Empirical heuristics for improving Intermittent Demand Forecasting


 Bennett Heath
 1 years ago
 Views:
Transcription
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 indeph 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, ockou 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 eayoimplemen 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 nonzero demand ize, while he econd erie coni of he repecive inerval beween wo conecuive nonzero 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 amoohing 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 inample 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, nonoverlapping aggregaion of inermien demand daa ino ime bucke o ha he reuling erie are more likely o be noninermien. 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, eayoapply 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 ouofample daa via producing oneepahead foreca; hu we calculaed 11 oneepahead 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 ouofample 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 inample 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 inample 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 E04 SMA(13) E04 SES(0.05) E04 Croon(0.05) E04 Croon(0.1) E04 Croon(0.15) E04 Croon(0.2) E04 SBA(0.05) E04 SBA(0.1) E04 SBA(0.15) E04 SBA(0.2) E04 Syneo(0.05) E04 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 inample MSE i eleced a he opimal, reuling in differen a value for each erie. The value of he inample 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 inample 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) E04 SBA( opimal a) E04 Syneo( opimal a) E04 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 avalue (numeraor) (denominaor) % % 13 inample % % obervaion % % % % 18 inample % % obervaion % % % % 23 inample % % obervaion % % Table 4. Diribuion of opimal avalue Table 4 preen he diribuion of he opimal avalue for boh demand and inerval in hree inance of he rolling procedure. In more deail, he number of ime erie elecing a opimal avalue 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 inample 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 avalue 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) E04 SBA(0.1, Round) E04 SBA(0.2, Round) E04 Syneo(0.05, Round) E04 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 ocalled hea line), whoe primary qualiaive characeriic i he beer approximaion of he longerm behavior of he daa or he augmenaion of horerm 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 imeerie 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 CroonThea could pick up rend of nonaionary erie, hu diplaying more poen predicive power. Mehod BIAS ACCURACY ME MASE MdASE CroonThea(0.05, Num & Denom) E04 CroonThea( opimal a, Num & Denom) E04 CroonThea( opimal a, Denom) E04 CroonThea( opimal a, Num) E04 CroonThea(0.05, Num) E04 CroonThea(0.05, Num, Round) E04 Table 6. Combining Croon wih Thea The reul of CroonThea 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 CroonThea combinaion doe no pay back in erm of accuracy. The reul indicae wore ouofample 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 elfimprovemen heuriic, offering noable improvemen in he reuling accuracy meric, while keeping he bia level conan. The moderae performance of CroonThea 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, nonineger 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 nonzero 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 nonzero 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, preproce 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, holdou 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 CroonThea). 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 webervice 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 windowbaed 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 lowmoving 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 nonconan a moohing parameer, via elecing he be a value for each erie hrough inample 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. CroonThea 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 CroonThea 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, McGrawHill, 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 lowmoving, 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 M3Compeiion: 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 811, 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 accuracyimplicaion 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 lowmoving demand, Journal of he Operaional Reearch Sociey, Vol. 35, pp
A Comparative Study of Linear and Nonlinear Models for Aggregate Retail Sales Forecasting
A Comparaive Sudy of Linear and Nonlinear Model for Aggregae Reail Sale Forecaing G. Peer Zhang Deparmen of Managemen Georgia Sae Univeriy Alana GA 30066 (404) 6514065 Abrac: The purpoe of hi paper i
More informationFortified financial forecasting models: nonlinear searching approaches
0 Inernaional Conference on Economic and inance Reearch IPEDR vol.4 (0 (0 IACSIT Pre, Singapore orified financial forecaing model: nonlinear earching approache Mohammad R. Hamidizadeh, Ph.D. Profeor,
More informationEquity Valuation Using Multiples. Jing Liu. Anderson Graduate School of Management. University of California at Los Angeles (310) 2065861
Equiy Valuaion Uing Muliple Jing Liu Anderon Graduae School of Managemen Univeriy of California a Lo Angele (310) 2065861 jing.liu@anderon.ucla.edu Doron Niim Columbia Univeriy Graduae School of Buine
More informationHow has globalisation affected inflation dynamics in the United Kingdom?
292 Quarerly Bullein 2008 Q3 How ha globaliaion affeced inflaion dynamic in he Unied Kingdom? By Jennifer Greenlade and Sephen Millard of he Bank Srucural Economic Analyi Diviion and Chri Peacock of he
More informationCHAPTER 11 NONPARAMETRIC REGRESSION WITH COMPLEX SURVEY DATA. R. L. Chambers Department of Social Statistics University of Southampton
CHAPTER 11 NONPARAMETRIC REGRESSION WITH COMPLEX SURVEY DATA R. L. Chamber Deparmen of Social Saiic Univeriy of Souhampon A.H. Dorfman Office of Survey Mehod Reearch Bureau of Labor Saiic M.Yu. Sverchkov
More informationForecasting, Ordering and Stock Holding for Erratic Demand
ISF 2002 23 rd o 26 h June 2002 Forecasing, Ordering and Sock Holding for Erraic Demand Andrew Eaves Lancaser Universiy / Andalus Soluions Limied Inroducion Erraic and slowmoving demand Demand classificaion
More informationHeat demand forecasting for concrete district heating system
Hea demand forecaing for concree diric heaing yem Bronilav Chramcov Abrac Thi paper preen he reul of an inveigaion of a model for horerm hea demand forecaing. Foreca of hi hea demand coure i ignifican
More informationTopic: Applications of Network Flow Date: 9/14/2007
CS787: Advanced Algorihm Scribe: Daniel Wong and Priyananda Shenoy Lecurer: Shuchi Chawla Topic: Applicaion of Nework Flow Dae: 9/4/2007 5. Inroducion and Recap In he la lecure, we analyzed he problem
More informationNew Evidence on Mutual Fund Performance: A Comparison of Alternative Bootstrap Methods. David Blake* Tristan Caulfield** Christos Ioannidis*** and
New Evidence on Muual Fund Performance: A Comparion of Alernaive Boorap Mehod David Blake* Trian Caulfield** Chrio Ioannidi*** and Ian Tonk**** June 2014 Abrac Thi paper compare he wo boorap mehod of Koowki
More informationCalculation of variable annuity market sensitivities using a pathwise methodology
cuing edge Variable annuiie Calculaion of variable annuiy marke eniiviie uing a pahwie mehodology Under radiional finie difference mehod, he calculaion of variable annuiy eniiviie can involve muliple Mone
More information6.003 Homework #4 Solutions
6.3 Homewk #4 Soluion Problem. Laplace Tranfm Deermine he Laplace ranfm (including he region of convergence) of each of he following ignal: a. x () = e 2(3) u( 3) X = e 3 2 ROC: Re() > 2 X () = x ()e d
More informationReporting to Management
CHAPTER 31 Reporing o Managemen Inroducion The success or oherwise of any business underaking depends primarily on earning revenue ha would generae sufficien resources for sound growh. To achieve his objecive,
More informationA Note on Using the Svensson procedure to estimate the risk free rate in corporate valuation
A Noe on Using he Svensson procedure o esimae he risk free rae in corporae valuaion By Sven Arnold, Alexander Lahmann and Bernhard Schwezler Ocober 2011 1. The risk free ineres rae in corporae valuaion
More informationRobust Bandwidth Allocation Strategies
Robu Bandwidh Allocaion Sraegie Oliver Heckmann, Jen Schmi, Ralf Seinmez Mulimedia Communicaion Lab (KOM), Darmad Univeriy of Technology Merckr. 25 D64283 Darmad Germany {Heckmann, Schmi, Seinmez}@kom.udarmad.de
More information2.4 Network flows. Many direct and indirect applications telecommunication transportation (public, freight, railway, air, ) logistics
.4 Nework flow Problem involving he diribuion of a given produc (e.g., waer, ga, daa, ) from a e of producion locaion o a e of uer o a o opimize a given objecive funcion (e.g., amoun of produc, co,...).
More informationOPTIMAL BATCH QUANTITY MODELS FOR A LEAN PRODUCTION SYSTEM WITH REWORK AND SCRAP. A Thesis
OTIMAL BATH UANTITY MOELS FOR A LEAN ROUTION SYSTEM WITH REWORK AN SRA A Thei Submied o he Graduae Faculy of he Louiiana Sae Univeriy and Agriculural and Mechanical ollege in parial fulfillmen of he requiremen
More informationMACROECONOMIC FORECASTS AT THE MOF A LOOK INTO THE REAR VIEW MIRROR
MACROECONOMIC FORECASTS AT THE MOF A LOOK INTO THE REAR VIEW MIRROR The firs experimenal publicaion, which summarised pas and expeced fuure developmen of basic economic indicaors, was published by he Minisry
More informationPROFIT TEST MODELLING IN LIFE ASSURANCE USING SPREADSHEETS PART TWO
Profi Tes Modelling in Life Assurance Using Spreadshees, par wo PROFIT TEST MODELLING IN LIFE ASSURANCE USING SPREADSHEETS PART TWO Erik Alm Peer Millingon Profi Tes Modelling in Life Assurance Using Spreadshees,
More informationThe Application of Multi Shifts and Break Windows in Employees Scheduling
The Applicaion of Muli Shifs and Brea Windows in Employees Scheduling Evy Herowai Indusrial Engineering Deparmen, Universiy of Surabaya, Indonesia Absrac. One mehod for increasing company s performance
More informationWhy Do Real and Nominal. InventorySales Ratios Have Different Trends?
Why Do Real and Nominal InvenorySales Raios Have Differen Trends? By Valerie A. Ramey Professor of Economics Deparmen of Economics Universiy of California, San Diego and Research Associae Naional Bureau
More informationExplore the Application of Financial Engineering in the Management of Exchange Rate Risk
SHS Web o Conerence 17, 01006 (015) DOI: 10.1051/ hcon/01517 01006 C Owned by he auhor, publihed by EDP Science, 015 Explore he Applicaion o Financial Engineering in he Managemen o Exchange Rae Rik Liu
More informationChapter 8 Student Lecture Notes 81
Chaper Suden Lecure Noes  Chaper Goals QM: Business Saisics Chaper Analyzing and Forecasing Series Daa Afer compleing his chaper, you should be able o: Idenify he componens presen in a ime series Develop
More informationThe naive method discussed in Lecture 1 uses the most recent observations to forecast future values. That is, Y ˆ t + 1
Business Condiions & Forecasing Exponenial Smoohing LECTURE 2 MOVING AVERAGES AND EXPONENTIAL SMOOTHING OVERVIEW This lecure inroduces imeseries smoohing forecasing mehods. Various models are discussed,
More informationSubsistence Consumption and Rising Saving Rate
Subience Conumpion and Riing Saving Rae Kenneh S. Lin a, HiuYun Lee b * a Deparmen of Economic, Naional Taiwan Univeriy, Taipei, 00, Taiwan. b Deparmen of Economic, Naional Chung Cheng Univeriy, ChiaYi,
More informationChapter 1.6 Financial Management
Chaper 1.6 Financial Managemen Par I: Objecive ype quesions and answers 1. Simple pay back period is equal o: a) Raio of Firs cos/ne yearly savings b) Raio of Annual gross cash flow/capial cos n c) = (1
More informationINTRODUCTION TO FORECASTING
INTRODUCTION TO FORECASTING INTRODUCTION: Wha is a forecas? Why do managers need o forecas? A forecas is an esimae of uncerain fuure evens (lierally, o "cas forward" by exrapolaing from pas and curren
More informationVector Autoregressions (VARs): Operational Perspectives
Vecor Auoregressions (VARs): Operaional Perspecives Primary Source: Sock, James H., and Mark W. Wason, Vecor Auoregressions, Journal of Economic Perspecives, Vol. 15 No. 4 (Fall 2001), 101115. Macroeconomericians
More informationThe International Investment Position of Jamaica: An Estimation Approach
WP/04 The Inernaional Invemen Poiion of Jamaica: An Eimaion Approach Dane Docor* Economic Informaion & Publicaion Deparmen Bank of Jamaica Ocober 2004 Abrac Thi paper eek o inroduce he inernaional invemen
More informationNanocubes for RealTime Exploration of Spatiotemporal Datasets
Nanocube for RealTime Exploraion of Spaioemporal Daae Lauro Lin, Jame T Kloowki, and arlo Scheidegger Fig 1 Example viualizaion of 210 million public geolocaed Twier po over he coure of a year The daa
More informationProcess Modeling for Object Oriented Analysis using BORM Object Behavioral Analysis.
Proce Modeling for Objec Oriened Analyi uing BORM Objec Behavioral Analyi. Roger P. Kno Ph.D., Compuer Science Dep, Loughborough Univeriy, U.K. r.p.kno@lboro.ac.uk 9RMW FKMerunka Ph.D., Dep. of Informaion
More informationCrosssectional and longitudinal weighting in a rotational household panel: applications to EUSILC. Vijay Verma, Gianni Betti, Giulio Ghellini
Croecional and longiudinal eighing in a roaional houehold panel: applicaion o EUSILC Viay Verma, Gianni Bei, Giulio Ghellini Working Paper n. 67, December 006 CROSSSECTIONAL AND LONGITUDINAL WEIGHTING
More informationOptimal Path Routing in Single and Multiple Clock Domain Systems
IEEE TRANSACTIONS ON COMPUTERAIDED DESIGN, TO APPEAR. 1 Opimal Pah Rouing in Single and Muliple Clock Domain Syem Soha Haoun, Senior Member, IEEE, Charle J. Alper, Senior Member, IEEE ) Abrac Shrinking
More informationEconomics 140A Hypothesis Testing in Regression Models
Economics 140A Hypohesis Tesing in Regression Models While i is algebraically simple o work wih a populaion model wih a single varying regressor, mos populaion models have muliple varying regressors 1
More informationChapter 13. Network Flow III Applications. 13.1 Edge disjoint paths. 13.1.1 Edgedisjoint paths in a directed graphs
Chaper 13 Nework Flow III Applicaion CS 573: Algorihm, Fall 014 Ocober 9, 014 13.1 Edge dijoin pah 13.1.1 Edgedijoin pah in a direced graph 13.1.1.1 Edge dijoin pah queiong: graph (dir/undir)., : verice.
More informationChapter 8: Regression with Lagged Explanatory Variables
Chaper 8: Regression wih Lagged Explanaory Variables Time series daa: Y for =1,..,T End goal: Regression model relaing a dependen variable o explanaory variables. Wih ime series new issues arise: 1. One
More informationFourier Series Solution of the Heat Equation
Fourier Series Soluion of he Hea Equaion Physical Applicaion; he Hea Equaion In he early nineeenh cenury Joseph Fourier, a French scienis and mahemaician who had accompanied Napoleon on his Egypian campaign,
More informationPredicting Stock Market Index Trading Signals Using Neural Networks
Predicing Sock Marke Index Trading Using Neural Neworks C. D. Tilakarane, S. A. Morris, M. A. Mammadov, C. P. Hurs Cenre for Informaics and Applied Opimizaion School of Informaion Technology and Mahemaical
More informationTwoGroup Designs Independent samples ttest & paired samples ttest. Chapter 10
TwoGroup Deign Independen ample e & paired ample e Chaper 0 Previou e (Ch 7 and 8) Ze z M N e (oneample) M N M = andard error of he mean p. 989 Remember: = variance M = eimaed andard error p. 
More informationHotel Room Demand Forecasting via Observed Reservation Information
Proceedings of he Asia Pacific Indusrial Engineering & Managemen Sysems Conference 0 V. Kachivichyanuul, H.T. Luong, and R. Piaaso Eds. Hoel Room Demand Forecasing via Observed Reservaion Informaion aragain
More informationJournal Of Business & Economics Research September 2005 Volume 3, Number 9
Opion Pricing And Mone Carlo Simulaions George M. Jabbour, (Email: jabbour@gwu.edu), George Washingon Universiy YiKang Liu, (yikang@gwu.edu), George Washingon Universiy ABSTRACT The advanage of Mone Carlo
More informationLong Term Spread Option Valuation and Hedging
Long Term Spread Opion Valuaion and Hedging M.A.H. Demper, Elena Medova and Ke Tang Cenre for Financial Reearch, Judge Buine School, Univeriy of Cambridge, Trumpingon Sree, Cambridge CB 1AG & Cambridge
More informationUSE OF EDUCATION TECHNOLOGY IN ENGLISH CLASSES
USE OF EDUCATION TECHNOLOGY IN ENGLISH CLASSES Mehme Nuri GÖMLEKSİZ Absrac Using educaion echnology in classes helps eachers realize a beer and more effecive learning. In his sudy 150 English eachers were
More informationFormulating CyberSecurity as Convex Optimization Problems Æ
Formulaing CyberSecuriy a Convex Opimizaion Problem Æ Kyriako G. Vamvoudaki,João P. Hepanha, Richard A. Kemmerer 2, and Giovanni Vigna 2 Cener for Conrol, Dynamicalyem and Compuaion (CCDC), Univeriy
More informationFormulating CyberSecurity as Convex Optimization Problems
Formulaing CyberSecuriy a Convex Opimizaion Problem Kyriako G. Vamvoudaki, João P. Hepanha, Richard A. Kemmerer, and Giovanni Vigna Univeriy of California, Sana Barbara Abrac. Miioncenric cyberecuriy
More informationPROFIT TEST MODELLING IN LIFE ASSURANCE USING SPREADSHEETS PART ONE
Profi Tes Modelling in Life Assurance Using Spreadshees PROFIT TEST MODELLING IN LIFE ASSURANCE USING SPREADSHEETS PART ONE Erik Alm Peer Millingon 2004 Profi Tes Modelling in Life Assurance Using Spreadshees
More informationCHARGE AND DISCHARGE OF A CAPACITOR
REFERENCES RC Circuis: Elecrical Insrumens: Mos Inroducory Physics exs (e.g. A. Halliday and Resnick, Physics ; M. Sernheim and J. Kane, General Physics.) This Laboraory Manual: Commonly Used Insrumens:
More informationII.1. Debt reduction and fiscal multipliers. dbt da dpbal da dg. bal
Quarerly Repor on he Euro Area 3/202 II.. Deb reducion and fiscal mulipliers The deerioraion of public finances in he firs years of he crisis has led mos Member Saes o adop sizeable consolidaion packages.
More informationThree Dimensional Grounding Grid Design
Three Dimenional Grounding Grid Deign Fikri Bari Uzunlar 1, Özcan Kalenderli 2 1 Schneider Elecric Turkey, Ianbul, Turkey bari.uzunlar@r.chneiderelecric.com 2 Ianbul Technical Univeriy, ElecricalElecronic
More informationNewton's second law in action
Newon's second law in acion In many cases, he naure of he force acing on a body is known I migh depend on ime, posiion, velociy, or some combinaion of hese, bu is dependence is known from experimen In
More informationThe Response of Term Rates to Fed Announcements *
Revied: June The Repone o Term Rae o Fed Announcemen Abrac In February 4, 994 he Federal Reerve began he pracice o announcing change in he argeed level or he ederal und rae immediaely aer uch deciion were
More informationIndividual Health Insurance April 30, 2008 Pages 167170
Individual Healh Insurance April 30, 2008 Pages 167170 We have received feedback ha his secion of he e is confusing because some of he defined noaion is inconsisen wih comparable life insurance reserve
More informationSKF Documented Solutions
SKF Documened Soluions Real world savings and we can prove i! How much can SKF save you? Le s do he numbers. The SKF Documened Soluions Program SKF is probably no he firs of your supplier parners o alk
More informationCSE202 Greedy algorithms
CSE0 Greedy algorihm . Shore Pah in a Graph hore pah from Princeon CS deparmen o Einein' houe . Shore Pah in a Graph hore pah from Princeon CS deparmen o Einein' houe Tree wih a mo edge G i a ree on n
More informationFourier series. Learning outcomes
Fourier series 23 Conens. Periodic funcions 2. Represening ic funcions by Fourier Series 3. Even and odd funcions 4. Convergence 5. Halfrange series 6. The complex form 7. Applicaion of Fourier series
More informationPROFITS AND POSITION CONTROL: A WEEK OF FX DEALING
PROFITS AND POSITION CONTROL: A WEEK OF FX DEALING Richard K. Lyon U.C. Berkeley and NBER Thi verion: June 1997 Abrac Thi paper examine foreign exchange rading a he dealer level. The dealer we rack average
More informationMath 201 Lecture 12: CauchyEuler Equations
Mah 20 Lecure 2: CauchyEuler Equaions Feb., 202 Many examples here are aken from he exbook. The firs number in () refers o he problem number in he UA Cusom ediion, he second number in () refers o he problem
More informationPerformance Center Overview. Performance Center Overview 1
Performance Cener Overview Performance Cener Overview 1 ODJFS Performance Cener ce Cener New Performance Cener Model Performance Cener Projec Meeings Performance Cener Execuive Meeings Performance Cener
More informationSAMPLE LESSON PLAN with Commentary from ReadingQuest.org
Lesson Plan: Energy Resources ubject: Earth cience Grade: 9 Purpose: students will learn about the energy resources, explore the differences between renewable and nonrenewable resources, evaluate the environmental
More informationRevisions to Nonfarm Payroll Employment: 1964 to 2011
Revisions o Nonfarm Payroll Employmen: 1964 o 2011 Tom Sark December 2011 Summary Over recen monhs, he Bureau of Labor Saisics (BLS) has revised upward is iniial esimaes of he monhly change in nonfarm
More informationpolicies are investigated through the entire product life cycle of a remanufacturable product. Benefiting from the MDP analysis, the optimal or
ABSTRACT AHISKA, SEMRA SEBNEM. Invenory Opimizaion in a One Produc Recoverable Manufacuring Sysem. (Under he direcion of Dr. Russell E. King and Dr. Thom J. Hodgson.) Environmenal regulaions or he necessiy
More informationPart 1: White Noise and Moving Average Models
Chaper 3: Forecasing From Time Series Models Par 1: Whie Noise and Moving Average Models Saionariy In his chaper, we sudy models for saionary ime series. A ime series is saionary if is underlying saisical
More informationCOMPARISON OF AIR TRAVEL DEMAND FORECASTING METHODS
COMPARISON OF AIR RAVE DEMAND FORECASING MEHODS Ružica Škurla Babić, M.Sc. Ivan Grgurević, B.Eng. Universiy of Zagreb Faculy of ranspor and raffic Sciences Vukelićeva 4, HR Zagreb, Croaia skurla@fpz.hr,
More informationUnderstanding Sequential Circuit Timing
ENGIN112: Inroducion o Elecrical and Compuer Engineering Fall 2003 Prof. Russell Tessier Undersanding Sequenial Circui Timing Perhaps he wo mos disinguishing characerisics of a compuer are is processor
More informationANALYSIS FOR FINDING AN EFFICIENT SALES FORECASTING METHOD IN THE PROCESS OF PRODUCTION PLANNING, OPERATION AND OTHER AREAS OF DECISION MAKING
Inernaional Journal of Mechanical and Producion Engineering Research and Developmen (IJMPERD ) Vol.1, Issue 2 Dec 2011 136 TJPRC Pv. Ld., ANALYSIS FOR FINDING AN EFFICIENT SALES FORECASTING METHOD IN
More informationAP Calculus AB 2013 Scoring Guidelines
AP Calculus AB 1 Scoring Guidelines The College Board The College Board is a missiondriven noforprofi organizaion ha connecs sudens o college success and opporuniy. Founded in 19, he College Board was
More informationBALANCE OF PAYMENTS. First quarter 2008. Balance of payments
BALANCE OF PAYMENTS DATE: 20080530 PUBLISHER: Balance of Paymens and Financial Markes (BFM) Lena Finn + 46 8 506 944 09, lena.finn@scb.se Camilla Bergeling +46 8 506 942 06, camilla.bergeling@scb.se
More information4. The Poisson Distribution
Virual Laboraories > 13. The Poisson Process > 1 2 3 4 5 6 7 4. The Poisson Disribuion The Probabiliy Densiy Funcion We have shown ha he k h arrival ime in he Poisson process has he gamma probabiliy densiy
More informationDuration and Convexity ( ) 20 = Bond B has a maturity of 5 years and also has a required rate of return of 10%. Its price is $613.
Graduae School of Business Adminisraion Universiy of Virginia UVAF38 Duraion and Convexiy he price of a bond is a funcion of he promised paymens and he marke required rae of reurn. Since he promised
More informationRealtime Particle Filters
Realime Paricle Filers Cody Kwok Dieer Fox Marina Meilă Dep. of Compuer Science & Engineering, Dep. of Saisics Universiy of Washingon Seale, WA 9895 ckwok,fox @cs.washingon.edu, mmp@sa.washingon.edu Absrac
More informationSupply Chain Management Using Simulation Optimization By Miheer Kulkarni
Supply Chain Managemen Using Simulaion Opimizaion By Miheer Kulkarni This problem was inspired by he paper by Jung, Blau, Pekny, Reklaii and Eversdyk which deals wih supply chain managemen for he chemical
More informationState Machines: Brief Introduction to Sequencers Prof. Andrew J. Mason, Michigan State University
Inroducion ae Machines: Brief Inroducion o equencers Prof. Andrew J. Mason, Michigan ae Universiy A sae machine models behavior defined by a finie number of saes (unique configuraions), ransiions beween
More informationThe Twin Agency Problems in Corporate Finance  On the basis of Stulz s theory 
The Twin Agency Problem in Corporae Finance  On he bai of Sulz heory  Von der Fakulä für Machinenbau, Elekroechnik und Wirchafingenieurween der Brandenburgichen Technichen Univeriä Cobu zur Erlangung
More informationUnderstanding the Brazilian Economic Growth Regime: A Kaleckian Approach. Bruno Thiago Tomio FAE Blumenau. Resumo
Underanding he Brazilian Economic Growh Regime: A Kaleckian Approach Bruno Thiago Tomio FAE Blumenau Reumo Denro da economia pókeyneiana, uma da erene principai é formada por auore que conam com o eudo
More informationTEMPORAL PATTERN IDENTIFICATION OF TIME SERIES DATA USING PATTERN WAVELETS AND GENETIC ALGORITHMS
TEMPORAL PATTERN IDENTIFICATION OF TIME SERIES DATA USING PATTERN WAVELETS AND GENETIC ALGORITHMS RICHARD J. POVINELLI AND XIN FENG Deparmen of Elecrical and Compuer Engineering Marquee Universiy, P.O.
More information4.8 Exponential Growth and Decay; Newton s Law; Logistic Growth and Decay
324 CHAPTER 4 Exponenial and Logarihmic Funcions 4.8 Exponenial Growh and Decay; Newon s Law; Logisic Growh and Decay OBJECTIVES 1 Find Equaions of Populaions Tha Obey he Law of Uninhibied Growh 2 Find
More informationReputation and Social Network Analysis in MultiAgent Systems
Repuaion and Social Neork Analyi in MuliAgen Syem Jordi Sabaer IIIA  Arificial Inelligence Reearch Iniue CSIC  Spanih Scienific Reearch Council Bellaerra, Caalonia, Spain jabaer@iiia.cic.e Carle Sierra
More informationInterest Rate Spreads and Mandatory Credit Allocations: Implications on Banks Loans to Small Businesses in Indonesia
Dicuion Paper No. 0402 Inere Rae Spread and Mandaory Credi Allocaion: Implicaion on Bank oan o Small Buinee in Indoneia Reza Y. Siregar January 2004 Indoneia Program Univeriy of Adelaide Adelaide 5005
More informationRC, RL and RLC circuits
Name Dae Time o Complee h m Parner Course/ Secion / Grade RC, RL and RLC circuis Inroducion In his experimen we will invesigae he behavior of circuis conaining combinaions of resisors, capaciors, and inducors.
More informationInfrastructure and Evolution in Division of Labour
Infrarucure and Evoluion in Diviion of Labour Mei Wen Monah Univery (Thi paper ha been publihed in RDE. (), 906) April 997 Abrac Thi paper udie he relaionhip beween infrarucure ependure and endogenou
More informationRepresenting Periodic Functions by Fourier Series. (a n cos nt + b n sin nt) n=1
Represening Periodic Funcions by Fourier Series 3. Inroducion In his Secion we show how a periodic funcion can be expressed as a series of sines and cosines. We begin by obaining some sandard inegrals
More informationModeling Energy American Options in the NonMarkovian Approach
Modeling Energy American Opion in he NonMarkovian Approach Valery Kholodnyi Vienna Auria 06.05.015 VERBUND AG www.verbund.com Ouline Ouline Inroducion Mehodology he NonMarkovian Approach Modeling Energy
More informationµ r of the ferrite amounts to 1000...4000. It should be noted that the magnetic length of the + δ
Page 9 Design of Inducors and High Frequency Transformers Inducors sore energy, ransformers ransfer energy. This is he prime difference. The magneic cores are significanly differen for inducors and high
More informationAn empirical analysis about forecasting Tmall airconditioning sales using time series model Yan Xia
An empirical analysis abou forecasing Tmall aircondiioning sales using ime series model Yan Xia Deparmen of Mahemaics, Ocean Universiy of China, China Absrac Time series model is a hospo in he research
More informationThe Kinetics of the Stock Markets
Asia Pacific Managemen Review (00) 7(1), 14 The Kineics of he Sock Markes Hsinan Hsu * and BinJuin Lin ** (received July 001; revision received Ocober 001;acceped November 001) This paper applies he
More informationModule 4. Singlephase AC circuits. Version 2 EE IIT, Kharagpur
Module 4 Singlephase A circuis ersion EE T, Kharagpur esson 5 Soluion of urren in A Series and Parallel ircuis ersion EE T, Kharagpur n he las lesson, wo poins were described:. How o solve for he impedance,
More information2.6 Limits at Infinity, Horizontal Asymptotes Math 1271, TA: Amy DeCelles. 1. Overview. 2. Examples. Outline: 1. Definition of limits at infinity
.6 Limis a Infiniy, Horizonal Asympoes Mah 7, TA: Amy DeCelles. Overview Ouline:. Definiion of is a infiniy. Definiion of horizonal asympoe 3. Theorem abou raional powers of. Infinie is a infiniy This
More informationTimeSeries Forecasting Model for Automobile Sales in Thailand
การประช มว ชาการด านการว จ ยด าเน นงานแห งชาต ประจ าป 255 ว นท 24 25 กรกฎาคม พ.ศ. 255 TimeSeries Forecasing Model for Auomobile Sales in Thailand Taweesin Apiwaanachai and Jua Pichilamken 2 Absrac Invenory
More informationDIFFERENTIAL EQUATIONS with TI89 ABDUL HASSEN and JAY SCHIFFMAN. A. Direction Fields and Graphs of Differential Equations
DIFFERENTIAL EQUATIONS wih TI89 ABDUL HASSEN and JAY SCHIFFMAN We will assume ha he reader is familiar wih he calculaor s keyboard and he basic operaions. In paricular we have assumed ha he reader knows
More informationOPTIMIZING PRODUCTION POLICIES FOR FLEXIBLE MANUFACTURING SYSTEM WITH NONLINEAR HOLDING COST
OPIMIZING PRODUCION POLICIE FOR FLEXIBLE MANUFACURING YEM WIH NONLINEAR HOLDING CO ABRAC Leena Praher, Reearch cholar, Banahali Vidayaeeh (Raj.) Dr. hivraj Pundir, Reader, D. N. College, Meeru (UP) hi
More informationDETERMINISTIC INVENTORY MODEL FOR ITEMS WITH TIME VARYING DEMAND, WEIBULL DISTRIBUTION DETERIORATION AND SHORTAGES KUNSHAN WU
Yugoslav Journal of Operaions Research 2 (22), Number, 67 DEERMINISIC INVENORY MODEL FOR IEMS WIH IME VARYING DEMAND, WEIBULL DISRIBUION DEERIORAION AND SHORAGES KUNSHAN WU Deparmen of Bussines Adminisraion
More informationStock Trading with Recurrent Reinforcement Learning (RRL) CS229 Application Project Gabriel Molina, SUID 5055783
Sock raing wih Recurren Reinforcemen Learning (RRL) CS9 Applicaion Projec Gabriel Molina, SUID 555783 I. INRODUCION One relaively new approach o financial raing is o use machine learning algorihms o preic
More informationDistributing Human Resources among Software Development Projects 1
Disribuing Human Resources among Sofware Developmen Proecs Macario Polo, María Dolores Maeos, Mario Piaini and rancisco Ruiz Summary This paper presens a mehod for esimaing he disribuion of human resources
More informationWhy Did the Demand for Cash Decrease Recently in Korea?
Why Did he Demand for Cash Decrease Recenly in Korea? Byoung Hark Yoo Bank of Korea 26. 5 Absrac We explores why cash demand have decreased recenly in Korea. The raio of cash o consumpion fell o 4.7% in
More informationAnalysis of the development trend of China s business administration based on time series
SHS Web of Conference 4, 000 7 (06) DOI: 0.05/ hconf/0640007 C Owned by he auhor, ublihed by EDP Science, 06 Analyi of he develomen rend of China buine adminiraion baed on ime erie Rui Jiang Buine School,
More informationA Reexamination of the Joint Mortality Functions
Norh merican cuarial Journal Volume 6, Number 1, p.166170 (2002) Reeaminaion of he Join Morali Funcions bsrac. Heekung Youn, rkad Shemakin, Edwin Herman Universi of S. Thomas, Sain Paul, MN, US Morali
More informationCVA calculation for CDS on super senior ABS CDO
MPRA Munich Personal RePEc Archive CVA calculaion for CDS on super senior AS CDO Hui Li Augus 28 Online a hp://mpra.ub.unimuenchen.de/17945/ MPRA Paper No. 17945, posed 19. Ocober 29 13:33 UC CVA calculaion
More informationTime Series Analysis Using SAS R Part I The Augmented DickeyFuller (ADF) Test
ABSTRACT Time Series Analysis Using SAS R Par I The Augmened DickeyFuller (ADF) Tes By Ismail E. Mohamed The purpose of his series of aricles is o discuss SAS programming echniques specifically designed
More informationYTM is positively related to default risk. YTM is positively related to liquidity risk. YTM is negatively related to special tax treatment.
. Two quesions for oday. A. Why do bonds wih he same ime o mauriy have differen YTM s? B. Why do bonds wih differen imes o mauriy have differen YTM s? 2. To answer he firs quesion les look a he risk srucure
More informationForecasting Daily Supermarket Sales Using Exponentially Weighted Quantile Regression
Forecasing Daily Supermarke Sales Using Exponenially Weighed Quanile Regression James W. Taylor Saïd Business School Universiy of Oxford European Journal of Operaional Research, 2007, Vol. 178, pp. 154167.
More informationForecasting. Including an Introduction to Forecasting using the SAP R/3 System
Forecasing Including an Inroducion o Forecasing using he SAP R/3 Sysem by James D. Blocher Vincen A. Maber Ashok K. Soni Munirpallam A. Venkaaramanan Indiana Universiy Kelley School of Business February
More information