歷屆優(yōu)秀匯總-2013年題獎1264隊題

第二屆“認證杯”數(shù)學(xué)中國頁參賽隊伍的參賽隊號：（請各個參賽隊提前填寫好競賽（由競賽送至評委團前競賽評 （由競賽評委團評閱前進 DynamicHR:Hermitcrabs’behaviorandthetheoryofvacancychainsgiveusabeneficialmethodwhichcanbeappliedinthemanagementofHR.Thismethodcanimprovetheeffectivenessandcontrolexpenditureswithinareasonablerangeatthesametime.Inourmodels,wedividetheproblemintothestatichumanresourcesprogramming,theshortestqueueofjobapplicantsandthedynamicmodelofhumanresourcesmanagement.HRallocationoffixednumberofemployeesandjobsisthebasisofdynamicmanagement.ly,inmodelI,wedefinethesystemofmeasuringemployees’workingeffectiveness.Basedonthis,wesetuptheprogrammingmodeltoachievetheoptimaltotaleffectiveness.Secondly,weareinspiredbythecrabs’behaviorofwaitingforacertainperiodoftime.Therefore,weestablishmodelIItodeterminetheshortestqueueofjobapplicants.Thefunctionofcost-effectivenessisthebasisofthismodel.ModelIIIisadynamicmodel.InitialjobvacanciesatthebeginningofperiodtarethedrivingforceofHRadjustment.WedefinethemechanismofthisdrivingforcetoguaranteetheoptimalHRallocation.WehavereferredtotheBPneuralnetworkalgorithmandgeneticalgorithm.AccordingtotherelationshipofdifferentperiodsandthecontinuousprocessofoptimizationofHR,wesimulatetheprocessandpredictthetrendinthefuturewithcomputers.Inthelast,wesuggestsomepossiblewaystoimproveourmodel,includingthedifficultyincollectinginformationaboutapplicantsandthechangeofworkingeffectivenesswithtime,etc.Thesearealsoourdirectioninthefuture.KeyEffectivenessoptimization,mechanismofdynamiccontrol,random Problem Variablesand ModelI:StaticHumanResources Definitionof IndexesofIndividualWorking IndexesofIndividualWorking IndexesofIndividualWorking ThePrimary TheObjective TheConstraint ThePrimary TheIntermediate TheAdvanced ModelII:TheShortestQueueofJob TheDistributionofHuman TheCost TheOptimalLengthofApplicant TheModelofSelectionsofmorethanone ModelIII:TheDynamic TheTimesofJob TheShortestTransferPathof ThePredictionofTransfer TransferofaSingle Transferofmorethanone UncertainTransferof PredictionsoftheChangeofHR Thegoalof ThePredictionofTransfer ysisofSolutionsand ysisofthe Solutionsofthe AnswertoQuestion AnswertoQuestion EvaluationoftheModelandPossible AdvantagesofOur DisadvantagesofOur Possible ApplicationofRandom TheChangeofeffectiveness Advertising ProblemWhenalonecrabencounteredoneofthebeautifulnewss,itbehavedspecially.Afteraseriesofbehavior,theresourcesallocationwithinthegroupreachesSociologistsandeconomistsusetheterm“vacancychain”todescribeasequentialexchangeofresourcesthatbenefitseveryindividualinthesequence.vacancychainsareanexcellentwaytodistributeresources.Soitmakessensethathermitcrabshaveevolvedsophisticatedsocialbehaviorstomakethemostofvacancychains.Therefore,thegoalhereEvolvesocialstrategiestoexchangejobsinqueuesothateveryonebenefitsfromit.Canweapplythemtoallindustries?Ifnot,whatconditionsneedtomeet?NowanewHumanResourcewebsitewantstoadoptthisidea,Howmanyjobapplicantsneedtosatisfybothemployersandemployees.RunittopredictthechangeofHRexpendsforsomeenterprisecustomerswithinthenextfiveyears.PrepareanadvertisingsheetforthewebsitehighlightingthestrategiesandPreliminaryHermitcrabs’behaviorofexchangeofsheltershassignificantmeaningstothemanagementandoptimizationofhumanresources.Thisbehaviorisbasedonthesatisfactoryofindividualdemandandtriestodistributeresourcesinthewholesocietyinthemostbeneficialway,thoughadynamicprocessofadjustment.Givenintheproblems,wearerequiredtosetupadynamicmodeltodescribethemovementofhumanresourcesinabusinessbasedontheysisofhermitcrabs’behaviorandvacancychain.Therearemanyreasonscausingjobvacanciesinabusiness.Generally,thesevacancieswilllybetakenupbyexistingemployees panytransferofjobs.Thenthevacanciesleftwillbefilledbynewstaffsthoughrecruitmentfromtheoutsideofthebusiness.Andthenthisprocesswillberepeatedinthenextjobadjustment.ThisprocessisshowninFigure1.Tosumup,thedynamicmovementofhumanresourcescanbedividedintothreesteps:Step1:Jobvacanciesarise.Weneedtoreallocateexistingemployeeswithinthebusinesstothedifferentjobstoreachoptimization.Step2:Afterthereallocation,thejobvacanciesleftwillbetakenupbynewemployeesrecruitedfromthesociety.Step3:whentherearenewjobvacanciesandineachbusinessperiod,repeatstage1and2abovetoadjusthumanresourcesallocation.Specifically,step1istheissueofallocatinghumanresourcesundertheconditionthatthenumberofjobsandemployeesareconstant.Wewilltreatthe izationofthetotaleffectivenessfunctionasourgoal.Inthisessay,wedescribethisprocessasthestaticmodelofhumanresourcesallocation.Step2ismainlyusedinanopenprocessofrecruitment.Thisincludesthedeterminationofthenumberofjobapplicantsinordertoachievethebalancebetweenthebestchoiceofemployeesandthesmallestnumberofapplicantsrequired.Theproblemofthebalanceisduetotherandomizationofprobabilityofeachapplicant’sStep3isadynamicmodelofhumanresourcesmanagementandallocation.WehavereferredtotheBPneuralnetworkalgorithmandgeneticalgorithm.Wesetupadynamicmodelwithmultipleinputandsingleoutput.TheflowchartisshownasFigure1:FlowChartoftheDynamicModelInthisprocess,weneedtoconsiderthefollowingfactors:Theinitialjobvacanciesarethedrivingforceofthisdynamicsystem.Theprobabilitiesofjobvacanciesvaryindifferentbusiness.(Herewedefinejobvacancyasthatthepreviousemployeeleftthejobandhenceavacancyarises.)Thechoiceofnewlyrecruitedemployeesisbasedonthedemandofthebusiness.Therefore,theindividualeffectivenessofthenewlyrecruitedemployeesdependsonthenatureofthejobvacanciesofthebusiness.Upontheappearanceofthejobvacancies,weshouldlyconsidertofillthesevacancieswithexistingemployees.Thismeansthattherewillbejobexchangesandreallocationofstaffswithinthebusiness.Thisprocessissimilarwiththebehaviorofhermitcrabs.Practicalsituationalsoapprovestheprocess.Mostjobvacanciesariseasaresultofretirementandothercommonfactors.Thesevacanciesareusuallyofhighlevelsandcannotbetakenupbynewemployees.Onlywhenthepreviousemployeesgetpromotedandleavethepreviousjoboflowlevelsvacant,thevacanciescanbefilledbynewlyemployedstaffs.Theninthenextperiod,newemployeesinthisperiodcanhavethechancetoexchangejobswithexistingemployees.Expendituresincurredintheprocessofrecruitmentisonlyrelatedtothenumberofapplicants.Thereisnocontrivedfactorsandotherlimitationsintheinternaladjustmentofhumanresources.Duringtheprocessofrecruitment,theemployerscanknowalltheinformationabouttheapplicants.TherearesufficientapplicantsintheVariablesandETheeffectivenessmatrixoftheexpectationoftotaltimesoftheexpectationoftotaltheefficiencyofThelengthofModelI:StaticHumanResourcesForagroupofemployeesoffixednumberandasetoffixedjobs,weneedtotakeaccountoftheirability,theirpreferencetodifferentjobs,thevaluetheemployeescanbringintothejobsandtheextenttowhichtheycaninfluencetheperformanceandefficiencyofthegroupasawhole.DefinitionofBeforetheexchangeandreallocationofjobs,themostimportanttaskistolearnaboutemployees’abilityandpreferenceandtrytoavoidinformationasymmetry.IndexesofIndividualWorkingAstheleadersofabusiness,itisnecessarytomakesurethateachemployeeispositionedinthejobwhichheisbestat.Intermsoftheconditionsabove,wemakethefollowingassumptions:Wecanknoweachemployee’sworkingabilityoneachjobthroughinterviewsandregularcheck,etc.Andalltheinformationwegetareaccurate.Thefactoroflearningcurveeffectwhichcanimproveemployees’abilityshouldbeignored.WedonotconsiderthetransferofbusinessandtasksamongdifferentWedividethelevelofeachemployee’sworkingabilityinto5degreesasfollows:Table1:LevelofWorkingAbilityABCD5432Inordertotransferthedegreeofworkingabilityintoavailablenumericalinformationforysispurposes,wemustknowthatthelevelofworkingabilityinpracticeisnonlinear.Accordingtofuzzyevaluationmethods,weapplyCausydistributefunctiontothedegreeofworkingabilitytodothenonlinearchange.Theequationsareas??={[1+??(??? 1≤??≤????????+ 3≤??≤WhereA,B,m,nareparameters,xisthevalueofworkingability,aisthevalueafterNowwedefinethefollowingWhenthedegreeisAandthevaluationofworkingabilityis5,thedegreeofmembershipis1,whieansf(5)=1.WhenthedegreeisCandthevaluationofworkingabilityis3,thedegreeofmembershipis0.8,whieansf(3)=0.8.Whenthevaluationofworkingabilityis1,thedegreeofmembershipis0.01, eansf(1)=0.01.Thenwecansolve??={??=??=??=Applythevalueoftheseparametersintotheequationaboveandwecangetthatthezationrangeofemployees’workingabilityis{1,0.9126,0.8,0.5245}.?? ?? ??= where??????istheworkingabilityofemployee??injobIndexesofIndividualWorkingEveryemployee’spreferencetowardsworkandjobsandtheiremotionwilltheirperformanceinthejobsandtheirFollowingthemethodusedin2.1.1,wesetupthematrixofindexesofemployees’workingpreferenceasfollows??=[??=[?????]where??????istheworkingpreferenceofemployee??injobIndexesofIndividualWorking???[ ????where??????istheworkingeffectivenessofemployee??injob??????=??×??????+(1???)× 0<??<whereαistheweightofworkingThePrimaryInthestaticprogrammingofhumanresources,weseektheizationofgroupeffectivenessandoptimization.Baseontheysisabove,wetakeintoconsiderationofemployees’workingabilityandpreferencetowardsjobsintheobjectivefunction,whichisrelatedtotheactualconditions.Hereweassumethatjobsinthebusinessandemployeesareone-to-onecorrespondent.TheObjectiveWedefinetheobjectivefunctionas??=

? where??????isa0-1variableanditsvalueisas

= ?????????????????????????????????????????????????? ??????????????????????????????????????Knownfromthequestion,ourequationofoptimizationofeffectiveness??????∑????????????=where??????istheindexesofemployee??’seffectivenessinjob??,??isthematrixofeffectiveness,??=[1 1](thenumberof1is??).TheConstraintTheconstraintsareasEveryemployeemusthaveajobinthe∑??????=Everyjobmustbetakenupbyan∑??????=Thedecisionvariableisa0-1variable,whi??????∈ThePrimaryConsideringthefactorsmentionedabove,ourmodelisas ??????∑∑????????=1∑??????=∑??????={??????∈TheIntermediateInpractice,theactualsituationswemeetwitharenotalwayssimilarwiththecasesinpart2.2.Inmostcases,thesupplyofemployeesisgreaterthandemand.Assumethatthenumberofjobsis??,thenumberofjobapplicantsis??and??>??.Thismeansthattherewillbe(?????)applicantswhocannotgetajob.??=[

? ??=[

]Inthismodel,weonlyneedtoconsidertheconstraintthateveryjobistakenupby ??????∑∑????????????=??=1∑??????=∑??????≤{??????∈where??isanm-orderrowTheAdvancedInactualsituations,weoftenhavetoconsidersomecontingencyfactors.contingencyfactorswilllimitthemanagementandallocationofhumanresources.Forinstance,someemployeesmaynothavetheabilitytotainjobsorsomecandoonlyapartofthejobs.Weneedtoaddthefollowingconstraintsintothemodel:??????=where??isa0-1{ ????????????????????????????????????????????????????{ ??????????????????????????????????????Similarly,theremaybefactorsofinter-relationshipbetweenemployees.Forexample,someemployeesmayfinishtheirworkonlyiftheyworktogetherwithcertainotheremployeeortheymayonlydotheirworkiftheyareseparatedfromcertainotheremployees.Consideringthis,weaddthefollowingconstraints:f(X)=wheref(X)istheequationoflimitationsofinter-relationshipofmatrixModelII:TheShortestQueueofJobThehermitcrabs’behaviorgivesusmuchenlightenment.Whentheyfindabeautifuls,theywilllywaitforacertainperiodoftimeandmakesurethatnootherhermitcrabssuitthesmorethanthemselves.Thentheywillclaimthesastheirowns.Inbusinesshumanresourcesmanagement,thisprocessisevenmorecomplex.Afterwemakesurethatthestructureofhumanresourceswithinthebusinessachievesoptimization,wewillconsiderrecruitingnewemployeesfromthesociety.Wecannotlearnabouttheinformationaboutalltheapplicantsinthesocietybeforerecruitmentsincethiswillbringhugecoststothebusiness.Similartohermitcrabs’behaviorthattheywillwaitforonlyacertainperiodoftime,wemustdetermineaproperlengthofthequeueofjobapplicants.Thislengthisthenumberofjobapplicantsaboutwhomweneedlearninformationindetail.Andweshouldassumethatwhenwesetthislength,weknownothingaboutallthejobapplicants.Basedontheysisabove,weassumethattheconditionofrecruitmentisThetotalnumberofjobapplicantsinthesocietyismuchlargerthanthenumberinthequeue.TheabilitystructureofapplicantsinthesocietyobeysnormalThetotaltimerequiredinrecruitingemployeesisfixed.Andtheexpendituresofrecruitmentisrelatedtothelengthoftheapplicantqueue.TheDistributionofHumanWeassumethattheabilityofjobapplicantsobeynormal??~??(0,where??istheabilityofeachFigure2:DistributionofAsisshowninFigure2,??0isthelowerlimitofjobabilityrequiredfortheapplicants.Here,??0,??1,??2,??3formfourranges,dividingtheabilityoftheapplicantsintofourdegrees.Inthediagramofthenormaldistribution,sectionA,B,CandDrepresentthedegreesofworkingabilityinModelI,whichis{2,3,4,5},shownasfollowsinTableTable2:RangeofEffectivenessDegreeofworkingDCBAEffectiveness-costTotalAccordingtotheconditionsabove,wedefinethatthelengthoftheapplicantqueue??.Undertheconditionthatweonlyknowabouttheinformationofthe applicants,ourgoalistoselectthebestoneapplicantasouremployeefromtheapplicantsinthequeue.Wesetupamatrixofrandomprobabilityasfollows????????= where??????????istheprobabilitythatthebestapplicantinthequeuewithalengthoffallsinthedegreeof????????1=1?(1?????????2=1?(1?????????3=1?(1?{????????4=1?(1?Thenwedefinethat??isthetotal??(??)=

3??2[??3where??(??)istheexpectationoftotaleffectiveness,????istheindexofworkingeffectivenessofemployeesinthedegreeof??.4??(??)=∑(1?(1?TheCostInthismodel,weconsiderthattheextensionoftheapplicantqueuewillincreaseexpenditures.Theseincludetheexpendituresonmaterialresourcesandhumanresourcesrequiredinlearningabouttheinformationaboutapplicants.Theexpendituresareindirectproportiontothelengthoftheapplicantqueue.E(??)=????+whereCisthecost,??isa??canbeestimatedbythehistoricalcosthappenedinthepastintheprocessofrecruitmentwithinthebusiness.Thenwedefinethat??isvaluemeasuredbymoneygeneratedbyemployeesundertheunitindexofeffectivenessinunittime. ??(??) ??(??) (????+ whereVisthereimbursedeffectivenessgeneratedfromtheprocessofTheOptimalLengthofApplicantWhenthemarginaleffectivenessisequaltomarginalcost,wecangettheoptimallengthofapplicantqueue.

= ThiscanbeshowninFigure3andFigure ee1ee 0 L

LFigure3:Influenceof Figure4:InfluenceofTheModelofSelectionsofmorethanoneTheysisaboveismainlyusedtosolvetheproblemwhentheenterpriseneedstorecruitonlyonenewemployee.Whenthenumberofnewemployeestheyneedtohireis??,wecansetupthefollowingmatrixofprobability:

????????=

]((??????????1=(1?1?????1)??????????????2=(1?(1?????2)??????????????3=(1?(1?????3)????{??????????4=(1?(1?????4)????Theexpectationoftotaleffectivenesswillbeas ??(??)=∑∑??=1HerethecostcurveisthesamewiththatinthesituationwhereonlyoneemployeeisModelIII:TheDynamicinthenextperiodInmodelI,weyzedtheallocationofhumanresourcesundertheconditionthatthenumberofemployeesandjobsarethesameandfixed.InmodelII,inthenextperiodStep1:Jobvacancies

finalvacancieswhichshouldbefilledbynewemployees.Figure5:StepsofModelInthisdynamicprocess,initialjobvacanciesarethedrivingforceofadjustmentofjobswithinthebusiness.ThentheoptimizationwillbecarriedoutthroughthemethodinmodelI.Afteraseriesofjobexchanges,thejobvacanciesleftwillbefilledbynewlyrecruitedemployeesfromthesociety.Afterthis,inthenextperiodwhenexistingemployeesleavetheirjobsandnewvacanciesarise,theadjustmentwillbeOurgoalistomakesurethatinthedynamicprocessofjobexchangeandrecruitment,highereffectivenessandlowerrateofstaffturnovercanbeachievedatthesametime.WecanshowtheprocessofjobadjustmentusingthefollowingFigure6:ChainofjobTheTimesofJobLet’sassumethatinanenterprisethetotalnumberofjobsisconstant.Beforethejobreallocation,theoptimaljoballocationmatrixisasfollows:

??(??)=[

? Thematrixofeffectivenessisas ??(??)=[

? Nowthereisthephenomenonthatsomeexistingemployeeswillleavetheenterprise.Assumethatthenumberofemployeesleavingtheirjobsandnewlyrecruitedemployeesis??.Replacetheindexesofeffectivenessoftheemployeeswholefttheenterprisewiththatofthenewemployees.Thentherebe??(??+1)andwecandefinenewoptimaljoballocationmatrix??(??+1).ApplythesefactorsintomodelIandwecanget: ??????∑∑??(??+1)??????(??+??=1∑??(??+1)????=∑??(??+1)????={??(??+1)????∈Theninperiod??+1,theoptimaljoballocationandthetimesoftransferofjobswill ??=∑??=1

|??(??+1)???????(??)????|Intheequationabove,duetotheparticularityofmatrix??(??+1)and??(??),wecansolvethetimesoftransferofjobsbymathematicaltransformations.TheShortestTransferPathofInthepracticalprocessofhumanresourcesmanagement,duetothecostoftransfersofjobswithinthegroup,wewillgenerallytrytoreducethetimesandrangeoftransfersandkeeptheeffectivenessatahighlevel.Therefore,theobjectivefunctioninperiod??+1canbeasfollows:

min{??????∑∑??(??+1)??????(??+??=1Theconstrains∑??(??+1)????=∑??(??+1)????={??(??+1)????∈WiththehelpofsoftwareLingo,wecansolve??(??+1),whichwillalsobeusedastheconditionsfor??(??+2).Thiswillguaranteethatineachadjustmentofhumanresources,ourgoalistoachievetheshortesttransferpathandthehighesttotalThePredictionofTransferInpracticalsituations,theappearanceofinitialjobvacanciesisrandom.Theindexesofnewlyrecruitedemployees’effectivenessarerandom,too.Therefore,theenterprisemustpredictthetrendofhumanresourcesinthesocietyforthenextperiod.TransferofaSingleInordertosimplifythemodel,wewilllylookatthepredictioninwhichonlyoneemployeeischangedforonetime.WemakethefollowingThetotalnumberofexistingemployeesis??,ofwhichthenumberofemployeesrequiredtobehiredfromthesocietyis??.??(??)istheeffectivenessmatrixofexistingemployees.??′(??)istheeffectivenessmatrixofapplicants.??(??)istheallocationofexistingemployees.Theprobabilityofleavingthejobsisthesameforalltheexistingemployees.Theprobabilityofrecruitmentisthesameforalltheapplicants.Thentheprobabilityofleavingthejobsforexistingemployees1????????1=Theprobabilityofrecruitmentofapplicants1????????2= ????= ??=[

] where??????isthetotaleffectivenessgeneratedwhenapplicant??takestheplaceofexistingemployee??.Wecanusemodel4.2tosolveeach??????inmatrix??.??????isleasttimesofjobtransferswhenapplicant??takestheplaceofexistingemployee??.Therefore,wecan

??(??)

11

??(??)= TransferofmorethanoneIfmorethanoneemployeesneedtoberecruited,thenumberofprobabletransferswillbeS=CgCg,wheregisthenumberofemployeesneedtoberecruitedfrommThenwecangetthefollowing??(??)=∑??(??)=∑UncertainTransferofUndertheconditionoftransfersofmorethanoneemployees,if??<??,thenumberofprobabletransferswillbeC1C1+C2C2+?+m m mLet??=??1+??2+?+????.Then??and??willbeS-ordervectors. expressionof??(??)and??(??)willbethesameastheequationsinPredictionsoftheChangeofHRThegoalofTopredictthesituationofhumanresourcesinperiod??,wearemainlygoingtoknowaboutthejobtransferpathandtotaleffectivenessinperiod??.Throughthemethodin4.3,wecangettheexpectationoftimesoftransferandtotaleffectivenessinperiod??+1basedonthejoballocationmatrixandeffectivenessmatrixinthebasicWedefinethefollowing ????????(??+?? where??istheratiobetweentotaleffectivenessandtimesoftransfer.Weconsiderthattheresultandefficiencyofhumanresourcesallocationwillbebetterifthevalueof??islarger.ThePredictionofTransferTheexpectationofefficiencyofhumanresourcesallocationinperiod??+1??(??)=Intermsofthepredictionoftransferpath,werefertothegreypredictionmodel.Weusethecombinationwhichistheclosesttotheefficiencyofhumanallocationand??(??)as??????{|??(??)???(1)|,|??(??)???(2)|,?,|??(??)?Weshouldfindtheonewhichistheclosesttotheexpectationastheinitialhumanresourcesallocationinperiod??+1.Thenbasedontheysisinperiod??+1,wecancontinuetopredictthemanagementofhumanresourcesinperiod??+2andsoon.Ourpredictionoftransferpathisledby??(??).5ysisofSolutionsandInordertoverifytheavailabilityofthemodelprecisely,weusecomputerstosimulatethedynamicprocessofhumanresourcesmanagement.ly,weassumethattherearedifferencesbetweenworkingeffectivenessofdifferentemployees.Nowwedefinetwotypesofhumanresourcesallocation:??1:??2::??3:??4=0.2:0.3:0.4:??1:??2::??3:??4=0.1:0.2:0.4:Itisobviousthathumanresourcesallocationtypea)isbetterthantypeForsomeenterprises,theeffectivenessofexistingemployeesisworsethanthatofthenewlyrecruitedemployeesfromthesociety.Forsomeotherenterprises,theaveragelevelofworkingabilityofnewlyrecruitedemployeesishigherthanthatofexistingWiththehelpofcomputers,wesimulatethetotaleffectivenesshumanresourcesandtimesofjobtransfersinthenext5yearsundertheconditionoftwotypesofhumanresourcesallocationrespectively.Intheprocessofsimulation,weestablishtherandomeffectivenessmatrixofexistingemployeesandnewlyrecruitedemployeesaccordingtotheweightmentionedrespectively.ThenwecanusethemethodinmodelIIItoyzeandpredictthechangeofhumanresourcesinthefuture.WesetupfourkindsofrandompatternstosimulatethepracticalhumanresourcesPattern1:Theperiodofadjustmentis1year.Thenumberofemployeeschangedis1.Theaverageeffectivenesslevelofexistingemployeesislowerthanthatofnewlyrecruitedemployees.Pattern2:Theperiodofadjustmentis1year.Thenumberofemployeeschangedis2.Theaverageeffectivenesslevelofexistingemployeesislowerthanthatofnewlyrecruitedemployees.Pattern3:Theperiodofadjustmentis1year.Thenumberofemployeeschangedis1.Theaverageeffectivenesslevelofexistingemployeesishigherthanthatofnewlyrecruitedemployees.Pattern4:Theperiodofadjustmentis1year.Thenumberofemployeeschangedis2.Theaverageeffectivenesslevelofexistingemployeesishigherthanthatofnewlyrecruitedemployees.Table4:expectationsofDifferentPatternPatternPatternPatternYear3434YearYearYearYearLong-1212ysisofthePatternonePatterntwoPatternonePatterntwo PatternonePatterntwoPatternonePatterntwo

0

Figure FigurePatternthreePatternfourPatternthreePatternfourPatternthreePatternfourPatternthreePatternfourPatternthreePatternfourPatternthreePatternfour

3

2

1 Figure FigureFigure7:changesofExpectationswithFromFigure7.1and7.2,wecanknowthatwhenthenewlyrecruitedemployees’abilityisbetterthantheexistingemployees,thetotaleffectivenessoftheenterpriseaswholewillshowaupwardtrendastimegoesby.Butthespeedoftheincreasewillslowdownandtendtobeclosetotheexpectationoftheoptimaleffectivenessoftheapplicantsinthesociety.Intheme,withtheprocessofthecombinationofexistingemployeesandnewemployees,theexpectationoftransfertimesineachperiodtendstobecloseto1.Toputitanotherway,internaladjustmentisnotrequiredsincethereisnodistinctionbetweentheeffectivenessofexistingemployeesandnewemployee.Thereforethereisnoneedtotransferjobswithinthebusiness.Situationsaredifferentinpattern3and4.Inthesetwopatterns,outsideapplicants’effectivenessislowerthanexistingemployees.Infactjobvacanciesinthesesituationsarethelossofhumanresources.Therefore,totaleffectivenessofoptimalallocationwillshowadownwardtrenduntilthetotaleffectivenessofexistingemployeesisthesamewiththatofthoseinthesociety.Inallthepatterns,timesofjobtransferswilldecreasewiththepassoftimeduetothereducedtodifferencesbetweenabilityofexistingemployeesandotherapplicants.Ineachperiod,thenumberoftransfersofemployeesdirectlydeterminesthespeedofhumanresourcesallocation.Soitcanbeseenfromgraph3andgraph4thatthepatternsinwh