A Bayesian Combination Forecasting Model for Retail Supply Chain Coordination

Transcription

1 A Bayesa Cobato Forecastg Model or Retal Supply Cha Coordato W.J. Wag* ad Q. Xu Glorous Su School o Busess ad Maageet, Doghua Uversty Shagha, P.R.Cha *wejew@dhu.edu.c ABSTRACT Retalg plays a portat part oder ecooc developet, ad supply cha coordato s the research ocus retal operatos aageet. Ths paper revews the collaboratve orecastg process wth the raework o the collaboratve plag, orecastg ad repleshet o retal supply cha. A Bayesa cobato orecastg odel s proposed to tegrate ultple orecastg resources ad coordate orecastg processes aog parters the retal supply cha. Based o sulato results or retal sales, the eectveess o ths cobato orecastg odel s deostrated or coordatg the collaboratve orecastg processes, resultg a proveet o dead orecastg accuracy the retal supply cha. Keywords: Keywords: Bayesa Cobato Forecastg Model, Retal Supply Cha Coordato, Collaboratve Forecastg, Forecastg Accuracy.. Itroducto The supply cha coordato aog parters throughout the etre supply cha has abstracted ore ad ore atteto ro both the dustres ad the acadecs []. Varous supply cha coordato solutos have bee developed to streale the supply cha aageet ad prove the supply cha operatos perorace [-4]. Collaboratve plag, orecastg ad repleshet (CPFR), whch s a retal supply cha coordato ovato, has bee adopted ad pleeted by ay world-reowed retalers ad auacturers, such as Wal-Mart ad Proctor & Gable. CPFR cocers the collaborato where two or ore partes the supply cha jotly pla a uber o prootoal actvtes ad work out sychrozed orecasts, o the bass o whch the producto ad repleshet processes are detered. The rst CPFR project was ploted by Wal-Mart wth ts supplers 995. The results o the two-year project showed that CPFR could sultaeously reduce vetory levels ad crease sales or both retalers ad supplers. Sce ts orgal applcato was tated, CPFR has had ay successul applcatos North Aerca, Europe ad Cha [5,6]. The collaboratve orecastg plays a portat part the CPFR pleetato procedure. I ths paper, we wll brely revew the CPFR cocept ad ts pleetato process at rst. The collaboratve orecastg process whch s the core part o CPFR wll the be aly dscussed. The collaboratve orecastg process s the bascs phase o the pleetato o CPFR ad the corerstoe to the success o CPFR projects. The collaboratve orecastg process o CPFR requres a sold orecastg approach to sythesze orato ad kowledge ro ultply partes the supply cha. The cobato orecastg ethod ca cobe orecastg odels ro deret partes to sooth the coordato the supply cha ad reduce orecastg dscrepaces. Thus, cosderg the ultple ors o orecastg resources the retal supply cha, the Bayesa cobato orecastg ethod s appled or CPFR collaboratve orecastg odelg wth proved orecastg accuracy ad supply cha collaborato perorace ths paper. Cobg orecasts s a well-establshed procedure or provg orecastg accuracy Joural o Appled Research ad Techology 35

2 A Bayesa Cobato Forecastg Model or Retal Supply Cha Coordato, W.J. Wag. / whch takes advatage o the avalablty o both ultple orato ad coputg resources or data tesve orecastg [7]. Sce Bates-Grager rst proposed the cobato orecastg ethod 969 [8], ay kds o cobato ethods have bee developed [9]. Bayesa cobato ethods [0, ] use the dstrbutoal propertes o the dvdual orecasts to costruct the cobato. May researches related to Bayesa cobato ethods have bee developed ay schees. Walz ad Walz [] copared the Bayesa ethodology ad ultple regresso coposte orecasts wth acroecooc data. Ad ther study oud that the Bayesa cobato procedure produces ore accurate coposte orecasts tha does the regresso cobato procedure. Hoogerhede et al [3] copared several Bayesa cobato schees ters o orecast accuracy ad ecooc gas. Fara ad Mubwadarkwa [4] studed a olear geoetrc cobato o Bayesa orecastg odels. The Bayesa cobato orecastg ca cobe the quattatve ad qualtatve data ad orecastg ethods [5]. Dead orecastg retal supply cha s pacted by ay actors such as product prooto or socal developet tred. Also, subjectve orecastg based o the expert experets s ote used retal arket orecastg. The Bayesa cobato orecastg odel s thereore cosdered to be a sutable collaboratve orecastg approach retal supply cha coordato. I the rst part o ths paper, the CPFR retal supply cha coordato ad collaboratve orecastg process are dscussed brely. I the secod part o the paper, a Bayesa cobato orecastg ethod s odeled to coordate orecastg process retal supply cha. Fally, the sulato o ths odel s copleted usg Carreour sales data. The sulato results showed the eectveess o ths Bayesa cobato orecastg odel retal supply cha collaborato process. CPFR Collaborato ad Forecastg CPFR, whch was proposed by VICS (Volutary Iter-dustry Coerce Stadards Assocato) 995, provdes retalers ad supplers wth a raework or sharg key supply cha orato ad coordato plas. Uder CPFR, supply cha parters or a cosesus orecast, ether by workg collaboratvely or by rst developg ther ow dvdual orecasts, whch are the used to create a cosesus orecast. The key to collaborato utlzg CPFR s the joted dead orecast betwee retalers ad auacturers, whch s the used to sychroze repleshet ad producto plas throughout the etre supply cha. Ths coordato ad orato sharg allows retalers ad supplers to optze ther supply cha actvtes. Drk Seert, a proessor at Harvard Busess School ad the Uversty o Massachusetts, deed CPFR as a tatve aog all partcpats the supply cha, teded to prove the relatoshps aog the through jotly aaged plag processes ad shared orato. [6]. The collaboratve orecastg process, whch s oe o a CPFR phases that cludes collaborated pla, orecastg ad repleshet phases, guaratees a precse dead by pleetg a joted orecastg process sde the retal corporato ad aog ts supply cha parters. The orecastg accuracy, a dex used to evaluate the perorace o CPFR collaboratve orecastg process, s detered by the orecastg dscrepaces betwee the orecastg results ad actual dead values. The orecastg dscrepaces ay be caused by accuracy o the put data or dereces aog orecastg odels used by deret parters. Iaccuracy o put data ay be resulted ro accurate ad utely sale data ad the u-tely coucato or chages caused by deads, such as alterato o advertseet pla or products prooto pla. A CPFR collaboratve orecastg process aog parters ca help to prove the accuracy o data or orecastg. I ths paper, we wll ocus o the dscusso o the ways to reduce dscrepaces caused by orecastg odels dereces. The Bayesa cobato orecastg odel s proposed to reduce ths kd o dscrepacy ad prove the dead orecastg accuracy ad collaborato the CPFR pleetato process. I the CPFR collaboratve orecastg process, parters the supply cha wll use deret orecastg odels ad orecastg cycles because o ther deret orecastg kowledge backgrouds ad resources. For exaple, order 36 Vol., Aprl 04

3 A Bayesa Cobato Forecastg Model or Retal Supply Cha Coordato, W.J. Wag. / to orecast products dead the retalers ay use the sple ovg average ethod, whle the auacturers ay use artcal eural etwork ethod. Also, the retaler s orecastg cycles could arrage ro several weeks to oe quarter, due to large dereces aog varous kds o sale tes. However, the auacturers ay take oe week as ther orecastg cycle due to ewer kds o products. Ths ay results ore accurate orecast results by auacturers because o shorter orecastg cycle ad ore sophstcated orecastg odels. Dead orecast results ay der by as uch as a actor o three betwee auactures ad retaler ro the sae product [7]. I order to reduce these orecastg dscrepaces ad sooth the collaboratve orecastg process aog CPFR parters, a joted orecastg odel whch ca cobe orecastg odels ro deret partes should be used. The cobato o the coplex orecastg odels ad proessoal orecastg kowledge used by auacturers ad tely sales data ad arket orato sourced ro retaler wll prove the orecastg accuracy ad eectve supply cha collaborato. The cobato orecastg ethod whch tres to cobe the deret orecastg approaches used by retalers ad auacturers s ecessary or ore accurate ad eectve collaboratve orecastg CPFR process.a sple approach ght be easy or orecastg, but the slghtly ore coplex cobato orecastg ethod ca prove orecastg accuracy the CPFR collaboratve orecastg process. The cobato orecastg approach that we developed ca reduce the orecastg dscrepaces resultg ro the deret terests o retalers ad auactures the supply cha. I geeral, retalers ght cocer ore wth sales loss caused by goods shortage, whle auacturers ay cocer ore about overstock cost resultg ro surplus stock ad trasportato cost caused by retured goods. A joted orecastg odel ca cobe both partes cosderatos the retal supply cha. The CPFR collaboratve orecastg process based o the cobato odel s showed as the lowchart Fg.. Based o the data ro pot-osale, tal orecastg results are calculated by cobato orecastg odel that cobes dvdual orecastg odels ro the retaler ad the auacturer. Ad the, the al optzed orecastg report s created ater correctg dscrepaces the orecastg result that caot be accepted accordg to the CPFR excepto stadard. The excepto stadard s jotly created by retalers ad auacturers. The collaboratve orecastg process aog the partes the supply cha ca help to reduce orecastg dscrepacy caused by accuracy o put data. The cobato orecastg ethod appled CPFR collaboratve orecastg process ca reduce orecastg dscrepacy resultg ro orecastg odels dereces betwee retalers ad auacturers. Data or Forecastg Retaler Mauacturer Cobato Forecastg Excepto Stadard Forecastg results accepted? Yes Error Correcto No Forecastg Report Output Fgure. CPFR Cobato Forecastg Process Flowchart. Joural o Appled Research ad Techology 37

4 A Bayesa Cobato Forecastg Model or Retal Supply Cha Coordato, W.J. Wag. / Bayesa Cobato Forecastg Modelg Idvdual orecastg ethods avalable to the orecaster rage ro applyg the robust sple average to the ar ore theoretcally coplex, such as ethods based o artcal eural etworks ethods [8]. Varous optal estato theores, such as the least squares, the weghted least square, u varace, ad u varace ubased estato procedures have bee appled to d out proper techques to cobe dvdual orecasts. Aog varous kds o cobato orulatos, the sple average cobato orecastg ethod has the vrtues o partalty ad robustess ecooc ad busess orecastg [9]. All the ethods adopt the lear orulato whereby a vector,, o dvdual orecasts are cobed va a lear weghtg vector, w. I the sple average ethod the weght o dvdual orecasts are the sae as w. The cobato ethod proposed by Bates ad Brager 969 s reerred to as the optal lear cobato odel or B-G ethod. Wth ths approach, the orecastg results c, c c are assued to be rado varables wth the covarace atrx. Based o the zg the varace crtera (MV), the optal orecastg results ca be calculated as the ollowg Eq.. c W k k k W T Here, the weghtg vector T T T W ( ) ( W, W..., W T (,,...,) ) () The Bayesa cobato orecastg odel ca be developed ro the B-G ethod, usg the dstrbutoal propertes o the dvdual orecasts to costruct the cobato. Suppose Y s a vector represetg sapled actual dead. The orecastg results obtaed ro the deret partes the supply cha whch are orecasted wth dvdual orecastg ethods are represeted by,,, j,,,. Ad,,,, preset deret orecastg te perods. The Bayesa cobato orecastg ethod akes use o the Bayesa rule to decde the optal cobato ways ad weghts o dvdual orecastg ethods cobato odel, resultg cobed orecastg results deret te perods ˆ c (,,, ), whch ca approxate actual dead values. T Set Z (,, ),,,,. The the jot probablty desty ucto o dvdual orecastg saples o depedet te z, z,, z ca be calculated as the ollowg Eq.. (,, ; ) z, ; ) z z Y ( z Y () Here s a paraeter vector, ad T Y ( y, y,, y ) s the vector o the actual dead saples o the deret orecastg te perods. Accordg to the Bayesa rule, the probablty desty ucto that Y s set as a specc vector value y ca be calculated as the ollowg Eq. 3: ( yz, z,, z ) ( z y ) ( y ) ( z y ) ( y ) dy AI (,, A (,, y ) ( y ) y ) ( y ) dy (3) Here, ( y )(,,, ) s the pror probablty dstrbuto o y, whch represets the pror estato or preerece o decso aker to y. A s the deto set o y. I oly oe orecastg te perod s cosdered as the geeral case ad pror dstrbuto ( y) s uor dstrbuto or, that s ( y), the Eq. ca be spled as the ollowg Eq. 4. (,, y) ( y,,, ) (4) (,, y) dy A 38 Vol., Aprl 04

5 A Bayesa Cobato Forecastg Model or Retal Supply Cha Coordato, W.J. Wag. / The orecastg error dstrbuto o dvdual orecastg results (,, ) s chose as oral dstrbuto or logarth oral dstrbuto ost cases. I ths paper, a ore geeral dstrbuto o orecastg error s troduced through Box Cox coverso, where Z ( ) 0 Z (5) l Z 0 Here, s coverso paraeter Supposed s the covarace atrx o (,, ) ad W represets the weghts o dvdual orecastg ethods. The, the weghts ca be calculated as ollowg Eq.6, based o the u error varace crtera: T T W, W W T W..., (6) Ad, olear cobato orecastg orula ca be obtaed through Bayesa aalyss as ollowg Eq.7, whch wll be used to calculate the optal cobato orecastg results approxatg to the actual values vector Y. w s e ( ) W W ˆ c 0 0 (7) T T Here,, ad W t S. Ad, the optal coverso paraeter * ca be calculated as the ollowg Eq.8. ) j t arg Y j ( W (8) j Where j s the orecastg result o j te perod through dvdual orecastg ethod. The weghts W ca be calculated by Eq. 6. The covarace atrx ca be detered ro pror value or estated by past approxate saple values. 4. Sulato Carreour s oe o the bggest superarket chas the world. Carreour shares the sales data wth ts supplers through the Iteret techology ad coordates the orecastg process wth the parters the retal supply cha. To deostrate our proposed odel, sulato o the Bayesa cobato orecastg approach wll be based o the sales data o oe kd o bscut products Carreour Cha. Detaled sales data o ths product or 39 weeks s showed table. Durg the sulato process, the sales data ro week to 8 were used to estate paraeters or the Bayesa cobato orecastg odel. The sales data ro week 9 to 39 were used as a coparso wth the orecastg results obtaed ro cobato orecastg ethods. The dstrbuto curve o bscut product sales data over the etre 39 weeks s showed Fgure. Through a statstcal aalyss o the bscut sales data, cludg saple autocorrelato ucto (ACF) testg ad partal correlato testg, t was oud that dstrbuto o the bscut sales values y s a rst order statoary sequece I(). 4. Idvdual Forecastg Method Selecto ad Bayesa Cobato Deterato Based o the Carreour bscut sale data ad statstcal aalyss, the Bayesa orecastg odel ca be created ollowg three a steps, whch cludes proper dvdual orecastg ethod selecto, cobato deterato ad optal paraeter estato. The characterstcs o dvdual orecasts cobg the odel has substatal plcatos o the overall orecastg perorace o odel, ad thus t s very portat to rgorously aalyze dvdual orecast errors. The rst step the cobato odelg process s to copare ad select sutable dvdual orecastg ethods or cobato. Joural o Appled Research ad Techology 39

6 A Bayesa Cobato Forecastg Model or Retal Supply Cha Coordato, W.J. Wag. / Week Actual Week Actual Week Actual Dead Dead Dead Table The Sales Data or Carreour Bscut Product. Week Actual Dead F F F3 F4 F Table. Forecastg Results o Fve Idvdual Forecastg Methods. I geeral, deret partes the retal supply cha ay use deret patters o orecastg. So, the deret patters o dvdual orecastg ethods, whch clude sple ovg average, expoetal soothg, tred extrapolato, ARIMA (autoregressve tegrated ovg average) ad artcal eural etwork ethods, are appled to create a cobed odel to orecast product dead ro week 9 to 39. Through a coparso study o orecastg results ro each dvdual orecastg ethod, the best paraeters o each dvdual orecastg ethod are estated. The orecastg results o ve dvdual orecastg ethods are dcated Table. The F colu dcates the best results orecasted by the sple ovg average ethod usg a ovg perod N =3. The F colu s the best results orecasted by the expoetal soothg ethod wth the soothg coecet a = 0.6. The F3 colu s the best results orecasted by the two polyoal regresso ethod (=). The F4 colu s the best results orecasted by the ARIMA ethod whe paraeter d =. The F5 colu dcates the best results orecasted by the artcal eural etwork ethod wth three euros ad two hdde layers the eural etwork. 30 Vol., Aprl 04

7 A Bayesa Cobato Forecastg Model or Retal Supply Cha Coordato, W.J. Wag. / Ater the ve dvdual orecastg ethods are selected, the secod step cobato odelg process s to detere sutable ways to cobe these dvdual ethods. Wth the Matlab sulato tool, the orecastg results are calculated usg deret ways o cobg these dvdual orecastg ethods, as show Table 3. As t s wdely accepted that oly ''good'' orecasts should be cluded a cobato, serous dereces orecast error varaces betwee the dvdual orecasts are ot to be expected [8]. Fro the orecastg results show Table 3, t ca be see that ay cobato ways that cluded F3 polyoal regresso ethod dd ot have good orecastg perorace. So, F3 dvdual orecastg ethod was dropped. ct W (9) t Whe, /, Bayesa cobato ors s as the ollowg Eq. 0, whch has the sae cobato or as the weghted average o square root. ct W t (0) Ad, whe, Bayesa cobato ors s as ollowg Eq., whch has the sae cobato or as the weghted average o haroca seres. Fally, the our dvdual ethods (F F F4 F5) were chose or the Bayesa cobato odel. ct W () t Cobato (F F F3 F4 F5) (F F F3 F4) (F F F3 F5) (F F F4 F5) (F F3 F4 F5) (F F3 F4 F5) (F F4 F5) (F F4 F5) (F F F5) Forecastg Results BAD BAD BAD GOOD BAD BAD GOOD GOOD GOOD Table 3. Deret Cobato o Idvdual Forecastg Methods. 4. Bayesa Cobato Model Sulato As the coverso paraeter the Bayesa cobato Eq. 7 vares, Bayesa cobato orula ca be spled to the deret ors o other sple cobato orecastg ethods. For exaple, whe =, Bayesa cobato or ca be approxated to the ollowg Eq. 9, whch has the sae cobato or as the weghted average o square su. * The optal coverso paraeter s calculated accordg to the Eq. 8. The ttg process o the optal paraeter * s show Fgure 3. Fro the ttg curve, t ca be see that the su o * square o orecastg error s zed whe = 6.949, whch could be rouded to * =7 or the Bayesa cobato odelg. Errors betwee orecastg result ad actual dead, represetg orecastg dscrepacy, are used as the evaluato stadards o orecastg ethods perorace. Here (see Table 4), we have used our a easure dces o orecastg error, whch are the su o squares error (SSE), the ea square error (MSE), the ea absolute percetage error (MAPE) ad the ea square percetage error (MSPE), to evaluate the accuracy o orecastg results ro Bayesa cobato orecastg odel. The Bayesa cobato odels wth deret paraeter are copared wth the sple average ethod ad optal lear ethod the sulato based o Carreour bscut sales data. The orecastg errors o deret cobato orecastg ethods are show the table 4. The easure o orecastg error wth the optal * Bayesa cobato ethod whe =7 are lower tha those o sple cobato ethods Joural o Appled Research ad Techology 3

8 A Bayesa Cobato Forecastg Model or Retal Supply Cha Coordato, W.J. Wag. / ad other Bayesa cobato ethods whe =-, =/, ad =, dcatg that these choces o are the ost sutable or cobato odels the retal collaboratve orecastg process. Ths research shows that the Bayesa cobato orecastg ethod s a eectve approach or tegratg ad coordatg the orecastg process aog parters the retal supply cha. Ad, the optal Bayesa cobato orecastg ethod ca hghly prove the dead orecastg accuracy o collaboratve orecastg actvty the retal supply cha Fgure. Product Sales Data Dstrbuto Curve 39 Weeks. 6 x S λ Fgure 3. Bayesa Paraeter Fttg Curve. Cobato Forecastg Methods SSE MSE MAPE MSPE Sple Average Method.64E+04.40E Optal Lear Method.5E+04.9E Bayesa Cobato =.83E+04.57E Bayesa Cobato =/.45E+04.3E Bayesa Cobato =-.37E+04.6E * Bayesa Cobato =7.9E+03.74E Table 4. The Coparso o Bayesa Cobato Models Forecastg Errors. 3 Vol., Aprl 04

9 A Bayesa Cobato Forecastg Model or Retal Supply Cha Coordato, W.J. Wag. / Cocluso The collaboratve plag, orecastg ad repleshet raework provdes a practcal roadap or retal supply cha coordato. Ths paper proposed a Bayesa cobato orecastg odel that ca cobe dvdual orecastg ethods ro deret partes the retal supply cha or CPFR collaboratve orecastg. Sulato results usg a real exaple dcate that orecastg dscrepaces are reduced ad collaboratve orecastg accuracy s proved whe the orecastg process are tegrated through the optal Bayesa cobato orecastg odel. Ths suggested that the Bayesa cobato orecastg ethod s a eectve approach or the collaboratve orecastg process retal supply cha. Further research o collaboratve orecastg ethodologes or supply cha coordato wll be exteded to ore coplex product dead stuatos the uture. Ackowledgeets Ths research was partly supported by grats ro the Shagha Scece Foudato Coucl (ZR400900), the Chese Natoal Scece Foudato Coucl (7774), Foudato o Mstry o Educato o Cha ( ), Iovato Progra o Shagha Mucpal Educato Cosso (ZS58) ad Natoal Key Techology R&D Progra o the Mstry o Scece ad Techology (0BAH9F00). Thaks to the edtor ad reerees at the Joural o Appled Research ad Techology. Reereces [] Y. Avv, The eect o collaboratve orecastg o supply cha perorace, Maageet Scece, vol. 47, o. 0, pp , 00. [] M. Cedllo-Capos, C. Sachez-Rarez, Dyac Sel-Assesset o Supply Chas Perorace: a Eergg Market Approach, Joural o Appled Research ad Techology, vol. 7, o. 3, pp , 03. [3] M. Fathollah, F. Taha, A. Ashour, Developg a Coceptual Fraework or Sulato Aalyss a Supply Cha Based o Coo Plator (SCBCP), Joural o Appled Research ad Techology, vol. 7, o., pp , 009. [4] M. M. Gl, P. M. Espñera, J. M. L. Cerquera, Supply cha aageet autootve teratoal logstcs: a scearo ad ts challeges, Joural o Syste ad Maageet Sceces, vol., o. 4, pp , 0. [5] X. Lu, Y. Su, Iorato Itegrato o CPFR Iboud Logstcs o Autootve Mauactures Based o Iteret o Thgs, Joural o Coputers, vol. 7, o., pp , 0. [6] P. Daese, Desgg CPFR collaboratos: sghts ro seve case studes, Iteratoal Joural o Operatos & Producto Maageet, vol. 7, o., pp. 8 04, 007. [7] D.W. Bu, Forecastg wth ore tha oe odel, Joural o Forecastg, vol. 8, o. 3, pp. 6-66, 989. [8] J.M. Bates, C. W. J Greager, Cobato o Forecasts, Operatoal Research Quarterly, vol. 0, o. 4, pp , 969. [9] P.J. Laberso, S.E., Page, Optal Forecastg Groups, Maageet Scece, vol. 58, o. 4, pp , 0. [0] D.W. Bu, A Bayesa approach to the lear cobato o orecasts, Operatoal Research Quarterly, vol. 6, o., pp , 975. []_R.T. Clee, R.L. Wkler, Aggregatg pot estates: A lexble odelg approach, Maageet Scece, vol. 39, o. 4, pp , 993 [] M. M. Gl, P. M. Espñera, J. M. L. Cerquera, Supply cha aageet autootve teratoal logstcs: a scearo ad ts challeges, Joural o Syste ad Maageet Sceces, vol., o. 4, pp , 0. [3] L. Hoogerhede, R. Klej, F. Ravazzolo, H.K. Va Djk, M. Verbeek, Forecast Accuracy ad Ecooc Gas ro Bayesa Model Averagg Usg Te- Varyg Weghts, Joural o Forecastg, vol. 9, o. -, pp. 5-69, 00. [4] A. E. Fara, E. Mubwadarkwa, The geoetrc cobato o Bayesa orecastg odels, Joural o Forecastg, vol. 7, o. 6, pp , 008. [5] R.X. Gao, S.Y. Zhag, B. Lu, A Bayesa approach to cobed orecasts, Joural o Systes Egeerg, vol., o., pp. 8-35, 996. [6] D. Seert, Collaboratve Plag, Forecastg, ad Repleshet: How to Create a Supply Cha Advatage, AMACOM. Aerca Maageet Assocato, pp. 7-40, pp.73-76, 003. [7] M. Katz, H.D. Bobb, A closer look at CPFR processes: Workg wth orecast exceptos, Joural o Appled Research ad Techology 33

10 A Bayesa Cobato Forecastg Model or Retal Supply Cha Coordato, W.J. Wag. / Iteratoal Joural o Physcal Dstrbuto & Logstcs Maageet, vol. 4, o. 0, pp. 78-8, 000. [8].L.M. de Meezes, D. W. Bu, J. W. Taylor, Revew o gudeles or the use o cobed orecasts, Europea Joural o Operatoal Research, vol. 0, o., pp , 000. [9] R.T. Clee, Cobg orecasts: a revew ad aotated bblography, Iteratoal Joural o Forecastg. vol. 5, o. 4, pp , Vol., Aprl 04