A Combining Forecasting Modeling and Its Application

Transcription

1 A Combg Forecastg Modelg ad Its Applcato Degme Qu, Weje Wag o cte ths verso: Degme Qu, Weje Wag. A Combg Forecastg Modelg ad Its Applcato. Kecheg Lu; Stephe R. Gullver; Wez L; Chagru Yu. 5th Iteratoal Coferece o Iformatcs ad Semotcs Orgasatos (ICISO), May 04, Shagha, Cha. Sprger, IFIP Advaces Iformato ad Commucato echology, AIC-46, pp.46-5, 04, Servce Scece ad Kowledge Iovato. <0.007/ >. <hal > HAL Id: hal Submtted o Aug 06 HAL s a mult-dscplary ope access archve for the depost ad dssemato of scetfc research documets, whether they are publshed or ot. he documets may come from teachg ad research sttutos Frace or abroad, or from publc or prvate research ceters. L archve ouverte plurdscplare HAL, est destée au dépôt et à la dffuso de documets scetfques de veau recherche, publés ou o, émaat des établssemets d esegemet et de recherche fraças ou étragers, des laboratores publcs ou prvés. Dstrbuted uder a Creatve Commos Attrbuto 4.0 Iteratoal Lcese

2 A Combg Forecastg Modelg ad Its Applcato Degme Qu, WeJe Wag* Glorous Su School of Busess ad Maagemet, Doghua Uversty Shagha, 0005, Cha Abstract. he supply cha coordato has abstracted more ad more atteto from dustres ad academcs. hs paper studes a Bayesa combato forecastg model to tegrate multple forecastg resources ad coordate forecastg process amog parters retal supply cha. he smulato results based o the retal sales data show the effectveess of ths Bayesa combato forecastg model to coordate the collaboratve forecastg process. hs Bayesa combato forecastg model ca mprove demad forecastg accuracy of supply cha. Keywords: Combato forecastg, Bayesa model, Supply cha. Itroducto Wth the developmet of formato ad etwork techology, varous ovatve supply cha solutos are created. Collaboratve plag, forecastg ad repleshmet (CPFR), whch s a retalg supply cha coordato ovato based o the etwork techology, has bee adopted ad mplemeted by may world-reowed retalers ad maufacturers, such as Wal-Mart, Proctor & Gamble, etc.. CPFR cocers the collaborato where two or more partes the supply cha jotly pla a umber of promotoal actvtes ad work out sychrozed forecasts, o the bass of whch the producto ad repleshmet processes are determed []. he frst CPFR project was ploted by Wal-Mart wth ts supplers 995. he results of two-year project showed that CPFR could smultaeously reduce vetory levels ad crease sales for both retalers ad supplers. Sce ts orgal applcato was tated, CPFR has had may successful applcatos North Amerca, Europe ad Cha []. he collaboratve forecastg plays a mportat part CPFR mplemetato procedure. We wll brefly revew the CPFR cocept ad ts mplemetato process at the begg of ths paper. Ad the, the collaboratve forecastg process whch s the core part of CPFR wll be maly dscussed. As the bascs phase of the mplemetato of CPFR, the collaboratve forecastg process s the corerstoe to the success of CPFR projects. he collaboratve forecastg process of CPFR requres a sold forecastg approach to sythess formato ad kowledge from multply partes the supply cha. he combato forecastg method ca combes

3 forecastg models from dfferet partes to smooth coordato the supply cha ad reduce forecastg dscrepaces. hus, cosderg the multple forms of forecastg resources the retal supply cha, the Bayesa combato forecastg method s appled for CPFR collaboratve forecastg modelg wth mproved forecastg accuracy ad supply cha collaborato performace ths paper. Combg forecasts s a well-establshed procedure for mprovg forecastg accuracy whch takes advatage of the avalablty of both multple formato ad computg resources for data tesve forecastg [3]. Sce Bates-Grager frst proposed the combato forecastg method 969 [4], may kds of combg methods have bee developed [3]. Zeg et al [5] studed the combato forecastg model wth error correcto ad chagg weght coeffcet. Hoogerhede et al [6] compared several Bayesa combato schemes terms of forecast accuracy ad ecoomc gas. Bayesa combato methods use the dstrbutoal propertes of the dvdual forecasts to costruct the combato. he demad forecastg retal supply cha s mpacted by may factors such as product promoto or socal developmet tred. Ad, subjectve forecastg based o the expert expermets s ofte used retal market forecastg. So, the Bayesa combato forecastg model s cosdered as the collaboratve forecastg approach retal supply cha coordato. I the frst part of ths paper, the CPFR retal supply cha coordato ad collaboratve forecastg process are dscussed brefly. I the secod part of the paper, a Bayesa combato forecastg method s modeled to coordate forecastg process retal supply cha. Fally, the smulato for ths model s completed based o the Carrefour sales data. he smulato results showed the effectve of ths Bayesa combato forecastg model retal supply cha collaborato process.. Bayesa Combato Forecastg Modelg for Collaboratve Forecastg Process he combato method proposed by Bates ad Brager 969 s ormally called as optmal lear combato model or B-G method. he forecastg results fc, fc f c are supposed as radom varables wth the covarace matrx ths model. Based o the mmzg the varace crtera (MV), the optmal forecastg results ca be calculated as the followg formula () f c W k k f k W f () Here,weghtg vector W ( ) ( W, W..., W ), (,,..., ). he Bayesa combato forecastg model s developed based o the B-G method ad uses the dstrbutoal propertes of the dvdual forecasts to costruct the combato. Supposed the Y s presetg the samples of actual demad. he forecastg results obtaed from the dfferet partes the supply cha whch are

4 forecasted wth m kds of dvdual forecastg methods are preseted by f, f, f m (j=,,,m).,,, preset dfferet forecastg tme perods. he Bayesa combato forecastg method makes use of the Bayesa rule to decde the optmal combato ways ad weghts of dvdual forecastg methods combato model ad get the combed forecastg results dfferet tme perods ˆ (,,, ), whch ca be fully approxmated to actual demad values. f c z Set f, f, f ),,,,, ad the the jot probablty desty ( m fucto of m dvdual forecastg samples o depedet tme be caculated as follows. z,, z, z ca I f ( z, z,, z Y; ) f ( z Y ; ) () Here s parameter vector, ad Y ( y, y,, y) s the vector of the actual demad samples o the dfferet forecastg tme perods. Accordg to the Bayesa rule, the probablty desty fucto that Y s specfed as a vector value y s as follows: f ( y z, z,, z ) A I f ( f A, f f ( f, f f ( z y ) f ( y ) f ( z y ) f ( y ) dy, f, f m m y ) f ( y ) y ) f ( y ) dy (3) Here f ( y )(,,, ) s the pror probablty dstrbuto of y, whch presets the pror estmato or preferece of decso maker to y. A s the defto set of y. If oly oe forecastg tme perod s cosdered as the geeral case ad pror f (y) dstrbuto s uform dstrbuto form, that s f ( y), the formula () ca be smplfed as the followg. f ( f, f, fm y) f ( y f, f,, fm) (4) f ( f, f, f y) dy A m

5 he forecastg error dstrbuto of dvdual forecastg results ( f, f, fm) s chose as ormal dstrbuto or logarthm ormal dstrbuto most case. I ths paper, more geeral dstrbuto of forecastg error s troduced through Box Cox coverso. Z ( ) 0 Z (5) l Z 0 Here, λ s coverso parameter Supposed s the covarace matrx of ( f, f, fm) ad W presets the weghts of dvdual forecastg f. he, weghts ca be calculated as followg formula based o the mmum error varace crtera: m m m W, W Wm W..., (6) Ad, olear combato forecastg formula ca be obtaed through Bayesa aalyss as follows, whch wll be used to calculate the optmal combato forecastg results approxmated to the actual values Y. m w s f e fˆ c m m ( W f W f ) 0 0 (7) Here,, m m m m ad W t S Ad, the optmal coverso parameter λ* ca be calculated as the followg formula. t arg m Y ( j j W f j ) (8) Here, f j preset the forecastg result o j tme perod by dvdual forecastg methods. he weghts W ca be calculated by formula (4). he covarace matrx ca be determed by pror value or estmated by past proxmate samples values.

6 3. Smulato he smulato of the Bayesa combato forecastg model wll be based o the sales data of oe kd of bscut product Carrefour Cha ths paper. he detaled sales data of ths bscut product 39 weeks Carrefour Cha s showed table. Durg the smulato process, the sales data from week to week 8 are used to estmate parameters Bayesa combato forecastg model creato. he sales data from week 9 to week 39 are used to compare wth the forecastg results obtaed from combato forecastg methods. able he Sales Data of Bscut Carrefour Supermarket Week Demad Week Demad Week Demad Based o the Carrefour bscut sale data ad statcs aalyss, the Bayesa forecastg model ca be created followg three ma steps, whch cludes proper dvdual forecastg methods selecto, combato ways determato ad optmal parameter estmato. he characterstcs of the dvdual forecasts combg the model has substatal mplcatos o the overall forecastg performace of model, ad thus t s very mportat to make a rgorous aalyss o the dvdual forecast errors. he frst step of combato modelg s to compare ad select proper dvdual forecastg methods for combato. able Forecastg Results of Fve Idvdual Forecastg Methods Week Actual Demad F F F3 F4 F

7 I geeral, dfferet partes the retal supply cha may use the dfferet patters of dvdual forecastg. So, the dfferet patters of dvdual forecastg methods, whch clude the smple movg average, the expoetal smoothg, the tred extrapolato method, ARIMA (autoregressve tegrated movg average) method ad artfcal eural etwork method, are appled to combe model to forecast Carrefour bscut demad from week 9 to week 39. hrough comparso study of forecastg results of each dvdual forecastg method, the best parameters of each dvdual forecastg method are estmated. he forecastg results of fve dfferet dvdual forecastg methods are dcated able. he F row data dcated the best result forecasted by the smple movg average method whe movg perod N equal to 3. he F row data dcated the best result forecasted by the expoetal smoothg method whe smoothg coeffcet a equal to 0.6. he F3 row data dcated the best result forecasted by the two polyomal regresso method (=). he F4 row data dcated the best result forecasted by the ARIMA method whe parameter d equal to. he F5 row data dcated the best result forecasted by the artfcal eural etwork method whe there are three euros ad two hdde layers the eural etwork. After the fve dvdual forecastg methods selected, the secod step of combato modelg s to determe proper combato ways of these dvdual methods. Wth the Matlab smulato tool, the forecastg results are calculated usg dfferet combato ways of these dvdual forecastg methods. As t s wdely accepted that oly ``good'' forecasts should be cluded a combato, strog dffereces forecast error varaces betwee the dvdual forecasts are ot to be expected [7]. Four dvdual methods (F F F4 F5) whch have good forecastg performace s decded to be combed to Bayesa combato model. he optmal coverso parameter λ * ca be calculated accordg to the formula (8). he sum of square of forecastg error s mmzed whe λ * = he optmal coverso parameter λ * could be smplfed as λ * =7 the Bayesa combato modelg. he forecastg error betwee forecastg result ad actual demad are used as the evaluato stadards of forecastg methods performace. here are may kds of measure dexes of forecastg errors [8]. I ths paper, four ma measure dexes of forecastg error, whch are the squares sum error (SSE), the mea square error (MSE), the mea absolute percetage error (MAPE) ad the mea square percetage error (MSPE), are appled to comprehesvely evaluate the forecastg accuracy of Bayesa combato forecastg model. able 3 he Comparso of Bayesa Combato Models Forecastg Accuracy Combato Forecastg SSE MSE MAPE MSPE Methods Smple Average Method.64E+04.40E Optmal Lear Method.5E+04.9E Bayesa Combato λ*=7.9e+03.74e he Bayesa combato models wth dfferet parameters λ are compared wth the smple average method ad optmal lear methods the smulato based

8 o Carrefour bscut sale data. he forecastg errors of dfferet combato forecastg methods are showed the table 3. It ca be foud that the four measure dexes of forecastg error of optmal Bayesa combato method whe λ * =7 are lower tha those of smple combato methods. So, the optmal Bayesa combato forecastg model performs better tha other combato models retal collaboratve forecastg process. hs smulato research proved that the optmal Bayesa combato forecastg method s a effectve approach to tegrate ad coordate the forecastg process amog parters retal supply cha. Bayesa combato forecastg method ca hghly mprove the demad forecastg accuracy of collaboratve forecastg actvty the retal supply cha. 4. Cocluso he collaboratve plag, forecastg ad repleshmet framework provdes the practcal roadmap for retal supply cha coordato. he collaboratve forecastg s take as the core part CPFR soluto mplemetato. A Bayesa combato forecastg method, whch ca combe dvdual forecastg methods from dfferet partes the retal supply cha, s modeled for CPFR collaboratve forecastg process. he smulato results showed that forecastg dscrepaces are reduced ad collaboratve forecastg accuracy s mproved after tegratg forecastg process wth the optmal Bayesa combato forecastg model. It s tured out that the Bayesa combato forecastg method s a effectve meas for collaboratve forecastg process retal supply cha. he further research o collaboratve forecastg methodology for supply cha coordato wll be exteded to dfferet statstc features of product demad stuato the future. Ackowledgmets. hs research was supported by a grat from the Shagha Scece Foudato Coucl (ZR400900) ad the Chese Natoal Scece Foudato Coucl (7774). Refereces. Lu, X., Su, Y., 0. Iformato Itegrato of CPFR Iboud Logstcs of Automotve Maufactures Based o Iteret of hgs. Joural of Computers, 7(): Daese, P., 007. Desgg CPFR collaboratos: sghts from seve case studes, Iteratoal Joural of Operatos & Producto Maagemet, 7(): Bu, D.W., 989. Forecastg wth more tha oe model. Joural of Forecastg, 8(3), Bates, J.M., Greager, C. W. J, 969. Combato of Forecasts, Operatoal Research Quarterly, 0(4): Zeg, Y., ag, X., Zheg, W., Combato forecastg based o Ste-rule

9 estmato ad error correcto, Joural of Maagemet Sceces Cha, 00,4 (6): Hoogerhede, L., Klej, R., Ravazzolo, F., Va Djk, H.K., Verbeek, M., Forecast Accuracy ad Ecoomc Gas from Bayesa Model Averagg Usg me-varyg Weghts, Joural of Forecastg, 00, 9(-): 5-69, 7. Meezes, L.M. de, Bu, D. W., aylor, J. W Revew of gudeles for the use of combed forecasts. Europea Joural of Operatoal Research, 0(): Zhag, C., Huag, L., Zhao, Z., 03. Research o combato forecast of port cargo throughput based o tme seres ad causalty aalyss. Joural of Idustral Egeerg ad Maagemet, 6():4-34