Chapter7

DemandForecasting

inaSupplyChainSupplyChainManagement

(3rdEdition)

7-1OutlineTheroleofforecastinginasupplychainCharacteristicsofforecastsComponentsofforecastsandforecastingmethodsBasicapproachtodemandforecastingTimeseriesforecastingmethodsMeasuresofforecasterrorForecastingdemandatTahoeSaltForecastinginpractice2RoleofForecasting

inaSupplyChainThebasisforallstrategicandplanningdecisionsinasupplychainUsedforbothpushandpullprocessesExamples:Production:scheduling,inventory,aggregateplanningMarketing:salesforceallocation,promotions,newproductionintroductionFinance:plant/equipmentinvestment,budgetaryplanningPersonnel:workforceplanning,hiring,layoffsAllofthesedecisionsareinterrelated3CharacteristicsofForecastsForecastsarealwayswrong.Shouldincludeexpectedvalueandmeasureoferror.Long-termforecastsarelessaccuratethanshort-termforecasts(forecasthorizonisimportant)Aggregateforecastsaremoreaccuratethandisaggregateforecasts4ForecastingMethodsQualitative:primarilysubjective;relyonjudgmentandopinionTimeSeries:usehistoricaldemandonlyStaticAdaptiveCausal:usetherelationshipbetweendemandandsomeotherfactortodevelopforecastSimulationImitateconsumerchoicesthatgiverisetodemandCancombinetimeseriesandcausalmethods5ComponentsofanObservationObserveddemand(O)=Systematiccomponent(S)+Randomcomponent(R)Level(currentdeseasonalizeddemand)Trend(growthordeclineindemand)Seasonality(predictableseasonalfluctuation)Systematiccomponent:ExpectedvalueofdemandRandomcomponent:Thepartoftheforecastthatdeviates

fromthesystematiccomponentForecasterror:differencebetweenforecastandactualdemand6TimeSeriesForecastingForecastdemandforthenextfourquarters.7TimeSeriesForecasting8ForecastingMethodsStaticAdaptiveMovingaverageSimpleexponentialsmoothingHolt’smodel(withtrend)Winter’smodel(withtrendandseasonality)9BasicApproachto

DemandForecastingUnderstandtheobjectivesofforecastingIntegratedemandplanningandforecastingIdentifymajorfactorsthatinfluencethedemandforecastUnderstandandidentifycustomersegmentsDeterminetheappropriateforecastingtechniqueEstablishperformanceanderrormeasuresfortheforecast10TimeSeries

ForecastingMethodsGoalistopredictsystematiccomponentofdemandMultiplicative:(level)(trend)(seasonalfactor)Additive:level+trend+seasonalfactorMixed:(level+trend)(seasonalfactor)StaticmethodsAdaptiveforecasting11StaticMethodsAssumeamixedmodel:Systematiccomponent=(level+trend)(seasonalfactor)Ft+l=[L+(t+l)T]St+l=forecastinperiodtfordemandinperiodt+lL=estimateoflevelforperiod0T=estimateoftrendSt=estimateofseasonalfactorforperiodtDt=actualdemandinperiodtFt=forecastofdemandinperiodt12StaticMethodsEstimatinglevelandtrendEstimatingseasonalfactors13EstimatingLevelandTrendBeforeestimatinglevelandtrend,demanddatamustbedeseasonalizedDeseasonalizeddemand=demandthatwouldhavebeenobservedintheabsenceofseasonalfluctuationsPeriodicity(p)thenumberofperiodsafterwhichtheseasonalcyclerepeatsitselffordemandatTahoeSalt(Table7.1,Figure7.1)p=414TimeSeriesForecasting

(Table7.1)Forecastdemandforthenextfourquarters.15TimeSeriesForecasting

(Figure7.1)16EstimatingLevelandTrendBeforeestimatinglevelandtrend,demanddatamustbedeseasonalizedDeseasonalizeddemand=demandthatwouldhavebeenobservedintheabsenceofseasonalfluctuationsPeriodicity(p)thenumberofperiodsafterwhichtheseasonalcyclerepeatsitselffordemandatTahoeSalt(Table7.1,Figure7.1)p=417DeseasonalizingDemand [Dt-(p/2)+Dt+(p/2)+S2Di]/2pforpevenDt= (sumisfromi=t+1-(p/2)tot+1+(p/2))

SDi/pforpodd

(sumisfromi=t-(p/2)tot+(p/2)),p/2truncatedtolowerinteger18DeseasonalizingDemandFortheexample,p=4isevenFort=3:D3={D1+D5+Sum(i=2to4)[2Di]}/8={8000+10000+[(2)(13000)+(2)(23000)+(2)(34000)]}/8=19750D4={D2+D6+Sum(i=3to5)[2Di]}/8={13000+18000+[(2)(23000)+(2)(34000)+(2)(10000)]/8=2062519DeseasonalizingDemandThenincludetrendDt=L+tTwhereDt=deseasonalizeddemandinperiodtL=level(deseasonalizeddemandatperiod0)T=trend(rateofgrowthofdeseasonalizeddemand)Trendisdeterminedbylinearregressionusingdeseasonalizeddemandasthedependentvariableandperiodastheindependentvariable(canbedoneinExcel)Intheexample,L=18,439andT=52420TimeSeriesofDemand

(Figure7.3)21EstimatingSeasonalFactors Usethepreviousequationtocalculatedeseasonalizeddemandforeachperiod St=Dt/Dt=seasonalfactorforperiodt Intheexample, D2=18439+(524)(2)=19487D2=13000 S2=13000/19487=0.67 Theseasonalfactorsfortheotherperiodsarecalculatedinthesamemanner22EstimatingSeasonalFactors

(Fig.7.4)23EstimatingSeasonalFactorsTheoverallseasonalfactorfora“season”isthenobtainedbyaveragingallofthefactorsfora“season”Iftherearerseasonalcycles,forallperiodsoftheformpt+i,1<i<p,theseasonalfactorforseasoniisSi=[Sum(j=0tor-1)

Sjp+i]/r

Intheexample,thereare3seasonalcyclesinthedataandp=4,soS1=(0.42+0.47+0.52)/3=0.47S2=(0.67+0.83+0.55)/3=0.68S3=(1.15+1.04+1.32)/3=1.17S4=(1.66+1.68+1.66)/3=1.6724EstimatingtheForecastUsingtheoriginalequation,wecanforecastthenextfourperiodsofdemand:F13=(L+13T)S1=[18439+(13)(524)](0.47)=11868F14=(L+14T)S2=[18439+(14)(524)](0.68)=17527F15=(L+15T)S3=[18439+(15)(524)](1.17)=30770F16=(L+16T)S4=[18439+(16)(524)](1.67)=4479425AdaptiveForecastingTheestimatesoflevel,trend,andseasonalityareadjustedaftereachdemandobservationGeneralstepsinadaptiveforecastingMovingaverageSimpleexponentialsmoothingTrend-correctedexponentialsmoothing(Holt’smodel)Trend-andseasonality-correctedexponentialsmoothing(Winter’smodel)26BasicFormulafor

AdaptiveForecastingFt+1=(Lt+lT)St+1=forecastforperiodt+linperiodt

Lt=Estimateoflevelattheendofperiodt

Tt=Estimateoftrendattheendofperiodt

St=Estimateofseasonalfactorforperiodt

Ft=Forecastofdemandforperiodt(madeperiodt-1orearlier)Dt=Actualdemandobservedinperiodt

Et=Forecasterrorinperiodt

At=Absolutedeviationforperiodt=|Et|MAD=MeanAbsoluteDeviation=averagevalueofAt

27GeneralStepsin

AdaptiveForecastingInitialize:Computeinitialestimatesoflevel(L0),trend(T0),andseasonalfactors(S1,…,Sp).Thisisdoneasinstaticforecasting.Forecast:Forecastdemandforperiodt+1usingthegeneralequationEstimateerror:ComputeerrorEt+1=Ft+1-Dt+1

Modifyestimates:Modifytheestimatesoflevel(Lt+1),trend(Tt+1),andseasonalfactor(St+p+1),giventheerrorEt+1intheforecastRepeatsteps2,3,and4foreachsubsequentperiod28MovingAverageUsedwhendemandhasnoobservabletrendorseasonalitySystematiccomponentofdemand=levelThelevelinperiodtistheaveragedemandoverthelastNperiods(theN-periodmovingaverage)Currentforecastforallfutureperiodsisthesameandisbasedonthecurrentestimateofthelevel Lt=(Dt+Dt-1+…+Dt-N+1)/N Ft+1=LtandFt+n=Lt

Afterobservingthedemandforperiodt+1,revisetheestimatesasfollows: Lt+1=(Dt+1+Dt+…+Dt-N+2)/N Ft+2=Lt+1

29MovingAverageExampleFromTahoeSaltexample(Table7.1)Attheendofperiod4,whatistheforecastdemandforperiods5through8usinga4-periodmovingaverage?L4=(D4+D3+D2+D1)/4=(34000+23000+13000+8000)/4=19500F5=19500=F6=F7=F8Observedemandinperiod5tobeD5=10000Forecasterrorinperiod5,E5=F5-D5=19500-10000=9500Reviseestimateoflevelinperiod5:L5=(D5+D4+D3+D2)/4=(10000+34000+23000+13000)/4=20000F6=L5=2000030SimpleExponentialSmoothingUsedwhendemandhasnoobservabletrendorseasonalitySystematiccomponentofdemand=levelInitialestimateoflevel,L0,assumedtobetheaverageofallhistoricaldata L0=[Sum(i=1ton)Di]/n Currentforecastforallfutureperiodsisequaltothecurrentestimateofthelevelandisgivenasfollows: Ft+1=LtandFt+n=Lt

AfterobservingdemandDt+1,revisetheestimateofthelevel: Lt+1=aDt+1+(1-a)Lt

Lt+1=Sum(n=0tot+1)[a(1-a)nDt+1-n]31SimpleExponentialSmoothingExampleFromTahoeSaltdata,forecastdemandforperiod1usingexponentialsmoothingL0=averageofall12periodsofdata=Sum(i=1to12)[Di]/12=22083F1=L0=22083Observeddemandforperiod1=D1=8000Forecasterrorforperiod1,E1,isasfollows:E1=F1-D1=22083-8000=14083Assuminga=0.1,revisedestimateoflevelforperiod1:L1=aD1+(1-a)L0=(0.1)(8000)+(0.9)(22083)=20675F2=L1=20675Notethattheestimateoflevelforperiod1islowerthaninperiod032Trend-CorrectedExponentialSmoothing(Holt’sModel)AppropriatewhenthedemandisassumedtohavealevelandtrendinthesystematiccomponentofdemandbutnoseasonalityObtaininitialestimateoflevelandtrendbyrunningalinearregressionofthefollowingform:

Dt=at+b T0=a L0=b Inperiodt,theforecastforfutureperiodsisexpressedasfollows: Ft+1=Lt+Tt

Ft+n=Lt+nTt

33Trend-CorrectedExponentialSmoothing(Holt’sModel)Afterobservingdemandforperiodt,revisetheestimatesforlevelandtrendasfollows:Lt+1=aDt+1+(1-a)(Lt+Tt)Tt+1=b(Lt+1-Lt)+(1-b)Tt

a=smoothingconstantforlevelb=smoothingconstantfortrendExample:TahoeSaltdemanddata.Forecastdemandforperiod1usingHolt’smodel(trendcorrectedexponentialsmoothing)Usinglinearregression,L0=12015(linearintercept)T0=1549(linearslope)34Holt’sModelExample(continued)Forecastforperiod1:F1=L0+T0=12015+1549=13564Observeddemandforperiod1=D1=8000E1=F1-D1=13564-8000=5564Assumea=0.1,b=0.2L1=aD1+(1-a)(L0+T0)=(0.1)(8000)+(0.9)(13564)=13008T1=b(L1-L0)+(1-b)T0=(0.2)(13008-12015)+(0.8)(1549)=1438F2=L1+T1=13008+1438=14446F5=L1+4T1=13008+(4)(1438)=1876035Trend-andSeasonality-CorrectedExponentialSmoothingAppropriatewhenthesystematiccomponentofdemandisassumedtohavealevel,trend,andseasonalfactorSystematiccomponent=(level+trend)(seasonalfactor)AssumeperiodicitypObtaininitialestimatesoflevel(L0),trend(T0),seasonalfactors(S1,…,Sp)usingprocedureforstaticforecastingInperiodt,theforecastforfutureperiodsisgivenby: Ft+1=(Lt+Tt)(St+1)andFt+n=(Lt+nTt)St+n

36Trend-andSeasonality-CorrectedExponentialSmoothing(continued)Afterobservingdemandforperiodt+1,reviseestimatesforlevel,trend,andseasonalfactorsasfollows:Lt+1=a(Dt+1/St+1)+(1-a)(Lt+Tt)Tt+1=b(Lt+1-Lt)+(1-b)TtSt+p+1=g(Dt+1/Lt+1)+(1-g)St+1

a=smoothingconstantforlevelb=smoothingconstantfortrendg=smoothingconstantforseasonalfactorExample:TahoeSaltdata.Forecastdemandforperiod1usingWinter’smodel.Initialestimatesoflevel,trend,andseasonalfactorsareobtainedasinthestaticforecastingcase37Trend-andSeasonality-CorrectedExponentialSmoothingExample(continued)L0=18439T0=524 S1=0.47,S2=0.68,S3=1.17,S4=1.67F1=(L0+T0)S1=(18439+524)(0.47)=8913Theobserveddemandforperiod1=D1=8000Forecasterrorforperiod1=E1=F1-D1=8913-8000=913Assumea=0.1,b=0.2,g=0.1;reviseestimatesforlevelandtrendforperiod1andforseasonalfactorforperiod5L1=a(D1/S1)+(1-a)(L0+T0)=(0.1)(8000/0.47)+(0.9)(18439+524)=18769T1=b(L1-L0)+(1-b)T0=(0.2)(18769-18439)+(0.