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1、Chapter5SeasonalForecasts5.1IntroductionSeasonalforecastsareneededwhenthedemandsoverayearhaveacyclicalflowsuchastheriseforlightclothingduringthesummers;heavyclothingduringthewinters,schoolsuppliesinlatesummers;antifreezeduringthewinters;golfballsinthesummers;coldtabletsinthewin
2、ters;andsunglassesinthesummers.Twofore-castmodelsaredescribed:theseasonalsmoothingmultiplicativeforecastmodel,andtheseasonalsmoothingadditiveforecastmodel.Perhapsthemostcommonapplicationofthemodeliswhenthedemandsaremonthlycovering12monthsinayear.Theseasonalmultiplicativemodelis
3、describedfullywithexampledata.Themodelhastwostages:firstistoinitializetheforecastsusingthemostcurrentNhis-torydemands,andsecondistorevisetheforecastsaseachnewmonthlydemandbecomesavailable.Themodelincludesatrendcomponentandtwelveseasonalra-tiosforeachmonthoftheyear.Thetrendcompo
4、nentcouldbeflat,risingorfalling,andtheseasonalratioscouldvaryforeachmonthoftheyearindicatinganincreaseordecreaseinthedemandsforthemonthrelativetothetrend.Themodelrequiresthreesmoothingparametersthatassignhigherweightstothemorerecentdemandsinthehistory.Thisway,theforecastscanrea
5、dilyreacttoanychangesinthedemandflowoftheitemsinforecast.Forbrevity,anabridgeddiscussionoftheseasonalad-ditivemodelispresented.5.2SeasonalMultiplicativeModelTheseasonal(exponentially)smoothingmultiplicativemodelapplieswhenthede-mandsfollowacyclicalpatternfromyeartoyear,likether
6、iseinthesaleofbathingsuitsduringthesummermonths.Thisdemandflowiscalledaseasonaldemand©SpringerInternationalPublishingSwitzerland201559N.T.Thomopoulos,DemandForecastingforInventoryControl,DOI10.1007/978-3-319-11976-2_5605SeasonalForecastspatternandcombinesbothseasonalandtrendcom
7、ponents.Theforecastmodelfortheτ-thfuturemonth,asofmontht,isbelow:f()τ=(a+τb)r(t+τ)τ=1,2,…where:tisthecurrentmonth,aisthelevelofthecurrentmonth,bistheslope,andr(t+τ)istheseasonalratiofortheτ-thfuturemonth.Theunderlyingtrendoftheseasonalpatternismeasuredby(a+bt).Theseasonalratios
8、specifyhowtheexpecteddemandforthemonthwillvarywithresp
