Empirical heuristics for improving Intermittent Demand Forecasting

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1 Empirical heuriic for improving Inermien Demand Forecaing Foio Peropoulo 1,*, Konanino Nikolopoulo 2, Georgio P. Spihouraki 1, Vailio Aimakopoulo 1 1 Forecaing & Sraegy Uni, School of Elecrical and Compuer Engineering, Naional Technical Univeriy of Ahen, Greece 2 The Buine School, Bangor Univeriy, Bangor, UK *correponding auhor Abrac Purpoe: Inermien demand appear poradically, wih ome ime period no even diplaying any demand a all. Even o, uch paern coniue coniderable proporion of he oal ock in many indurial eing. Forecaing inermien demand i a raher difficul ak bu of criical imporance for correponding co aving. The curren udy examine he empirical oucome of hree heuriic oward he modificaion of eablihed inermien demand forecaing approache. Deign/mehodology/approach: Fir, opimizaion of he moohing parameer ued in Croon approach i empirically explored, in conra o he ue of an a priori fixed value a in earlier udie. Furhermore, he effec of ineger rounding of he reuling foreca i conidered. Laly, we evaluae he performance of Thea model a an alernaive of SES eimaor for exrapolaing demand ize and/or inerval. The propoed heuriic are implemened ino forecaing uppor yem. Finding: The experimen i performed on 3,000 real inermien demand erie from he auomoive indury, while evaluaion i made boh in erm of bia and accuracy. Reul indicae increaed forecaing performance. Originaliy/Value: The curren reearch explore ome very imple heuriic which have a poiive impac on he accuracy of inermien demand forecaing approache. While, ome of hee iue have been parially explored in he pa, he curren reearch focue on a complee in-deph analyi of eay o employ modificaion o well eablihed inermien demand approache. By hi, we enable he applicaion of uch heuriic on an indurial environmen, which may lead ino ignifican invenory and

2 producion co reducion and oher benefi. Keyword: inermien demand; moohing parameer; rounding; hea mehod; empirical inveigaion 1. Inroducion Demand and invenory foreca are required for virually all deciion making iuaion regarding fuure even, from hor erm foreca dealing wih invenorie and cheduling o medium and long erm one needed for raegy and planning. Accurae foreca are of grea pracical imporance, linking invenory co wih revenue, cuomer aifacion, ock-ou co and lead ime (for example Huang e al., 2011). Inermien demand paern are characerized by infrequen demand arrival coupled wih variable demand ize, whenever demand occur. Inermien demand iem may be engineering pare par or oher iem wihin he range of produc offered by any organizaion and a any level of he upply chain. Spare demand creae ignifican problem in he manufacuring and upply environmen a far a forecaing i concerned. I i no only he variabiliy of he demand ize, bu alo he variabiliy of he inerval beween demand ha make inermien demand o difficul o foreca. If he fac ha low moving iem may coniue up o 60% of he oal ock in any indurial eing (Johnon e al., 2003) i alo aken ino accoun, i become obviou ha mall improvemen can inigae ubanial co aving. The curren udy examine hree empirical heuriic ued wih eablihed and commonly ued forecaing approache for inermien demand (Croon, 1972; Syneo and Boylan, 2001; Syneo, 2001). Firly, opimizaion iue, regarding he opimal moohing parameer ued, are looked ino. Secondly, an inuiively aracive and pracically indipenable heuriic i inveigaed: rounding of he final foreca, a all demand ize of SKU are whole number. Laly, an approach ha combine Croon mehod for inermien demand wih Thea model (Aimakopoulo and Nikolopoulo, 2000) i horoughly inveigaed. All hree heuriic reul in very promiing reul when applied o daa characerized by inermien demand paern, where he preence of zero demand i eviden. Taking ino accoun ha uch daa arie in many indurie, i come wihou aying ha he

3 curren reearch aim a improving eing and procedure by eay-o-implemen modificaion on convenional echnique. Furhermore, o our knowledge i i he fir ime ha he effecivene of independenly elecing he moohing value for he numeraor and he denominaor of each one of he erie, via a widely ued co funcion (MSE), i being empirically inveigaed. Laly, he full poenial of uilizing he Thea model in Croon framework for he exrapolaion of i componen i analyzed and dicued. The remainder of he curren paper i rucured a follow. Firly, a hor lieraure review on widely ued inermien demand forecaing echnique i preened a Secion 2, followed by he experimenal rucure of our reearch and he decripion of he daa e ued (Secion 3). Empirical reul regarding he hree heuriic examined are preened and dicued in Secion 4. The implemenaion of he propoed hree heuriic i explored in Secion 5, hrough a dedicaed forecaing uppor yem. Finally, ome managerial implicaion are menioned (Secion 6), while concluion are ummed up and avenue for fuure work are propoed in Secion Inermien demand forecaing approache Inermien demand daa or coun daa are frequenly oberved in indurial and invenory eing. William (1984) inroduced a number of claificaion rule in order for a pare par o be characerized a low moving, inermien or lumpy. According o Teuner and Sani (2009), i i no an eay ak o foreca inermien demand, baically due o i erraic, and omeime lumpy, naure. Neverhele, i i very urpriing ha o lile work ha been done on forecaing inermien demand daa (Gooijer and Hyndman, 2005), wih everal indurie and organizaion relying on he ingle exponenial moohing (SES) mehod in order o foreca demand in a rouine ock conrol yem (Brown, 1959). A fir hown by Croon (1972), he ue of SES generally lead o inappropriae ock level. A an alernaive, Croon propoed he decompoiion of he original inermien erie ino wo eparae erie. The fir one include all non-zero demand ize, while he econd erie coni of he repecive inerval beween wo conecuive non-zero demand. Each line i exrapolaed eparaely, while he final foreca i imply calculaed a a raio of he wo. Auming ẑ and pˆ o be he foreca of demand ize and inerval, repecively, for period, Croon foreca i given by:

4 z Yˆ ˆ pˆ In fac, laer reearch in hi field i heavily baed on hi ingle reearch by Croon. Willemain e al. (1994) and Johnon and Boylan (1996) have underaken accuracy comparion beween SES and Croon mehod, demonraing he uperioriy of he laer, epecially when he inerval beween demand exceed 1.25 ime he updae period. Syneo and Boylan (2001) proved ha Croon mehod i poiively biaed. Toward he correcion of hi behavior, hey propoed a modificaion of he original Croon mehod (Syneo and Boylan, 2005), beer known a Syneo and Boylan Approximaion (SBA). Thi new eimaor i given by: Yˆ a zˆ 1 2 pˆ where a i he value of he exponenial moohing conan ued in he exrapolaion of he inerval erie. Syneo, in hi PhD Thei (2001), propoed anoher unbiaed eimaor, which can be obained a follow: ˆ a zˆ Y 1 2 a pˆ 2 Previou empirical udie (Syneo and Boylan, 2001) have hown ha he biaed behavior of Croon mehod i more apparen in he cae of daa wih high inermiency (i.e. many period wih zero demand) when high moohing value (a) are ued. A a reul, Croon mehod i no recommended o be ued wih a value above Thi reul wa verified by Teuner and Sani (2009), who analyzed he circumance under which Croon mehod and SBA approach end o be biaed. According o heir finding, Croon original mehod preen maller bia if few demand are zero, wherea SBA modificaion ha a maller bia if many demand are zero. Moreover, i i argued ha foreca derived from Syneo mehod are ouperformed in erm of forecaing variance by he SB mehod (Syneo, 2001; Teuner and Sani, 2009). Teuner and Sani (2009) ugge he ue of Syneo mehod a an alernaive o Croon and SBA mehod, bu heir finding are only baed on imulaed daa. In all hree cae, he demand ize and inerval are exrapolaed uing SES, while foreca are updaed only in period wih poiive demand. The eimae of he demand under he SES mehod i given by (Makridaki e al., 1998):

5 Yˆ ˆ ˆ i 1 Y ( Y Y ) (1 ) i0 Alhough a-moohing value in he range [ ] are viewed a realiic (Croon, 1972; Willemain e al., 1994; Johnon and Boylan, 1996), mo of he empirical udie inveigaing inermien demand aumed a conan value for a. The ue of a moohing conan i no a uual echnique in fa moving erie, where an opimizaion procedure ake place oward he elecion of an opimal moohing parameer which minimize he in-ample MSE. Moreover, Snyder (2002) argued for he ue of differen moohing parameer for he demand ize and inerval, a well a propoed he ue of oher compaible model and mehod. Recen reearch on inermien demand forecaing ha focued, oher han forecaing performance in erm of accuracy, on he variabiliy of inermien demand eimae (Syneo and Boylan, 2010), he imporance of invenory obolecence (Teuner e al., 2011) and invenory performance under differen ype of informaion haring (Ali e al., 2012). Anoher new reearch roue ha been he emporal, non-overlapping aggregaion of inermien demand daa ino ime bucke o ha he reuling erie are more likely o be non-inermien. Thi echnique ha proven o be very promiing in erm of forecaing accuracy (Nikolopoulo e al., 2011) and cuomer ervice level (Babai e al., 2012). However, depie any reearch during he la 40 year, Croon mehod i very ofen applied in pracice (Filde e al., 2008) and incorporaed in commercial forecaing uppor yem. A a reul, eay-o-apply modificaion on he original framework ha will lead in performance improvemen are conidered a beneficial. Y i 3. Empirical Daa & Experimenal Srucure The empirical daabae ued for he purpoe of our reearch coni of he individual monhly demand hiorie of 3,000 SKU from he auomoive indury, over wo year (24 conecuive monhly demand obervaion). The ame daabae ha been ued in earlier udie (Syneo and Boylan, 2005; Syneo e al., 2005). Deailed decripive aiic (o he econd decimal place) on he demand daa erie characeriic are preened in Table 1. I i worh menioning ha he daa in hand are conidered a fa inermien, where he inermien demand inerval are a any ime le han 2, wih

6 a median value a The low degree of inermience in hi daa e i coupled wih low demand ize wih low degree of variance. A a reul, he daa e i conidered uiable a i conain erie falling in all four clae of demand, according o Syneo e al. (2005): erraic, lumpy, mooh or inermien. A he ame ime, he empirical daa are no o be relaed wih iue regarding variabiliy of he eimae and invenory obolecence. Thi empirical daae will no heavily affec he biaed behavior of he Croon mehod, due o i low degree of inermiency. 3,000 Demand Size Demand Inerval Demand per period SKU Mean SDev Mean SDev Mean SDev Min % ile Median % ile Max Table 1. Demand daa decripive aiic For he imulaion purpoe of he curren reearch we held ou he la 11 obervaion of each erie, iniializing all mehod over he fir 13 period. We performed a liding imulaion (rolling evaluaion) over he ou-of-ample daa via producing one-epahead foreca; hu we calculaed 11 one-ep-ahead error for each erie, for each of he forecaing mehod conidered. The evaluaion of he reul wa performed by meauring he bia and accuracy of he examined mehod. Mean Error (ME) offer a way o deermine if an examined mehod i conienly poiively or negaively biaed, depending on he ign of he reuling value. ME can be calculaed acro all erie uing he following equaion: where Y and 1 mean( ME) n h n h Y Yˆ 1 1 Yˆ are he acual and foreca value, repecively, of erie a ime period, n i he oal number of erie conidered and h i he number of ou-of-ample period (horizon), hu n=3,000 and h=11. Accordingly, accuracy wa calculaed uing average value of Mean a well a Median Abolue Scaled Error (MASE and MdASE repecively, Hyndman and Koehler, 2006). Thee wo meric are widely applicable, cale independen and eay o inerpre: value of MASE greaer han one indicae ha

7 foreca are wore, on average, han in-ample one ep foreca of he Naive mehod. The average value of MASE and MdASE are given by: 1 mean( MASE ) n h 1 mean( MdASE ) n n 1 n h n 1 Y k i1 Y median 1 n 1 where k i he number of in-ample period, hu k=13. Three eimaor were ued in erm of benchmarking: Naive, SES and Simple Moving Yˆ k Y i2 i Yˆ Y Y i i1 Y Average (SMA). Naive foreca are equal o he la acual demand, o: Yˆ 1 Y SES foreca were generaed uing a conan level moohing parameer, equal o La, SMA a lengh of 13 period wa ued becaue hi wa he eimaion procedure employed by he ofware manufacurer ha provided he empirical daa erie ued in hi reearch (Syneo and Boylan, 2005). The eimae of he demand under he SMA(13) i given by: 13 1 Yˆ Y 13 i1 i i1 4. Empirical Inveigaion & Dicuion Bia and accuracy reul for he hree benchmark are repored in Table 2. Reul for inermien demand mehod are alo preened, when a moohing conan in he range [ ] i eleced, he ame for demand ize and inerval. Overall, he mo unbiaed mehod for he examined daae would be SBA mehod wih a=0.05, followed by Naïve and SES. Boh in Croon and SBA mehod, an increae in value of he a moohing conan lead o a greaer abolue value of ME, reuling in more biaed foreca. ME for Croon mehod i negaive, denoing a poiively biaing behavior, wherea in he cae of SBA he bia ha a negaive direcion. In erm of accuracy, SBA core he lowe value for MASE and MdASE, a a=0.15 and 0.2, repecively. I i worh noing ha, in conra o bia, increaed value of a moohing conan have a poiive effec on he meaured (via MdASE) accuracy for boh Croon

8 and SBA mehod. Furhermore, we hould alo noe he overall good performance of SES mehod, which cored he ame accuracy level wih SBA a a=0.05. Empirical reul of Table 2 indicae ha Syneo mehod i no uiable for he examined daa, being ouperformed from Croon and SBA in erm of boh bia and accuracy. A a reul, furher analyi of he curren reearch i baically baed on he performance of he laer mehod. Mehod BIAS ACCURACY ME MASE MdASE Naive E-04 SMA(13) E-04 SES(0.05) E-04 Croon(0.05) E-04 Croon(0.1) E-04 Croon(0.15) E-04 Croon(0.2) E-04 SBA(0.05) E-04 SBA(0.1) E-04 SBA(0.15) E-04 SBA(0.2) E-04 Syneo(0.05) E-04 Table 2. Reul of benchmark and andard inermien demand mehod 4.1. Opimizing a moohing parameer The fir heuriic of our reearch examine he opimizaion of a moohing parameer, raher han uing a conan value for demand ize and inerval acro all erie. A linear opimizaion procedure ake place, where all value in he range [ ] are examined eparaely uing a ep of 0.01, and he one minimizing he in-ample MSE i eleced a he opimal, reuling in differen a value for each erie. The value of he in-ample MSE i given by: 1 MSE k k Y Yˆ 1 Thi linear opimizaion i a common pracice for fa moving erie, where moohing parameer are eleced in order o be fi he in-ample foreca model. In hi cae, 2

9 he opimizaion procedure i applied direcly and excluively o he decompoed erie, i.e. he demand ize and inerval, which may lead o differen opimal a value, a uggeed by Snyder (2002). Mehod BIAS ACCURACY ME MASE MdASE Croon( opimal a) E-04 SBA( opimal a) E-04 Syneo( opimal a) E-04 Table 3. Opimizing a moohing value The reul of hi empirical heuriic for each inermien demand mehod (Croon, SBA and Syneo) are preened in Table 3. In erm of accuracy, he reul are almo idenical wih hoe of he implemenaion of he mehod where conan a moohing value i e equal o 0.05 acro all erie. However, here i a ignifican reducion of he value of ME meric in he cae of SBA mehod. The calculaed bia drop o 0.021, which mean a 25% error improvemen. There i however no ignifican evidence ha opimizaion benefi Croon and Syneo mehod. Demand Inerval a-value (numeraor) (denominaor) % % 13 in-ample % % obervaion % % % % 18 in-ample % % obervaion % % % % 23 in-ample % % obervaion % % Table 4. Diribuion of opimal a-value Table 4 preen he diribuion of he opimal a-value for boh demand and inerval in hree inance of he rolling procedure. In more deail, he number of ime erie elecing a opimal a-value in he range [ ], [ ] and [ ] along wih he relevan

10 percenage are demonraed. The hree inance conidered in hi analyi were compleed by 13, 18 and 23 in-ample obervaion repecively. A cloe obervaion of Table 4 make i clear ha maller value of a are generally eleced (inide he range [ ]), epecially in he cae of hor available hiory. A more obervaion become available, opimizaion enable a elecive choice of greaer a-value a well, for up o 17% of he ime erie The effec of rounding When forecaing SKU, providing decimal foreca value doe no make much ene. Thi imple idea lead u o round he produced foreca o ha he reporing value would be whole number. Table 5 preen he reul of he rounding effec, when indicaive implemenaion of inermien demand mehod are ued. In comparion wih Table 2, he bia meaured in all cae i almo a he ame level (if no even lower). Furhermore, here are noable improvemen in erm of accuracy, a compued via MASE, where he calculaed foreca are approximaely 2% more accurae for all mehod eed. Mehod BIAS ACCURACY ME MASE MdASE Croon(0.1, Round) E-04 SBA(0.1, Round) E-04 SBA(0.2, Round) E-04 Syneo(0.05, Round) E-04 Table 5. Rounding SKU foreca 4.3. Combining Croon mehod wih Thea model The ue of SES mehod in order o exrapolae he decompoed Croon erie ha been criicized in many udie (ee for example Snyder, 2002). We conider he ue of an alernaive, modern forecaing echnique, he Thea model (he winner of M3 forecaing compeiion, Makridaki and Hibon, 2000), inroduced by Aimakopoulo and Nikolopoulo (2000). Thea mehod decompoe he original erie in wo (or more) eparae erie (he o-called hea line), whoe primary qualiaive characeriic i he beer approximaion of he long-erm behavior of he daa or he augmenaion of hor-erm feaure, depending on he value of he Thea coefficien.

11 Thee hea line are exrapolaed eparaely. A he curren udy, we implemen he Claic Thea model, a a hree ep procedure: 1. Each ime-erie i decompoed ino wo Thea line, he linear regreion line (which i referred alo a Thea Line (Θ=0)) and he Thea Line (Θ=2), which i calculaed a follow: TheaLine( 2) 2Y LRL Where Y refer o he -h acual obervaion of he raw daa, while LRL denoe he -h obervaion of he linear regreion line, expreing he linear relaionhip beween raw daa and ime. 2. The linear regreion line i exrapolaed in he uual way while he econd line i exrapolaed via Single Exponenial Smoohing. 3. The foreca produced from he exrapolaion of he wo line are combined wih equal weigh. Thu, we inveigae he ue of Thea model, which can replace SES mehod in eiher numeraor or denominaor of Croon raio, or even in boh. Originally, he combinaion of Croon wih Thea wa propoed by Nikolopoulo e al. (2007), where Thea model wa applied ju for he exrapolaion of he demand ize (numeraor). The inuiion for uing hi combinaion wa ha Croon-Thea could pick up rend of non-aionary erie, hu diplaying more poen predicive power. Mehod BIAS ACCURACY ME MASE MdASE Croon-Thea(0.05, Num & Denom) E-04 Croon-Thea( opimal a, Num & Denom) E-04 Croon-Thea( opimal a, Denom) E-04 Croon-Thea( opimal a, Num) E-04 Croon-Thea(0.05, Num) E-04 Croon-Thea(0.05, Num, Round) E-04 Table 6. Combining Croon wih Thea The reul of Croon-Thea combinaion are preened in Table 6. Each row of he able diplay he reul for a eparae implemenaion of he approach, in erm of he eleced a moohing value (0.05 or opimal, a dicued in Subecion 4.1), he level a which Thea wa applied (numeraor, denominaor or boh) and, la, he applicaion

12 (or no) of he rounding heuriic (a dicued in Subecion 4.2) a he final foreca. The reul indicae ignifican improvemen in erm of bia, when Thea model i ued for he exrapolaion of inerval (denominaor). Specifically Croon- Thea( opimal a, Denom) implemenaion ha he be bia performance in comparion o all oher implemenaion preened in he curren udy, wih an improvemen cloe o 50% from he econd be implemenaion (SBA( opimal a)). On he oher hand, he Croon-Thea combinaion doe no pay back in erm of accuracy. The reul indicae wore ou-of-ample accuracy performance han he inample accuracy under Naïve, when Thea model i applied o he denominaor. Laly, he rounding effec eem o work once again a a imple elf-improvemen heuriic, offering noable improvemen in he reuling accuracy meric, while keeping he bia level conan. The moderae performance of Croon-Thea combinaion in erm of accuracy could be inerpreed a lack of he rend componen in he examined empirical daae. Even if he rend componen i almo zero for he majoriy of inermien demand erie, he preence of a deerminiic rend would coniderably favor he ue of Thea model over SES Dicuion The ue of differen moohing parameer for he demand and inerval ha been previouly uggeed (Snyder, 2002). However, appropriaely chooing moohing value independenly for he numeraor and he denominaor of each one of he erie, via a widely ued co funcion (MSE), ha no been previouly propoed nor inveigaed. In fac, hi pracice drive in coniderable gain in erm of bia, while a he ame ime no negaive impac on accuracy are recorded. The mo imporan obervaion, however, derive from comparing Table 2 and 3. I i prey clear, ha a he aic value of he moohing parameer (a) raie from 0.05 o 0.20, here i a ignifican deerioraion of he bia meric (meaured a ME). However, elecing he mo uiable moohing value independenly for each erie, hrough minimizing inample error, lead o ignificanly beer reul (up o 25%). Thi pracically mean ha he ue of a co funcion for elecing he be moohing parameer per erie can make a difference. In many indurial applicaion, epecially hoe involving ime erie of pare par or SKU, non-ineger poin foreca are conidered a non realiic. The impac of rounding he final poin foreca derived from inermien demand mehod are

13 empirically examined in hi reearch. The mo ignifican reul i ha hi echnique reul in beer accuracy level (up o 2%) while a he ame ime no deerioraion in erm of bia i recorded. A a reul, we rongly recommend he ue of hi heuriic, which i regarded a appealing in boh empirical and pracical erm. Finally, an alernaive o he radiional Croon mehod wa examined in Subecion 4.3. Originally, Croon propoed he ue of SES a he exrapolaion procedure for boh decompoed erie (demand and inerval). Given ha boh decompoed erie repreen equence of non-zero value, we conider, for he fir ime, he full poenial of uing if he Thea model a he exrapolaion echnique of eiher he nominaor, denominaor or boh. In fac, he choice of hi model lie in i uperior performance, a recorded in pa major inernaional forecaing compeiion. Thi imple echnique allow Croon framework ac almo in an unbiaed way (improvemen up o 90% from he original approach), when Thea model i ued for he exrapolaion of he inerval beween non-zero demand. 5. The forecaing uppor yem (FSS) In many applicaion, aiical foreca are produced via dedicaed and auonomou forecaing uppor yem (FSS). Thi direcion erve muliple purpoe. Firly, manager and praciioner may no be familiar wih he neceary aiical background. Secondly, an auomaed FSS can handle, pre-proce and foreca houand of ime erie (ale or order for SKU) in ju a few econd. Laly, many feaure of he modern FSS, uch a aiical analyi, handling he impac of pecial period and inegraion of judgmenal inervenion, are regarded a neceary o he forecaing proce of any indury. The need of he empirical analyi of he curren reearch led u o he deign and developmen of a unique and dedicaed forecaing uppor yem for handling daa of inermien naure. The purpoe of he curren ecion i o give he general guideline oward he implemenaion of a FSS ha fully implemen he propoed heuriic analyzed in he curren reearch, o enabling he manager o have direc acce o any gain derived hrough heir pracice in any manufacuring or indurial eing. Moreover, we aim o give inigh o praciioner already uilizing cuomized ofware a o which direcion of addiional implemenaion or exernal module hould hey arge for exploiing hee heuriic.

14 The Inermien Demand Forecaing Syem (IDFS) wa deigned following a hreeier phyical archiecure (viualizaion, aiical/buine and daa). The main advanage of hi archiecure i ha i i eaily erviceable and expandable. The fir layer of he archiecure i he uer inerface, where boh graphical and numerical inerpreaion of he daa and he reul are diplayed. Furhermore, hi layer enable uer oward a deailed elecion of he parameer relaed o he forecaing proce (forecaing mehod, horizon, hold-ou ample, error meric), along wih he uage of he hree heuriic preened in hi paper. Figure 1 and Figure 2 how wo ypical creen diplay of he propoed yem. The econd layer i he aiical/buine ier. All he aiical and mehodological procedure are modeled and implemened in he middle layer, which include he funcion relaed o he forecaing proce. Thi layer include all original forecaing mehodologie (for example SES, Thea model, Croon, SBA and Syneo) and alo allow mehod o inerac wih each oher (for example, oward he formaion of Croon-Thea). Addiional adjumen, uch a he ue of opimized over conac moohing value or he rounding of he final foreca, are paing a exernal variable, hrough he ineracion wih he fir layer. In addiion, a middle ier i ued o creae he bae for furher exenion wih exernal ofware, encompaing inerface, wrapper and web-ervice neceary for daa exchange. Laly, he hird layer coni of he daa ier of he applicaion. The daa bae managemen yem (daabae, view and relaion) i lying on he daa bae erver, a window-baed machine iolaed from he inerne in order o avoid hrea and provide aifacory repone ime. The daa layer provide he aiic/buine layer wih he required hiorical daa and ore any foreca and accuracy reul.

15 Figure 1. Graphical viualizaion of he inpu daa and parameer iniializaion Figure 2. Forecaing mehod/parameer and graphical inerpreaion of he empirical reul

16 IDFS wa developed uing Microof Viual Baic.NET 2008 while he Dunda Char, for Viual Baic.NET, wa employed for he yem implemenaion, in regard o i advanced charing funcionaliy and uperior graphic opion. Finally, he Microof SQL Server 2008 R2 daabae i uilized by IDFS o ore and rerieve he required informaion for he daa analyi and forecaing. 6. Managerial Implicaion Heuriic linked wih he impliciy of preadhee are conidered managerial appealing and flexible, epecially in he cae of low-moving iem and when dealing wih problem of differen ize (Hummel and Jee, 1990). A a reul, opimizing a moohing parameer and rounding final foreca eem alo o be inereing from a managerial poin of view. Boh heuriic can eaily be implemened by manager and praciioner, while offering noable gain regarding accuracy and/or bia. To begin wih, opimizing procedure for moohing parameer of exponenial moohing mehod are implemened and auomaed in major forecaing package. In ha ene, hee procedure can eaily be employed in a pracical invenory eing, reuling in ubanial improvemen for he bia of SBA eimaor (up o 25%), while coring good accuracy level (compared o SBA(0.05) implemenaion). Moreover, he ak of rounding he final foreca derived from any inermien demand mehod can be eaily done by ue of ordinary preadhee. Thi imple heuriic offer remarkable improvemen in meaured forecaing accuracy, keeping, a he ame ime, bia a lower level. Foreca for inermien demand SKU call for rounding, o a o make foreca inerpreable and direcly uable for real upply chain managemen applicaion, uch a order placemen. 7. Concluion & Perpecive The curren udy examined he empirical effecivene of hree empirical heuriic oward he modificaion of commonly ued forecaing approache for inermien demand. We propoed he ue of non-conan a moohing parameer, via elecing he be a value for each erie hrough in-ample opimizaion. Moreover, hee value may be differen for he demand ize and he inerval (Snyder, 2002). The ue of SES mehod for he exrapolaion of he decompoed erie in Croon framework i alo examined. We conidered a an alernaive he Thea model, a echnique ha

17 ouperformed all exponenial moohing mehod in he M3 forecaing compeiion. Laly, an inuiively appealing heuriic, concerning he rounding of he final foreca, wa propoed. The reul indicae ha opimal elecion of a moohing value reul in almo idenical accuracy level, while in ome cae here are ignifican improvemen on he bia. Thu, model opimizaion i feaible and doe pay back. Rounding eem o work urpriingly well, offering noable improvemen in erm of accuracy and keeping bia conan. Thee reul render hi imple heuriic uiable in cae of daa e coniing of SKU. Croon-Thea performance wa moderae, a i performed well a far a bia i concerned, bu eemed problemaic in erm of accuracy. A la, a pecialized FSS for inermien demand daa wa propoed. Furher reearch hould involve he ineracion of he rounding heuriic from a heoreical poin of view. Moreover, all experimen of hi udy could be replicaed wih differen daa e, o a o reach more general concluion abou he hree propoed heuriic. Specifically, he Croon-Thea combinaion hould be eed horoughly wih imulaed and field rended daa. Finally, i i recenly argued (Syneo e al., 2010) ha in an invenory forecaing eing exrapolaion mehod hould no only be evaluaed wih repec o heir foreca accuracy bu alo in erm of heir ock conrol implicaion, a meaured hrough accuracy implicaion meric (uch a invenory co and ervice level achieved). Exploring he effec of he examined heuriic on ock conrol i an inereing line for furher reearch and cerainly worhwhile puruing from a praciioner perpecive. Reference Ali M.M., Boylan J.E. and Syneo A.A. (2012), Foreca error and invenory performance under foreca informaion haring, Inernaional Journal of Forecaing, Vol. 28, pp Aimakopoulo V. and Nikolopoulo N. (2000), The hea model: a decompoiion approach o forecaing, Inernaional Journal of Forecaing, Vol. 16, pp Babai M.Z., Ali M.M. and Nikolopoulo K. (2012), Impac of emporal aggregaion on ock conrol performance of inermien demand eimaor: Empirical analyi, Omega, Vol. 40, pp Brown R. (1959) Saiical Forecaing for Invenory Conrol, McGraw-Hill, New York. Croon J.D. (1972), Forecaing and Sock Conrol for Inermien Demand, Operaional Reearch Quarerly, Vol. 23, pp

18 De Gooijer J.G and Hyndman R.J. (2005), 25 year of ime erie forecaing, Inernaional Journal of Forecaing, Vol. 22, pp Filde R., Nikolopoulo K., Crone S.F. and Syneo A.A. (2008) Forecaing and operaional reearch: A review, Journal of he Operaional Reearch Sociey, Vol. 59, pp Huang L.T., Hieh I.C. and Farn C.K. (2011), On ordering adjumen policy under rolling foreca in upply chain planning, Compuer and Indurial Engineering, Vol. 60, pp Hummel J.W. and Jee R.R. (1990), A preadhee heuriic approach for he ocking and reenion of low-moving, obolecen iem, Compuer and Indurial Engineering, Vol. 18, pp Hyndman R.J. and Koehler A.B. (2006), Anoher look a meaure of foreca accuracy, Inernaional Journal of Forecaing, Vol. 22, pp Johnon F.R. and Boylan J.E. (1996), Forecaing inermien demand: A comparaive evaluaion of Croon mehod, Inernaional Journal of Forecaing, Vol. 12, pp Johnon F.R., Boylan J.E. and Shale E.A. (2003), An examinaion of he ize of order from cuomer, heir characerizaion and he implicaion for invenory conrol of low moving iem, Journal of he Operaional Reearch Sociey, Vol. 54, pp Makridaki S., Wheelwrigh S.C. and Hyndman R.J. (1998), Forecaing: Mehod and Applicaion (3rd ed.), Wiley, New York, NY. Makridaki S. and Hibon M. (2000), The M3-Compeiion: reul, concluion and implicaion, Inernaional Journal of Forecaing, Vol. 16, pp Nikolopoulo K., Syneo A.A. and Babai M.Z. (2007), A new inermien demand approach via combining Croon mehd and he Thea model, paper preened a he 22nd European Conference on Operaional Reearch EURO XXII, July 8-11, 2007, Prague, Czech Republic. Nikolopoulo K., Syneo A.A., Boylan J.E., Peropoulo F. and Aimakopoulo V. (2011), An aggregae diaggregae inermien demand approach (ADIDA) o forecaing: an empirical propoiion and analyi, Journal of he Operaional Reearch Sociey, Vol. 62, pp Snyder R. (2002), Forecaing ale of low and fa moving invenorie, European Journal of Operaional Reearch, Vol. 140, pp Syneo A.A. and Boylan J.E. (2001), On he bia of inermien demand eimae, Inernaional Journal of Producion Economic, Vol. 71, pp Syneo A.A. (2001), Forecaing for Inermien Demand. Brunel Univeriy: Unpublihed Ph.D hei. Syneo A.A. and Boylan J.E. (2005), The accuracy of inermien demand eimae, Inernaional Journal of Forecaing, Vol. 21, pp Syneo A.A., Boylan J.E. and Croon J.D. (2005), On he caegorizaion of demand paern, Journal of he Operaional Reearch Sociey, Vol. 56, pp

19 Syneo A.A and Boylan J.E. (2010), On he variance of inermien demand eimae, Inernaional Journal of Producion Economic, Vol. 128, pp Syneo A.A., Nikolopoulo K. and Boylan J.E. (2010), Judging he judge hrough accuracy-implicaion meric: he cae of invenory forecaing, Inernaional Journal of Forecaing, Vol. 26, pp Teuner R. and Sani B. (2009), On he bia of Croon forecaing mehod, European Journal of Operaional Reearch, Vol. 194, pp Teuner R.H., Syneo A.A. and Babai M.Z. (2011), Inermien demand: Linking forecaing o invenory obolecence, European Journal of Operaional Reearch, Vol. 214, pp Willemain T.R., Smar C.N., Shockor J.H. and DeSauel P.A. (1994), Forecaing inermien demand in manufacuring: A comparaive evaluaion of Croon mehod, Inernaional Journal of Forecaing, Vol. 10, pp William T.M. (1984), Sock conrol wih poradic and low-moving demand, Journal of he Operaional Reearch Sociey, Vol. 35, pp

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