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传播优秀Word版文档,希望对您有帮助,可双击去除!传播优秀Word版文档,希望对您有帮助,可双击去除!/传播优秀Word版文档,希望对您有帮助,可双击去除!外文原文StudyonHumanResourceAllocationinMulti-ProjectBasedonthePriorityandtheCostofProjectsLinJingjing,ZhouGuohuaSchoolofEconomicsandmanagement,SouthwestJiaotongUniversity,610031,ChinaAbstractThispaperputforwardtheaffectingfactorsofproject’spriority.whichisintroducedintoamulti-objectiveoptimizationmodelforhumanresourceallocationinmulti-projectenvironment.Theobjectivesofthemodelweretheminimumcostlossduetothedelayofthetimelimitoftheprojectsandtheminimumdelayoftheprojectwiththehighestpriority.ThenaGeneticAlgorithmtosolvethemodelwasintroduced.Finally,anumericalexamplewasusedtotestifythefeasibilityofthemodelandthealgorithm.IndexTerms—GeneticAlgorithm,HumanResourceAllocation,Multi-project’sproject’spriority.INTRODUCTIONMoreandmoreenterprisesarefacingthechallengeofmulti-projectmanagement,whichhasbeenthefocusamongresearchesonprojectmanagement.Inmulti-projectenvironment,thesharearecompetitionofresourcessuchascapital,timeandhumanresourcesoftenoccur.Therefore,it’scriticaltoscheduleprojectsinordertosatisfythedifferentresourcedemandsandtoshortentheprojects’durationtimewithresourcesconstrained,asin[1].Formanyenterprises,thehumanresourcesarethemostpreciousasset.Soenterprisesshouldreasonablyandeffectivelyallocateeachresource,especiallythehumanresource,inordertoshortenthetimeandcostofprojectsandtoincreasethebenefits.Someliteratureshavediscussedtheresourceallocationprobleminmulti-projectenvironmentwithresourcesconstrained.Reference[1]designedaniterativealgorithmandproposedamathematicalmodeloftheresource-constrainedmulti-projectscheduling.Basedonworkbreakdownstructure(WBS)andDantzig-Wolfedecompositionmethod,afeasiblemulti-projectplanningmethodwasillustrated,asin[2].References[3,4]discussedtheresource-constrainedprojectschedulingbasedonBranchDelimitationmethod.Reference[5]putforwardtheframeworkofhumanresourceallocationinmulti-projectinLong-term,medium-termandshort-termaswellasresearchanddevelopment(R&D)environment.Based传播优秀Word版文档,希望对您有帮助,可双击去除!传播优秀Word版文档,希望对您有帮助,可双击去除!传播优秀Word版文档,希望对您有帮助,可双击去除!onGPSSlanguage,simulationmodelofresourcesallocationwasbuilttogettheproject’sdurationtimeandresourcesdistribution,asin[6].Reference[7]solvedtheengineeringproject’sresourcesoptimizationproblemusingGeneticAlgorithms.Theseliteraturesreasonablyoptimizedresourcesallocationinmulti-project,butallhadthesameprerequisitethattheproject’simportanceisthesametoeachother.Thispaperwillanalyzetheeffectsofproject’spriorityonhumanresourceallocation,whichistobeintroducedintoamathematicalmodel;finally,aGeneticAlgorithmisusedtosolvethemodel.EFFECTSOFPROJECTSPRIORITYONHUMANRESOUCEALLOCATIONANDTHEAFFECTINGFACTORSOFPROJECT’SPRIORITYResourcesharingisoneofthemaincharacteristicsofmulti-projectmanagement.Theallocationofsharedresourcesrelatestotheefficiencyandrationalityoftheuseofresources.Whenresourceconflictoccurs,theresourcedemandoftheprojectwithhighestpriorityshouldbesatisfiedfirst.Onlyafterthat,cantheprojectswithlowerprioritybeconsidered.Basedontheideaofprojectclassificationmanagement,thispaperclassifiestheaffectingfactorsofproject’spriorityintothreecategories,astheproject’sbenefits,thecomplexityofprojectmanagementandtechnology,andthestrategicinfluenceontheenterprise’sfuturedevelopment.Thepriorityweightoftheprojectisthefunctionoftheabovethreecategories,asshownin(1).W=f(I,c,s…)(1)Wherewreferstoproject’spriorityweight;Ireferstothebenefitsoftheproject;creferstothecomplexityoftheproject,includingthetechnologyandmanagement;sreferstotheinfluenceoftheprojectonenterprise.Thebiggerthevaluesofthethreecategories,thehigherthepriorityis.HUMANRESOURCEALLOCATIONMODELINMULTI-PROJECTENVIRONMENT传播优秀Word版文档,希望对您有帮助,可双击去除!传播优秀Word版文档,希望对您有帮助,可双击去除!传播优秀Word版文档,希望对您有帮助,可双击去除!ProblemDescriptionAccordingtotheconstrainttheory,theenterpriseshouldstrictlydifferentiatethebottleneckresourcesandthenon-bottleneckresourcestosolvetheconstraintproblemofbottleneckresources.Thispaperwillstressonthelimitedcriticalhumanresourcesbeingallocatedtomulti-projectwithdefinitedurationtimesandpriority.Tosimplifytheproblem,wesupposethatthatthreeexistseveralparallelprojectsandasharedresourcesstorehouse,andtheenterprise’soperationonlyinvolvesonekindofcriticalhumanresources.Thesupplyofthecriticalhumanresourceislimited,whichcannotbeobtainedbyhiringoranyotherwaysduringacertainperiod.whenresourceconflictamongparallelprojectsoccurs,wemayallocatethehumanresourcetomulti-projectaccordingtoproject’spriorities.Theallocationofnon-criticalindependenthumanresourcesisnotconsideredinthispaper,whichsupposesthattheindependentresourcesthateachprojectneedscanbesatisfied.Engineeringprojectsusuallyneedmassivecriticalskilledhumanresourcesinsomecriticalchain,whichcannotbesubstitutedbytheotherkindofhumanresources.Whenthecriticalchainsofprojectsatthesametimeduringsomeperiod,thereoccurresourceconflictandcompetition.Thepaperalsosupposesthatthecorrespondingnetworkplanningofvariousprojectshavealreadybeenestablished,andthepeaksofeachproject’sresourcesdemandhavebeenoptimized.Thedelayofthecriticalchainwillaffectthewholeproject’sdurationtime.3.2ModelHypothesesThefollowinghypotheseshelpustoestablishamathematicalmodel:Thenumberofmutuallyindependentprojectsinvolvedinresourceallocationprobleminmulti-projectisN.EachprojectisindicatedwithQi,whilei=1,2,…N.Thepriorityweightsofmulti-projecthavebeendetermined,whicharerespectivelyw传播优秀Word版文档,希望对您有帮助,可双击去除!传播优秀Word版文档,希望对您有帮助,可双击去除!传播优秀Word版文档,希望对您有帮助,可双击去除!1,w2…wn.ThetotalnumberofthecriticalhumanresourcesisR,withrkstandingforeachperson,whilek=1,2,…,RΔki=Resourcescapturingbyseveralprojectsbeginsontime.tEiistheexpecteddurationtimeofprojectIthatneedsthecriticalresourcestofinishsometaskaftertimet,onthepremisethatthehumanresourcesdemandcanbesatisfied.tAiistherealdurationtimeofprojectIthatneedsthecriticalresourcetofinishsometaskaftertimet.Accordingtothecontract,ifthedelayoftheprojecthappensthedailycostlossduetothedelayis△ciforprojectI.Accordingtotheproject’simportance,thedelayofaprojectwillnotonlycausethecostloss,butwillalsodamagetheprestigeandstatusoftheenterprise.(whilethelatentcostisdifficulttoquantify,itisn’tconsideredinthisarticletemporarily.)Fromthehypothesis(5),wecanknowthataftertimet,thetime-gapbetweentherealandexpecteddurationtimeofprojectIthatneedsthecriticalresourcestofinishsometaskis△ti,(△ti=tAi-tEi).Forthereexistsresourcescompetition,thetime–gapisnecessarilyapositivenumber.Accordingtohypotheses(6)and(7),thetotalcostlossofprojectIisCi(Ci=△ti*△Ci).Thedurationtimeofactivitiescanbeexpressedbytheworkloadofactivitiesdividedbythequantityofresources,whichcanbeindicatedwithfollowingexpressionoftAi=ηi/Ri*,.Intheexpression,ηireferstotheworkloadofprojectsIduringsomeperiod,whichissupposedtobefixedandpre-determinedbytheprojectmanagersonprojectplanningphase;Ri*referstothenumberofthecriticalhumanresourcesbeingallocatedtoprojectsIactually,withtheequationR传播优秀Word版文档,希望对您有帮助,可双击去除!传播优秀Word版文档,希望对您有帮助,可双击去除!传播优秀Word版文档,希望对您有帮助,可双击去除!i*=existing.DuetotheresourcecompetitiontheresourcedemandsofprojectswithhigherPrioritiesmaybeguarantee,whilethoseprojectswithlowerprioritiesmaynotbefullyguaranteed.Inthissituation,thedecreaseoftheresourcesupplywillleadtotheincreaseofthedurationtimeofactivitiesandtheproject,whiletheworkloadisfixed.OptimizationModelBasedontheabovehypotheses,theresourceallocationmodelinmulti-projectenvironmentcanbeestablished.Here,theoptimizationmodelis:Fi=minZi=min=min(2)=min=minZ2=min=min(3)Wherewj=max(wi),()(4)Subjectto:0=R(5)Themodelisamulti-objectiveone.Thetwoobjectivefunctionsarerespectivelytominimizethetotalcostloss,whichistoconformtotheeconomictarget,andtoshortenthetimedelayoftheprojectwithhighestpriority.Thefirstobjectivefunctioncanonlyoptimizetheapparenteconomiccost;thereforethesecondobjectivefunctionwillhelptomakeupthislimitation.Fortheprojectwithhighestpriority,timedelaywilldamagenotonlytheeconomicbenefits,butalsothestrategyandtheprestigeoftheenterprise.Thereforeweshouldguaranteethatthemostimportantprojectbefinishedontimeoraheadofschedule.传播优秀Word版文档,希望对您有帮助,可双击去除!传播优秀Word版文档,希望对您有帮助,可双击去除!传播优秀Word版文档,希望对您有帮助,可双击去除!SOLUTIONTOTHEMULTI-OBJECTIVEMODELUSINGGENETICALGORITHMThemulti-objectiveoptimizationproblemisquitecommon.Generally,eachobjectiveshouldbeoptimizedinordertogetthecomprehensiveobjectiveoptimized.Thereforetheweightofeachsub-objectiveshouldbeconsidered.Reference[8]proposedanimprovedantcolonyalgorithmtosolvethisproblem.Supposedthattheweightsofthetwooptimizingobjectivesareαandβ,whereα+β=1.ThenthecomprehensivegoalisF*,whereF*=αF1+βF2.ThePrincipleofGeneticAlgorithmGeneticAlgorithmrootsfromtheconceptsofnaturalselectionandgenetics.It’sarandomsearchtechniqueforglobaloptimizationinacomplexsearchspace.Becauseoftheparallelnatureandlessrestrictions,ithasthekeyfeaturesofgreatcurrency,fastconvergenceandeasycalculation.Meanwhile,itssearchscopeisnotlimited,soit’saneffectivemethodtosolvetheresourcebalancingproblem,asin[9].ThemainstepsofGAinthispaperareasfollow:EncodingAnintegerstringisshort,directandefficient.Accordingtothecharacteristicsofthemodel,thehumanresourcecanbeassignedtobeacodeobject.Thestringlengthequalstothetotalnumberofhumanresourcesallocated.ChoosingthefitnessfunctionThispaperchoosetheobjectivefunctionasthefoundationoffitnessfunction.Toratethevaluesoftheobjectivefunction,thefitnessofthen-thindividualis1/传播优秀Word版文档,希望对您有帮助,可双击去除!传播优秀Word版文档,希望对您有帮助,可双击去除!传播优秀Word版文档,希望对您有帮助,可双击去除!。GeneticoperationIt’sthecoreofGA.Thisprocessincludesthreebasicoperators:selectionoperator,crossoveroperator,andmutationoperation.Selectionoperationistoselectthegoodindividualsamongthegroup.Theprobabilityofastringtobeselectedasaparentisproportionaltoitsfitness.Thehigherthestring’sfitnessis,thegreatertheprobabilityofthestringtobeselectedasaparentwillbe.CrossoveroperatorTheso-calledcrossoveristhatthepatenchromosomesexchangesomegenestoyieldtwooffspringstringsinsomerule.Wecanuseuniformcrossover,thatthetwochromosomesexchangethegenesonthesamepositionswiththesamecrossoverprobabilitytoyieldtwonewindividuals.MutationoperatorMutationaddstothediversityofapopulationandtherebyincreasesthelikelihoodthatthealgorithmwillgenerateindividualswithbetterfitnessvalues.ThemutationoperatordeterminesthesearchabilityofGA,maintainthediversityofapopulation,andavoidtheprematurity.Thereareseveralmutationisquiteeasy.StandardfortheterminalofGAWithouthumancontrol,theevolutionprocessofthealgorithmwillneverend.Thepopulationsizeaffectsthefinalresultandtheoperationspeed.Ifthesizeisgreater,thediversityofthepopulationcanbeadded,andthebestresultcanbeobtainedeasier.However,theefficiencyisreduced.Recently,inmostGAprogress,thebiggestevolvementalgebraisdeterminedbyhuman-beingstocontrolthecoursethealgorithm.NUMERICALEXAMPLE传播优秀Word版文档,希望对您有帮助,可双击去除!传播优秀Word版文档,希望对您有帮助,可双击去除!传播优秀Word版文档,希望对您有帮助,可双击去除!WeuseanumericalexampletoillustratetheeffectivenessofGeneticAlgorithm.Assumethattherearethreeprojectswiththesamenetwork,andthepriorityweightshavebeenputforward.Thereisonlyonecriticalpathineachproject.ThedatawehaveknownareshowninTable1.Table1DataoftheThreeProjectsProjectPriorityweightwtECostloss(humanyuan/day)Workload(person*day)10.421010010020.3181508030.271280120ThestepsofGeneticAlgorithmtosolvethemodelareasfollow:Step1:Anintegerstringisadopted.Encodewith[0,1,2]fortherearethreeprojects.Thelengthofthechromosomeis16,thetotalnumberofhumanresourcetobeallocated.Step2:Theinitialpopulationsizeis50.Step3:Doinggeneticoperation.AdoptRouletteWheelandElitisttactictodeterminedselectionoperator.Theoffspringcanbeyieldedbyuniformcross-over.Themutationoperatorcanbedeterminedbyuniformmutation.Weassumethatthemutationprobabilityequalto0.001.Step4:Adoptthemaximumpopulationsizeis100whenterminated.Afterthecomputersimulation,wecanobtainthePare-toresultswithdifferentimportanceweightsofthetwoobjectivefunctions,asshowninTable2:Table2TheSolutionResultoftheModelR1*R2*R3*F1(HundredYuan)F2(Day)α=1,β=0655911.22.8α=0.7,β=0.3754940.81.8α=0.4,β=0.68441051.81.05α=0.1,β=0.910331472.80传播优秀Word版文档,希望对您有帮助,可双击去除!传播优秀Word版文档,希望对您有帮助,可双击去除!传播优秀Word版文档,希望对您有帮助,可双击去除!Fromtable2wecanlearnthat,whenαandβchange,theresultisdifferent.HoweverwecanobtainaseriesofParetoresults.CONCLUSIONHumanresourceallocationinmulti-projectenvironmentisacomplicatedproblem.Thispaperanalyzestheimportanceofproject’spriorityinresourceallocationandestablishesahumanresourceallocationmodelbasedonpriorityandcostofprojects.Finally,geneticAlgorithmisadoptedtosolvethemodel.Duringtheconstructionprocessoftheallocationmodel,wehaveputforwardsomehypothesesinordertosimplifytheproblem.However,whentheenterprisespracticallyallocatetheresources,heywillfacemorecomplexity,whichisthefocusofourfuturestudy.传播优秀Word版文档,希望对您有帮助,可双击去除!传播优秀Word版文档,希望对您有帮助,可双击去除!传播优秀Word版文档,希望对您有帮助,可双击去除!中文翻译:在项目优先权和成本的基础上对多项目中人力资源配置的研究林晶晶,周国华中国西南交通大学经济和管理学院,610031摘要本文提出项目优先次序的影响因素,为多项目环境配置人力资源引入一个多目标优化模型。这一模型的目标是使得由于项目时间限制的延误损失的成本最低和具有最高优先顺序项目的延迟最小。然后用遗传算法求解该模型。最后,用一个数值例子证明该模型和算法的可行性。关键字遗传算法;人力资源配置;多项目、项目的优先权;1、引言越来越多的企业面临的挑战是多项目管理,这已经成为项目管理研究的焦点。多项目环境中,诸如资金,时间和人力等资源的共享和竞争经常发生。因此合理安排项目的进度,以满足不同资源的需求并缩短项目造成的资源约束。对于许多企业来说,人力资源是最宝贵的资产。所以企业应合理有效分配每个资源,尤其是人力资源,用以缩短时间减少项目的成本和增加效益。一些文献中曾讨论的存在资源约束的多项目环境中资源分配问题。设计一个迭代算法,并提出了资源约束的多项目调度的数学模型。基于工作分解结构(wbs)和dantzig-wolf的分解方法,人们曾演示过一个可行的多项目规划方法。讨论基于分支定界的方法的资源受限项目的调度。提出在长期、中期和短期的多项目及研究和开发(R&D)环境中人力资源配置框架。在gpss语言的基础上,为了获得该项目的持续时间和资源的分配而建立仿真模型的资源配置。用遗传算法解决了工程项目的资源优化问题。这些文献虽然合理优化了多项目的资源配置,但它们都有相同的先决条件即该项目的重要性是一样。本文将引进数学模型用以分析项目优先权在人力资源配置中的作用。最后,用遗传算法求解这一模型。2.项目优先权对人的资源分配的作用和影响项目优先权的因素传播优秀Word版文档,希望对您有帮助,可双击去除!传播优秀Word版文档,希望对您有帮助,可双击去除!传播优秀Word版文档,希望对您有帮助,可双击去除!资源共享是是多项目管理一个主要特点。共享资源的分配涉及到资源使用的效率和合理性,当资源发生冲突时,应该首先满足最高优先权项目的资源的需求。在此之后,较低优先权的项目才予以考虑。基于项目分类管理的思想,本文将归类项目的优先次序的影响因素分为三类。正如项目的利润一样,复杂的项目管理和技术以及战略都影响着企业的未来发展。优先权的重量级取决于该项目上述三大类因素。公式为:W=f(I,c,s…)(1)其中w是指项目的优先权重;i指该项目的利润,;c指项目中技术和管理的复杂性;s指该项目对企业的影响。三类因素的价值越大,其优先级越高。3、在多项目环境下的人力资源分配模型。3.1、问题描述根据约束理论,企业应严格区分瓶颈资源和非瓶颈资源来解决瓶颈资源的约束问题。本文将着力研究被分配在多项目中有限且关键的人力资源,而这些多项目都有明确的期限和时代优先权。为了简化问题,我们假设存在平行的几个项目和一个共享的资源库,且企业的运作只涉及一种重要的人力资源。关键人力资源的供应是有限的,在一定期限内是不能通过雇用或凭借任何其他方式获得的。当资源之间的冲突在并行项目中发生时,我们可能会根据项目的优先次序分配人力资源。本文不考虑非关键独立的人力资源的配置问题,这是假定这些独立的资源可以满足每个项目的需求。工程项目通常在一些关键链需要大量的关键技术熟练的人力资源,而这些资源是由其他人力资源所不能取代。在某时期内,当项目的几个关键环节同时需要同一种关键性人力资源时就会发生资源的冲突和竞争。本文还假设认为,各个项目已经建立相应的网络规划,并且每个项目的资源需求的高峰期已得到优化。关键环节的延误将会影响整个项目的持续时间。3.2模型假设

以下假说帮助我们建立一个数学模型:(1)介入多项目的资源分配问题的相互独立项目的数量是N。每个项目Q用表示,而i=1,2,…N。传播优秀Word版文档,希望对您有帮助,可双击去除!传播优秀Word版文档,希望对您有帮助,可双击去除!传播优秀Word版文档,希望对您有帮助,可双击去除!(2)确定了多项目优先权重量,各自是w1,w2…wn。(3)重要人力资源的总数是R,用rk代表每个人,而k=1,2,…,R(4)ki=(5)几个项目共用的资源从时间ts开始。tEi是人力资源的需求可以得到满足的前提下项目i的预计持续时间,项目i在ts后需要关键资源来完成某些任务。(6)根据合同,如果该项目延误则由延误对项目i造成的每日成本损失为△Ci。根据该项目的重要性,工程延误后不但会造成成本的损失,而且还会损害企业的威望和地位。(而潜在的成本是难以量化的,这在本文中暂时不做考虑)。(7)从假说(5),我们可以知道在时间ts后,项目i真正持续时间和预期持续时间的时间差距为△ti,(△ti=tAi-tEi)。由于存在着资源的竞争,时间的差距必然是一个正数。(8)根据假说(6)和(7),项目i总的成本损失是Ci(Ci=△ti*△Ci)。(9)活动持续时间可以用活动的工作量除以资源的数量表达,用下面的表达式表示为tAi=ηi/R*i。在这个表达式中,ηi指在某一时期项目i的工作量,它应该是固定和预先确定的。R*i是指在项目经理对项目的规划阶段被实际上分配给项目i中的关键人力资源的数量。于是存在方程Ri*=。由于资源的竞争,具有较高优先权项目的资源需求可能得到保障,而那些较低的优先权的项目可能无法得到充分保障。在这种情况下当工作量是固定的,减少了资源的供应将导致活动和项目持续时间的增加。3.3优化模型基于上述的假设确立多项目环境的资源分配模型。这里的优化模型表示为:Fi=minZi=min=min(2)传播优秀Word版文档,希望对您有帮助,可双击去除!传播优秀Word版文档,希望对您有帮助,可双击去除!传播优秀Word版文档,希望对您有帮助,可双击去除!=min=minZ2=min=min(3)Wherewj=max(wi),()(4)Subjectto:0=R(5)该模型是一个多目标形式的。这两个目标函数一个是为符合经济目标以尽量减少总的成本损失,另一个是以缩短有最高优先权项目的延迟时间。由于第一个目标函数只能优化明显的经济成本,因此第二个目标函数将有助于弥补此限制。

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