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 2004
Inroducion and Overview... 2 Forecasing and Supply Chain Planning... 2 Forecasing Pracice... 3 Supply Chain Improvemens for Beer Forecass... 4 Forecasing Mehods... 5 Qualiaive Inpu... 5 Quaniaive Inpu... 6 Simple Time Series Models... 7 Projecion... 7 Simple Moving Average (MA)... 7 Weighed Moving Average (WMA)... 8 Basic Exponenial Smoohing (BES)... 8 Simple Time Series Example... 9 Forecas Accuracy... 0 Average Error and Bias... Mean Absolue Deviaion... 2 Mean Absolue Percenage Error... 2 Mean Squared Error... 2 Tracking Signal... 2 Forecas Error Example... 3 Smoohed Error Measures... 3 Errors as an Esimae of Forecas Uncerainy... 4 A Reacion-o-Error Inerpreaion of Exponenial Smoohing... 5 Muli-Facor Time Series Mehods... 5 Trend-Enhanced Forecasing Models... 6 Exponenial Smoohing Updaes Hol s Model... 6 Trend- and Seasonaliy-Enhanced Forecas Models... 7 Exponenial Smoohing Updaes Winers Model... 7 Model Iniiaion and Forecasing... 7 Hol s Addiive Trend Model Example... 8 Winers Addiive Trend, Muliplicaive Seasonaliy Model Example... 20 Deseasonalizing Demand... 20 Deermining he Iniial Forecasing Facors... 22 Forecasing wih Winers Model... 23 Forecasing References... 26 Time Series Forecasing Problems... 27 Forecasing wih SAP R/3... 29 Loading Hisorical Daa... 29 Forecasing Wih SAP R/3: Seps and Inpu Requiremens... 33 User Selecion Approach o Forecasing... 33 Sysem Selecion Approach o Forecasing... 36 Summary 40 Creaing Par Numbers...4 Glow-Brigh Corporaion Case... 44
Inroducion and Overview A key par of supply chain planning involves demand planning and he associaed demand forecasing process. The focus here is on he various issues involved in forecasing and heir use in he SAP R/3 sysem. The objecives of his documen are o highligh he need for forecasing o manage he supply chain, provide saisical ime series models for shor-erm forecasing, review forecasing performance merics and racking procedures, and illusrae how forecasing is done in he SAP R/3 sysem. To help develop an undersanding of he saisical mehods, some example problems are included. I should be noed ha his module does no cover regression mehods as his opic is covered in deph in many oher places. Forecasing and Supply Chain Planning Supply chain planning, o a large degree, sars wih forecasing. Maching supply and demand is an imporan goal for mos firms and is a he hear of operaional planning. I is also of significan imporance as he overly opimisic Cisco found in 200 when i ook a $2.2 Billion invenory wrie-down because of heir abiliy o forecas demand wih near-scienific precision. Since mos producion sysems can respond o consumer demand insananeously, some esimae, or forecas, of fuure demand is required so ha he efficien and effecive operaional plans can be made. Plan, process, and labor capaciy are all se based on he forecass of fuure demand. Capaciy planning and faciliy decisions would be based primarily on longer erm, aggregae forecass. However, forecass are also needed o plan proper invenory levels, which in general, end o require shorer-erm forecass a a disaggregaed level since specific componens, pars, and end-iems mus be socked for immediae consumer demand. Forecass affec mos funcional areas of he firm and are he saring poin for resource allocaion decisions. For example, manufacuring mus plan producion on a day o day basis o mee cusomer orders, while purchasing needs o know how o align supplier deliveries wih he producion schedules. Finance needs o undersand he forecass so ha he proper levels of invesmen can be made in plan, equipmen, and invenory and so ha budges can be consruced o beer manage he business. The markeing funcion needs o know how o allocae resources for various produc groups and markeing campaigns. Forecass also deermine he labor requiremens required by he firm so ha he human resources funcion can make proper hiring and raining decisions when demand is expeced o grow. Cisco s Comeback, Business Week Online, November 24, 2003 2
Forecasing Pracice Forecass are always wrong, bu some are more wrong han ohers. Forecasing he demand for innovaive producs, fashion goods, and he like is generally more difficul han forecasing demand for more commodiy-like producs ha are sold on a daily basis. Aggregae forecass of a group of similar producs are generally more accurae han individual forecass of he individual producs ha make up he group. Finally, he longer he forecas ino he fuure, he less reliable he forecas will be. Forecasing pracice is based on a mix of qualiaive and quaniaive mehods. When planning occurs for innovaive producs, lile demand daa are available for he produc of ineres and he degree o which like produc demand daa are similar is unknown. Thus a large amoun of judgmen is needed by expers who can use heir indusry experise o predic demand. These expers, hough, will undoubedly use hisorical demand daa, even if no direcly, in heir judgmen. Commodiy-like producs ha are sold everyday, on he oher hand, are much more suiable for quaniaive models and need very lile judgmen o forecas demand. Sill, when knowledge of cerain evens leads one o believe ha fuure demand migh no rack hisorical rends, some judgmen may be warraned o make adjusmens in he models which use pas daa. In his case, a heavy reliance on pas daa wih adjusmens based on exper judgmen should be he mehod used for forecasing. Forecasing should be done primarily for end-iem demand. In manufacuring siuaions, his means here is no real need for forecasing componen pars which make up he final iem. When producion quaniies for he end iem have been deermined, componen demand can be compued based on he producion plan of he end iem and knowledge of he bill of maerials (BOM). Aggregaing forecass across muliple iems reduces forecasing errors. A clohing sore, for insance, migh be able o esimae wihin a prey narrow range wha he demand will be for men s dress shirs. Bu when ha sore ries o esimae he demand for individual syles, colors, and sizes of shirs, he accuracy of heir forecass will be considerably worse. Firms handle his kind of forecasing problem usually in one of hree ways; hey eiher forecas from he boom up, from he op down, or hey sar in he middle and work boh up and down. The op down forecas essenially esimaes oal sales demand and hen divides hose sales dollars level by level unil he sock keeping uni (SKU) is reached. The boom up mehod, as one migh expec, sars wih forecass a he SKU level and hen aggregaes hose demand esimaes level by level o reach a company level forecas. Anoher mehod, one migh call he in-beween mehod, sars forecass a he caegory level (like men s dress shirs), and hen works up o deermine sore sales and works down o divide up he forecas ino syles, colors and SKUs. The use of managemen ime o make forecass is relaively expensive when compared o he cos of using saisical forecasing models, and he difference beween he coss of hese wo mehods has been increasing in recen years due o he auomaed acquisiion of daa from poin of sale sysems and compuer power in general. There can be no 3
subsiue for human inpu in he forecasing process; however, human inpu can be expensive. In addiion, research indicaes ha for some everyday commodiy-ype iems, simple saisical models work well and in fac work beer when no massaged by managers. Sill, some managers believe ha spending ime o make forecass perfec will solve mos of heir supply chain problems. There are imes when managerial inpu is needed, bu here comes a poin where i is beer o undersand he inaccuracy in he forecas and plan accordingly. Once a good forecasing process (procedures, echniques, models and managemen oversigh) has been pu in place, coninual refinemen has lile value and can even hur he forecasing process. Supply Chain Improvemens for Beer Forecass Since forecass are never accurae, wo common soluions are ofen proposed o fix forecas errors. The firs is o reduce he lead ime o reac sooner o changes. This is a good parial soluion, bu reducing lead imes is no always easy o do and is ofen expensive. In addiion, shorening he lead ime, in many cases, jus moves he problems from one par of he supply chain o anoher. The second is o make o order so ha invenory doesn need o be produced in advance of demand. This soluion is also good, bu like shorening he lead ime, ends o shif demand o he nex level of he supply chain. Furhermore, producing o order sill requires forecass, o be able o keep he righ quaniies of raw maerial on hand. So while hese ideas help improve cerain aspecs of he forecasing problem, hey do no eliminae he need for some kind of forecasing mehods. A more recen proposal o fix forecas errors is o use collaboraion. The idea is ha if differen pars of he supply chain collaborae on a common forecas and everyone plans based on ha single forecas; hen here is lile need for one par of he chain o hedge based on he uncerainy of wha is done in oher pars of he chain. Inra-firm collaboraion, you would hink, would be common place seems ha a lile common sense would dicae ha everyone in a firm come ogeher wih a common se of forecas figures. Bu his is rarely he case. Markeing has a se of forecass, so oo does operaions. Sales has heir forecas and i s possible ha for budgeing purposes Finance uses sill anoher. The advancemen of enerprise resource planning (ERP) sysems is helping ensure ha here is only one forecas, based upon he principles of a single daa reposiory used by all areas of he enerprise. Once funcional areas wihin a firm agree on a common forecas, he nex sep is for iner-firm agreemen. This ype of collaboraion is ougher, bu many believe i is an essenial sep in he coninual improvemen of he supply chain. The collaboraive planning, forecasing, and replenishmen (CPFR) muli-indusry iniiaive is aimed a providing his kind of inegraive forecas beween so-called rading parners differen levels in he supply chain. Supply chain advanced planning sysem (APS) models and sofware packages are designed o connec he various supply chain players so ha his collaboraion can be compleed successfully. Bu here is much o do in his area o end he second guessing ha is so prevalen oday. 4
Forecasing Mehods Forecasing is based on a mix of qualiaive and quaniaive inpus. The ype of produc and ha produc s impac on supply chain coss deermine how much human inpu is used and how sophisicaed he forecasing model should be. Qualiaive Inpu Human judgmen can be capured in a number of ways. Three common approaches include an Individual Marke Exper, Group Consensus, and he Delphi Mehod. All of hese are someimes referred o as Exper Opinion mehodologies since hey require people wih some knowledge of he producs and markes developing forecas esimaes for planning needs. Individual Marke Expers can be hired o wach for indusry rends, perhaps even by geographic area, and migh even work wih sales people o esimae fuure demand for producs. Individuals, hough, have biases ha hey may no be aware of and here is a limi o how much informaion one person can obain. To overcome his, even hough i can be considerably more expensive, is o use groups of expers. Group Consensus involves bringing ogeher a eam of expers, hopefully from differen funcional areas, o reach consensus on fuure forecass for a produc or a group of producs. Group Consensus forecass end o bring ogeher differen facions of he company so ha everyone ends o buy-in he final numbers. The group ges o make sure ha over-zealous managers don over-forecas jus o ry o mee firm expecaions for growh. The group also ges o make sure someone doesn play conservaive and under-forecas because ha person hinks i is less risky o low-ball he forecas. Bu, building consensus has is pifalls as well. When people from differen ranks in he firm come ogeher, here can be a endency for low-ranking personnel o a some poin acquiesce o he higher-ranking managers in he group. This defeas he poin of coming o a consensus agreemen and can be a real problem wih cerain personaliies. One way o overcome his issue is o come o an anonymous consensus by using somehing known as he Delphi Mehod. The Delphi Mehod requires one person o adminiser and coordinae he process and poll he eam members (respondens) hrough a series of sequenial quesionnaires. While he eam members need o be people who have some experise in he area of ineres o he forecas, he adminisraor only needs o have some knowledge of how o coordinae he effor wihou unduly influencing he resuls. The quesionnaires ha are sen o he members involve no only esimaes of demand, bu hey are aimed a deermining how he member is reaching ha esimae. Once everyone has reurned he quesionnaires, he adminisraor mus summarize he resuls and send a summary repor o all of he members, bu, wih he ideniy of who made which forecas hidden from he eam. Along wih he summary is anoher quesionnaire which in some ways builds off of he previous forecass and assumpions used in hose forecass. This process of quesionnaire, summary, quesionnaire, summary coninues unil he paricipans reach some consensus on he forecas. Obviously his mehod can be boh ime consuming and 5
raher expensive o adminiser bu i can lead o good forecass and in addiion, i esablishes over ime he imporan inpus o he process. Three rounds seems o be a good compromise beween forecas qualiy and he cos and effor involved. Quaniaive Inpu Quaniaive analysis ypically involves wo approaches: causal models and ime-series mehods. Causal models esablish a quaniaive link beween some observable or known variable (like adverising expendiures) wih he demand for some produc. Time series analysis involves looking a hisorical demand for a produc o forecas fuure demand. The mos common ypes of Causal Models are regression analysis and economeric models. While regression models can be quie involved, simple linear regression is ofen used, whereby a sraigh line of he form Y mx + b is used o describe he relaionship beween he dependen variable Y and he independen variable X. The line is fi hrough a se of poins such ha he squared disance from he line is minimized, hus a leas square fi. Economeric models are usually some form of mulivariae regression model where he independen variables (many Xs) represen facors like disposable income and indusrial oupu from he economy. The mahemaical deails of regression are no covered here. There are a number of differen kinds of Time Series Models, mos of which work on he assumpion ha hisorical demand can be smoohed by averaging and ha pas demand paerns will coninue o occur in he fuure. Simple ime series analysis includes models such as he Weighed Moving Average and Basic Exponenial Smoohing. More complex ime series mehods include facors for rends, seasonal paerns, and economic cycles. The remainder of his reading focuses on hese ime series models. 6
Simple Time Series Models Some of he mos popular forecasing mehods, especially in sofware packages, are commonly referred o as ime series models. These models make use of pas daa o predic fuure demand. This ype of forecasing mehod is especially relevan for iems which are coninuously ordered as hese mehods can be auomaed in compuer informaion sysems o a large degree. The models assume ha each observed demand daa poin is comprised of some sysemaic componen and some random componen. The ime series model is designed o predic he sysemaic componen bu no he random componen. The idea is similar o he logic of qualiy conrol chars in ha you don ry o reac o he process variabiliy as long as i is wihin he conrol limis. Reacing (or changing he forecas model) because of errors ha are random is only likely o increase he error in fuure forecass. Wha is needed is o ry o predic he range or variaion of his random error. Models can be designed for jus abou any ype of sysemaic change in demand, bu here is real danger in rying o predic he random componen. Projecion The easies ime series mehod simply projecs fuure demand based on he las period s demand. The forecas for he nex period +, F +, is simply a projecion of his period demand, D F + D () This mehod, alhough easy o use, doesn make use of daa ha is easily available o mos managers; hus, using more of he hisorical daa should improve he forecas. Averages of pas demand migh be more useful and are discussed nex. Simple Moving Average (MA) The simple moving average forecas makes use of more of he hisorical demand daa han jus he las period s demand. An n-period moving average uses he las n periods of demand as a forecas for nex periods demand: F + D + D + D 2 +... + D n+ (2) n This forecas model is mos useful where he demand level is fairly consan over ime. The model hen makes simple adjusmens o his average level raher han assuming ha he level is forever consan. Is advanage over he projecion model is ha by averaging, he forecas won end o flucuae as much. The average of he previous n periods can be viewed as he esimae of he average level of demand as of period. Thus, one could define he level, L, as 7
L D + D + D 2 +... + D n+ (3) n and hus he forecas, F +, is jus he las esimae of he level of demand. F + L (4) This forecas is no differen han he direc forecas given above in Equaion 2, bu he inerpreaion allows for an easier presenaion of he more advanced forecasing models o come. Weighed Moving Average (WMA) One shorcoming of he simple moving average is he equal weighing of daa. For insance, a 5-period moving average weighs each of he pas 5 demand observaions he same each has a 20% impac on he forecas. This runs couner o ones inuiion ha he mos recen daa is he mos relevan. Thus, he weighed moving average allows for more emphasis o be placed on he mos recen daa. This forecas is: w D + w D + w D +... + w 2 2 n+ n+ F + L (5) w + w + w 2 +... + w n+ D where w is he weigh applied o he demand incurred in period, w - is he weigh given o ha of period -, and so on Inuiively, he expecaion would be ha he more recen demand daa should be weighed more heavily han older daa; so, generally, one would expec he weighs o follow he relaionship w w - w -2. Basic Exponenial Smoohing (BES) Nice properies of a weighed moving average would be one where he weighs no only decrease as older and older daa are used, bu one where he differences beween he weighs are smooh. Obviously he desire would be for he weigh on he mos recen daa o be he larges. The weighs should hen ge progressively smaller he more periods one considers ino he pas. The exponenially decreasing weighs of he basic exponenial smoohing forecas fi his bill nicely. The forecas equaion is given by: F ) + L αd + ( α F (6) where α is a smoohing parameer beween 0 and. To show ha his forecas is in fac a weighed average forecas, i is insrucive o look a he algebraic expansion of his model. Since F α D + ( α) F 8
F F + α D + α D ( ) + ( α)[ αd + ( α) F ] 2 + α α ) D + ( α F This oo can be expanded since F α D 2 + ( α) F 2 F F + α D + α D ( 2 ) 2 2 + α ( α ) D + ( α ) [ αd 2 + ( α ) F 2 ] 2 3 + α α ) D + α ( α ) D + ( α F Coninuing his expansion, he model can be wrien as: F + ( 2 3 + 2 3 α D + α α ) D + α ( α ) D + α ( α ) D... (7) Thus, he exponenial smoohing model is acually a weighed moving average model wih special weighs. These weighs ge coninuously smaller as hey are applied o periods farher away from he curren period. Wih some algebra, i can be shown ha hese weighs sum o one 2 α + α( α) + α( α) + α( α) 3 +... (8) Even hough hese weighs have nice properies, i is no necessary o keep rack of each of he weighs. In addiion, a sysem running he model does no need o sore he hisorical daa or does i need o compue anyhing based on old daa. The only hing ha is needed is he smoohing facor α, las period s demand, and las period s forecas. The nice hing abou he model is ha all pas demand daa is effecively sored in he las period s forecas. Simple Time Series Example Weigh 0.35 0.3 0.25 0.2 0.5 0. 0.05 0 Weighs vs. Time Period: α0.3 - -2-3 -4-5 -6-7 -8-9 -0 Time Period Figure : Effecive Weighs for BES The models presened above are now illusraed using a simple daa se. Eigh periods of demand daa for a produc are given for January hrough Augus in Table. The period designaion in he able is he same as referred o in he models. Table : Seasonal Esimaes and Iniial Seasonal Facors 9
The firm wishes o forecas demand for Sepember (period +). These calculaions are presened below. Simple Projecion F + D ; F + 48. Simple Moving Average (using 4 periods) F D + D + D +... + D n+ 48 + 4+ 47 + 55 4 2 + n Weighed Moving Average (using 4 periods wih w 0.4, w - 0.3 w -2 0.2, w -3 0.) F + w D + w D w + w + w 2 + w 2 2 +... + w +... + w n+ n+ n+ 0.4(48) + 0.3(4) + 0.2(47) + 0.(55) 46. Basic Exponenial Smoohing (wih α0.2) D To employ BES, he firm uses he pas demand daa o rain he model. To do his raining, forecass need o be compued for each period for which here is demand daa. Table 2 shows he forecas for Sepember of 46.4 and he compuaions needed o obain ha forecas using he exponenial model. By leing he forecasing model run hrough pas daa, a sor of smoohing akes place so ha fuure forecass are based on good weighs. This raining wih pas daa also allows he forecaser o measure he forecas errors based on he model assuming ha i Table 2: BES Calculaions was acually used in he pas o make forecass. D 47 Forecas Accuracy Since forecass are always wrong, an esimae of he inaccuracy of he forecas can be jus as helpful as he forecas of he expeced demand. So a good forecas needs o include a mean and an esimae of how he forecas will vary around he mean. This measure helps us undersand he risk of he forecas and allows us o make decisions allowing for 0
variabiliy ha is presen. Forecasing involves esimaing more han he expeced demand i involves rying o esimae he uncerainy as well. To ascerain how well a forecas model is working, acual pas demand informaion is compared o he forecas for ha period. These forecas errors, no only ell a firm how well heir forecas sysem is working, hey also provide informaion abou how much risk here is in he forecas by helping a manager undersand he inheren variaion in he demand. An esimae of he fuure forecas variaion is based, a leas in par, on he variaion of pas forecass. Many imes his esimae of he accuracy of a forecas is consisen over ime and can be used o esablish upper and lower esimaes of expeced demand. The forecas error for period is defined as 2 E F D (9) Several differen error merics are used in pracice, wih differen srenghs. They are based on various funcional sums of hese individual period- forecas errors as explained below. Average Error and Bias The simple average error over n periods is AE n n E i n i (0) bu one would expec ha a good forecas would be such ha he expeced value of AE n is zero since posiive and negaive deviaions should cancel each oher ou. In fac, i would be good o know he value of AE n, since i indicaes how good he forecas is racking he acual demand. A similar more common measure, known as he bias, is usually used o rack his sysemaic error and is given as: n bias n E i i () Managers are ineresed in forecass wih no bias. When a bias exiss, i is likely ha he wrong funcional forecas model is being used. Sysemaic bias should, heoreically, be somehing ha can be eliminaed by inroducing some facor in he model o remove i from he forecas. Thus, his simple error measure can be one of he mos imporan in deermining if he correc forecasing model is being used. 2 Some auhors define error as E D F. This definiion requires he user o be aware of how o inerpre he posiive or negaive sign of he errors.
Mean Absolue Deviaion A common average error measuremen used in many companies is known as he mean absolue deviaion, or MAD. Mahemaically, i is represened as MAD n n E i n i (2) where E i is he absolue value of E i. By aking he absolue value of he error erms, his error measuremen capures he posiive and negaive deviaions beween he forecas and he acual demand. Mean Absolue Percenage Error A measure which is closely relaed o he MAD, bu which expresses he magniude of he error relaive o he magniude of he demand is known as he mean absolue percenage error, or MAPE. To express his relaive measure as a percen, he average raio is muliplied by 00. n Ei MAPE n 00 (3) n D i i Mean Squared Error Anoher measure of average error is known as he mean squared error, or MSE. This erminology should be a familiar o hose who have used regression models. Here, insead of simply averaging he deviaions of he forecas as compared o he acual demand, he deviaions are squared, giving more weigh o hose errors which are he farhes from he acual demand. MSE n 2 n E n i (4) Tracking Signal To auomaically deec when a forecas model is no longer producing good forecass, a measure known as a racking signal is ofen used. bias Tracking Signal (5) MAD This racking signal is a measure ha can be used in a conrol-char-like manner so ha when an ou-of-conrol sae is reached, he forecasing model can be revised o ge hings 2
back in conrol. By dividing he bias by he MAD, he conrol limis for his uni-less measure are he same for every produc being forecas and herefore separae conrol limis need no be kep for each produc. Insead, a common rule of humb is when he racking signal reaches a value of posiive or negaive 6, i is ime o invesigae he forecasing model. Forecas Error Example To illusrae some of hese error measures, he demand daa and forecass from he example problem presened in Table 2 will be used. The demand is compared o he forecas for each period wih he resuling errors give in Table 3. This provides values for he error, E i, for each period from January hrough Augus. The las wo columns of his able show he forecas error and he squared forecas error for each of he periods of ineres. Table 3: Seasonal Facors bias Jan Aug Aug Ei i Jan 2.0 3.4 + 5.3 + 0.2 5.8 + 0.3 + 6.3 2.0 2.9 MAD Jan Aug Aug Ei n i Jan 2.0 + 3.4 + 5.3 + 0.2 + 5.8 + 0.3 + 6.3 + 2.0 25.3 3.2 8 8 MSE Jan Aug Aug E n i Jan 2 2.0 2 + 3.4 2 + 5.3 2 + 0.2 2 + 5.8 8 2 + 0.3 2 + 6.3 2 + 2.0 2 20.8 5. 8 bias 2.9 Tracking Signal (as of Aug) 0.9 MAD 3.2 Smoohed Error Measures Since errors are someimes used o esimae demand variaion, i is useful o hink abou an exponenially smoohed MAD so ha recen errors are weighed more heavily. Smoohing he error is very similar o he basic exponenial forecasing echnique. Thus, each period a new MAD is compued as MAD δ E + δ MAD (6) ( ) where δ is a smoohing parameer beween 0 and. 3
Errors as an Esimae of Forecas Uncerainy Forecass usually consis of jus a mean; bu, an esimae of he sandard deviaion of he uncerainy of fuure forecass can be jus as imporan. The firm needs o know how much risk is in he forecas. For example, good invenory models need some measure of demand uncerainy, or more accuraely, forecas uncerainy, o deermine he proper levels of safey sock invenory. Invenory models which use pas demand variaion are likely calling for oo much safey sock; a good forecas may be able o predic some of his uncerainy and he safey sock is only needed for he unpredicable par. Two common measures of he sandard deviaion of he forecas errors are presened nex. One of hese is based on he absolue deviaion. When forecas errors are normally disribued and have no bias, he MAD can be used o esimae he sandard deviaion, σ.25mad. (7) The oher measure is based on he direc esimae of mean squared deviaion saisic and is given as n 2 ( E E ) σ n. (8) 4
A Reacion-o-Error Inerpreaion of Exponenial Smoohing Since F E + D, he forecas using he exponenial smoohing model can be rewrien as F + α( F E ) + ( α) F (9) which, wih a lile algebra, can be rewrien as F + F αe (20) Thus, each new forecas can be inerpreed as he pas forecas adjused by some percenage of he las forecas s error. When he forecas error is posiive, he forecas overesimaed he demand; herefore, he nex forecas needs o be reduced. The smoohing parameer α deermines by how much he forecas should be modified. Muli-Facor Time Series Mehods Forecass for demand which include some paern like rend or seasonaliy require facors for such paerns. The simple ime series models above include only one facor, which for he average level of demand. When he underlying demand has for insance a rend, hese simple models do no perform well here can be a significan bias in he forecas. The daa presened in numerical and graphical form Figure 2: Bike 3023 Demand Daa wih Trend in Figure 2, for an iem known as Bike 3023, has a definie rend componen. If he basic exponenial smoohing model wih a smoohing facor of α0.2 is used o forecas, he forecas values, along wih he associaed errors and bias are as shown in Table 4. Noe ha one can observe he bias wihou he calculaions since he error is always negaive saring in period 2. This shows ha he forecas model is always underesimaing he demand and is a good indicaion ha he wrong forecas model is being used. One can observe his paern in Figure 3 where he forecas is shown along wih he demand and he forecas Table 4: Example Daa wih Forecas 5
is always under forecasing or lagging he demand. Therefore, demand ha has some paern like a rend or seasonaliy should be forecas wih a model ha conains he adjusmen facor for he paern. Trend-Enhanced Forecasing Models Figure 3: Demand and Forecas Informaion The funcional form of a model which forecass demand wih a rend parameer requires wo componens, a level componen, L, and a rend componen, T. When T is used o represen an esimae of he rend as of period, he model for forecasing one period ino he fuure is F + + L T (2) The addiive rend adjusmen is one of he mos commonly used and is someimes referred o as Hol s Model. To forecas he r h period ino he fuure, he model is F + + r L rt (22) Exponenial Smoohing Updaes Hol s Model Each period when more informaion becomes available, he level and rend facors can be updaed. This is done wih equaions very similar o he equaions for he basic exponenial smoohing model presened earlier. For he basic exponenial smoohing model, a smoohing parameer α was used o deermine how much of he new demand informaion should be included in he level facor. Since here are now wo facors, level and rend, a second smoohing parameer β is needed for deermining he amoun of smoohing o be done on he rend facor. Values for β are beween 0 and. The updaing equaions for each facor for he case of addiive rend (Hol s model) are L ( + α D + α)( L T ) (23) T ( L L ) + ( β ) T β (24) 6
Trend- and Seasonaliy-Enhanced Forecas Models When boh rend and seasonal facors are presen, along wih he average level facor, he forecas equaion is a combinaion of he hree facors. The mos common model and one known as Winers Model, assumes an addiive rend facor and a muliplicaive seasonaliy facor. This model for forecasing one period ino he fuure is F (25) + ( L + T ) S+ The facor for seasonaliy, S +r, is he seasonal facor for he period +r, r periods in he fuure. Noe ha here is a seasonal facor for every season. If he forecas is quarerly, hen here are four seasonal facors. If he forecas is done monhly or weekly, hen here are welve or 52 seasonal facors respecively. In some shor-erm forecasing siuaions, where demand varies by he day of he week, here could be a seasonal facor for each day of he week, or seven facors. For forecasing r periods ino he fuure, he form is F + r L + rt ) S+ r ( (26) Exponenial Smoohing Updaes Winers Model Jus as was done for he addiive rend model (Hol s model), he facors for addiive rend and muliplicaive seasonaliy (Winers model) can be updaed as new informaion becomes available. In addiion, since here are now hree facors, a hird smoohing parameer γ is needed for seasonaliy. The updaing equaions are hen L D α + ( α)( L + T ) (27) S ( L L ) + ( β ) T T β (28) D S + p γ + ( γ ) S L (29) where p is he number of seasons (e.g., p2 for monhly daa wih a yearly cycle). Model Iniiaion and Forecasing Jus as was he case for he basic exponenial smoohing model, i is imporan o find good iniial saring facors and hen rain he model. Bu for he muli-facor models, his is a lile more involved. Two ses of example daa are used below o illusrae his iniiaion on Hol s and Winers models. 7
Hol s Addiive Trend Model Example Managers a Dynosasio wan o se up forecasing models for heir mos popular producs. The demand for one of heir producs which has seen phenomenal growh since is inroducion is shown in Table 5. This produc has been on he marke since January of 2003 and hus he here is demand daa for his produc for eleven periods hrough November of 2003. An analys for he firm has decided o use Hol s Model o forecas fuure demand and in paricular come up wih an esimae of demand for December of 2003. Since he model assumes an addiive rend, a sraigh line can be fi o he daa o esimae he iniial level Table 5: Dynosasio Monhly Demand facor (he inercep) and he iniial rend facor (he slope of he line). A linear regression yields he following Inercep: 297 Slope: 87.9 These wo erms hen become he esimaes of L and T as of period 0 (demand was regressed agains he period numbers hrough ) so ha L 0 297 T 0 87.9 Using he forecas equaion, he forecas for period becomes F 297 + 87.9 + L + T F L0 + T0 384.9 To coninue, he firm now observes he firs period of demand, D 404. Wih his informaion, he level and rend facors can now be updaed so ha hey are curren as of period. The analys has chosen a smoohing parameer of α0.2 for he level facor. L L α D + ( )( + α L T ) α D + α)( L + T ) 0.2(404) + ( 0.2)(297 + 87.9) ( 0 0 Similarly, wih a smoohing parameer of β0.3 for he rend facor T β L L ) + ( β T T ( ) β ( L L0 ) + ( β ) T0 0.3(388.7 297) + ( 0.3)87.9 A forecas for period 2 can now be made F 388.7 + 89.0 477.8 + L + T F2 L + T * 388.7 89.0 (* Noe ha some calculaions will be slighly affeced by rounding.) 8
The res of he calculaions are shown in Table 6, including he forecas for period 2, December of 2003. Noe ha he period 0 numbers are he iniial values of he level and rend obained from he regression. Table 6: Forecass and Level and Trend Facor Updaes Also in Table 6 are he errors calculaed by using he model o forecas he pas daa. Mos imporanly, i can be observed ha here is no a paern o hese errors. Thus, here is no sysemaic bias ha would indicae he use of a wrong model. 9
Winers Addiive Trend, Muliplicaive Seasonaliy Model Example The disribuion manager of Jackes-and-Such wans o se up a forecasing model for one of he firm s more popular producs. The demand for his produc is shown in Table 7. A plo of his daa indicaes a significan seasonaliy along wih growh over he las four years, as can be seen in Figure 4. The manager has decided ha he appropriae forecasing model should be one wih addiive rend and muliplicaive seasonaliy (Winers Model). Iniializaion for his model is much like ha of he rend only model shown above. The goal is o fi a sraigh line o he daa and hen see how far off ha line each of he seasons are, hus finding he seasonal facors. One way would be o hand fi a line o he daa. Anoher way would Figure 4: Plo of Demand Showing Trend and Seasonaliy be o use regression, like in Hol s model, bu in order o use linear regression; he daa mus firs be deseasonalized. Deseaso nalizing Demand Deseasonalizing daa essenially requires wo seps:. Finding he average seasonal demand over a complee se of seasons for all daa available. 2. Ensuring ha he averages are cenering on he appropriae period. For demand daa, seasons can be quarers of he year, monhs of he year, 4-week periods of a year, weeks of he year, and any oher collecion of periods where one could possibly observe a recurring paern. When seasons are aken o be quarers for insance, one can 20
find he average deseasonalized quarerly demand by aking averages over any four consecuive quarers. Using he daa from Jackes-and-Such, he average quarerly demand over he firs year is Since his is he average over he firs four periods, his demand average is cenered on period 2.5, which is he subscrip on he average demand. This can be seen in Table 8 where he firs se of dark diagonal lines show he.5 as he average over he demand daa from 98 o 33. In similar fashion, he average value of 3.5 is found by aking he average over four consecuive quarers saring wih period 2. D 98 + 06 + 09 + 33 4 2.5.5 Table 8: Deseasonalized Calculaions D 06 + 09 + 33 + 07 4 3.5 3.8 So ha he deseasonalized demand is cenered on each period and no beween hem, each pair of he deseasonalized averages above and below each period mus be averaged o ge he deseasonalized esimae is as of a cerain period, and no beween he periods. D D + D 2.5 + 3.8 2 2.5 2.5 3 2.6 This cenered, deseasonalized demand average is shown in he las column of Table 8 where he se of ligh lines indicae he resul of he average of he wo numbers,.5 and 3.8. The res of he cenered, deseasonalized averages are also shown in his column. I should be noed ha his procedure o deseasonalize he demand is appropriae for seasonal siuaions where he number of seasons is even. An even number of seasons requires he deseasonalized daa be cenered. If he number of seasons is odd, as would be he case if he daa were broken ino say hireen four-week seasons, hen when all of he seasons are averaged, he resuling average would occur on he middle period (in he case of hireen periods, he sevenh period of he daa being averaged) and here would be no reason o cener he average. 2
Deermining he Iniial Forecasing Facors Once he daa has been deseasonalized, finding he level and rend facors is he same as wih Hol s rend only model. The deseasonalized averages can be regressed on he period number wih he resul for his daa ha L 0 00.8 T 0 3.5 Finally, he iniial seasonal facors mus be deermined o complee he model. This requires hree seps.. Finding an esimae of he sraigh line fi of deseasonalized demand, 2. Deermining an esimae of he seasonaliy for each period. 3. Averaging he esimaes across all similar seasons. Sep can be done by finding he sraigh line esimae of deseasonalized demand Dˆ ˆ D L + T (30) 0 0 For insance, for period 4 he esimae is ˆ 4 D 00.8 + 4 3.5 4.8 The esimae of seasonaliy from Sep 4 for any period is he raio of he acual demand o he demand forecas D Dˆ S ~ (3) Again, using period 4, his esimae is D 33 4.8 ~ 4 S 4 ˆ D4 This number indicaes ha he acual demand for period 4 is approximaely 6% higher han he sraigh-line deseasonalized fi..6 22
Once an esimae has been calculaed for each demand observaion (as shown in Figure 5 wih arrows indicaing all quarer 4 differences), Sep 3 is used o find he iniial seasonal facors. For any given season, all esimaes for ha season are averaged for an Figure 5: Seasonal Facor for Q4 overall iniial seasonal facor for he given season. Thus, one seasonal facor is obained for each of he p seasons by averaging over k observaions of ha season. S {,2, K, p} ~ S ~ + S + p ~ + S + 2 p k ~ + S + 3 p + K (32) For he 4 h quarer, his would be S S ~ ~ + S + S 4 ~ + S.6 +.3 +.+.3 4 4 8 2 6 4.3 Doing his for each season, he four seasonal facors are found as S 0.94 ; S 0.96 ; S 0.98 ; S4.3 These calculaions are summarized in Table 9. Forecasing wih Winers Model Now ha he iniial level, rend, and seasonal facors have been obained for Winers model, he model can be rained and hen used o forecas he desired fuure periods. 23
Table 9: Seasonal Esimaes and Iniial Seasonal Facors To rain he model, he iniial facors are used o forecas for he firs period. In his case, he firs forecas is for Quarer of 2000. This forecas is obained using Equaion (27) and F ( L + T ) S F ( L0 + T0 ) (00.8 + 3.5)0.94 98.0 + + S Once his forecas has been made, he assumpion is ha ime moves forward and he period demand is observed o be 98. Wih he observaion of more demand, he level, rend and seasonal facors can be updaed as was he case wih he previous rend only model. To do his, Equaions (32)-(34) are used. Firs, he level facor is updaed wih he assumpion ha α0.25 as D L α + ( α)( L + T ) S L D α S + ( α)( L 0 + T 98 0.25 + 0.75(00.8 + 3.5) 04.3 0.94 Nex, he rend facor is updaed wih he assumpion ha β0.20 as T β ( L L ) + ( β ) T T β ( L L ) + ( β ) T 0 0.2(04.3 00.8) + 0.8 3.5 3.5 0 ) 0 24
Finally, he seasonal facor for period, which happens o be he one used for any firs quarer forecass, is updaed. The smoohing parameer is γ0.5. S S + p 5 D γ L D γ L + ( γ ) S + ( γ ) S 98 0.5 + ( 0.5)0.94 0.94 04.3 Noe ha his updae didn change any of he facors and his is because he forecas was very accurae for he firs period. Once he parameers have been updaed, Equaion 27 can be used once again o forecas he nex period, period 2. The res of he compuaions for his forecasing and updaing are shown in Table 0. Table 0: Forecasing and Updaing for Jackes-And-Such Summary The prior secions have provided he reader wih an inroducion o a number of fundamenal approaches and models o ime series forecasing and illusraed heir compuaional process. Some forecas models like Winers are complicaed, involving numerous mahemaical equaions wih he inheren required noaion o manage he needed compuaions. Bu as complicaed as hey migh be, using hese saisical models can help reduce forecas errors o manageable levels wihou significan levels of every- 25
day human ineracion. These models are designed o remove sysemaic error and can be helpful in doing jus ha when implemened correcly. While more elaborae models like ARIMA and X have been proposed 3, he se described above have proved o be he primary forecasing ools used in pracice. Pracice has also shown ha forecass, no maer how sophisicaed a model employed, will sill have forecas errors. Perfec forecass, while a laudable goal, can be aained because random behavior and dynamic change is always presen. The soluion? Human inpu is a criical componen o es for reasonableness and handle unforeseeable evens. Therefore, he forecas sysem design needs o combine human oversigh managemen wih saisical forecasing models on compuer-based sysems like SAP s R/3 sysem, so ha managemen ime can be spen mos producively on he numerous asks wihin he supply chain. Forecasing References Armsrong, J. S. (200c), Exrapolaion for ime-series and cross-secional daa, in J. S. Armsrong (ed.), Principles of Forecasing. Norwell, MA: Kluwer Academic Press. Box, G. E. P., Jenkins, G. M., and Reinsel, G. C. (994). Time Series Analysis, Forecasing and Conrol, 3rd ed. Prenice Hall, Englewood Clifs, NJ. Chafield, C. (996). The Analysis of Time Series, 5h ed., Chapman & Hall, New York, NY. Gardner, E. S. Jr. (985), Exponenial smoohing: The sae of he ar, Journal of Forecasing, 4, -28. C. C Hol (957) Forecasing seasonals and rends by exponenially weighed moving averages, ONR Research Memorandum, Carnegie Insiue 52. Nelson, C. R. (973). Applied Time Series Analysis for Managerial Forecasing, Holden- Day, Boca-Raon, FL. Makradakis, S., Wheelwrigh, S. C. and McGhee, V. E. (983). Forecasing: Mehods and Applicaions, 2nd ed., Wiley, New York, NY. P. R. Winers (960) Forecasing sales by exponenially weighed moving averages, Managemen Science 6, 324 342. 3 The ineresed reader can use he ciaions lised in he references o explore heir feaures. 26
Time Series Forecasing Problems. Using he daa above in Table 4 for Bike 3023, forecas demand using he BES model, bu wih an α0.4. Compare his forecas o he example wih an α0.2. 2. Using he daa above in Table 4 for Bike 3023, forecas demand using a five-period moving average and a five period weighed moving average for periods 7 hrough 3. For he weighed moving average, use he weighs 0.5, 0.4, 0.3, 0.2, and 0.. Compare hese wo forecass o he wo BES models for Bike 3023, especially wih respec o he MAD, MSE, Bias, and TS for periods 7 hrough 2. 3. Using he daa above in Table 4 for Bike 3023, fi an addiive rend model o he daa and forecas periods 7 hrough 5. Compare his forecas model o he wo BES models and he wo MA models in problems and 2 by commening on he errors. 4. Table P4 conains wo years of demand informaion for a recenly inroduced food produc. Use a addiive rend model o forecas demand for his new produc for he firs hree monhs of 2004. 5. Table P5 conains four years of demand informaion for iem X503A2. I is believed ha since he demand shows some seasonal paern ha Winers Model is he forecasing Table P4: Demand for New Food Produc model ha should be used for his iem. Forecas 2004 Quarer demand for X503A2 based on he forecas model fi wih he firs four years of daa. Use α 0.4, β0.3, and γ0.2 as smoohing parameers. Table P5: Quarerly Demand Daa for X503A2 27
Table P6: Monhly Demand Daa for Rain Jacke 6. Table P6 conains hree years of monhly demand informaion for a popular classic rain jacke. Forecas he firs six monhs of demand for his jacke based on forecas model fi wih he firs four years of daa. Use α 0.4, β0.3, and γ0.2 as smoohing parameers. 28
Forecasing wih SAP R/3 Inroducion and Background The prior secion presened a uorial on basic ime series forecasing logic, procedures and performance measures. While we could program hese procedures using ools like Visual Basic or Excel spreadshees, here are several commercial packages available o suppor business planning. This secion illusraes how o employ he SAP R/3 sysem o conduc forecasing. I shows how o load daa, define forecas parameers, obain forecass, and review he resuls from R/3 s forecasing process. The Glow-Brigh Corporaion case (included in a laer secion) provides an opporuniy o demonsrae he forecasing sysem wihin he SAP R/3 sysem. Below is an example plo of sales in R/3 for par number 40-00C of Glow-Brigh. Noe ha he daa exhibis seasonaliy and an upward rend in hisorical sales. The R/3 forecasing sysem employs a ime series analysis approach o forecasing, and as such, aemps o find a paern over ime in he hisorical daabase, and hen exends his paern ino he fuure. As discussed above, here are a number of models ha users may chose o aemp o mach hisorical paerns. Therefore, he sysem mus firs have hisorical daa o do he ime series analysis for he forecass. Loading Hisorical Daa The firs sep o using he forecas feaure of R/3 requires populaing he Maerial Maser wih hisorical sales daa. Since he sysem used in a learning environmen is no an acive sysem wih real sales daa, his hisorical daa mus be enered before any forecasing can be done. To ener his daa, navigae hrough he Dynamic Menu wihin 29
R/3 down o he plan level by making he appropriae enries, as shown below. This will evenually lead o he Forecasing ab wihin he Maerial Maser which allows one o use he Forecas Module. Nex, open he Forecasing ab of he record for par 40-00C and click on he Consumpion Vals buon. This opens he able of hisorical daa, as shown below. Noe ha he firs ime his able is opened he record will be empy. 30
One of he mos imporan issues in using he R/3 forecasing module is he ime orienaion of he daa. This arises because he R/3 sysem is an operaional sysem wih a running clock. Any ime you use he sysem, he sysem clock will be he curren ime and dae. Thus, he firs hing ha has o be deermined is he curren R/3 sysem ime clock dae. This will be he ime origin reference for forecasing. Anoher imporan issue is ha he hisorical daa needs o be sequenced from mos recen o oldes. The Glow Brigh hisorical sales daa is organized in an oldes-o-mos recen forma as shown below and his is he opposie of wha is needed. Assume ha he curren R/3 sysem ime is Augus of 2003. This will be assumed o be he ime origin poin for he sales hisory. Tha is, he las monh of he sales daa should be Augus of 2003. Nex, he daa needs o be re-sequenced from mos recen o oldes. This can be done very easily in Excel, saring wih he daa from Augus 2003 (Period 68 wih a demand of 52,88). 3
The daa is hen ransferred o he R/3 sysem by using he Excel COPY command (Noe ha his is he only way of ransferring daa from Excel o he R/3 sysem). This daa ransfer mus be done by copying no more han eleven cells a a ime. Thus, one needs o go o he Excel shee and highligh he firs cells of daa, and hen go o he R/3 Consumpion Page and highligh he firs cell in he Correced Values column, and pase he firs hisorical daa figures ino R/3. Please noe ha you have o use CTRL-V (simulaneously pressing he CTRL key and he V key) o pase. Coninue ransferring daa from he Excel shee by repeaing he COPY command for he appropriae daa (again, remembering o highligh no more han eleven cells a a ime) 32
and going o he R/3 Consumpion Page and highlighing he nex empy cell in he Correced Values column before placing he daa wih he CTRL-V enry. When all he daa have been ransferred, i should be saved in he sysem by clicking he save icon in he upper lef corner of he screen (This is he orange disk icon). Forecasing Wih SAP R/3: Seps and Inpu Requiremens Wih he hisorical daa loaded ino he maerial maser forecasing record for an iem, wo forecasing opions are available o he user: User Selecion Approach (USA) all forecas parameers and models are manually enered by user. Sysem Selecion Approach (SSA) a se of specific forecas parameers and models (e.g., smoohing consan values, simple versus enhanced smoohing, ec.) are deermined by R/3 sysem and he remainder is user deermined. These wo approaches are illusraed nex. User Selecion Approach o Forecasing Firs, here is a need o reurn o he Forecasing ab wihin he Dynamic Menu of he R/3 sysem as shown below. 33
Once he Forecasing ab has been reached, he forecasing model mus be chosen. There are many forecasing models wihin R/3 and clicking on he dropdown buon beside Forecas model presens he opions, as shown below. The user approach requires he analys o deermine and selec he model ha is appropriae for he daa. Besides selecing he desired forecasing model, he user also needs o inpu he forecasing parameers discussed earlier in his documen. These requiremens are illusraed below. Once he parameers have been enered, he Save buon (The orange disk icon) is used before proceeding wih he forecas. 34
When he forecas seup is complee, he Execue Forecas buon is used o iniiae he forecas process. The forecas execuion requires esablishing he forecas ime origin and confirming ha he correc parameers are se, as shown wih he following screen shos. Wih he forecasing execuion compleed, he Forecas Resuls are displayed. The resuls provide he forward looking forecass, basic error merics and messages. Clicking on he char buon provides a plo of he hisorical demand and forecased daa. 35