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1、Chapter3HorizontalForecasts3.1IntroductionPerhapsthemosttypicaldemandpatternisthehorizontalwherethemonth-to-monthdemandsfluctuateaboveandbelowapath(calledthelevel)withoutanytrendorseasonalinfluence.Thischapterdescribesfivehorizontalforecastingmodels.Theseforecastmodelsar
2、eherecalledthefollowing:horizontalfore-cast,horizontalmovingaverageforecast,horizontaldiscountforecast,horizontalsmoothingforecast,andforecastsusing2stages.Inallsituations,theconceptofrawandintegerforecastsisshown.Foreachofthemodels,monthlyrawforecastsaregeneratedinfract
3、ionalform.Acorrespondingsetofforecastsiscalledintegerforecastsandtheseareconvertedfromtherawforecastsbywayoftheroundingalgorithm.Akeymeasureoftheforecastsisthestandarddeviationofthe1-monthforecasterrors.Thismeasureisneededsubsequentlywheninventorydecisionarecomputed.Anot
4、herusefulmeasure,thecoefficient-of-variation,isarelativewaytomeasuretheforecasterror.3.2HorizontalForecastsWhentheleastsquaremethodisusedtogenerateahorizontalforecastmodel,apa-rameterNspecifiesthenumberofhistorydemandstouseintheforecast.ThemostrecentNdemandsaredenotedasx
5、(1),…,x(N)wherex(t)isthedemandinmontht,t=1istheoldestmonth,andt=Nisthemostrecentmonth.Theforecastfortheτ-thfuturemonthisf()aττ=,=1,2...whereaiscalledthelevelrepresentingtheaveragedemandpermonth.©SpringerInternationalPublishingSwitzerland201523N.T.Thomopoulos,DemandForeca
6、stingforInventoryControl,DOI10.1007/978-3-319-11976-2_3243HorizontalForecastsTheestimateofthelevelisobtainedbyformulatingtheexpressiononthesumofsquares,S(e),asbelow,N2Se()=−Σ[]xt()at=1wheree(t)=[x(t)−a]istheresidualerrorathistorymontht.Thevalueofthelevel,a,thatyieldsthem
7、inimumofS(e)iscalledtheleastsquaresestimate,andinthissituation,thelevelbecomes,NaN`=Σxt()/t=13.3RawForecastsTheforecastsfortheτ-thfuturemonthisthereby,f()τ=a`1,2τ=,...Thisforecastisherecalledarawforecastsincetheforecastvaluesaremostlikelyfractions,sameasthevalueofa`.3.4C
8、umulativeRoundingAlgorithmInmostsystems,therawforecasts,f(τ),areconvertedtointegerforecasts,denotedasx`
