1、毕业论文（设计）外文翻译外文原文ONTHEVARIANCEOFINTERMITTENTDEMANDESTIMATESINTERMITTENTDEMANDOCCURSATRANDOMWITHMANYTIMEPERIODSSHOWINGNODEMANDATALLFORECASTINGSUCHDEMANDPATTERNSCONSTITUTESACHALLENGINGEXERCISEBECAUSEOFTHEASSOCIATEDDUALSOURCEOFVARIATIONDEMANDINTERVALSANDDEMANDSIZESRESEARCHINTHISAREAHASDEVELOPEDRAPIDLYIN
2、RECENTYEARSWITHNEWRESULTSIMPLEMENTEDINTOSUPPLYCHAINSOFTWARESOLUTIONSBECAUSEOFITSPRACTICALIMPLICATIONSINANINVENTORYCONTEXT,BOTHTHEACCURACYOFTHEFORECASTSANDTHEIRVARIABILITYSAMPLINGERROROFTHEMEANHAVEEQUALIMPORTANCEINTERMSOFSERVICELEVELACHIEVEMENTAND/ORINVENTORYCOSTMINIMISATIONALTHOUGHTHEFORMERISSUEHASB
3、EENSTUDIEDEXTENSIVELYMAINLYBUILDINGUPONCROSTONSMODEL,1972THELATTERHASBEENLARGELYIGNOREDTHEPURPOSEOFTHISPAPERISTOANALYSETHEMOSTWELLCITEDINTERMITTENTDEMANDESTIMATIONPROCEDURESINTERMSOFTHEVARIANCEOFTHEIRESTIMATESDETAILEDDERIVATIONSAREOFFEREDALONGWITHADISCUSSIONOFTHEUNDERLYINGASSUMPTIONSASSUCH,WEHOPETHA
4、TOURCONTRIBUTIONMAYCONSTITUTEAPOINTOFREFERENCEFORFURTHERANALYTICALWORKINTHISAREAASWELLASFACILITATEABETTERUNDERSTANDINGOFISSUESRELATEDTOMODELLINGINTERMITTENTDEMANDSINTRODUCTIONINTERMITTENTDEMANDFORPRODUCTSAPPEARSSPORADICALLY,WITHSOMETIMEPERIODSSHOWINGNODEMANDATALLWHENDEMANDOCCURS,THEDEMANDSIZEMAYBECO
5、NSTANTORVARIABLE,PERHAPSHIGHLYSOINTERMITTENTDEMANDITEMSMAYBEANYSTOCKKEEPINGUNITSKUWITHINTHERANGEOFPRODUCTSOFFEREDBYANORGANISATIONATANYLEVELOFTHESUPPLYCHAINSUCHITEMSMAYCOLLECTIVELYACCOUNTFORUPTO60OFTHETOTALSTOCKVALUEJOHNSTONETAL,2003ANDAREPARTICULARLYPREVALENTINTHEAEROSPACE,AUTOMOTIVE,MILITARYANDITSE
6、CTORSTHEYAREOFTENTHEITEMSATGREATESTRISKOFOBSOLESCENCEINVENTORYCONTROLDECISIONSFORINTERMITTENTITEMSARENEEDEDTODETERMINEINVENTORYREPLENISHMENTRULESTHESEDECISIONSCANBEMADEMOREINTELLIGENTLYIFSUPPORTEDBYMOREACCURATEANDLESSVARIABLEDEMANDFORECASTSIMPROVEMENTSINFORECASTINGANDSTOCKCONTROLMAYBETRANSLATEDTOSIG
7、NIFICANTREDUCTIONSINWASTAGEORSCRAP,ANDVERYSUBSTANTIALCOSTSAVINGSWITHFURTHERIMPLICATIONSFORTHEEFFECTIVEMANAGEMENTOFTHERELEVANTSUPPLYCHAINSREPLENISHMENTREQUIREMENTSARECALCULATEDACCORDINGTOANANTICIPATEDPROBABILITYDISTRIBUTIONOFDEMANDOVERLEADTIMEMANYORGANISATIONSTHATDEALWITHINTERMITTENTDEMANDITEMSFACESI
8、GNIFICANTDIFFICULTIESINORGANISINGTHEIRSTOCKINSUCHAWAYASTOMINIMISEINVENTORYHOLDINGSWHILSTACHIEVINGSATISFACTORYSERVICEINTERMITTENTDEMANDPATTERNSAREBUILTFROMCONSTITUENTELEMENTS,ADEMANDARRIVALPROCESSTHATRESULTSINASEQUENCEOFINTERDEMANDINTERVALSANDTHEDEMANDSIZES,WHENDEMANDOCCURSTHEDUALSOURCEOFVARIATIONUND
9、ERCONCERNCONSTITUTESTHEMAINDIFFICULTYINFORECASTINGTHEREQUIREMENTSFORSUCHITEMSINADDITION,THEINAPPROPRIATENESSOFSTANDARDDISTRIBUTIONSSAYNORMALFORREPRESENTINGTHESEPATTERNSINTRODUCESFURTHERCOMPLICATIONSINTOTHEIRMANAGEMENTTHESTANDARDMETHODUSEDININDUSTRYTOFORECASTINTERMITTENTDEMANDREQUIREMENTSISCROSTONSME
10、THODCROSTON,1972THEMETHODISINCORPORATEDINSTATISTICALSUPPLYCHAINFORECASTINGSOFTWAREPACKAGESEGFORECASTPRO,ANDDEMANDPLANNINGMODULESOFCOMPONENTBASEDENTERPRISEANDMANUFACTURINGSOLUTIONSEGINDUSTRIALANDFINANCIALSYSTEMSIFSABITISALSOINCLUDEDININTEGRATEDREALTIMESALESANDOPERATIONSPLANNINGPROCESSESEGSAPADVANCEDP
11、LANNINGANDOPTIMISATIONAPO40CROSTON1972PROVEDTHEBIASEDNATUREOFSIMPLEEXPONENTIALSMOOTHINGSESWHENAPPLIEDINANINTERMITTENTDEMANDCONTEXTANDHEPROPOSEDAMETHODTHATRELIESEXPLICITLYUPONESTIMATESOFTHEINTERDEMANDINTERVALSANDDEMANDSIZESTHEMETHODWASCLAIMEDTOBEUNBIASED,BUTSYNTETOSANDBOYLAN2001SHOWEDITTOBEPOSITIVELY
12、BIASEDIEOVERFORECASTINGMEANDEMANDANDTHEYSUBSEQUENTLYPROPOSEDANAPPROXIMATELYUNBIASEDESTIMATORSBASYNTETOSBOYLANAPPROXIMATION,SYNTETOSANDBOYLAN,2005THISESTIMATIONPROCEDUREAPPLIESADEFLATINGFACTORTOTHECROSTONESTIMATESINORDERTOTAKEAWAYTHEBIASALITTLEBIASTHOUGHSTILLREMAINS,ONTHEOPPOSITESIDEIESLIGHTLYUNDERES
13、TIMATINGMEANDEMANDSYNTETOS2001ALSOPROPOSEDANEXACTLYUNBIASEDMODIFICATIONOFCROSTONSMETHODSYMETHODTHISPROCEDUREWASFURTHEREVALUATEDBYTEUNTERAND2009ANDITWASFOUNDTOPERFORMVERYWELLFORACOMPREHENSIVEACCOUNTOFALLRECENTDEVELOPMENTSININTERMITTENTDEMANDSUPPLYCHAINFORECASTINGPLEASEREFERTOFILDESETAL2008ANDSYNTETOS
14、ETALTHEFOCUSOFTHEABOVESTUDIESHASBEENTHEBIASORTHELACKOFITOFMEANDEMANDESTIMATESHOWEVER,THESAMPLINGERROROFTHEMEANIEVARIABILITYOFTHEESTIMATESWHICHISOFEQUALIMPORTANCEFORBOTHFORECASTINGANDSTOCKCONTROLPURPOSESHASNOTBEENEXPLICITLYDISCUSSEDTHEACHIEVEMENTOFTHESERVICETARGETISANIMPORTANTOBJECTIVE,ANDREQUIRESANU
15、NBIASEDFORECASTOFMEANDEMAND,ASSUMINGTHATTHEDISTRIBUTIONOFDEMANDISKNOWNEGPOISSON,NEGATIVEBINOMIALMINIMISATIONOFINVENTORYHOLDINGSISACHIEVEDBYAPPROPRIATESTOCKRULESNOTDISCUSSEDINTHISPAPERANDBYUSINGAMINIMUMVARIANCEESTIMATOROFTHEMEANDEMANDCONSEQUENTLY,ITWOULDBEHIGHLYDESIRABLETOOBTAINMINIMUMVARIANCEUNBIASE
16、DESTIMATORSOFMEANDEMANDINTHISPAPER，THEISSUEOFTHEVARIANCEOFINTERMITTENTDEMANDESTIMATESISEXPLICITLYADDRESSEDFORSES,CROSTONSMETHOD,SYANDSBAWEHOPETHATTHISPAPERMAYSERVEASADATAREPOSITORYFORFURTHERANALYTICALWORKINTHISAREAANDFORFACILITATINGABETTERUNDERSTANDINGOFPERTINENTISSUESOURPAPERCONCLUDESWITHADISCUSSIO
17、NOFTHEIMPLICATIONSOFOURWORKFORSUPPLYCHAINFORECASTINGPRACTICESREFERRINGALSOTOTHEBULLWHIPEFFECTANDANAGENDAFORFURTHERRESEARCHINTHISAREATHEREMAINDEROFOURPAPERISSTRUCTUREDASFOLLOWSSECTION2THEUNDERLYINGMODELASSUMEDFORTHEPURPOSESOFTHISRESEARCHISPRESENTEDALONGWITHTHECORRESPONDINGVARIANCEOFSESESTIMATESTHEVAR
18、IANCEOFTHEESTIMATESPRODUCEDBYTHECROSTONSMETHOD,SYANDSBAARESUBSEQUENTLYDISCUSSEDINSECTIONS35,RESPECTIVELYTHETHEORETICALRESULTSPRESENTEDINTHISPAPERARESUMMARISEDINSECTION6WHERETHEIMPLICATIONSOFTHISWORKFORREALWORLDSUPPLYCHAINPRACTICESAREALSODISCUSSEDFINALLY,INSECTION7,WEPRESENTTHECONCLUSIONSOFTHISRESEAR
19、CHALONGWITHSOMEIMPORTANTLINESOFFURTHERENQUIRYINTHISAREAANINTERMITTENTDEMANDMODELCROSTONADVOCATEDSEPARATINGTHEDEMANDINTOTWOCOMPONENTS,THEINTERDEMANDTIMEANDTHESIZEOFDEMAND,ANDANALYSINGEACHCOMPONENTSEPARATELYHEASSUMEDASTATIONARYMEANMODELFORREPRESENTINGTHEUNDERLYINGDEMANDPATTERN,NORMALDISTRIBUTIONFORTHE
20、SIZEOFDEMANDANDABERNOULLIDEMANDGENERATIONPROCESS,RESULTINGINGEOMETRICALLYDISTRIBUTEDINTERDEMANDINTERVALSTHREEMOREASSUMPTIONSIMPLICITLYMADEBYCROSTONINDEVELOPINGHISMODELARETHEFOLLOWINGINDEPENDENCEBETWEENDEMANDSIZESANDINTERDEMANDINTERVALS,INDEPENDENCEOFSUCCESSIVEDEMANDSIZESANDINDEPENDENCEOFSUCCESSIVEIN
21、TERDEMANDINTERVALSASFARASTHELASTASSUMPTIONISCONCERNEDITISIMPORTANTTONOTETHATTHEGEOMETRICDISTRIBUTIONISCHARACTERISEDBYAMEMORYLESSPROCESSTHEPROBABILITYOFADEMANDOCCURRINGISINDEPENDENTOFTHETIMESINCETHELASTDEMANDOCCURRENCE,SOTHATTHISDISTRIBUTIONALASSUMPTIONISCONSISTENTWITHINDEPENDENTINTERDEMANDINTERVALST
22、HENORMALITYASSUMPTIONISTHEMOSTRESTRICTIVEONEFORTHEANALYSISCONDUCTEDBYCROSTON,SINCETHEDEMANDSIZESMAYBE,THEORETICALLY,REPRESENTEDBYANYPROBABILITYDISTRIBUTIONWITHOUTAFFECTINGTHERESULTSTHEREMAININGASSUMPTIONSARERETAINEDFORTHEANALYSISTOBECONDUCTEDINTHISPAPERTHEVARIANCEOFSESESTIMATESCROSTON1972PROVEDTHEIN
23、APPROPRIATENESSOFEXPONENTIALSMOOTHINGASAFORECASTINGMETHODWHENDEALINGWITHINTERMITTENTDEMANDSANDHEEXPRESSEDINAQUANTITATIVEFORMTHEBIASASSOCIATEDWITHTHEUSEOFTHISMETHODWHENDEMANDOCCURSACCORDINGTOTHEMODELDESCRIBEDABOVEEXPONENTIALSMOOTHINGISUNBIASEDIFWECONSIDERTHEESTIMATESMADEATTHEENDOFEVERYFORECASTREVIEWP
24、ERIODALLPOINTSINTIMEITISBIASEDTHOUGHIFWEISOLATETHEESTIMATESMADEAFTERADEMANDOCCURRENCEISSUEPOINTSONLYTHEFORMERSCENARIOCORRESPONDSTOAREORDERINTERVAL/PERIODICREVIEWSTOCKCONTROLSYSTEMWHEREASTHELATTERTOAREORDERLEVEL/CONTINUOUSREVIEWMODELTHEBIASPROPERTIESOFSESARESUMMARISEDIN3SUMMARYOFTHEORETICALRESULTSAND
25、DISCUSSIONTHESTATISTICALPROPERTIESOFTHEMETHODSDISCUSSEDTHUSFARINTHISPAPERARESUMMARISEDINTABLE1INPARTICULAR,WEINDICATETHEEXPECTEDESTIMATEPRODUCEDBYEACHOFTHESEMETHODSALONGWITHTHEVARIANCEOFTHEIRESTIMATESSAMPLINGERROROFTHEMEANTHEVARIANCEOFDEMANDITSELFISPRESENTEDASWELLSUCHRESULTSENABLETHECALCULATIONOFTHE
26、THEORETICALONESTEPAHEADMEANSQUAREDERRORMSEASSOCIATEDWITHSES,CROSTON,SYANDSBASUCHRESULTSMAYBEOFPARTICULARVALUEFORCOMPUTERISEDSUPPLYCHAIN/INVENTORYMANAGEMENTSYSTEMSRELYINGUPONANALYTICALVARIANCEEXPRESSIONS,ASOPPOSEDTOESTIMATIONTHROUGHSMOOTHEDMSEORMEANABSOLUTEDEVIATIONMADPROCEDURESINADDITION,ANALYTICALM
27、SEEXPRESSIONSENABLETHEDIRECTCOMPARISONOFTHEPERFORMANCEOFTHESEMETHODSTHROUGHTHECONSIDERATIONOFBOTHBIASANDSAMPLINGERROROFTHEMEANSEEALSOSYNTETOSETAL,2005TEUNTERANDSANI2009COMMENTEDONTHEUNBIASEDNATUREOFTHESYMETHODANDRECOMMENDEDTHATTHEESTIMATORUNDERCONCERNRECEIVESMOREATTENTIONASACOMPETITIVEALTERNATIVETOS
28、BAALTHOUGHSYISINDEEDUNBIASED,ADETAILEDANALYSISCONDUCTEDBYSYNTETOS2001SHOWEDTHATTHISMETHODCOMPARESUNFAVOURABLYTOSBAWITHREGARDSTOTHEIRMSEPERFORMANCEDUETOTHEINCREASEDVARIANCEOFTHERELEVANTESTIMATESTHISISAVERYIMPORTANTPOINTBOTHFROMATHEORETICALANDAPRACTITIONERSPERSPECTIVESINCE,TYPICALLY,GREATEREMPHASISISB
29、EINGPLACEDONTHEBIASORTHELACKOFITASSOCIATEDWITHANESTIMATIONPROCEDURERATHERTHANTHEVARIANCEOFTHEESTIMATESIDEALLYTHOUGH,BOTHSHOULDBEEQUALLYCONSIDEREDSINCETHEYCOLLECTIVELYDETERMINETHESUPPLYCHAINIMPLICATIONSOFUSINGTHEMETHODUNDERCONCERNFORSTOCKCONTROLPURPOSES31IMPLICATIONSFORSUPPLYCHAINMANAGEMENTTHEBULLWHI
30、PEFFECTISATERMPROMOTEDBYLEEETAL1997BUTWASOBSERVEDANDMODELLEDDECADESEARLIERBYFORRESTER1958ITOCCURSWHENEVERDEMANDBECOMESMOREVARIABLEASITPROCEEDSTHROUGHTHESUPPLYCHAIN,AWAYFROMTHECONSUMERANDTOWARDSTHESUPPLIERLEEETAL2000DISCUSSEDFOURCAUSESOFTHEBULLWHIPEFFECT,NAMELYDEMANDSIGNALPROCESSING,RATIONING/SHORTAG
31、EGAMING,ORDERBATCHINGANDPRICEFLUCTUATIONSDEMANDSIGNALPROCESSINGINPARTICULARREFERSTOTHEMAGNIFICATIONINVARIANCETHATOCCURSTHROUGHTHEFORECASTERRORANDTHEINTERACTIONBETWEENFORECASTINGPROCEDURESANDINVENTORYRULESATEACHSTAGEOFTHESUPPLYCHAINSEEALSOCHENETAL,2000A,BFORAREVIEWOFSTUDIESINTHISAREAPLEASEREFERTOSYNT
32、ETOSETAL,2009SUCHINTERACTIONSACCOUNTFORSIGNIFICANTDISCREPANCIESBETWEENTHEACTUALPERFORMANCEOFANINVENTORYSYSTEMANDWHATISTHEORETICALLYEXPECTEDTHEYAREPARTICULARLYPREVALENTINANINTERMITTENTDEMANDCONTEXTWHEREVERYLARGEFORECASTERRORSAREALLTOOCOMMONDUETOTHEDIFFICULTIESASSOCIATEDWITHTHEFORECASTINGTASKFOREXAMPL
33、E,MAJORDEVIATIONSHAVEBEENREPORTEDINTHELITERATUREBETWEENTHETARGETANDACHIEVEDCUSTOMERSERVICELEVELSINSUCHACONTEXTOFAPPLICATIONSYNTETOSANDBOYLAN,2008FORECASTVARIANCEISAKEYCONTRIBUTORYFACTORTOTHEBULLWHIPEFFECT,ANDASSUCHANYRESEARCHORIENTEDTOVARIANCERELATEDISSUESSHOULDBEOFDIRECTINTERESTTOSUPPLYCHAINPRACTIT
34、IONERSHAVINGMENTIONEDTHAT,NORESEARCHHASBEENCONDUCTEDTODATEONTHEBEHAVIOUROFTHEBULLWHIPEFFECTFORSUPPLYCHAINSDEALINGWITHINTERMITTENTDEMANDPRODUCTS,FOREXAMPLESERVICEPARTSSUCHPRODUCTSHAVEBECOMEUBIQUITOUSINMODERNSOCIETIESANDSTUDYINGTHERELEVANTSUPPLYCHAINSSHOULDBEVERYIMPORTANTBOTHFROMANACADEMICANDPRACTITIO
35、NERPERSPECTIVE1CONCLUSIONSANDEXTENSIONSTHEAREAOFINTERMITTENTDEMANDFORECASTINGHASRECEIVEDANUMBEROFTHEORETICALCONTRIBUTIONSINTHERECENTYEARS,MOSTOFWHICHHAVEBEENFOCUSINGONTHEISSUEOFBIASOFTHERELEVANTESTIMATIONPROCEDURESINTHISPAPER,WEHAVEARGUEDFORTHEADDITIONALCONSIDERATIONOFTHEVARIANCEOFINTERMITTENTDEMAND
36、ESTIMATESSINCETHISISEQUALLYIMPORTANTINTERMSOFAMETHODSIMPLICATIONSFORSTOCKCONTROLANALYTICALEXPRESSIONSAREOFFEREDWITHREGARDSTOTHESAMPLINGERROROFTHEMEANFORFOURESTIMATIONPROCEDURESSES,CROSTON,SYANDSBATHEBIASPROPERTIESOFTHESEESTIMATORSAREALSOPRESENTEDANDTHERESULTSCOLLECTIVELYPERMITTHECALCULATIONOFTHERELE
37、VANTMEANSQUAREDERRORMSEEXPRESSIONSMSEISTHEONLYMATHEMATICALLYTRACTABLEFORECASTACCURACYMETRICANDITSQUANTIFICATIONALLOWSCOMPARISONSTOBEPERFORMEDBETWEENVARIOUSESTIMATORSINADDITION,SUCHRESULTSMAYBEPARTICULARLYUSEFULFORCOMPUTERISEDSYSTEMSTHATRELYUPONANALYTICALVARIANCEEXPRESSIONSFORSTOCKREPLENISHMENTPURPOS
38、ES译文关于间歇需求的估计方差间歇性需求伴随着许多完全没有显示需求的时间段随机发生。预测这样的需求模式成了一项富有挑战性的工作，这是由于相关双源的变异（需求的时间间隔和需求的大小）。最近几年，在这方面的研究因为它的实际影响，随着新成果落实到供应链软件的解决方案而迅速发展。在库存方面，无论是预测或是其可变性（抽样平均误差）的准确性，在服务水平上的成就和/或库存成本最小化方面上都具有同等重要性。尽管前一个问题已得到广泛的研究（主要依靠克罗斯顿的模式，1972年建设），但后者却在很大程度上被忽略。本文的目的是，对最受欢迎的间歇性需求估算的方差方面的估算程序进行分析。因此，我们希望我们的贡献可以构成这
39、一领域的进一步分析工作中的一个参考点，同时也能促进有关间歇性需求建模问题的更好理解。详细的推导，读者们可以看其中一个基本假设的讨论。1简介间歇性的产品需求偶尔会伴随着一些完全没有需求显示的时段而出现。间歇性的产品需求偶尔会伴随着一些完全没有需求显示的时段而出现。当需求发生时，需求的大小可能是常量或变量，也可能是高度等。间歇需求项目可能是任一级供应链上的其中一个组织提供的产品供应范围内的任何存货单位（SKU）。这些项目集体可以占股票价值（约翰斯顿等人。，2003）总数的60，在航空航天，汽车，军事和IT行业尤其普遍。这些项目往往面临着过时的最大风险。间歇性项目的库存控制决策可以用来确定库存补充原
40、则。如果需求预测更加准确且减少变动，这些决策可以更明智。预测和库存控制的改进，可翻译成在流失或报废方面非常重要的减少，以及进一步影响相关供应链有效管理的非常可观的成本节约。补货要求是根据交货时间的一个预计概率分布来计算的。许多处理间歇需求项目的组织在用这样的方式组织他们的股票，以减少库存持有量，而达到满意服务方面面临着重大困难。间歇性的需求模式是根据到达过程要求（即在一间需求间隔序列结果）的构成要素和需求发生时需求的大小而建立的。关注下的双源变异构成了预测这些项目要求的主要困难。此外，代表这些模式的标准分布（例如正常）的不当引入使得他们的管理变得更加复杂。用于预测间歇性需求要求的应用于行业的标
41、准方法是克罗斯顿的想法（克罗斯顿，1972）。该方法已纳入统计的供应链预测软件包（如预测专业版），以及基于构件的企业和制造解决方案（如工业和金融系统IFS的AB）的计划模块。它也包含在集成的实时销售和运营规划流程（例如SAP先进规划与优化载脂蛋白40）中。克罗斯顿（1972）在适用于间歇需求这个角度时证明了简单平滑指数的偏颇性（SES），而且他依靠明确的跨时点播的时间间隔和需求规模的估计提出了一个明确的方法。该方法自称是不偏不倚，但SYNTETOS和伊兰（2001年）表明它是正偏压（即过预测平均需求），而且他们随后提出了一个近似无偏估计校本评核（SYNTETOS伊兰逼近，SYNTETOS和伊兰
42、，2005年）。这种估算程序适用于克罗斯顿估计中的一个减缓物价变动因素，从而纠正偏差。但另一方面（即稍微低估平均需求），有一点偏差仍然存在。SYNTETOS（2001）也提出了一项克罗斯顿的准确无偏修正搭档方法（石荫法）。这一程序通过TEUNTER和SANI（2009年）的进一步评估，证明了表现非常好。2009出于对最近所有间歇性需求供应链预测的发展的综合考虑，请参阅菲尔德斯埃塔尔。（2008年）和SYNTETOS埃塔尔。（2009）。上述研究的重点一直是偏差（或缺乏）的平均需求估算然而，对双方预测和库存控制的目的同样重要的抽样误差的平均值还没有被明确讨论。该服务指标的实现是一个重要的目标，假
43、设需求分布是已知的（如泊松分布，负二项）以及估算需求的方差，它需要平均需求的一个无偏预测。库存持有最小化是通过适当的股票规则（本文不讨论）以及平均需求最小方差估计来实现的。因此，这对获得平均需求最低无偏方差的估算将是非常可取的。在这个文件中，间歇性需求的估计方差问题明确阐述了SES，克罗斯顿方法，SY和SBA。我们希望，这份文件可以作为一个数据库为这一领域的进一步分析工作和促进了相关问题的了解提供帮助。我们的论文总结讨论了我们的工作对供应链预测方法（指也对牛鞭效应）产生的影响，以及在这一方面的进一步研究的一个议程。我们论文的其余部分结构如下第2节中本研究目的假设的基本模式，提出了相应的SES估
44、算方差。由克罗斯顿方法，SY和SBA产生的估算方差，分别在其后35节中讨论。这个文件中提出的理论结果在第6节中有总结，同时第六节中还讨论了真正的全球供应链实践这项工作的影响。最后在第七节，我们提出了这项研究的结论，其中有几行说明了在这一领域的进一步调查。2间歇性的需求模型克罗斯顿主张将需求分离成间隔需求时间和需求规模两部分，并每个部分逐个进行分析。他假定一个代表基本需求模式的固定均值模型中，需求规模的正态分布和需求生成过程中的正常伯努利分配，引起间隔需求的几何分布。三个隐含在克罗斯顿制定其模型的假设如下需求规模和需求间隔之间的独立性，连续需求规模独立性和连续需求间隔的独立性。至于最后一个假设提
45、醒我们注意，是由于内存少过程的特点引起了几何分布，这一点非常重要这项需求发生的几率是上一次需求发生以来单独时间，这使得这一具有自主分配的假设与相互独立的间隔需求相一致。常态假设是由克罗斯顿进行分析最具限制性的一个，因为需求量的大小在理论上由不影响结果的任意概率分布来表示。其余的假设对分析有所保留，这在本文中有介绍。21SES的估算方差克罗斯顿（1972）证明了处理间歇性要求时预测方法的指数平滑不恰当，他以定量的形式说明当上述模型中的需求发生时，该方法的相关偏差。如果我们考虑到每个预测期（在所有时间点）结束时的估算，指数平滑就不会有偏差。但即使我们对需求发生（问题点只）后所作的估算进行隔离也还是有偏差的。前者对应方案通过重新排序间隔/定期审查股票来控制系统，而后者是通过重新重新排序的水平/连续审查模式。TABLE1SES的偏差性在表一中有所总结。3理论结果与讨论的总结这些方法的统计特性迄今为止在本文中讨论的在表1中有总结。特别是，我们指出了每一个方法随着他们的估计（抽样平均误差）方差产生的预期估算。这样的结果使与SES,克罗斯顿，SY和SBA相关的理论的前一步均方误差（MSE）得以计算。需求本身的方差也有提出。这些结果可能成为依托于分析方差表达式的电脑化供应链/库存管理系统的特殊价值，而与平滑估算的MSE或平均绝对差（MAD）的程序不同。
