ANALYSIS FOR FINDING AN EFFICIENT SALES FORECASTING METHOD IN THE PROCESS OF PRODUCTION PLANNING, OPERATION AND OTHER AREAS OF DECISION MAKING

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1 Inernaional Journal of Mechanical and Producion Engineering Research and Developmen (IJMPERD ) Vol.1, Issue 2 Dec TJPRC Pv. Ld., ANALYSIS FOR FINDING AN EFFICIENT SALES FORECASTING METHOD IN THE PROCESS OF PRODUCTION PLANNING, OPERATION AND OTHER AREAS OF DECISION MAKING Mr. M A HANNAN, Mr. M G MORSELIN, Mr. M M RAHMAN and Mr. M S ISLAM Deparmen of Mechanical Engineering, Dhaka Universiy of Engineering & Technology, Gazipur. Bangladesh. Corresponding Auhors: hannan05@gmail.com ABSTRACT Forecasing is he firs major aciviy needed in planning and scheduling process. Accuracy measures and he evaluaion are he vial poins of he forecass. Many forecasers and decision makers such as execuive managers, planners, producion managers, sales managers, and invenory managers have differen needs in erms of he following: The iming of an even, e.g., when he nex recession will sar; he magniude of a variable (e.g., sales volume nex monh); he iming and quaniies of some variables (e.g., when and how many raw maerials o order); and he monioring of some quaniy (e.g., marke share). Managers need he above predicions and are faced wih he problem of having o selec forecasing echniques among he many ha are available. Forecasing echniques range from naive models, moving average, exponenial smoohing (single, double, ec.), adapive echniques and economeric models o sophisicaed echniques (Box-Jenkins, Parzen's Mehod, ec.). In addiion, forecass can be made judgmenally. The obvious quesion is wha is he bes way of predicing he fuure. This paper deals wih he differen accuracy measures and forecasing echnique evaluaion, based on he pas sales daa of a

2 Mr. M A Hannan, Mr. M G Morselin, Mr. M M Rahman and Mr. M S Islam 2 manufacuring company. A review of research sudies in he area of forecasing mehods and heir implicaion in evaluaing forecass have been provided and he reliabiliy of he daa sources available for forecasing is discussed. The differen accuracy measures described and he field of heir uses are summarized. The paper hen considers he selecion of he few parameers and he adjusmen of he forecass hrough monioring of forecas accuracy on a coninuous basis. Finally, a general discussion has been made before drawing a conclusions along wih fuure direcions of research. KEY WORDS: POM: Producion and Operaions, Managemen, Forecasing, Demand Daa, Regression, TSA: Time Series Analysis, ESM: Exponenial Smoohing Mehod, MAD: Mean Absolue Deviaion, MSE: Mean Squared Error, TS: Tracking Signal SE: Sum Error, BIAS: Mean Error, CFE: Cumulaive Forecas Error. 1. INTRODUCTION Forecasing [1] is a echnique for ranslaing pas experience ino esimaes of he fuure. Forecasing involves careful sudy of pas daa and presen scenario. The main purpose of forecasing is o esimae he occurrence, iming, or magniude of fuure.evens. For example, he rend of pas en years in he demand of cars and corresponding purchasing power of he consumers may form a basis of forecasing he demand of cars during nex year. Once, he reliable forecas for he demand is available, a good planning of aciviies is needed o mee he fuure demand. Forecasing hus provides he inpu o he planning and scheduling process. Precise forecasing of economic aciviies, such as produc demand, is almos impossible because of many ineracive facors, which are difficul o model. Despie he fac ha highly reliable forecasing is unrealisic, he approximae esimae forms he basis of planning process.

3 3 Analysis for Finding an Efficien Sales Forecasing Mehod in he Process of Producion Planning, Operaion and Oher Areas of Decision Making The objecives of his sudy are: a. To idenify he characerisics of he pas sales daa colleced and o check each se of daa for suiabiliy of use in he forecas mehods according o he characerisics and o idenify which model of forecasing would be used o projec he fuure demand of each of he iems. Precisely and finally b. To show he mehod of comparison of he forecasing mehods by calculaing he errors associaed wih each mehod of forecas. 2. BRIEF REVIEW OF RESEARCH MATERIALS IN THE AREA OF FORECASTING ACCURACY AND EVALUATION There have been many research sudies which summarize he accuracy and he performance of quaniaive and qualiaive forecasing echniques [1-16]. For [ 1-11, 13] example, numerous sudies have indicaed ha quaniaive echniques perform beer han qualiaive echniques while ohers have found he opposie resul or ha heir performance is abou he same. Oher research has evaluaed he performance of a paricular model relaive o oher models. Many sudies have indicaed ha simple forecasing echniques do as well as sophisicaed echniques and in some cases hey do beer. Oher researchers have showed he imporance of using combining forecasing echniques and he impac on improving he accuracy wheher using a simple combining approach or a weighed approach. Deailed informaion on many of he findings is summarized in an aricle by Mahmoud (1984), summarizes briefly some of he mos imporan findings. The pas research suggess ha quaniaive mehods ouperform qualiaive mehods. This is of obvious significance o praciioners wishing o improve heir forecasing accuracy. Forecasers or praciioners mus, however, be aware of he paricular circumsances under which empirical research has demonsraed he superioriy of quaniaive mehods. Only where he circumsances are similar in pracice can more accurae forecass using quaniaive echniques be expeced. For insance, when he forecaser is dealing wih a limied number of pas observaions, he applicabiliy of qualiaive

4 Mr. M A Hannan, Mr. M G Morselin, Mr. M M Rahman and Mr. M S Islam 4 mehods migh be more appropriae. Armsrong (1985) suggesed ha i is advanageous o experimen wih more han one qualiaive mehod as some are more accurae han ohers. Anoher ineresing conclusion from he praciioners' poin of view ha many pas sudies have revealed is ha simple forecasing mehods perform equally as accuraely as do sophisicaed mehods. This has been illusraed by a variey of sudies. Examples are Makridakis and Hibon (1979) and Makridakis e. al. (1982). The implicaion of hese findings is o encourage praciioners o view forecasing mehodologies as a se of mehods wihin heir abiliy o undersand and use hem. This may be especially so in he case of 'mnagers who wish o predic and cope wih fuure uncerainies bu do no have he raining or experise o deal wih he very complex forecasing echniques. For heoriss, he implicaions are o concenrae heir effors on he developmen and refining of simplifier forecasing models, and on he simplificaion of more complex echniques. The Reliabiliy of he Daa Sources [13] A major consideraion in he selecion of a forecasing mehod for a paricular applicaion is he ype of paern in he daa. Normally, here are four differen daa paerns: horizonal, seasonal, cyclical and rend. However, one may find ha one or more of hese paerns could exis in a paricular imeseries. Idenifying he ype of daa would enable he forecaser o concenrae on a group of mehods which is more suiable o a paricular daa paern. However, before a daa paern is idenified, i is imporan ha he forecaser recognizes he dependence of any forecasing mehod upon a 3-reliable daabase. For example, Mahmoud (1982) and Rice and Mahmoud (1985) provided informaion on a variey of daa bases available which would be useful for organizaions or inernaional businesses. The liss idenified he ype of daa available and is applicabiliy in forecasing. Also, hey discussed he imporance of measuring he accuracy of he daabases and how one would idenify heir reliabiliy for a paricular source. Proper operaion and mainenance of an accurae and imely

5 5 Analysis for Finding an Efficien Sales Forecasing Mehod in he Process of Producion Planning, Operaion and Oher Areas of Decision Making daa sysem gives he forecaser an insrumen wih which o conrol and minimize he shorcomings of various forecasing mehods. I is, herefore, essenial o evaluae he daabases available o verify he reliabiliy of he daa before analyzing he daa paern. Finally, from a pracical sandpoin, if valuable resuls are o be obained from applying forecasing models, managers and forecasers mus remember ha a forecas is only as accurae as he daa se upon which is based. Measures of Forecasing Accuracy plays an imporan role in evaluaing forecasing mehods. Accuracy can refer o "goodness of fi" which in urn measures how well he forecasing model is able o reproduce he daa ha were used o develop he forecasing model. Mos imporanly, however, i should refer o he fuure (pos-sample). ha is, for daa ha have no been used o develop he forecasing model. Perceived accuracy varies from one applicaion o anoher or from one decision maker o anoher as described by Wheelwrigh and Makridakis (1985). For some decision siuaions, plus or minus 10% may be sufficien; in ohers, a variaion of as lile as 5% could spell disaser. Thus, being familiar wih he differen accuracy measures and heir pros and cons would enable hose decision makers seeking high levels of accuracy o acheive more accurae forecass. While accuracy is a significan facor in evaluaing forecass, i is difficul o define i. The difficuly is associaed wih he absence of a single universally acceped measure of accuracy (Gardner and Dannenbring, 1980; Mahmoud, 1984; Makridakis and Wheelwrigh, 1979; Makridakis and Winkler; This is due o he fac ha specific accuracy measures are appropriae for differen ypes of forecasing applicaions. For example, accuracy measures are defined by Granger (1969) as loss funcions and can be in he form of linear, quadraic, or non-symmeric funcions. Suppose a forecasing model could be bes fied using a quadraic model and an accuracy model such as Mean Absolue Error (MAE) was used which is more suiable for measuring linear or non-symmeric funcions. In his case an accuracy measure is no

6 Mr. M A Hannan, Mr. M G Morselin, Mr. M M Rahman and Mr. M S Islam 6 appropriae for he ype of daa used. This problem can be avoided wih a clear undersanding of he differen accuracy measures. Unforunaely, here is no single accuracy measure ha can be implemened in every forecasing siuaion. Also, i has been shown in many sudies ha he bes model fied (ex-ane) in erms of accuracy does no necessarily provide he bes forecas in he forecased phase (ex-pos) (see Mahmoud, 1982; Makridakis and Wheelwrigh, 1979). For example, he performance of hireen forecasing models esed wih a represenaive series of weekly sales daa covering a 104 week ime horizon, in which 12 periods were used for he ex-pos phase (Mahmoud, 1984). The hireen forecasing models ranged from he simplisic naive forecasing mehod o he complex Box-Jenkins approach. The hireen forecasing models are lised in he order of he Mean Square Error (MSE) of forecasing accuracy. The rank order of he MSE is from low o high. Noe ha he rank order of he Mean Square Error (ex-ane) and he U-Saisic are usually closely relaed. There is lile associaion beween he rank order of he accuracy measures a he ex-ane and ex-pos phases. The cos of forecasing error does no appear o be relaed o any of he oher accuracy measures used a he forecased phase. Some of he mos widely applied measures will be discussed o show heir advanages and disadvanages. I should be noed ha one common goal is o minimize he error in he forecas. Thus, he error [9] is defined as: Error = Acual - Forecas or e = A - F, where, e represens he error a period. A represens he acual value a period and F represens he forecased value a period. For a ime series of a variable such as he sales of produc A, he acual value of he monhly sales of he produc from January 1980 o December 1985, ha is, 72 periods. By idenifying he daa paern and choosing he appropriae model, he forecaser can measure he performance of he model by calculaing he oal errors from January 1980 o December 1985 (fied phase). The

7 7 Analysis for Finding an Efficien Sales Forecasing Mehod in he Process of Producion Planning, Operaion and Oher Areas of Decision Making difference beween he wo values (acual forecas) is a measure of he error in forecasing his variable for each period. In his fashion, 1 = January 2005 and n December Remember ha December 2011 represens he curren 3. BENEFITS OF FORECASTING ACCURACY IN INDUSTRY Good forecas of maerial, labor and oher resources for operaion are essenially needed by he managers. If good projecion of fuure demand is available, he managemen may ake suiable acion regarding invenory. Similarly, if producion aciviies are accuraely forecased, hen balanced workload may be planned. Good labor relaions may be mainained, as here would be lesser hiring and firing aciviies by he managemen wih beer manpower planning. Therefore, forecasing is useful due o following benefis, like: Effecive handling of uncerainy, Beer labor relaions, Balanced workload, Minimizaion in he flucuaions of producion, Beer use of producion faciliies, Beer maerial managemen, Beer cusomer service, Beer uilizaion of capial and resources, Beer design of faciliies and producion Figure 1 : Balance of forecasing Effecs

8 Mr. M A Hannan, Mr. M G Morselin, Mr. M M Rahman and Mr. M S Islam 8 Effors in forecasing aciviy involve wo ypes of coss [7]. While more effor in forecasing causes increased cos due o daa collecion and analysis; lesser forecasing aciviy involves los revenue, which may be due o unplanned labor, unplanned maerial or unplanned capial cos. Therefore, each firm should mainain a balance in is forecasing effor and sick o a zone near o accuracy cos rade off. Several demolishmen (besides some developmen) have been occurred during he pas few years in he indusrial field ha offers all of us an opporuniy o inegrae forecasing and decision-making. This case sudy research work has been done wih he aim o improve undersanding and awareness abou he erm Sales Forecasing. Almos all managerial decisions are based on forecass. Every decision becomes operaional a some poin in he fuure, so i should be based on forecass of fuure condiions. Forecass are needed hroughou an organizaion -- and hey should cerainly no be produced by an isolaed group of forecasers. Neiher is forecasing ever "finished". Forecass are needed coninually, and as ime moves on, he impac of he forecass on acual performance is measured; original forecass are updaed; and decisions are modified, and so on. So, Forecasing is a mehod for ranslaing pas experience ino esimaes of he fuure. 4. LITERATURES SURVEY FOR THE PRESENT WORK The componens of ime serious demand forecas: a. average: he mean of he observaions over ime b. rend: a gradual increase or decrease in he average over ime c. seasonal influence: predicable shor-erm cycling behavior due o ime of day, week, monh, season, year, ec. d. cyclical movemen: unpredicable long-erm cycling behavior due o business cycle or produc/service life cycle

9 9 Analysis for Finding an Efficien Sales Forecasing Mehod in he Process of Producion Planning, Operaion and Oher Areas of Decision Making e. random error: remaining variaion ha canno be explained by he oher four componens. [11, 17] 5. VARIOUS METHODS OF FORECASTING (i) Simple Moving Average(SMA) Mehod The Simple moving average is a discree averaging mehod, where periods in he pas beyond a cerain number are considered irrelevan for he analysis. Simple moving averages echnique reires he old daa and inducs fresh daa in o is calculaion a every forecasing period. a moving average can be use o averages ou seasonaliy if he number of periods included in he averages id equal o he amoun of ime required for he seasonal paen o sar o repea is self ha is welve monhs of monhly daa from quarers of quarerly daa and so on if he seasonal paen repeas is year. moving average echniques forecas demand by calculaing an average of acual demands from a specified number of prior periods each new forecas drops he demand in he oldes period and replaces i wih he demand in he mos recen period; hus, he daa in he calculaion "moves" over ime simple moving average Simple Moving Average compues using he equaion, SMA +1 = ( n 1 ) A i i= + 1= n Where, SMA +I = he simple moving Average a he end of he period. A = Acual demand in period. N = he number of periods included in each average forecas for period +1: SMA +1 = F +1 = A

10 Mr. M A Hannan, Mr. M G Morselin, Mr. M M Rahman and Mr. M S Islam 10 Key Decision: n - How many periods should be considered in he forecas

11 11 Analysis for Finding an Efficien Sales Forecasing Mehod in he Process of Producion Planning, Operaion and Oher Areas of Decision Making (ii) Weighed Moving Average(WMA) Mehod [11,17] Equal weighs where assigned o all periods in he compuaion of a simple moving Average. A weighed moving average assigns more weigh o some values han o ohers. The raionale for varying weighs in usually o allow recen daa o influence he forecas more han older daa if here is a long-run rend in demand, a weighed average wih heavier emphasis on recen daa is an improvemen over a simple average, bu i will sill lag behind demand. Therefore, weighed moving average is a moving average where each hisorical demand may be weighed differenly: Weighed moving average = A = Where, ( D * w ) D = Demand in period n ; W = Weigh applied o period s demand for period n w v W v = sum of weighs value; N = number of observaion Sum of all he weighs = 1 forecas: F +1 = A = forecas for period +1 The choice of weighs are some wha arbirary, because here is no any se of formula o deermine hem. The mos curren period weighs heavily han previous. [11, 17] (iii) Exponenial Smoohing(ES) Mehod A smoohing echnique in ime-series analysis ha weighs all observaions prior o he prior in ime a which a smoohing value is desired. A modified version of he weighed moving average echnique is he exponenial smoohing mehod.

12 Mr. M A Hannan, Mr. M G Morselin, Mr. M M Rahman and Mr. M S Islam 12 The new base = previous base + a (new demand previous base) Or saed in symbols. The Mahemaical Model of Exponenial Smoohing Mehod (ESM) may be given as: _ S = S 1 +α (D - S ). (1) 1 Smoohing consan, α, is beween 0 o 1, wih used of 0.01 o D = Acual demand for period. _ S = Forecas of he demand made for he presen period =F 1 _ S = Forecas for he nex period made during he presen period =F α = Weighed facor for he curren demand basis) The equaion (1) is: New basic = α (new demand) + (1- α) (previous Or, _ S = α D + (1- α) S _ 1 Or, F -1 = αd + (1-α) F.. (2) The advanage of his mehod over he moving average mehod is ha one needs o have only wo figures one for he old forecas and anoher for he acual sales observaions I is no necessary o sore he on a number of periods. Smoohing consan focuses more on presen period han ha of previous periods. Exponenial smoohing(1s) order smoohing mehod): F -1 = α D + (1- α) F = α D + (1- α) { α D -1 +(1- α) F -1 } The weighages for each of he demands in he pas is discouned by a facor of (1- α). The las erm is negligible for a very large n. In effec exponenial

13 13 Analysis for Finding an Efficien Sales Forecasing Mehod in he Process of Producion Planning, Operaion and Oher Areas of Decision Making smoohing is a weighed average of all he demands in he pas, he weigh ages decreasing exponenially by he facor (1- α). The exend of smoohing. ha is, he filering ou process for random flucuaion, depend upon he alpha facor, When his facor is small, i leads o giving lower weigh ages o recen demands and more consideraion o old demands. If alpha is large, he reverse is rue. An approximae relaion of alpha facor (α) o he moving average, which needs o menion: Alpha facor (α) = 2 n + 1 Where, n = Number of periods in he moving average. (iv) Double Exponenial Smoohing (Trend Adjused Exponenial Smoohing) Mehod [17] When a rend exiss, he forecasing echnique mus consider he rend as well as he series average ignoring he rend will cause he forecas o always be below (wih an increasing rend) or above (wih a decreasing rend) acual demand double exponenial smoohing smoohes (averages) boh he series average and he rend forecas for period +1: F +1 = A + T Where, average: A = ad + (1 - a) (A -1 + T -1 ) = ad + (1 - a) F average rend: T = β CT + (1 - β ) 1 curren rend: CT = A - A -1 forecas for p periods ino he fuure: F +p = A + p T where: A = exponenially smoohed average of he series in period T = exponenially smoohed average of he rend in period

14 Mr. M A Hannan, Mr. M G Morselin, Mr. M M Rahman and Mr. M S Islam 14 CT = curren esimae of he rend in period a = smoohing parameer beween 0 and 1 for smoohing he averages β = smoohing parameer beween 0 and 1 for smoohing he rend. (v) Linear or Addiive Trend Model [11,17] The apparen linear rend in exponenially smoohing averages is he difference beween he successive values, _ S - S _ 1 By being can smooh _ S - no same as he value of α. Equaion (2) modified, _ S series wih componen β (bea) which is 1 S = α D + (1- α) ( S +T -1 ) (3) 1 The upward value of T, he smoohed is T = β (S -1 +T -1 ) (1- α) + (1- α) T -1.. (4) Where, T = The smoohed rend in presen period, T +1 = The smoohed rend in previous period of. Forecas he upcoming period by adding T o he curren smoohed average _ S, as Followings: Forecas for he nex period = F,1 = _ S + T Forecas for in period ahead = F,m = S + mt... (5) _

15 15 Analysis for Finding an Efficien Sales Forecasing Mehod in he Process of Producion Planning, Operaion and Oher Areas of Decision Making (vi) Linear Regression(LR) Model [11,17] The regression forecas is based on he assumpion of a model consising of a consan and a linear rendsraigh line equaion: For he purposes of a forecas where he parameers of he model may change, i is more convenien o express he model as a funcion of is he posiive displacemen from a reference ime T., where The forecas is based on esimaed parameers. 6. MEASURING FORECASTING ERRORS Diagnosic Measures of Forecas Accuracy [8] is almos impossible o obain in exacly righ forecas every ime. This is due o many facors, which affec he rend in daa. I is difficul o capure he exac inerrelaion of hese influencing facors. Therefore, some error in forecased value and acual value is quie common. Someimes, i is imporan o know if he forecaser (a forecasing echnique) is unbiased or no. An unbiased model should overesimae or underesimae he forecas in almos equal raio. Four useful measures of forecas accuracy ofen referred o as measures of forecas error, are discussed below. There are mainly wo aspecs of forecasing errors o be concerned abou - Bias and Accuracy Bias - A forecas is biased if is errors are more in one direcion han in he oher: - The mehod ends o under-forecass or over-forecass.

16 Mr. M A Hannan, Mr. M G Morselin, Mr. M M Rahman and Mr. M S Islam 16 Accuracy - Forecas accuracy refers o he disance of he forecass from acual demand ignore he direcion of ha error. Crieria for selecing a Forecasing Mehod [16] Objecives are 1. Maximize Accuracy and 2. Minimize he Bias However, poenial Rules for selecing a ime series forecasing mehod is o selec he mehod ha i. gives he smalles bias, as measured by cumulaive forecas error (CFE); or, ii. i gives he smalles mean absolue deviaion (MAD); or iii. gives he smalles racking signal; or iv. suppors managemen's beliefs abou he underlying paern of demand or v. ohers. I appears obvious ha some measure of boh accuracy and bias should be used ogeher. How? Wha abou he number of periods o be sampled? if demand is inherenly sable, low values of and higher values of N are suggesed if demand is inherenly unsable, high values of??? and lower values of N are suggesed The main Diagnosic Measures of Forecasing are: 6.1 Mean Absolue Deviaion (MAD) [5] A common measure of forecas error is he mean absolue deviaion, (MAD). The MAD is he mean of he errors made by he forecas model over a series of ime Periods, wihou regard o wheher an error was an overesimae or an

17 17 Analysis for Finding an Efficien Sales Forecasing Mehod in he Process of Producion Planning, Operaion and Oher Areas of Decision Making underesimae. The MAD is someimes called he mean absolue error or MAE. To calculae a Ineres, change all he signs o posiive, adds hen and divides by he member of Values ha were used o obain he sum. The expression for hese operaions in Equaion: MAD= n 1 ( D F ) n Where, D = Acual demand in period. F = Forecas demand in period. n= Number of periods considered for calculaing he error. 6.2 Mean Square Error (MSE) or, MSE (Mean Sum of Square Error) [5] The average of square of all errors in he forecas is ermed as MSE. Is inerpreaion is same as MAD. MSE = n =1 D - F 2 / n The mean square error (MSE) can also be used as a measure of forecas error. The MAE in found by squaring is of a series of errors made by he forecas model. Summing hese squared errors and dividing by he number of errors used in he Calculaion. Using he symbols defined above for he MAD, he equaion for he MAE is: MSE= n 1 ( D F ) n 2

18 Mr. M A Hannan, Mr. M G Morselin, Mr. M M Rahman and Mr. M S Islam BIAS [5] Bias is a measure of over-esimaion or under-esimaion. A posiive bias indicaed under-esimaion while a negaive bias indicaes over-esimaion. BIAS = n =1 D - F / n 6.4 Mean Forecas Error (MFE) [5] The average forecas value several imes period, however, should be very close o he average of he acual values over hese same ime periods. he MFE is calculae by summing he forecas errors over a series of period and dividing his sum by he number of errors used o compue he sum. Again using he same symbols, he equaion for he mean forecas error as: MFE= n 1 ( D F ) n 6.5 Mean Absolue Percenage Error (MAPE) [5] The mean absolue percenage error (MAPE) is a relaive measure ha is compued by dividing he forecas error for period by he acual demand for period and hereby compuing he Percenage Error in period. Percenage error in period = D F D 100 Where D -F = Forecas error in period. The percenage error is now summed by ignoring he algebraic sign (ha is, by aking is absolue value) and his sum is divided by he number of observaions o obain MAPE.

19 19 Analysis for Finding an Efficien Sales Forecasing Mehod in he Process of Producion Planning, Operaion and Oher Areas of Decision Making MAPE= 100 n n = 1 D F D 6.6 Tracking Signal (TS) [5] A racking signal indicaes if he forecas is consisenly biased high or low. I is compued by dividing he cumulaive error by he cumulaive mean absolue deviaion, or MAD: The racking signal is recompued each period, wih updaed, "running" values of cumulaive error and MAD. The movemen of he racking signal is compared o conrol limis; as long as he racking signal is wihin hese limis, he forecas is in conrol. Conrol limis of ±2 o ±5 are used mos frequenly. Some imes Tracking Signals (TS) is measured as: I is used o idenify hose iems, which do no keep pace wih eiher posiive or negaive bias or rend. TS = n =1 (D - F ) / (MAD) n = (BIAS) n / (MAD) n where; (MAD) n = Mean absolue deviaion ill period n (BIAS) n = BIAS ill period n The racking signal can be hough of as a scaled deviaion of he forecas from he acual sales figures. The plo of he racking signal shows i flucuaes abou zero. If he company uses ±2 conrol limis, he forecasing echnique has o be recalibraed or changed afer period 6, as indicaed by he racking signal falling below he lower conrol limi.

20 Mr. M A Hannan, Mr. M G Morselin, Mr. M M Rahman and Mr. M S Islam THE SALES DATA PROCESSING AND PRESENTATION The Characerisics of daa: Pas sales daa had been colleced and used for forecasing he nex period. The demand paern is ime depended - i varies wih ime. The ime series daa has wo considerable componens, i.e., rend and seasonal componen. In he company here are wo seasonal paerns in he daa, Lo of pas sales daa have been colleced for all he producs. The POM Sofware (By N. Gaiher ) was used for calculaions of hose daa for each of he Producs, a very small par of hem are shown here as a sample, as presenaion of all he calculaions and resuls are beyond he scope of his paper. Table 1 : The acual quaniies of Sales daa for he las seven years for Iem I No. of year Sales acual value(tons)

21 21 Analysis for Finding an Efficien Sales Forecasing Mehod in he Process of Producion Planning, Operaion and Oher Areas of Decision Making 2. RESULTS AND DISCUSSION Using he exponenial smoohing mehod, he forecas errors such as MAD, MSE, BIAS, TS and SE were compued and compared wih he acual demand and forecased demand. The compuer oupu is shown below in Table 2.The variaion of he smoohing consan α is shown in he Figure no. 1. Table 2 : Compuer Oupu of Exponenial Mehod of ( E.S.M) Mehod **EXPONENTIAL SMOOTHING FORECASTING *** PROBLEM NAME: FORECASTING OF AMIT (Iem-I) Sales Sales ABSOLUTE PERIOD ACTUAL FORECAST ERROR THE VALUE OF ALPHA USED IS = 0.9 BEGINNING FORECAST IS = MEAN ABSOLUTE DEVIATION (MAD) FOR THE LAST 7 PERIODS = MEAN SQUARED ERROR (MSE) FOR ALL PAST PERIODS = MEAN ERROR (bias) FOR ALL PAST PERIODS = TRACKING SIGNAL=1 STANDARD ERROR (sigmasubyx) IS =

22 Mr. M A Hannan, Mr. M G Morselin, Mr. M M Rahman and Mr. M S Islam 22 From he calculaed forecased error, he difference in acual demand (61820) and forecased demand ( ) is so big. Beside he sandard error, racking signal, bias are also high. So he mehod is no preferable. I is shown by using he exponenial smoohing mehod o deermine he forecased error MAD, MSE, BIAS, TS and SE given in Table 3 and compared i beween he acual demand and forecased demand for he specific Iem - I. Using he POM sofware, he errors were calculaed and hose are presened in he following Table 3: Table 3 : Presenaion of Mehod Errors for Exponenial Smoohing (E.S.M) Mehod Error M.A.D M.S.E BIAS S.E T.S E.S.M SMOOTHING CONSTANT VS STANDARD ERROR CURVE STANDARDERROR SMOOTHING CONSTANT Figure 3 : Smoohing consan variaion for Exponenial Smoohing Mehod for Iem-I

23 23 Analysis for Finding an Efficien Sales Forecasing Mehod in he Process of Producion Planning, Operaion and Oher Areas of Decision Making DEMAND ACTUAL =0.4 =0.5 =0.6 = YEAR Figure 4 : Demand in differen years in Exponenial Smoohing for a paricular iem (Iem- I) Figure 4 shows a clear variaion of demand wih years. Curve 1 of his figure represens he acual value of demand in relaion o ime variaion.. Curves 2, 3 and 4 have been drawn by using exponenial smoohing mehod. From hese curves, i is observed ha he curve 2 (Smoohing value) shows beer wih α = 0.9 resuls rend curves are curve 2 and 3. From i is clear ha he Mean Absolue deviaion beween curve 1 and 2, 1 and 3, 1 and 4 are moderae.

24 Mr. M A Hannan, Mr. M G Morselin, Mr. M M Rahman and Mr. M S Islam 24 Table 4 : Compuer Oupu of Time Series Regression ( T.S.R) Mehod *** TIME SERIES REGRESSION FORECASTING *** PROBLEM NAME: FORECASTING OF AMIT (Iem -I) Sales Sales ABSOLUTE PERIOD ACTUAL FORECAST ERROR Sales CONFIDENCE INTERVAL ( 95%) PERIOD FORECAST LOWER BOUND UPPER BOUND REGRESSION EQUATION: Y = a + bx WHERE: Y = Sales X = TIME PERIOD a = b = R = R-SQUARE = MEAN ABSOLUTE DEVIATION (MAD) FOR THE LAST 7 PERIODS = MEAN SQUARED ERROR (MSE) FOR ALL PAST PERIODS = MEAN ERROR (bias) FOR ALL PAST PERIODS = 0.0

25 25 Analysis for Finding an Efficien Sales Forecasing Mehod in he Process of Producion Planning, Operaion and Oher Areas of Decision Making TRACKING SIGNAL= 0 STANDARD ERROR (sigmasubyx) IS = Using he Sofware POM, he errors were calculaed and hose are presened in he following Table 5. Table 5: Calculaion of Errors for he Time Serious Regression (T.S.R) Mehod Mehod Error M.A.D M.S.E BIAS S.E T.S T.S.R From he calculaed forecased error, he difference beween acual demand (61820) and forecased demand ( ) is so far. Beside sandard error, racking signal, bias are also high. So he mehod is no preferable. In he similar way, calculaions were performed for oher mehods of forecasing and only he errors were found ou for making he forecas opimized wih opimal deviaion. The errors are furnished below in Table -6. In urn, hose errors are graphically presened in Figure 4. Table 6 : Compued Errors in differen mehods of forecasing models Mehod Error M.A.D M.S.E BIAS S.E T.S S.M.A W.M.A E.S.M E.S.T T.S.R

26 Mr. M A Hannan, Mr. M G Morselin, Mr. M M Rahman and Mr. M S Islam 26 METHOD VS ERROR BAR CHART FOR AMIT ERROR S.M.A W.M.AE.S.M E.S.T T.S.R METHOD M.A.D M.S.E BIAS S.E T.S Figure 4: Presenaion of Forecasing mehod vs Error bar 00000Char for he specific Iem( Iem -I). From his graph of Figure 4, i is clear ha he Simple Average Mehod is obviously projecing maximum errors in all mehods of Forecasing, in case of he Iem # ANALYSIS OF THE RESULTS The bar char in Figure 3 Shows he mean square error(m.s.e) of ime series regression mehod is smaller han simple moving average, weighed moving average, exponenial smoohing and exponenial smoohing wih read mehod.beside, mean absolue deviaion(m.a.d), mean error (BIAS), racking signal, sandard error of ime series regression is also smaller han simple moving average mehod, weighed moving average mehod, exponenial smoohing mehod and exponenial smoohing wih read mehod. Selecing he ime series regression mehod ha gives he smalles bias, as measured by cumulaive forecas error (CFE); or gives he smalles mean absolue deviaion (MAD); or gives he smalles racking signal; or suppors managemen's beliefs abou he underlying paern of demand or ohers. I appears obvious ha some measure of boh accuracy and bias should be used ogeher by demand is inherenly sable, low values and higher values of number of period are

27 27 Analysis for Finding an Efficien Sales Forecasing Mehod in he Process of Producion Planning, Operaion and Oher Areas of Decision Making suggesed or demand is inherenly unsable, high values and lower values of number of period are suggesed. If he forecasing model performing well, he racking signal should be nearly zero which would indicae ha here have been abou as many acual daa poins above he forecass as bellow. The abiliy of racking signal o indicae he direcion of forecased error is very helpful because wheher forecass should be reduced or increased is indicaed. If he racking signal is posiive, increase he forecass, if i is negaive, reduce he forecass. In char he racking signal is zero hen ime series regression mehod will be performing well. Among hese mehods, ime series regression mehod is preferable for forecasing. The forecased value for ami(iem-i) is Le us consider anoher se of Sales Daa for anoher Iem III Table 7: The acual quaniies of Sales daa for he las seven years for Epiclon (Iem - III) No. of year Sales acual value

28 Mr. M A Hannan, Mr. M G Morselin, Mr. M M Rahman and Mr. M S Islam 28 Table 8 : Using Simple Moving Average mehod wih FOUR Year-Period demand :*** SIMPLE MOVING AVERAGE FORECASTING *** PROBLEM NAME: FORECASTING OF EPICLON Sales Sales ABSOLUTE PERIOD ACTUAL FORECAST ERROR THE NUMBER OF AVERAGING PERIODS IS = 4 MEAN ABSOLUTE DEVIATION (MAD) FOR THE LAST 3 PERIODS = MEAN SQUARED ERROR (MSE) FOR ALL PAST PERIODS = MEAN ERROR (bias) FOR ALL PAST PERIODS =

29 29 Analysis for Finding an Efficien Sales Forecasing Mehod in he Process of Producion Planning, Operaion and Oher Areas of Decision Making TRACKING SIGNAL=1 STANDARD ERROR (sigmasubyx) IS = By using he Simple Moving Average mehod, he various errors were deermined. The forecas error (MAD, MSE, BIAS, TS and SE) and compared i beween acual demand and forecased demand. The Sofware POM, Norman Gaiher, was used o find he errors were calculaed and hose are shown in he following Table 10. Table 9 : Forecasing Errors for he Iem III Mehod Error M.A.D M.S.E BIAS S.E T.S S.M.A From he calculaed forecased error, he difference acual demand (189118) and forecased demand ( ) is so far. Beside sandard error, racking signal, bias are also high. So he mehod is no preferable. DEMAND A C T U A L S M A = 3 S M A = Y E A R Figure 5 : Demand in Differen Year in Simple Moving Average for Epiclon

30 Mr. M A Hannan, Mr. M G Morselin, Mr. M M Rahman and Mr. M S Islam 30 Using he Sofware POM, Norman Gaiher, he errors were calculaed and hose are shown in he following able: Table 10: Calculaion of Errors for (E.S.M) Mehod Error M.A.D M.S.E BIAS S.E T.S E.S.M From he calculaed forecased error, he difference acual demand (189118) and forecased demand ( ) is so far. Beside sandard error, racking signal, bias are also high. So he mehod is no preferable. SMOOTHING CONSTANT VS STANDARD ERROR CURVE STANDARDERROR SMOOTHING CONSTANT Figure 6 : Errors wih respec o smoohing consan variaion for Exponenial Smoohing Mehod (for Epicon: Iem-III)

31 31 Analysis for Finding an Efficien Sales Forecasing Mehod in he Process of Producion Planning, Operaion and Oher Areas of Decision Making A C T U A L = 0. 5 = = = DEMAND Y E A R Figure 7 : Demand versus year in Exponenial Smoohing wih rend for Epiclon (Iem - III) Figure 6 shows The Variaion of Demand wih Year. Curve 1 of his figure represens he acual value of demand in relaion o ime. By exponenial soohing mehod curves 2, 3 and 4 are drawn. From hese curves, i is experienial ha he curve 2 (Soohing value) shows beer (0.9) resuls read curve 2 and 3. Table 11 : Compued Errors in differen mehods of Forecasing Mehod Error M.A.D M.S.E BIAS S.E T.S S.M.A W.M.A E.S.M E.S.T T.S.R

32 Mr. M A Hannan, Mr. M G Morselin, Mr. M M Rahman and Mr. M S Islam 32 METHOD VS ERROR BAR CHART FOR EPICLON ERROR S.M.A W.M.A E.S.M E.S.T T.S.R METHODS M.A.D M.S.E BIAS S.E T.S Figure 8 : Mehod versus Error bar Char for Epiclon From showing he bar char mean square error(m.s.e) of ime series regression mehod is smaller han simple moving average, weighed moving average, exponenial smoohing and exponenial smoohing wih read mehod.beside, mean absolue deviaion(m.a.d),mean error (BIAS),racking signal, sandard error of ime series regression is also smaller han simple moving average mehod, weighed moving average, exponenial smoohing and exponenial smoohing wih rend mehod. Selecing he ime series regression mehod ha gives he smalles bias, as measured by cumulaive forecas error (CFE); or gives he smalles mean absolue deviaion (MAD); or gives he smalles racking signal; or suppors managemen's beliefs abou he underlying paern of demand or ohers. I appears obviously ha some measure of boh accuracy and bias should be used ogeher by demand is inherenly sable, low values and higher values of number of period are suggesed or demand is inherenly unsable, high values and lower values of number of period are suggesed. If he forecasing model performing well, he racking signal should be nearly zero which would indicae ha here have been abou as many acual daa poins above he forecass as bellow. The abiliy of racking signal o indicae he direcion of forecased error is very helpful because wheher forecass should be reduced or increased is indicaed. If he racking signal is

33 33 Analysis for Finding an Efficien Sales Forecasing Mehod in he Process of Producion Planning, Operaion and Oher Areas of Decision Making posiive, increase he forecass, if i is negaive, reduce he forecass. In char he racking signal is zero hen ime series regression mehod will be performing well. Among hese mehods, ime series regression mehod is preferable for forecasing. The forecased value for epiclon is In way, hrough he measuremen of he diagnosic errors, he bes mehod of forecasing ha bes fis he rend, can be found ou o have he bes projecion of he fuure demand, Iem by Iem.. 9. STEPS TO BE TAKEN FOR IMPROVING OVERALL CONDITIONS The following measures should be aken in he respecive concern 1. Organizaion mus know how much demand i has o saisfy o design and run an operaing sysem ha will saisfy cusomers. Tha leads o wo imporan quesions 2. Imporan maer is ha performance measures are no o be confusing wih forecas. I is necessary ha each manager up he line o reduce he so-called forecas slighly so ha i can easily me or even exceeded 3. Anoher imporan issue, who should make he forecas? May be markeing secion, operaions, finance or a cenral corporaion office depending on he size of he organizaion. Bu imporan hing is ha all managers should have an inpu o and knowledge of he assumpion behind he forecass. And company s sraegy should be clear o all. The forecasing aciviies mus be carefully coordinaed and moniored, oherwise inflaed in invenories and missed delivery daes could be in resul. 4. Finally i should be remembered ha prophesy is a good line of business bu i s full of risk smar managers recognize his realiy and find ways o updae heir plan when unexpeced even occurs.

34 Mr. M A Hannan, Mr. M G Morselin, Mr. M M Rahman and Mr. M S Islam CONCLUSION Decision-making process involves he selecion of a course of acion (means) in pursui of he decision maker's objecive. The way ha our course of acion affecs he oucome of a decision depends on how he forecass and oher inpus are inerrelaed and how hey relae o he oucome. In Forecasing, overall demand, ypically, is originaed by markeing. Bu inernal cusomers hroughou he organizaion depend on forecass o formulae and execue heir plans. The daa found are ime dependen, so he relaed ime series model is used o find ou forecasing he nex period, i is clearly known ha he ime series forecasing model used in aggregae planning ha is medium range in ime horizon. The fac ha pas canno be a perfec guide o he fuure. I warns o us ha sales forecasing should no be hough of as a rouine applicaion of some echniques and heoreical idea o a lis of unchanging variables. Successful forecasing requires exper blending of economic heory and hrough familiariy wih he relevan saisical daa, consequenly he economic forecass, he echnological forecass and analyses of a firm s inernal and exernal environmens are combined wih previous demand daa o develop demand forecass. REFERENCES 1. Fildes, Rober, Forecasing: The Issues, The Handbook of Forecasing: A Manager's Guide, Edied by Makridakis, S. and Wheelwrigh, S. C. New York: John Wiley and Sons, 1982, pp Beaumon, C.; Mahmoud, E. and McGee, V., Microcompuer Forecasing Sofware: A Survey. Journal of Forecasing, vol. 4, pp Armsrong, J. S., Long-Range Forecasing: From Crysal Ball o Compuer, John Wiley, Second Ediion, 1985

35 35 Analysis for Finding an Efficien Sales Forecasing Mehod in he Process of Producion Planning, Operaion and Oher Areas of Decision Making 4. Gardner, E. S., Exponenial Smoohing: The Sae of he Ar, Journal of Forecasing, Vol. 4, No.1,1985, pp Gardner, E. S., Auomaic Monioring of Forecas Errors, Journal of Forecasing, Vol. 2, No. 1, 1993 Figure 1: Smoohing consan variaion for Exponenial Smoohing Mehod for Iem-I, pp Gardner, E. S. and Dannenbring, Forecasing wih Exponenial Smoohing: Some Guidelines for Model Selecion, Decision Sciences, Vol. 11, 1990, pp Granger, C. W. J., Predicion Wih a Generalized Cos of Error Funcion: Operaions Research Quarerly, Vol. 20, No. 2, 1900, pp Mahmoud, Essam, Accuracy in Forecasing: A Survey, Journal of Forecasing, Vol. 3, No. 3, 1994, pp Mahmoud, Essam; Goyal, Suresh K.; and Shalchi, H., Loss-cos Funcions for Measuring he Accuracy of Sales Forecasing Mehods, (working paper), Makridakis, Sypros, The Ar and Science of Forecasing: An Assessmen and Fuure Direcions, Inernaional Journal of Forecasing, Forhcoming, Makridakis, S.; Wheelwrigh, S.; and McGee, V.E., Forecasing: Mehods and Applicaions, Second Ediion, New York: John Wiley and Sons, Makridakis, S.; Andersen, A.; Carbone,R.; Fildes, R.; Hibon, M.; Lewandowski, R.; Parzen, E. and Winkler, R., The Accuracy of Exrapolaion (Time Series) Mehods: Resuls of Forecasing Compuaion, Journal of Forecasing, Vol 1, 1992, pp

36 Mr. M A Hannan, Mr. M G Morselin, Mr. M M Rahman and Mr. M S Islam Makridakis, S. and Wheelwrigh, S. C., Forecasing: Framework and Overview, Forecasing TIMS Sudies in Managemen Science, Vol 12, S. Makridakis and S. C. Wheelwrigh, eds. Norh-Holland Publishing Company, [14] Rice, Gillian and Mahmoud, Essam, Forecasing and he Daabase: An Analysis of Daabases for Inernaional Business, Journal of Forecasing, Vol. 4, 1985, pp Seece, Ber, Evaluaion of Forecass, The Handbook of Forecasing: A Manager's Guide, edied by Spyros Makridakis and Seven C. Wheelwrigh, New York: John Wiley and Sons, 1998, pp Wrigh, David J., Evaluaion of Forecasing Mehods for Decision Suppor, The Inernaional Journal of Forecasing, Forhcoming, Wheelwrig'h, S. and Makridakis,-S., Forecasing Mehods for Managemen, 4h ediion, New York: John Wiley and Sons, Norman, G and F. Gaiher, An Inroducion o Producion and Operaions Managemen, 8 h edn, Harper and Row Pub, 2003, Morselin,M. G, M M Rahman, M S Islam: Deerminaion of Efficien Sales Forecasing Mehod in he Process of Producion Planning, Operaion and Oher Areas of Decision Making, an unpublished Research work carried ou in he ME Dep. a DUET for awarding B.Sc. Engineering. Degree, 26 Jan, 2010, Dhaka. Bangladesh. ACKNOWLEDGEMENT: The Auhor of his paper, M A Hannan, has been working as a Faculy member in he Deparmen of Mechanical Engineering, Dhaka Universiy of Engineering & Technology(DUET), Gazipur 1700, Dhaka, Bangladesh. His specializaion is in Operaions Research, POM, QC, TCM ec. of Indusrial Engineering Discipline. The auhor would like o hank Mr.

37 37 Analysis for Finding an Efficien Sales Forecasing Mehod in he Process of Producion Planning, Operaion and Oher Areas of Decision Making Morselin,M. G, M M Rahman, M S Islam are he hree of his undergraduae sudens who carried ou a research work on Efficien selecion of Forecasing Mehod in 2010 for obaining he B.Sc. Engineering Degree under his direc supervision. They successfully compleed he research work showing ha how an efficien forecasing mehod can be seleced for precise projecion of fuure ha is needed for proper planning of all business aciviies.