B(MMSE) in (). Together, they imly that reucing the lea time has the most imact when eman autocorrelation is ositive an away from zero an unity. Fig.. Relationshi between B(MMSE) an eman autocorrelation IV. COMPARISON OF THE THREE FORECASTING MATHODS A. Comare MA an ES Fig.. eicts the comarison between bullwhi measures X/05/$ IEEE. 7

4 Fig.. Comarison of B(MA) an B(ES) with equal average ata age when =4 of MA an ES forecast methos with ata ages =4. Because the san an the smoothing factor α can be selecte arbitrarily, we cannot, in general, establish this efinitive relationshi. The average ata is efine as the weighte average of the age of ata oints use for one-erio-ahea forecast, where the weights are ientical to those use to combine the historical ata in the forecast []. The average ata age is (+)/ for the MA an /α for the ES metho. When the average ata is equal, that is α=/(+), we can rove that the bullwhi effect of EP is larger than MA. Therefore the lea time has a more significant imact on the bullwhi effect measure when the ES metho is use to forecast lea-time eman. Finally, a ouble moving average forecasting technique can also be use to forecast eman rocesses with a linear tren. In this case, it can be shown that, for equivalent values of an α = α, that is, for an α = α chosen such that the average ata age of the two techniques are ientical, B(ES)>B(MA). For a etaile iscussion of the ouble moving average forecast, see Chen, et al. [7]. B. Comare ES an MMSE To comare the bullwhi effect of ES an MMSE, Fig. 3. eicts these two ifferent measures as a function of ρ, for ρ 0; =,, an 3, an a fixe value α =0.4; in which the soli curves correson to B(MMSE) an the ashe curves reresent B(ES). We can see that: ) There is a bullwhi effect for -<ρ< for B(ES), while there is no bullwhi effect when -<ρ<0 for B(MMSE); ) B(ES) is a ecreasing function of ρ, an it converges to one as ρ aroaches one; 3) ES forecasting can lea to less orer variance than MMSE forecasting when ρ is near one. Fig. 3. Comarison of B(MMSE) an B(ES) C. Comare MA an MMSE To comare the imact of ρ on B(MA), an B(MMSE), Fig. 4. an Fig. 5. eict these two ifferent measures as a function of ρ for =,, an 3, with =4 an 5 resectively. The following roerties can be obtaine immeiately from Fig. 4. an Fig. 5. as well as from the formulae for B(MA) an B(MMSE): ) B(MA) is a quaratic function of an increases without boun as the lea time increases. B(MMSE) aroaches to a finite limit of +ρ/(-ρ) as the lea time increases. Fig. 4. Comarison of B(MMSE) an B(MA) for =4 Fig. 5. Comarison of B(MMSE) an B(MA) for = X/05/$ IEEE. 8

5 ) With MA forecasting, there is a bullwhi effect for all values of ρ an : The effect is most ronounce when ρ is near zero for even or when ρ is near negative one for o. 3) B(MA) is insensitive to changes in ρ near zero as reflecte by the flatness of the curve on both sies of the origin. 4) B(MA) is a symmetric function of ρ when the san is even. 5) For the secifie values of an ; B(MA) is less than B(MMSE) when ρ is near one, inicating that MA forecasting can lea to less orer variance than MMSE forecasting. V. CONCUSIONS AND FUTURE DIRECTIONS This aer attemts to make a review of the revious literatures on the imact of forecasting methos on the bullwhi effect. The moeling results an comarison rovie several key management guielines: ) It is clear that the bullwhi effect is ue, in art, to the retailer's nee to forecast. We also see clearly that the increase in variability will be greater for longer lea times. However, the size of the imact oes een on the forecasting methos. ) If MA forecasting metho is use, the more eman information use to construct the forecast, the smaller the increase in variability. For ES forecasting metho, negatively correlate emans can lea to a larger increase in variability than ositively correlate emans. The more weight the forecast laces on a single observation, the larger the increase in variability. This result also imlies that a retailer facing a longer lea time must use a smaller smoothing arameter α in orer to reuce the bullwhi effect. For MMSE forecasting metho, there is no bullwhi effect for a negatively correlate rocess. When the correlation arameter is greater than 0.5 an less than, the bullwhi effect is most significant. 3) When using EP an MA forecasting scheme, we can rove that the bullwhi effect of EP is larger than MA with the same average ata age an for certain eman rocesses. 4) For a negatively correlate rocess, we shoul use MMSE metho so that we can eliminate bullwhi effect. If the correlation arameter is near zero, MMSE metho can still yiel better results. If the correlation arameter is near one, EP or MA yiels better results. The research can be generalize in several irections that are likely to enhance our unerstaning of how eman signals are transmitte along a suly chain. From our oint of view, ossible future irections in this area are as follows: ) A more general secification of the eman rocess such as an ARMA(, q) rocess can be emloye to stuy how ifferent forecasting methos filter the eman signal. ) More general inventory olicies can be incororate. The simle orer-u-level olicy can be misleaing when a significant fixe orering cost exists. Aroriate measures of the bullwhi effect for the general (s,s) olicy woul be of interest. 3) The moels stuie here consiere only the relatively simle forecasting technique an has not consiere more sohisticate methos such as such as Box-Jenkins. It is interesting to exlore the imact of more sohisticate methos on the bullwhi effect. REFERENCES [] J.W. Forrester, Inustrial ynamics a major breakthrough for ecision making, Harvar Business Review, vol. 36, no. 4, , 958. [] O.J. Blanchar, The rouction an inventory behavior of the American automobile inustry, Journal of Political Economy, vol. 9, , 983. [3] A.S. Bliner, Inventories an sticky rices, Am Econ Rev, vol. 7, , 98. [4] J. Kahn, Inventories an the volatility of rouction, Am Econ Rev, vol. 77, , 987. [5] J. D. Sterman, Moeling managerial behavior: misercetions of feeback in a ynamic ecision making exeriment, Management Science, vol. 35, , 989. 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