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Topic 10

Demand Forecasting in POM

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FORECASTING

1. Forecasting s. Prediction!

Forecasting! Estimating F"t"re #$ Casting For%ard Past Data.

Prediction! Estimating F"t"re #ased on S"#&ectie

Considerations ot'er t'an &"st Past Data.

(. T'ree )ee*s o+ Forecasting in Operations Management!

)ong Range Forecasting +or Aggregate Demand.

Intermediate Range Forecasting +or Prod"ct Gro"ps.

S'ort Range Forecasting +or Indiid"a* Item.

,. Forecasting O#&ecties!

Forecasting in POM! Item Demand -or/*oad +or Capacit$

P*anning

Forecasting in Finance! Do**ars Reen"e -Cas' F*o%

Re"irement

Forecasting in Mar/eting! 2nit o+ Sa*es -Se**ing Capa#i*it$

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Forecasting in Operations

Forecast for

operations

Time horizon MGT level

Product & Processdesign

Long range Top

Capacity RequirementPlanning

Long!ntermediate

Top middle

"ggregate ProductionPlanning

!ntermediate Middle

Production #cheduling #hort Lo$

Impact o+ Inacc"rate Demand Forecasting!

-Prod"ction P*anning #ased on Demand Forecasting

1. I+ Forecasting is consistent*$ 'ig'er t'an Act"a* Demand!

(. I+ Forecasting is consistent*$ *o%er t'an Act"a* Demand!

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Forecasting S$stems

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Forecasting Tec'ni"es

3"a*itatie Approac'!

1. De*p'i Met'ods! -E4pert5s S"#&ectie Ratings

(. Mar/eting Researc' and Ana*$sis! -C"stomer S"re$

,. 6istorica* Ana*og$! -7no%*edge o+ Simi*ar Prod"cts

8. ...................

3"antitatie Approac'! -T%o Genera* Tec'ni"es

A! Time Series Ana*$sis!

1. Simp*e Moing Aerage

(. eig'ted Moing Aerage

,. E4ponentia* Smoot'ing

8. .................

9! Ca"sa* Re*ations'ip Mode*s!

1. Regression Ana*$sis

(. Econometric Mode*s,. ................

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Se*ection o+ Forecasting Tec'ni"es

Princip*e o+ Forecasting!

: 'en Past Data are 7no%n as Good Indicator +or t'e F"t"re.

: T'e Pattern o+ t'e F"t"re can #e recogni;ed +rom Past Data.

3"a*itatie Tec'ni"es! -S"#&ectie and

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T'ree Simp*e Time Series Mode*s

1. Simp*e Moing Aerage! Gien N"m#er o+ Periods -n to #e

Aeraged.

(. eig'ted Moing Aerage! Gien -n and eig'ts -%i

,. Simp*e E4ponentia* Smoot'ing! Gien ? -smoot' Constant.

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E4ercise @1

Ass"me t'at $o"r stoc/ o+ merc'andise is maintained #ased on t'e

+orecast demand. I+ t'e distri#"tors sa*es personne* ca** on t'e +irstda$ o+ eac' mont'> comp"te $o"r +orecast sa*es #$ eac' o+ t'e t'ree

met'ods re"ested 'ere.

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Forecasting Error Meas"rement

1. Forecasting Error in -t!

Et -At Ft

(. 9ias -Mean Error!

9ias H -Et=n

H -At Ft=n

-9ias is a Meas"re o+ t'e Direction o+ Forecasting Error.

,. MAD -Mean A#so*"te Deiation!

MAD H-At Ft=n

-MAD is a Meas"re o+ t'e Si;e o+ Forecasting Error.

8. Trac/ Signa*!

TS 9ias=MAD - 1 JTS JK1

-TS is a Meas"re o+ Forecasting Error in terms o+ #ot' t'e

LDirectionL and t'e LSi;eL.

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E4ercise @(

Mont' 1 ( , 8 B

Act"a*

Demand

( ,( , 80 ,B 8 0

a 'at is t'e +orecast +or period 10 "sing t'e +o**o%ing mode*s

i Fo"r period moing aerage

ii Fo"r period %eig'ted moing aerage %it' %eig'ts o+ 0.1>

0.1> 0.( and 0. +or mont' > > B and respectie*$

iii Simp*e e4ponentia* smoot'ing %it' a*p'a 0.(> ass"ming

t'at t'e +orecast +or mont' is 0.

# I+ t'e +orecasts +or period 1 to period %ere ,0> ,> 8(> 8(> 80> 0>

,> 1> > respectie*$> determine t'e #ias> MAD and trac/ing

signa*. 6o% %o"*d $o" improe t'e +orecasting acc"rac$ in t'is

sit"ation

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Regression Forecasting Mode*s

In man$ cases> t'e Demand o+ an Item -dependent aria#*es is more

dependent "pon ot'er )eading Factors -independent aria#*es t'an

t'e Past Demand.

Regression Mode*s are dee*oped #ased on )eastS"are met'od.

1. )inear Regression Mode*s! -Simp*e s. M"*tip*e

a K #1:Q1 K #(:Q( K ...... K #n:Qn

'en n1> it #ecomes t'e Simp*e Regression Mode*>

a K #:Q -a! Intercept> #! S*ope

(. Non)inear Regression Mode*s! -no genera* mode*

a K #1:Q1K #(:Q(1

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Practica* Forecasting Pro#*ems

1. Practica* Forecasting Iss"es!

Inacc"rac$

Inconsistenc$

Cost and Acc"rac$ Tradeo++ -Simp*e mode* ma$ per+orm

#etter t'an comp*icated ones.

Data 2naai*a#i*it$

Fitness and Predicta#i*it$

A mode* t'at #est L+itsL t'e past data ma$ not #e t'e #est

LPredictieL one +or t'e +"t"re> d"e to demand pattern c'anges.

(. Ne% Direction in Forecasting! Integrated -P$ramid Forecasting S$stem! To Red"ce

Inconsistenc$.

Com#inationa* Forecasting Mode*s! To Red"ce Inacc"rac$

t'ro"g'!

o Mode* Com#inations

o Res"*t Com#inations

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Criteria +or Se*ecting a Forecasting Met'od

Cost and Acc"rac$

A tradeo++ #et%een cost and acc"rac$ more acc"rac$ at a

cost.

6ig'acc"rac$ %it' disadantages o+! need more data=data

ma$ #e di++ic"*t to o#tain=mode*s are more cost*$ to design>

imp*ement> and operate=ta/e *onger time to "se.

)o%Cost approac'es statistica* mode*s> 'istorica*

ana*ogies> e4ec"tiecommittee consens"s 6ig'Cost Approac'es comp*e4 econometric mode*s>

De*p'i> and mar/et researc'

Data Aai*a#i*it$

Is t'e data aai*a#*e=or #e economica**$ o#tained

For a ne% prod"ct> a c"stomer s"re$ ma$ not #e practica*.

Time Span 'at operations reso"rce #e +orecasted and +or %'at p"rpose

S'ortterm #est #e +orecast %it' simp*e time series mode*.

)ongterm #est #e predicted %it' regression or simi*ar mode*s.

Nat"re o+ prod"cts and serices

Is t'e prod"ct=serice 'ig' cost or 'ig' o*"me

'ere is t'e prod"ct=serice in its *i+e c$c*e

Does t'e prod"ct=serice 'ae seasona* demand +*"ct"ations

Imp"*se response and noise dampening

An appropriate #a*ance m"st #e ac'ieed #et%een!

6o% responsie t'e mode* to c'ange in t'e act"a* demand data

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Desire to s"ppress "ndesira#*e noise in t'e demand data.

ExercisesDemand Forecasting- Simpe !egression

1" Fine# $eaters %nc" is a mid si&ed man'(act'rer o( residentia )ater *eaters" Saes *a+e gro)nd'ring t*e ast se+era #ears, and t*e compan#s prod'ction capacit# needs to .e increased" T*ecompan#s management )onders i( nationa *o'sing starts mig*t .e a good indicator o( t*ecompan#s saes"

/ear ationa $o'sing Startsmiions

Fine# $eaters nn'aSaes miions o( doars

1 6"2 57

2 5"1 593 6"5 65

4 7"9 78

5 6"3 72

6 7"4 80

7 7"0 86

a" De+eop a simpe inear regression ana#sis .et)een Fine# $eaters saes and nationa*o'sing starts" Forecast Fine# $eaters saes (or t*e next t)o #ears" T*e ationa $ome'iders ssociation estimates t*at nationa *o'sing starts )i .e 7"1 miion and 8"0miion (or t*e next t)o #ears"

." *at percentage o( +ariation in Fine# $eaters saes is expained .# nationa *o'singstarts

c" o'd #o' recommend t*at Fine# $eaters management 'se (orecast (rom art a to pan(aciit# expansion *# or )*# not *at co'd .e done to impro+e t*e (orecast

2" *ase)ood partments is a 300'nit compex near Fair)a# :ni+ersit# t*at attracts most#'ni+ersit# st'dents" ;anager

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8 6"7 246

a" :se a simpe regression ana#sis to de+eop a mode to (orecast t*e n'm.er o( apartment'nits eased, .ased on 'ni+ersit# enroment" %( t*e enroment (or next semester isexpected to .e 6,600 st'dents, (orecast t*e n'm.er o( apartment 'nits t*at )i .e eased"

." *at percent o( +ariation in apartment 'nits eased is expained .# 'ni+ersit#enromentc" $o) 'se(' do #o' t*in? 'ni+ersit# enroment is (or (orecasting t*e n'm.er o( apartment

'nits eased

Demand Forecasting- ;o+ing +erages

3" %s pant estimates )ee?# demand (or its man# materias *ed in in+entor#" @ne s'c*

part, t*e T! 5922, is .eing st'died" T*e most recent 12 )ee?s o( demand (or t*e T! 5922are=

ee? Demand'nits

ee? Demand'nits

ee? Demand'nits

ee? Demand'nits

1 169 4 171 7 213 10 158

2 227 5 163 8 175 11 188

3 176 6 157 9 178 12 169

a" :se t*e mo+ing a+erage met*od o( s*ort-range (orecasting )it* an a+eraging period o(t*ree )ee?s to de+eop a (orecast o( t*e demand (or t*e !T 5922 component in )ee?

13"." %( a smoot*ing constant o( 0"25 is 'sed and t*e exponentia smoot*ing (orecast (or )ee?

11 )as 170"76 'nits, )*at is t*e exponentia smoot*ing (orecast (or )ee? 13c" *ic* (orecasting met*od is pre(erred- t*e A3 mo+ing a+erage met*od or t*e BA0"25

exponentia smoot*ing met*od T*e criterion (or c*oosing .et)een t*e met*ods is meana.so'te de+iation ;D o+er t*e most recent nine )ee?s" ss'me t*at t*e exponentiasmoot*ing (orecast (or )ee? 3 is t*e same as t*e act'a demand"

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4" T*e n'm.er o( Texas tax a'ditors needed .# t*e %nterna !e+en'e Ser+ice +aries (rom C'arterto C'arter" T*e past 12 C'arters o( data are s*o)n .eo)=

/ear 'arter 'ditors1 1 132

2 139

3 136

4 140

2 1 134

2 142

3 140

4 139

3 1 135

2 137

3 1394 141

a" :se mo+ing a+erages to (orecast t*e n'm.er o( a'ditors needed next C'arter i( A2,A4, and A6"

." *ic* o( t*ese (orecasts ex*i.it t*e .est (orecast acc'rac# o+er t*e past six C'arters o(*istorica data .ased on mean a.so'te de+iation

Demand Forecast- Exponentia Smoot*ing

5" to# compan# .'#s arge C'antities o( pastic peets (or 'se in t*e man'(act're o( itsprod'cts" rod'ction manager

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c" :se t*e .est ap*a +a'e (rom part . to comp'te t*e (orecasted pastic peets price (ormont* 17"

Demand Forecast- Seasona Forecast

6" comp'ter man'(act'rer )ants to de+eop next #ears C'arter# (orecasts o( saes re+en'es

(or its ine o( persona comp'ters" T*e compan# .eie+es t*at t*e most recent eig*t C'arters o(saes s*o'd .e representati+e (or next #ears saes=

/ear 'arter Saesmiions o(doars

/ear 'arter Saesmiions o(doars

1 1 9"2 2 1 10"3

1 2 5"4 2 2 6"4

1 3 4"3 2 3 5"4

1 4 14"1 2 4 16"0

:se seasonai&ed time series regression ana#sis to de+eop a (orecast o( next #ears C'arter#saes re+en'e (or t*e ine o( persona comp'ters"

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Tec'ni"es to S"pport 9etter Forecasting

ompan# eaders at a man'(act'rer o( ind'stria ('e p'mps decided to discontin'e some o(

t*eir G prod'cts" T*e# dismissed +endors and canceed a existing agreements reated to t*e p*ased-o't p'mps" ot ong a(ter, a .oom in sma, diese eectricit# generators ca'sed t*e p'mps to .e .ac? in*ig* demand" T*e man'(act'rer t*'s *ad to start (rom scratc* in order to re+i+e a prod'ct t*atot*er)ise co'd *a+e .een a cas* co)"

E+er# operations management pro(essiona *as a (orecasting nig*tmare o( *is or *er o)nresem.ing t*is one" ;ar?et conditions c*ange at an incredi.e pace, and t*e price and a+aia.iit# o(ra) materia o(ten +aries at a speed de(#ing ogic" (ood s*ortage, a ts'nami, terrorism, rising ('eprices, and co'ntess ot*er e+ents *a+e t*e potentia to compete# ater t*e .asic r'es o( .'siness"E+en t*e smaest incidents can *a+e a dramatic impact" Hi+en t*ese d#namic conditions, *o) is anacc'rate (orecast ac*ie+ed

orma# associated )it* n'm.ers and (orm'as, (orecasting is a ?ind o( magic .ox t*at 'ses

certain inp'ts to determine t*e prod'cts t*at t*e mar?et expects" T*ere are more t*an 100 di((erentC'antitati+e (orecasting met*ods a+aia.e, )*ic* a .egin )it* t*e simpe ass'mption t*at t*e past)i repeat in t*e ('t're"

Time-series met*ods extrapoate existing trends and inc'de seasona and c#cica indices, i(necessar#" T*e# aso ass'me t*at t*e trend, season, or c#ce )i *a+e a predicta.e and simiar e((ecte+er# time" ompex econometric and regression-.ased met*ods tr# to isoate t*e indi+id'acomponents ca'sing demand in order to create a (orecasting mode" 't t*ese modes *a+e an in*erentimitation in t*e n'm.er o( (actors t*e# 'se .eca'se it is impossi.e to inc'de a t*e ?e# data" ;oreo+er,somet*ing t*at seems insigni(icant toda# a o( a s'dden ma# .ecome a ?e# dri+er"

T*ere is no do'.t t*at (orecasting is critica# importantI *o)e+er, re#ing soe# on t*esen'merica (orecasting met*ods to dri+e .'siness )o'd .e an exercise in corporate *ara-?iri"

T'e +o"ndations!

@+er t*e #ears, (orecasting *as e+o+ed (rom a set o( principes to a set o( toos" *ie principesare generic and do not c*ange, toos are prone to inacc'rac# and, *ence, create a negati+e impression"

Somet*ing o.+io's# *as to .e done" @ne idea is to create .etter (orecasting modes t*at aremonitored and impro+ed in rea time" d+anced so(t)are toos *a+e at east pro+ided t*e a.iit# toc*ange (orm'as go.a# in t*e (raction o( a second" 't, gi+en t*e nat're o( a.r'pt c*anges, creatingan acc'rate mode seems e+en more di((ic't" %n+esting e((orts and reso'rces into seeming# .ettertoos aso )o'd ead to destr'ction-a.eit more so)#" T*e point is= *en t*e pat* is )rong, ac*ange in )a?ing s*oes does not impro+e an#t*ing"

@perations management pro(essionas m'st ater t*e )a# (orecasting is 'sed, not t*e )a# it is done"etter processes are reC'ired, and t*e# m'st .e resistant to inacc'rate (orecasts" T*e idea sit'ation )o'd.e to *a+e processes t*at are responsi+e to c'stomer needs and do not reC'ire a (orecast to ('nction"Foo)ing are some )a#s to .egin"

Recogni;e t'e c'ange. @perations management pro(essionas *a+e to appreciate t*e+aria.iit# in a sit'ation" T*e# m'st .ear in mind t*at sporadic e+ents can occ'r and c*ange t*eir.'sinesses-and t*ese peope m'st 'nderstand t*at s'c* e+ents cannot .e (orecast"

Instit"te +*e4i#i*it$. ;an'(act'ring (aciities, +endors, prod'ct design, and ot*er ?e# eementss*o'd .e de+eoped )it* an e#e (or (exi.iit#" Jendors m'st .e a.e to respond to a c*ange o( scaeand scope )it*o't a maKor impact on t*eir pricing" ants s*o'd .e a.e to prod'ce m'tipe prod'cts"Empo#ees and managers m'st *a+e t*e necessar# s?i and-more important#-t*e rig*t attit'de to .e a.e

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to c*ange t*eir responsi.iities according to c'rrent reC'irements" T*e .ene(its o( instit'ting (exi.iit#amost a)a#s o't)eig* t*e costs"

Standardi;e prod"cts.Standardi&ation is not t*e anton#m o( (exi.iit#" %t essentia# means t*att*e c*anges to a .ase prod'ct m'st .e incrementa" 'stomers expect m'tipe, 'niC'e prod'cts, and acompan# m'st .e a.e to c*ange t*e +o'me o( t*ese prod'cts as necessar#" Segment prod"cts.ot a prod'cts c*ange reg'ar#" :ness a (irm is in a +er# d#namic mar?et,

t*ere a)a#s )i .e prod'cts t*at are more sta.e t*an ot*ers" 'tting t*ese items aside and setting astandard sc*ed'e (or t*em red'ces compexit#" For exampe, i( 70 percent o( o'tp't can .epredicted )it* 95 percent acc'rac#, t*at means 25 percent o( t*e errors in t*e remaining 30 percento( t*e o'tp't )o'd *a+e a ess signi(icant impact"

Postpone.T*is is more important-and more possi.e t*an e+er .e(ore" Tec*noog# ena.es 's to do(ina assem.# m'c* coser to t*e c'stomer and )it*o't an# maKor increase in cost" Forecasting s*o'd.e mo+ed 'pstream, as )e" %( compan# eaders at t*e ('e p'mp man'(act'rer (rom t*e .eginning o(t*is artice *ad ?ept .asic prod'ct design constant and imited +ariation to mod'es, t*en t*e (irm co'd*a+e a.sor.ed mar?et ('ct'ations m'c* more easi#"

Ma/e Lsma**L %or/.T*e s*orter t*e term, t*e .etter t*e (orecast" s s'c*, e+er# aspect o( .'sinessm'st .e re)ired to ena.e sma .atc* si&es" Smaer +e*ices can .e 'sed to transport materia more(reC'ent#" Dei+ering or pic?ing 'p goods (rom m'tipe sites and t*en ret'rning to t*e origina

ocation )it* t*em s*o'd .e considered" !at*er t*an )aiting (or a .atc* o( goods, )or? m'st .e a.eto proceed on indi+id'a piecesI and, )*ere+er sma .atc* si&es are not economica, t*e processess*o'd .e c*anged to ma?e t*em )or?" eep in mind= ;a?ing sma )or? means t*at goods )i reac*t*e mar?et m'c* (aster" So, i( t*e c'm'ati+e ead time is 30 da#s, t*e mar?et *as to .e approximated.# at east 30 da#s" %( sma .atc*es can red'ce t*is time to 10 da#s, t*e mar?et *as to .e pre-empted .#on# 10 da#s"

Increase t'e speed o+ in+ormation trans+er. cc'rate and (ast in(ormation is t*e i(eine o( astrong .'siness" Data on act'a c'stomer 'sage s*o'd .e trac?ed )*ene+er possi.e, and tec*noog#toos s*o'd .e 'sed to ena.e in+ormation entr# once, at t*e point o( occ'rrence" @perating )it* *ig*speed and acc'rac# ens'res t*e (orecasting mode )i )or? on c'rrent in(ormation" 's, it .ecomesm'c* more i?e# t*at empo#ees can react acc'rate#"

Re%or/ #"siness r"*es.Hi+en t*at t*e sta?es o( t*e game *a+e c*anged, t*e r'es need to .e

atered, as )e" For exampe, an a(ter-saes ser+ice (irm stored (ast-mo+ing components at a itsregiona depots" ompan# eaders decided to s*i(t a t*e so)-mo+ing spare parts to a centra)are*o'se" T*en, t*e# )o'd .e (o)n to t*e di((erent regions on an as-needed .asis" %nstead o((orecasting a t*e components at eac* ocation, a (e) components no) are stored and (orecaston# at t*e centra ocation, signi(icant# increasing acc'rac#"

Monitor internationa* po*itics.'#ing and seing internationa# in+o+es a ot o( ris?"oitics, socia iss'es, and economics *a+e to .e monitored to create scenarios o( possi.e impact"Forecasting ne+er can predict s'c* e+ents, and operations management pro(essionas m'strecogni&e t*is and .'((er t*e (orecasts )*en necessar#"

E*eate +orecasting.Forecasting cannot .e mere# an operationa too" Senior managers m'strecogni&e t*e imitations o( t*e process and ead t*e necessar# c*anges in design, man'(act'ring,and distri.'tion" !es'ts o( (orecasting processes m'st .e monitored at t*e *ig*est e+e in order to

de+eop ot*er processes and red'ce dependence on (orecasts"Recogni;e t'e goa*.Firms are not in .'siness to ma?e acc'rate (orecastsI t*e#Lre in .'siness to

ma?e more mone#" Forecasting is mere# a too t*at *eps aong t*e )a#"Forecasting is .o'nd to .e inacc'rate, .'t it is nonet*eess necessar# (or a (irmLs s'r+i+a-especia#

)*en an organi&ation *as m'tip#ing prod'ct +ariants in a d#namic go.a mar?etpace" So(t)areso'tions o((er some assistance, .'t t*e c'rrent toos ne+er )i .e 100 percent e((ecti+e" T*'s,operations management pro(essionas m'st re(oc's t*eir e((orts to create processes t*at can dei+erstandard o'tp't )it* (orecasts o( imited acc'rac#"

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3"estion! S"mmari;e %'at $o" 'ae *earned +rom reading t'is artic*e.

O2T)OO7arm and S"nn$

By Nada R. Sanders, PhD.

Getting the best forecast by combining judgmental and statistical methods

cc'rate (orecasting a)a#s *as .een a critica organi&ationa capa.iit# (or e((ecti+e.'siness panning" Hood (orecasts are essentia (or identi(#ing and ne) mar?et opport'nities,anticipating ('t're demands, e((ecti+e# sc*ed'ing prod'ction, and red'cing in+entories"

@+er t*e past (e) #ears, *o)e+er, t*e roe o( (orecasting *as .ecome especia#signi(icant d'e to more competiti+e mar?et press'res" %n(ormation tec*noog# *as ena.ed(orecasts to dri+e entire s'pp# c*ains and enterprise reso'rces panning s#stems"Sim'taneo's#, go.a competition *as created an en+ironment c*aracteri&ed .# 'ncertaint#,rapid# s*i(ting mar?ets, and compressed c#ce times" 'stomers are demanding increasing#s*orter response times, impro+ed C'ait#, and greater prod'ct c*oice" T*e res't *as .een as*arp rise in (orecastingLs compexit# and *istorica data t*at are o(ten o( imited +a'e (orpredicting t*e ('t're"

!e#ing on statistica (orecasts aone can .e ine((ecti+e in t*is *ig*# compexen+ironment" onsider t*e case o( i?eLs 400 miion (ai're in 2000 )it* demand(orecasting so(t)are" ccording to t*e

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A %inning com#ination

;ore and more, s'ccess(' (orecasting 'ses composite met*odoogies"

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s'pport s#stem is *ep(' in (orecasting and decision ma?ing"

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Reie% 3"estions +or Topic 10!

N DE;D F@!EST%HO

e prepared to disc'ss t*e (oo)ing cases=

1 Di((erentiate .et)een qualitativeand C'antitati+e (orecasting tec*niC'es" Disc'ss - 'nder

)*at conditions t*ese t)o tec*niC'es )i .e pre(erred to 'se in practice"

2 e prepared to comp'te a (orecast 'sing a simpe mo+ing a+erage, a )eig*ted mo+ing

a+erage, and exponentia smoot*ing"

3 *at is t*e Pprincipe o( (orecastingQ rie( expain"

4 *# are t*ere di((erent considerations in seecting a (orecasting mode regarding t*ree

di((erent (orecasting *ori&ons= s*ort-term, medi'm-term, and ong-term"

5 $o) is t*e mean a.so'te de+iation ;D o( a (orecast series comp'ted *# is it

comp'ted

7 *at is t*e impact o( 'sing a arge or a sma +a'e o( in comp'ting an exponentia#

)eig*ted (orecast

8 *at is t*e impact o( 'sing a arge n'm.er o( period or a sma n'm.er o( n in

comp'ting a simpe or )eig*ted mo+ing a+erage (orecast

9 Henera#, *o) are seasona e((ects inc'ded in exponentia smoot*ing

10 Expain t*e di((erences .et)een M.iasM, ;D, Ptrac?ing signaQ and Mrandom errorsM in

(orecasting"

11 *at is t*e primar# di((erence .et)een a ca'sa mode and a time series mode (or

(orecasting

12 Di((erentiate .et)een t*e proKection t#pe o( (orecasting and t*e predicti+e t#pe o(

(orecasting"