数据、模型与决策（第12版）课件 第15章 预测

ForecastingChapter15Copyright©2016PearsonEducation,Inc.

ForecastingComponentsTimeSeriesMethodsForecastAccuracyTimeSeriesForecastingUsingExcelRegressionMethodsDataMiningChapterTopicsCopyright©2016PearsonEducation,Inc.

Avarietyofforecastingmethodsareavailableforusedependingonthetimeframe

oftheforecastandtheexistenceofpatterns.TimeFrames: Short-range(onetotwomonths) Medium-range(twomonthstooneortwoyears) Long-range(morethanoneortwoyears)Patterns: Trend Randomvariations Cycles SeasonalpatternForecastingComponentsCopyright©2016PearsonEducation,Inc.

Trend-Along-termmovementoftheitembeingforecast.Randomvariations-movementsthatarenotpredictableandfollownopattern.Cycle-Amovement,upordown,thatrepeatsitselfoveralengthytimespan.Seasonalpattern-Oscillatingmovementindemandthatoccursperiodicallyintheshortrun.ForecastingComponentsPatterns(1of2)Copyright©2016PearsonEducation,Inc.

Figure15.1(a)Trend;(b)Cycle;(c)Seasonal;(d)TrendwithSeasonForecastingComponentsPatterns(2of2)Copyright©2016PearsonEducation,Inc.

ForecastingComponentsForecastingMethodsTimesSeries-Statisticaltechniquesthatusehistoricaldatatopredictfuturebehavior.RegressionMethods-Regression(orcausal)methodsthatattempttodevelopamathematicalrelationshipbetweentheitembeingforecastandfactorsthatcauseittobehavethewayitdoes.QualitativeMethods-Methodsusingjudgment,expertiseandopiniontomakeforecasts.Copyright©2016PearsonEducation,Inc.

ForecastingComponentsQualitativeMethods“Juryofexecutiveopinion,”aqualitativetechnique,isthemostcommontypeofforecastforlong-termstrategicplanning.Performedbyindividualsorgroupswithinanorganization,sometimesassistedbyconsultantsandotherexperts,whosejudgmentsandopinionsareconsideredvalidfortheforecastingissue.Usuallyincludesspecialtyfunctionssuchasmarketing,engineering,purchasing,etc.,inwhichindividualshaveexperienceandknowledgeoftheforecasteditem.SupportingtechniquesincludetheDelphiMethod,marketresearch,surveys,andtechnologicalforecasting.Copyright©2016PearsonEducation,Inc.

TimeSeriesMethodsOverviewStatisticaltechniquesthatmakeuseofhistoricaldatacollectedoveralongperiodoftime.Methodsassumethatwhathasoccurredinthepastwillcontinuetooccurinthefuture.Forecastsbasedononlyonefactor-time.Copyright©2016PearsonEducation,Inc.

TimeSeriesMethodsMovingAverage(1of6)Movingaverageusesvaluesfromtherecentpasttodevelopforecasts.Thisdampensrandomincreasesanddecreases.Usefulforforecastingrelativelystableitemsthatdonotdisplayanytrendorseasonalpattern.Formulaformovingaverage(MA):Copyright©2016PearsonEducation,Inc.

Example:InstantPaperClipSupplyCompanywantstoforecastordersforthemonthofNovember.Developthree-monthandfive-monthmovingaveragesusingthedata.TimeSeriesMethodsMovingAverage(2of6)Table15.1Ordersfor10-monthperiodCopyright©2016PearsonEducation,Inc.

Example:InstantPaperClipSupplyCompanywantstoforecastordersforthemonthofNovember.Three-monthmovingaverage:Five-monthmovingaverage:TimeSeriesMethodsMovingAverage(3of6)Copyright©2016PearsonEducation,Inc.

Table15.1Three-andfive-monthmovingaveragesTimeSeriesMethodsMovingAverage(4of6)Copyright©2016PearsonEducation,Inc.

Figure15.2Three-andfive-monthmovingaveragesTimeSeriesMethodsMovingAverage(5of6)Copyright©2016PearsonEducation,Inc.

TimeSeriesMethodsMovingAverage(6of6)Longer-periodmovingaveragesreactmoreslowlytochangesindemandthandoshorter-periodmovingaverages.Theappropriatenumberofperiodstouseoftenrequirestrial-and-errorexperimentation.Amovingaveragedoesnotreactwelltochanges(trends,seasonaleffects,etc.)butiseasytouseandinexpensive.Goodforshort-termforecasting.Copyright©2016PearsonEducation,Inc.

Inaweightedmovingaverage,weightsareassignedtothemostrecentdata.Determiningpreciseweightsandthenumberofperiodsrequirestrial-and-errorexperimentation.TimeSeriesMethodsWeightedMovingAverageCopyright©2016PearsonEducation,Inc.

Exponentialsmoothingweightsrecentpastdatamorestronglythanmoredistantdata.Twoforms:simple

exponentialsmoothingandadjustedexponentialsmoothing.Simpleexponentialsmoothing: Ft+1=

Dt+(1-

)Ft where: Ft+1=theforecastforthenextperiod Dt=actualdemandinthepresentperiod Ft=thepreviouslydeterminedforecastforthepresentperiod

=aweightingfactor(smoothingconstant).TimeSeriesMethodsExponentialSmoothing(1of12)Copyright©2016PearsonEducation,Inc.

Themostcommonlyusedvaluesof

arebetween0.10and0.50.Determinationof

isusuallyjudgmentalandsubjectiveandoftenbasedontrial-and-errorexperimentation.TimeSeriesMethodsExponentialSmoothing(2of12)Copyright©2016PearsonEducation,Inc.

Table15.3DemandforpersonalcomputersTimeSeriesMethodsExponentialSmoothing(3of12)Copyright©2016PearsonEducation,Inc.

Example:PMComputerServices(seeTable15.4).Exponentialsmoothingforecastsusingsmoothingconstantof.30.Forecastforperiod2(February): F2=

D1+(1-

)F1=(.30)(.37)+(1-.30)(.37)=37unitsForecastforperiod3(March): F3=

D2+(1-

)F2=(.30)(.40)+(1-.30)(37)=37.9unitsTimeSeriesMethodsExponentialSmoothing(4of12)Copyright©2016PearsonEducation,Inc.

Table15.4Exponentialsmoothingforecasts,

=.30and

=.50TimeSeriesMethodsExponentialSmoothing(5of12)Copyright©2016PearsonEducation,Inc.

Theforecastthatusesthehighersmoothingconstant(.50)reactsmorestronglytochangesindemandthandoestheforecastwiththelowerconstant(.30).Bothforecastslagbehindactualdemand.Bothforecaststendtobeconsistentlylowerthanactualdemand.Lowsmoothingconstantsareappropriateforstabledatawithouttrend;higherconstantsappropriatefordatawithtrends.

TimeSeriesMethodsExponentialSmoothing(6of12)Copyright©2016PearsonEducation,Inc.

Figure15.3ExponentialsmoothingforecastsTimeSeriesMethodsExponentialSmoothing(7of12)Copyright©2016PearsonEducation,Inc.

Adjustedexponentialsmoothing:exponentialsmoothingwithatrendadjustmentfactoradded.Formula AFt+1=Ft+1+Tt+1 where:T=anexponentiallysmoothedtrendfactorTt+1+

(Ft+1-Ft)+(1-

)TtTt=thelastperiodtrendfactor

=smoothingconstantfortrend(avaluebetweenzeroandone).Reflectstheweightgiventothemostrecenttrenddata.Determinedsubjectively.

TimeSeriesMethodsExponentialSmoothing(8of12)Copyright©2016PearsonEducation,Inc.

Example:PMComputerServicesexponentiallysmoothedforecastswith

=.50and=.30(seeTable15.5nextslide).Adjustedforecastforperiod3: T3=

(F3-F2)+(1-

)T2

=(.30)(38.5-37.0)+(.70)(0)=0.45 AF3=F3+T3=38.5+0.45=38.95TimeSeriesMethodsExponentialSmoothing(9of12)Copyright©2016PearsonEducation,Inc.

Table15.5AdjustedexponentiallysmoothedforecastvaluesTimeSeriesMethodsExponentialSmoothing(10of12)Copyright©2016PearsonEducation,Inc.

Theadjustedforecastisconsistentlyhigherthanthesimpleexponentiallysmoothedforecast.Itismorereflectiveofthegenerallyincreasingtrendofthedata. TimeSeriesMethodsExponentialSmoothing(11of12)Copyright©2016PearsonEducation,Inc.

Figure15.4AdjustedexponentiallysmoothedforecastTimeSeriesMethodsExponentialSmoothing(12of12)Copyright©2016PearsonEducation,Inc.

Whendemanddisplaysanobvioustrendovertime,aleastsquaresregressionline,or

lineartrendline,canbeusedtoforecast.Formula: TimeSeriesMethodsLinearTrendLine(1of5)Copyright©2016PearsonEducation,Inc.

Example:PMComputerServices(seeTable15.6)TimeSeriesMethodsLinearTrendLine(2of5)Copyright©2016PearsonEducation,Inc.

Table15.6LeastsquarescalculationsTimeSeriesMethodsLinearTrendLine(3of5)Copyright©2016PearsonEducation,Inc.

Atrendlinedoesnotadjusttoachangeinthetrendasdoestheexponentialsmoothingmethod.Thislimitsitsusetoshortertimeframesinwhichthetrendwillnotchange.TimeSeriesMethodsLinearTrendLine(4of5)Copyright©2016PearsonEducation,Inc.

Figure15.5LineartrendlineTimeSeriesMethodsLinearTrend(5of5)Copyright©2016PearsonEducation,Inc.

Aseasonalpattern

isarepetitiveup-and-downmovementindemand.Seasonalpatternscanoccuronaquarterly,monthly,weekly,ordailybasis.Aseasonallyadjustedforecastcanbedevelopedbymultiplyingthenormalforecastbyaseasonalfactor.Aseasonalfactorcanbedeterminedbydividingtheactualdemandforeachseasonalperiodbytotalannualdemand:Si=Di/

DTimeSeriesMethodsSeasonalAdjustments(1of4)Copyright©2016PearsonEducation,Inc.

Seasonalfactorsliebetweenzeroandoneandrepresenttheportionoftotalannualdemandassignedtoeachseason.Seasonalfactorsaremultipliedbyannualdemandtoprovideadjustedforecastsforeachperiod.TimeSeriesMethodsSeasonalAdjustments(2of4)Copyright©2016PearsonEducation,Inc.

S1=D1/D=42.0/148.7=0.28 S2=D2/D=29.5/148.7=0.20 S3=D3/D=21.9/148.7=0.15 S4=D4/D=55.3/148.7=0.37Table15.7DemandforturkeysatWishboneFarmsExample:WishboneFarmsTimeSeriesMethodsSeasonalAdjustments(3of4)Copyright©2016PearsonEducation,Inc.

Multiplyforecasteddemandforanentireyearbyseasonalfactorstodeterminethequarterlydemand.Forecastforentireyear(trendlinefordatainTable15.7): y=40.97+4.30x=40.97+4.30(4)=58.17Seasonallyadjustedforecasts: SF1=(S1)(F5)=(.28)(58.17)=16.28SF2=(S2)(F5)=(.20)(58.17)=11.63SF3=(S3)(F5)=(.15)(58.17)=8.73SF4=(S4)(F5)=(.37)(58.17)=21.53TimeSeriesMethodsSeasonalAdjustments(4of4)Copyright©2016PearsonEducation,Inc.

Forecastswillalwaysdeviatefromactualvalues.Differencebetweenforecastsandactualvaluesarereferredtoasforecasterror.Wewouldlikeforecasterrortobeassmallaspossible.Ifforecasterrorislarge,eitherthetechniquebeingusedisthewrongone,ortheparametersneedadjusting.Measuresofforecasterrors: MeanAbsolutedeviation(MAD) Meanabsolutepercentagedeviation(MAPD) Cumulativeerror(Ebar) Averageerror,orbias(E) ForecastAccuracyOverviewCopyright©2016PearsonEducation,Inc.

MADistheaverageabsolutedifferencebetweentheforecastandactualdemand.Themostpopularandsimplest-to-usemeasuresofforecasterror.Formula:

ForecastAccuracyMeanAbsoluteDeviation(1of7)Copyright©2016PearsonEducation,Inc.

Example:PMComputerServices(seeTable15.8).CompareaccuraciesofdifferentforecastsusingMAD:

ForecastAccuracyMeanAbsoluteDeviation(2of7)Copyright©2016PearsonEducation,Inc.

Table15.8ComputationalvaluesforMADanderrorForecastAccuracyMeanAbsoluteDeviation(3of7)Copyright©2016PearsonEducation,Inc.

ThelowerthevalueofMADrelativetothemagnitudeofthedata,themoreaccuratetheforecast.Whenviewedalone,MADisdifficulttoassess.MADmustbeconsideredinlightofmagnitudeofthedata.ForecastAccuracyMeanAbsoluteDeviation(4of7)Copyright©2016PearsonEducation,Inc.

Canbeusedtocomparetheaccuracyofdifferentforecastingtechniquesworkingonthesamesetofdemanddata(PMComputerServices):Exponentialsmoothing(

=.50):MAD=4.04Adjustedexponentialsmoothing(

=.50,

=.30):MAD=3.81Lineartrendline:MAD=2.29ThelineartrendlinehasthelowestMAD;increasing

from.30to.50improvedthesmoothedforecast.

ForecastAccuracyMeanAbsoluteDeviation(5of7)Copyright©2016PearsonEducation,Inc.

AvariationonMADisthemeanabsolutepercentdeviation(MAPD).Measurestheabsoluteerrorasapercentageofdemandratherthanperperiod.Eliminatestheproblemofinterpretingthemeasureofaccuracyrelativetothemagnitudeofthedemandandforecastvalues.Formula:ForecastAccuracyMeanAbsoluteDeviation(6of7)Copyright©2016PearsonEducation,Inc.

MAPDforotherthreeforecasts: Exponentialsmoothing(

=.50):MAPD=8.5% Adjustedexponentialsmoothing(

=.50,

=.30): MAPD=8.1% Lineartrend:MAPD=4.9%ForecastAccuracyMeanAbsoluteDeviation(7of7)Copyright©2016PearsonEducation,Inc.

Cumulativeerror

isthesumoftheforecasterrors(E=

et).Arelativelylargepositivevalueindicatestheforecastisbiasedlow,alargenegativevalueindicatestheforecastisbiasedhigh.Ifthepreponderanceoferrorsarepositive,theforecastisconsistentlylow;andviceversa.Thecumulativeerrorforatrendlineisalwaysalmostzero,andisthereforenotagoodmeasureforthismethod.ThecumulativeerrorforPMComputerServicescanbereaddirectlyfromTable15.8.E=

et=49.31,indicatingtheforecastsarefrequentlybelowactualdemand.ForecastAccuracyCumulativeError(1of2)Copyright©2016PearsonEducation,Inc.

Cumulativeerrorforotherforecasts: Exponentialsmoothing(

=.50):E=33.21 Adjustedexponentialsmoothing(

=.50,

=.30): E=21.14Averageerror(bias)istheper-periodaverageofcumulativeerror.Averageerrorfortheexponentialsmoothingforecast:Alargepositivevalueofaverageerrorindicatesaforecastisbiasedlow;alargenegativeerrorindicatesitisbiasedhigh.

ForecastAccuracyCumulativeError(2of2)Copyright©2016PearsonEducation,Inc.

Resultsconsistentforallforecasts: Largervalueofalphaispreferable. Adjustedforecastismoreaccuratethanexponentialsmoothing. Lineartrendismoreaccuratethanalltheothers.Table15.9ComparisonofforecastsforPMComputerServicesForecastAccuracyExampleForecastsbyDifferentMeasuresCopyright©2016PearsonEducation,Inc.

Exhibit15.1TimeSeriesForecastingUsingExcel(1of4)=G21/11=B3*B8+(1-B3)*C8=C9+D9=B9-E9=ABS(B9-E9)=SUM(F9:F20)Copyright©2016PearsonEducation,Inc.

Exhibit15.2TimeSeriesForecastingUsingExcel(2of4)Toaccessthiswindow,clickon“Data”onthetoolbarribbonandthenthe“DataAnalysis”add-inCopyright©2016PearsonEducation,Inc.

Exhibit15.3TimeSeriesForecastingUsingExcel(3of4)Demandvaluesa=0.5CellsinwhichtheforecastedvalueswillbeplacedCopyright©2016PearsonEducation,Inc.

Exhibit15.4TimeSeriesForecastingUsingExcel(4of4)Copyright©2016PearsonEducation,Inc.

Exhibit15.5ExponentialSmoothingForecastwithExcelQMClick“ExcelQM”toaccessforecastingmacrosInputproblemdataintocellsB7andB10:B21Copyright©2016PearsonEducation,Inc.

TimeSeriesForecastingSolutionwithQMforWindows(1of2)Exhibit15.6Copyright©2016PearsonEducation,Inc.

Exhibit15.7TimeSeriesForecastingSolutionwithQMforWindows(2of2)Copyright©2016PearsonEducation,Inc.

Timeseriestechniquesrelateasinglevariablebeingforecasttotime.Regressionisaforecastingtechniquethatmeasurestherelationshipofonevariabletooneormoreothervariables.Thesimplestformofregressionislinearregression.RegressionMethodsOverviewCopyright©2016PearsonEducation,Inc.

Linearregression

relatesdemand(dependentvariable)toanindependentvariable.RegressionMethodsLinearRegressionCopyright©2016PearsonEducation,Inc.

StateUniversityAthleticDepartment.RegressionMethodsLinearRegressionExample(1of3)Table15.10LeastsquarescomputationsCopyright©2016PearsonEducation,Inc.

RegressionMethodsLinearRegressionExample(2of3)Copyright©2016PearsonEducation,Inc.

Figure15.6LinearregressionlineRegressionMethodsLinearRegressionExample(3of3)Copyright©2016PearsonEducation,Inc.

Correlationisameasureofthestrengthoftherelationshipbetweenindependentanddependentvariables.Formula:Valueliesbetween+1and-1.Valueofzeroindicateslittleornorelationshipbetweenvariables.Valuesnear1.00and-1.00indicateastronglinearrelationship.RegressionMethodsCorrelation(1of2)Copyright©2016PearsonEducation,Inc.

ValueforStateUniversityexample: Sincethevalueisclosetoone,wehaveevidenceofastronglinearrelationship.RegressionMethodsCorrelation(2of2)Copyright©2016PearsonEducation,Inc.

Thecoefficientofdetermination

isthepercentageofthevariationinthedependentvariablethatresultsfromtheindependentvariable.Computedbysquaringthecorrelationcoefficient,r.FortheStateUniversityexample:r=.948,r2=.899Thisvalueindicatesthat89.9%oftheamountofvariationinattendancecanbeattributedtothenumberofwinsbytheteam,withtheremaining10.1%duetoother,unexplained,factors.RegressionMethodsCoefficientofDeterminationCopyright©2016PearsonEducation,Inc.

RegressionAnalysiswithExcel(1of6)Exhibit15.8=INTERCEPT(B5:B12,A5:A12)=CORREL(B5:B12,A5:A12)Copyright©2016PearsonEducation,Inc.

RegressionAnalysiswithExcel(2of6)Exhibit15.9Clickon“Insert”toaccess“Charts”Copyright©2016PearsonEducation,Inc.

Exhibit15.10RegressionAnalysiswithExcel(3of6)Copyright©2016PearsonEducation,Inc.

Exhibit15.11RegressionAnalysiswithExcel(4of6)Copyright©2016PearsonEducation,Inc.

Exhibit15.12RegressionAnalysiswithExcel(5of6)Copyright©2016PearsonEducation,Inc.

Exhibit15.13RegressionAnalysiswithQMforWindows(6of6)Copyright©2016PearsonEducation,Inc.

MultipleRegressionwithExcel(1of4) Multipleregression

relatesdemandtotwoormoreindependentvariables. Generalform: y=

0+

1x1+

2x2+...+

kxk where

0=theintercept

1...

k=parametersrepresenting contributionsoftheindependent variables x1...xk=independentvariablesCopyright©2016PearsonEducation,Inc.

StateUniversityexamplerevisited;doestheadditionofpromotionalandadvertisingexpenditurestowinsimprovethepredictionofattendance?MultipleRegressionwithExcel(2of4)Copyright©2016PearsonEducation,Inc.

Exhibit15.14MultipleRegressionwithExcel(3of4)r2,thecoefficientofdeterminationRegressionequationcoefficientsforx1andx2Copyright©2016PearsonEducation,Inc.

Exhibit15.15MultipleRegressionwithExcel(4of4)Includesx1andx2columnsDataMiningCopyright©2016PearsonEducation,Inc.Dataminingisaprocessandsetoftoolsthathelpsforecastersusetoday’swealthofdatatodevelopusefulforecasts.Dataminingforbusinessforecastingpurposesisdifferentfromtimeseriesandcausalmethods.Ratherthanselectingatoolbyfirstdeterminingifapatternexistsinthedata,dataminingletsthedataidentifypatterns.Dataarestoredindatabases,datawarehouses,anddatamartsSoftwarepackagessuchasSAS,SPSS,Excel,RandothersareusedSometechniquesinclude:AssociationrulelearningClusteringanalysisClassificationPredictionCopyright©2016PearsonEducation,Inc.

ProblemStatement:Forthedatabelow,developanexponentialsmoothingforecast using

=.40,andanadjustedexponentialsmoothingforecast using

=.40and

=.20.ComparetheaccuracyoftheforecastsusingMADandcumulativeerror.ExampleProblemSolutionComputer