第九章网络计划技术(MBA讲义)课件

Chapter12PERT/CPMModelsfor

ProjectManagement§1

ProjectNetworks计划网络图§2SchedulingaProjectwithPERT/CPM

网络时间与关键路线§3DealingwithUncertainActivityDurations§4网络优化1Chapter12PERT/CPMModelsfo1项目管理ProjectManagement项目特征CharacteristicsofProjectsUnique,one-timeoperationsInvolvealargenumberofactivitiesthatmustbeplannedandcoordinatedLongtime-horizonGoalsofmeetingcompletiondeadlinesandbudgetsExamplesBuildingahousePlanningameetingIntroducinganewproductPERT—ProjectEvaluationandReviewTechnique计划评审技术

CPM—CriticalPathMethod关键路线法Agraphicalornetworkapproachforplanningandcoordinatinglarge-scaleprojects.项目管理ProjectManagement项目特征Cha2可信建筑公司项目ReliableConstructionCompanyProjectP285TheReliableConstructionCompanyhasjustmadethewinningbidof$5.4milliontoconstructanewplantforamajormanufacturer.可信建筑公司中标540万美元的项目Thecontractincludesthefollowingprovisions:Apenaltyof$300,000ifReliablehasnotcompletedconstructionwithin47weeks.如果不能在47周内完成项目，将被罚款30万美元。如果能在40周内完成，将获得15万美元的奖励Abonusof$150,000ifReliablehascompletedtheplantwithin40weeks.Questions:286Howcantheprojectbedisplayedgraphicallytobettervisualizetheactivities?如何用图来表示项目中活动流程Whatisthetotaltimerequiredtocompletetheprojectifnodelaysoccur?Whendotheindividualactivitiesneedtostartandfinish?Whatarethecriticalbottleneckactivities?对于非关键的活动Forotheractivities,howmuchdelaycanbetolerated承受?Whatistheprobabilitytheprojectcanbecompletedin47weeks?Whatistheleastexpensivewaytocompletetheprojectwithin40weeks?Howshouldongoingcostsbemonitoredtotrytokeeptheprojectwithinbudget?如何对成本进行实时监控，使项目成本控制在预算内可信建筑公司项目ReliableConstruction3活动明细表

ActivityListforReliableConstructionActivityActivityDescription紧前Immediate

Predecessors估计工期(Weeks)AExcavate挖掘—2BLaythefoundation打地基A4CPutuptheroughwall承重墙施工B10DPutuptheroof封顶C6EInstalltheexteriorplumbing安装外部管道C4FInstalltheinteriorplumbing安装内部管道E5GPutuptheexteriorsiding外墙施工D7HDotheexteriorpainting外部粉刷E,G9IDotheelectricalwork电路铺设C7JPutupthewallboard竖墙板F,I8KInstalltheflooring铺地板J4LDotheinteriorpainting内部粉刷J5MInstalltheexteriorfixtures设施H2NInstalltheinteriorfixtures安装内部设备K,L6活动明细表ActivityListforReliab4项目网络

ProjectNetworks表示整个项目的网络称为项目网络Anetworkusedtorepresentaprojectiscalledaprojectnetwork.Aprojectnetworkconsistsofanumberof节点nodesandanumberofarcs.Twotypesofprojectnetworks:Activity-on-arc(AOA弧表示活动):eachactivityisrepresentedbyanarc.Anodeisusedtoseparateanactivityfromitspredecessors.Thesequencingofthearcsshowstheprecedencerelationships.Activity-on-node(AON节点表示活动):eachactivityisrepresentedbyanode.Thearcsareusedtoshowtheprecedence优先relationships.AdvantagesofAON(usedinthistextbook):P288considerablyeasiertoconstruct易于构建easiertounderstand易于理解easiertorevisewhentherearechanges更便于修改项目网络ProjectNetworks表示整个项目的网络5ReliableConstruction

ProjectNetworkReliableConstruction

Project6MicrosoftProjectGanttChart甘特图W1/1表示第一周第一天；W2/5表示第二周第五天；MicrosoftProjectGanttChart7MicrosoftProject

—ProjectNetwork活动名称编号工期最早开始时间最早结束时间P290W1/1第一周第一天开始W2/5第二周第五天完成二周MicrosoftProject

—ProjectNet8AOAProjectNetwork1235ABCD6GEI4871011139H12FJKLNMAOAProjectNetwork1235ABCD6G9关于AOA计划网络图

统筹方法的第一步工作就是绘制计划网络图，也就是将工序（或称为活动）进度表转换为统筹方法的网络图。下面用一个例子来说明例3、某公司研制新产品的部分工序与所需时间以及它们之间的相互关系都显示在其工序进度表如表12-8所示，请画出其统筹方法网络图。

工序代号工序内容所需时间（天)紧前工序abcde产品设计与工艺设计外购配套零件外购生产原料自制主件主配可靠性试验601513388-aacb,d2表12-8关于AOA计划网络图工序代号工序内容所需时间（天)紧10网络图中的节点表示一个事件，是一个或若干个工序的开始或结束，是相邻工序在时间上的分界点，点圆圈表示，数字表示点的编号。弧表示一个工序（或活动），弧的方向是从工序开始指向工序的结束，弧上是各工序的代号，下面标以完成此工序所需的时间（或资源）等数据，即为对此弧所赋的权数．虚工序：只表示相邻工序的前后逻辑关系。需要人力、物力等资源与时间。画网络图的规则：两节点之间只能有一条弧（箭线）。两事件一工序网络图只能有一个开始节点（事项）和一个终点事项不允许有回路，不能有缺口

abcb,c的紧前工序为aabcdc,d的紧前工序为a,babcdc的紧前工序为a。d的紧前工序为a和b3网络图中的节点表示一个事件，是一个或若干个工序的开始或结束11绘制网络图分3步：(1)任务分解WBS

WorkbreakdownStructure

工作项目明细表：工序名称，代号；前后逻辑关系，消耗资源。(2)按表绘制网络图。（3）节点统一编号。采用平行和交叉作业技术

例４、把例３的工序进度表做一些扩充，如表12-9，请画出其统筹方法的网络图。

表12-9工序代号所需时间（天）紧前工序工序代号所需时间（天）紧前工序abcd60151338－aacefgh810165b，ｄdde，ｆ，ｇ１２４５３abcde601383815图12-44绘制网络图分3步：(1)任务分解WBSWorkbr12

解：我们把工序ｆ扩充到图12-4发生了问题，由于ｆ的紧前工序是ｄ，故ｄ的结束应该是ｆ的开始，所以代表ｆ的弧的起点应该是④，由于工序ｂ的结束也是④，所以工序ｂ也成了工序ｆ的紧前工序，与题意不符。为此我们利用虚工序。由于e的紧前工序是b和ｄ，在④和⑤之间加入虚工序

8e15243a60b151013dc38f图12-55解：我们把工序ｆ扩充到图12-4发生了问题，由于ｆ的紧前工13

在网络图上添加ｇ、ｈ工序得网络图12-6。

在统筹方法的网络图中不允许两个点之间多于一条弧，因此增加了一个点和虚工序如图12-7。615243a60b158e1013dc38fg16h515243a60b158e1013dc38fg16h5768在网络图上添加ｇ、ｈ工序得网络图12-6。615243a141ActivityTime(Weeks)Immediate

PredecessorsActivityTime(Weeks)Immediate

PredecessorsABCDE241064－ABCCHIJKL97845E,GCF,IJJF5EM2HG7DN6K,L2A23B4C4105D67EI46G87F7510J89H9KLM542111312N61ActivityTime(Weeks)Immediate15关键路线TheCriticalPathApaththroughanetworkisoneoftheroutesfollowingthearrows(arcs)fromthestartnodetothefinishnode.路是指沿着箭头从开始点到终点的一条路线Thelengthofapath

isthesumofthe(estimated)durationsoftheactivitiesonthepath.路长度为路上所有活动时间总和The(estimated)projectdurationequalsthelengthofthelongestpaththroughtheprojectnetwork.项目工期等于项目网络中最长路的长度Thislongestpathiscalledthecriticalpath.(Ifmorethanonepathtieforthelongest,theyallarecriticalpaths.)项目网络中最长路称为关键路关键路线TheCriticalPathApathth16ThePathsforReliable’sProjectNetworkPathLength(Weeks)StartABCDGHMFinish2+4+10+6+7+9+2=40StartABCEHMFinish2+4+10+4+9+2=31StartABCEFJKNFinish2+4+10+4+5+8+4+6=43StartABCEFJLNFinish2+4+10+4+5+8+5+6=44StartABCIJKNFinish2+4+10+7+8+4+6=41StartABCIJLNFinish2+4+10+7+8+5+6=42关键路线criticalpathP292ThePathsforReliable’sProje17最早开始时间和最早结束时间Thestartingandfinishingtimesofeachactivityifnodelaysoccuranywhereintheprojectarecalledtheearlieststarttimeandtheearliestfinishtime.用ES表示一个活动最早开始时间；EF表示一个活动最早结束时间。最早可能开始时间和结束时间。

EarliestStartTimeRule:ES=LargestEFoftheimmediatepredecessors.最早开始时间=所有紧前工序EF的最大者ABCiES=Max{20,23,19}=23EF=20EF=23EF=19HCBAHEF=20EF=23EF=19ES=23最早开始时间和最早结束时间Thestartingand18计算所有活动的ES时间:Foreachactivitythatstartstheproject(includingthestartnode),setitsES=0.项目的最早开始时间为0最早结束时间EF=ES+活动工期ForeachactivitywhoseEShasjustbeenobtained,calculateEF=ES+duration对于每个新活动，用最早开始时间法则求ESForeachnewactivitywhoseimmediatepredecessorsnowhaveEFvalues,obtainitsESbyapplyingtheearlieststarttimerule.Applystep2tocalculateEF.重复上述3个步骤Repeatstep3untilESandEFhavebeenobtainedforallactivities.最早结束时间EF=最早开始时间ES+活动工期从开始(左)向后计算ES计算所有活动的ES时间:最早结束时间EF=最早开始时间E19只有单个紧前工序的工序ES与EF的计算只有单个紧前工序的工序ES与EF的计算20ESandEFTimesforReliableConstruction多个紧前工序的ES与EF的计算ES=Max{25,23}=25ES=Max{29,20}=29ESandEFTimesforReliableC21最迟开始时间和最迟结束时间Thelateststarttimeforanactivityisthelatestpossibletimethatitcanstartwithoutdelayingthecompletionoftheproject(sothefinishnodestillisreachedatitsearliestfinishtime).在不影响项目完成总时间的前提下，一个活动最晚必须开始的时间。对于终点，最晚时间仍然是最早结束时间,LF=EFLS=Lateststarttimeforaparticularactivity最晚开始时间LF=Latestfinishtimeforaparticularactivity最晚结束时间LatestFinishTimeRule:

LF=SmallestLSoftheimmediatesuccessors.最晚时间等于其所有紧后活动最晚开始时间的最小者ABCLF=Min{30,28,27}=27LS=30LS=28LS=27HCBAHLS=30LS=28LS=27LF=27最迟开始时间和最迟结束时间Thelateststart22LSandLFTimesforReliable’sProjectMin{20,33}=20F[20,25][20,25]EFLSLFESH[29,38][33,42]EFLSLFESLSandLFTimesforReliable’s23TheCompleteProjectNetworkCriticalpath:StartABCEFJLNFinish{ES，LS}{EF，LF}TheCompleteProjectNetworkCr24TimesforReliable’sProjectAOA1235ABCD6GEI4871011139H12FJKLNM[0,2][0,2]2[2,6][2,6]4[6,16][6,16]107[16,23][16,20]4[16,22]67[22,29][29,38]9[38,40]25[20,25][25,33]85[33,38][33,37]4[38,44]6[38,44][42,44][34,38][33,38][31,42][25,33][20,25][18,25][16,20][24,31][18,24]TimesforReliable’sProject25SlackforReliable’sActivities活动（工序）的时差活动LSESLFEF总时差(LS–ES)是否关键工序A00220YesB22440YesC4416160YesD201626224NoE161620200YesF202025250YesG262233294NoH332942384NoI181625232NoJ252533330YesK343338371NoL333338380YesM423844404NoN383844440Yes总时差=最迟开始时间－最早开始时间=最迟结束时间－最早结束时间TS=LS－

ES=LF－EFTheslackofanactivitySlackforReliable’sActivitie26

例、某公司装配一条新的生产线，具体过程如表12-10,求：完成此工程的最少时间，关键路线及相应的关键工序，各工序的最早开始时间和非关键工序在不影响工程完成时间的前提下，其开始时间与结束时间可以推迟多久。7工序代号工序内容所需时间（天）紧前工序abcdefghij生产线设计外购零配件下料、锻件工装制造1木模、铸件机械加工1工装制造2机械加工2机械加工3装配调试60451020401830152535/aaaacdd,egb,i,f,h例、某公司装配一条新的生产线，具体过程如表12-10,求27解：据表12-10,绘制网络图如图12-8。图12-8关键路线：如图12-8,①-②-③-⑦-⑧就是一条关键路线，我们要干完所有的工序就必须走完所有这样的路线，由于很多工序可以同时进行，所以网络中最长的路线就决定了完成整个工程所需的最少时间，这条路线称为关键路线。12346785a60b45echj35ig1030d204025f18159解：据表12-10,绘制网络图如图12-8。1234678528

图12-10其次,从网络的收点开始计算出在不影响整个工程最早结束时间的情况下各个工序的最晚开始时间(缩写为LS)和最晚结束时间（缩写为LF),显然对同一工序有

LS=LF-t1236785a[0,60]60b[60,105]45e[60.100]c[60,70]h[100,115]j[135,170]35i[110.135]g[80,110]30d[60.80]204025f[70,88]1841015111236785a[0,60]60b[60,105]45e[29

运用此法则，可以从首点开始计算出每个工序的LF与LS，如图12-11所示。

接着，可以计算出每一个工序的时差，把在不影响工程最早结束时间的条件下，工序最早开始（或结束）的时间可以推迟的时间，成为该工序的时差，对每个工序来说其时差记为Ts有Ts=LS-ES=LF-EF1236785a[0,60]60[0,60]b[60,105]45[90,135]e[60.100]c[60,70]h[100,115]j[135,170]35[135,170]i[110.135]g[80,110]30[80,110]d[60.80]20[60,80]40[80,120]25[110,135]f[70,88]18[117,135]410[107,117]15[120,135]12运用此法则，可以从首点开始计算出每个工序的L30最后将各工序的时差，以及其他信息构成工序时间表如表12-11所示。这样就找到了一条由关键工序a,d,g,i和j依次连接成的从发点到收点的关键路线。13最后将各工序的时差，以及其他信息构成工序时间表如表12-1131ThePERT三种估计方式Mostlikelyestimate(m)=Estimateofmostlikelyvalueoftheduration最大可能估计

Optimisticestimate(o)=Estimateofdurationundermostfavorableconditions.乐观估计时间

Pessimisticestimate(p)=Estimateofdurationundermostunfavorableconditions.悲观估计时间处理不确定活动工期分布时间ThePERT三种估计方式Mostlikelyest32均值和标准差MeanandStandardDeviationAnapproximateformulaforthevariance活动时间方差(2)ofanactivityis Anapproximateformulaforthemean活动时间的均值(m)ofanactivityis

乐观估计P和悲观估计时间O的差大致为6个标准差均值和标准差MeanandStandardDeviat33可信公司活动的均值和方差ActivityompMeanVarianceA12321/9B23.5841C6918104D45.51061E14.5544/9F441051G56.51171H581794I37.5971J39981K44440L15.5751M12321/9N55.5964/9P306可信公司活动的均值和方差ActivityompMeanVar34PessimisticPathLengthsforReliable’sProject悲观估计时间的路径与路径长度PathPessimisticLength(Weeks)采用悲观估计时间StartABCDGHMFinish3+8+18+10+11+17+3=70StartABCEHMFinish3+8+18+5+17+3=54StartABCEFJKNFinish3+8+18+5+10+9+4+9=66StartABCEFJLNFinish3+8+18+5+10+9+7+9=69StartABCIJKNFinish3+8+18+9+9+4+9=60StartABCIJLNFinish3+8+18+9+9+7+9=63PessimisticPathLengthsforR35三个简化的近似PERT/CPMP306Themeancriticalpathwillturnouttobethelongestpaththroughtheprojectnetwork.假设均值关键路是项目中最长的一条路统计独立性Thedurationsoftheactivitiesonthemeancriticalpatharestatisticallyindependent.Thus,thethreeestimatesofthedurationofanactivitywouldneverchangeafterlearningthedurationsofsomeoftheotheractivities.正太分布假设Theformoftheprobabilitydistributionofprojectdurationisthenormaldistribution.Byusingsimplifyingapproximations1and2,thereissomestatisticaltheory(oneversionofthecentrallimittheorem)thatjustifiesthisasbeingareasonableapproximationifthenumberofactivitiesonthemeancriticalpathisnottoosmall（活动数至少5个）.三个简化的近似PERT/CPMP306The36计算项目的均值和方差ActivitiesonMeanCriticalPathMeanVarianceA21/9B41C104E44/9F51J81L51N64/9Projectdurationmp=44s2p=9计算项目的均值和方差ActivitiesonMeanC37ProbabilityofMeetingDeadlinez为d超过μp的标准差个数，查统计表可得概率值ProbabilityofMeetingDeadlin38ProbabilityofMeetingaDeadlineP(T≤

d)P(T≤d)–3.00.001400.50–2.50.00620.250.60–2.00.0230.50.69–1.750.0400.750.77–1.50.0671.00.84–50.89–1.033–0.750.231.750.960–0.50.312.00.977–0.250.402.50.993800.503.00.9986ProbabilityofMeetingaDeadl39SpreadsheetforPERTThree-EstimateApproachSpreadsheetforPERTThree-Est40时间和成本权衡ConsideringTime-CostTrade-OffsQuestion:Ifextramoneyisspenttoexpeditetheproject,whatistheleastexpensivewayofattemptingtomeetthetargetcompletiontime(40weeks)?CPMMethodofTime-CostTrade-Offs:Crashinganactivity赶工完成一项活动referstotakingspecialcostlymeasurestoreducethedurationofanactivitybelowitsnormalvalue.Specialmeasuresmightincludeovertime,hiringadditionaltemporaryhelp,usingspecialtime-savingmaterials,obtainingspecialequipment,etc.Crashingtheproject赶工完成项目referstocrashinganumberofactivitiestoreducethedurationoftheprojectbelowitsnormalvalue.时间和成本权衡ConsideringTime-CostT41Time-CostGraphforanActivity赶工常规赶工成本正常成本活动成本常规常规时间赶工时间活动时间Time-CostGraphforanActivit42Time-CostTrade-OffDataforReliable’sProject

Time(weeks)

成本Cost

Maximum

Reduction

inTime(weeks)CrashCost

perWeek

SavedActivityNormalCrashNormalCrashA21$180,000$280,0001$100,000B42320,000420,000250,000C107620,000860,000380,000D64260,000340,000240,000E43410,000570,0001160,000F53180,000260,000240,000G74900,0001,020,000340,000H96200,000380,000360,000I75210,000270,000230,000J86430,000490,000230,000K43160,000200,000140,000L53250,000350,000250,000M21100,000200,0001100,000N63330,000510,000360,000Sumofnormalcost=4550,000;Sumofcrashcost=6150,000P400Time-CostTrade-OffDataforR43MarginalCostAnalysisforReliable’sProject

InitialTableLengthofPathActivity

to

CrashCrash

CostABCDGHMABCEHMABCEFJKNABCEFJLNABCIJKNABCIJLN403143444142最长路MarginalCostAnalysisforRel44MarginalCostAnalysisforReliable’sProject

TableAfterCrashingOneWeekLengthofPathActivity

to

CrashCrash

CostABCDGHMABCEHMABCEFJKNABCEFJLNABCIJKNABCIJLN403143444142J$30,000403142434041MarginalCostAnalysisforRel45MarginalCostAnalysisforReliable’sProject

TableAfterCrashingTwoWeeksLengthofPathActivity

to

CrashCrash

CostABCDGHMABCEHMABCEFJKNABCEFJLNABCIJKNABCIJLN403143444142J$30,000403142434041J$30,000403141423940J只大只能赶工2天MarginalCostAnalysisforRel46MarginalCostAnalysisforReliable’sProject

TableAfterCrashingThree

WeeksLengthofPathActivity

to

CrashCrash

CostABCDGHMABCEHMABCEFJKNABCEFJLNABCIJKNABCIJLN403143444142J$30,000403142434041J$30,000403141423940F$40,000403140413940MarginalCostAnalysisforRel47MarginalCostAnalysisforReliable’sProject

FinalTableAfterCrashingFourWeeksLengthofPathActivity

to

CrashCrash

CostABCDGHMABCEHMABCEFJKNABCEFJLNABCIJKNABCIJLN403143444142J$30,000403142434041J$30,000403141423940F$40,000403140413940F$40,000403139403940MarginalCostAnalysisforRel48ProjectNetworkAfterCrashingProjectNetworkAfterCrashing49UsingLPtoMakeCrashingDecisionsRestatmentoftheproblem:Considerthetotalcostoftheproject,includingtheextracostofcrashingactivities.Theproblemthenistominimizethistotalcost,subjecttotheconstraintthatprojectdurationmustbelessthanorequaltothetimedesiredbytheprojectmanager.Thedecisionstobemadearethefollowing:Thestarttimeofeachactivity.每一个活动的开始时间Thereductioninthedurationofeachactivityduetocrashing.每个活动工期的减少量Thefinishtimeoftheproject(mustnotexceed40weeks).Theconstraintsare:TimeReduction≤MaxReduction(foreachactivity).ProjectFinishTime≤DesiredFinishTime.ActivityStartTime≥ActivityFinishTimeofallpredecessors(foreachactivity).ProjectFinishTime≥FinishTimeofallimmediatepredecessorsoffinishnode.UsingLPtoMakeCrashingDeci50SpreadsheetModelSpreadsheetModel51Mr.Perty’sConclusionsTheplanforcrashingtheprojectonlyprovidesa50percentchanceofactuallyfinishingtheprojectwithin40weeks,sotheextracostoftheplan($140,000)isnotjustified.Therefore,Mr.Pertyrejectsanycrashingatthisstage.Theextracostofthecrashingplancanbejustifiedifitalmostcertainlywouldearnthebonusof$150,000forfinishingtheprojectwithin40weeks.Therefore,Mr.PertywillholdtheplaninreservetobeimplementediftheprojectisrunningwellaheadofschedulebeforereachingactivityF.Theextracostofpartorallofthecrashingplancanbeeasilyjustifiedifitlikelywouldmakethedifferenceinavoidingthepenaltyof$300,000fornotfinishingtheprojectwithin47weeks.Therefore,Mr.PertywillholdthecrashingplaninreservetobepartiallyorwhollyimplementediftheprojectisrunningfarbehindschedulebeforereachingactivityForactivityJ.Mr.Perty’sConclusionsThepla52SchedulingandControllingProjectCostsPERT/Costisasystematicprocedure(normallycomputerized)tohelptheprojectmanagerplan,schedule,andcontrolcosts.Assumption:AcommonassumptionwhenusingPERT/Costisthatthecostsofperforminganactivityareincurredataconstantratethroughoutitsduration.SchedulingandControllingPro53BudgetforReliable’sProjectActivityEstimated

Duration(weeks)Estimated

CostCostperWeek

ofItsDurationA2$180,000$90,000B4320,00080,000C10620,00062,000D6260,00043,333E4410,000102,500F5180,00036,000G7900,000128,571H9200,00022,222I7210,00030,000J8430,00053,750K4160,00040,000L5250,00050,000M2100,00050,000N6330,00055,000BudgetforReliable’sProjectA54PERT/CostSpreadsheet(EarliestStartTimes)PERT/CostSpreadsheet(Earlies55PERT/CostSpreadsheet(EarliestStartTimes)PERT/CostSpreadsheet(Earlies56PERT/CostSpreadsheet(LatestStartTimes)PERT/CostSpreadsheet(Latest57PERT/CostSpreadsheet(LatestStartTimes)PERT/CostSpreadsheet(Latest58CumulativeProjectCostsCumulativeProjectCosts59PERT/CostReportafterWeek22ActivityBudgeted

CostPercent

CompletedValue

CompletedActualCost

toDateCostOverrun

toDateA$180,000100%$180,000$200,000$20,000B320,000100320,000330,00010,000C620,000100620,000600,000–20,000D260,00075195,000200,0005,000E410,000100410,000400,000–10,000F180,0002545,00060,00015,000I210,00050105,000130,00025,000Total$2,180,000$1,875,000$1,920,000$45,000PERT/CostReportafterWeek2260四、网络优化得到初始的计划方案，但通常要对初始方案进行调整与完善。根据计划目标，综合考虑资源和降低成本等目标，进行网络优化，确定最优的计划方案。1.时间-资源优化做法：1）优先安排关键工序所需的资源。2）利用非关键工序的时差，错开各工序的开始时间。3）统筹兼顾工程进度的要求和现有资源的限制，多次综合平衡。下面列举一个拉平资源需要量最高峰的实例。在例5中，若加工工人为65人，并假定这些工人可完成这5个工序任一个，下面来寻求一个时间-资源最优方案。如表12-16所示：四、网络优化61表12-16工序需要人数最早开始时间所需时间时差d5860200f22701847g428030h391001520i26110250若上述工序都按最早开始时间安排，那么从第60天至第135天的75天里，所需的机械加工工人人数如图12-17所示。表12-16工序需要人数最早开始时间所需时间时差d5860262在图的上半部中，工序代号后的数字是人数，线下面的数字是非关键工序时差长度。图的下半部表示从第60天至135天内的75天里，所需机械加工工人数，这样的图称为资源负荷图。58人64人80人81人42人26人65人6080100120130274635f(22人）18h(39人)15d(58人）i(26人）g(42人）302025图12-17在图的上半部中，工序代号后的数字是人数，线下63同时我们应优先安排关键工序所需的工人，再利用非关键工序的时差，错开各工序的开始时间，从而拉平工人需要量的高峰。经过调整，我们让非关键工序f从第80天开始，工序h从第110天开始。找到了时间-资源优化的方案，如图12-18所示，在不增加工人的情况下保证了工程按期完成。246753f(22人）h(39人）d(58人）i(26人）g(42人）工人数65人608010012013058人42人64人26人65人图12-18同时我们应优先安排关键工序所需的工人，再利用64Chapter12PERT/CPMModelsfor

ProjectManagement§1

ProjectNetworks计划网络图§2SchedulingaProjectwithPERT/CPM

网络时间与关键路线§3DealingwithUncertainActivityDurations§4网络优化1Chapter12PERT/CPMModelsfo65项目管理ProjectManagement项目特征CharacteristicsofProjectsUnique,one-timeoperationsInvolvealargenumberofactivitiesthatmustbeplannedandcoordinatedLongtime-horizonGoalsofmeetingcompletiondeadlinesandbudgetsExamplesBuildingahousePlanningameetingIntroducinganewproductPERT—ProjectEvaluationandReviewTechnique计划评审技术

CPM—CriticalPathMethod关键路线法Agraphicalornetworkapproachforplanningandcoordinatinglarge-scaleprojects.项目管理ProjectManagement项目特征Cha66可信建筑公司项目ReliableConstructionCompanyProjectP285TheReliableConstructionCompanyhasjustmadethewinningbidof$5.4milliontoconstructanewplantforamajormanufacturer.可信建筑公司中标540万美元的项目Thecontractincludesthefollowingprovisions:Apenaltyof$300,000ifReliablehasnotcompletedconstructionwithin47weeks.如果不能在47周内完成项目，将被罚款30万美元。如果能在40周内完成，将获得15万美元的奖励Abonusof$150,000ifReliablehascompletedtheplantwithin40weeks.Questions:286Howcantheprojectbedisplayedgraphicallytobettervisualizetheactivities?如何用图来表示项目中活动流程Whatisthetotaltimerequiredtocompletetheprojectifnodelaysoccur?Whendotheindividualactivitiesneedtostartandfinish?Whatarethecriticalbottleneckactivities?对于非关键的活动Forotheractivities,howmuchdelaycanbetolerated承受?Whatistheprobabilitytheprojectcanbecompletedin47weeks?Whatistheleastexpensivewaytocompletetheprojectwithin40weeks?Howshouldongoingcostsbemonitoredtotrytokeeptheprojectwithinbudget?如何对成本进行实时监控，使项目成本控制在预算内可信建筑公司项目ReliableConstruction67活动明细表

ActivityListforReliableConstructionActivityActivityDescription紧前Immediate

Predecessors估计工期(Weeks)AExcavate挖掘—2BLaythefoundation打地基A4CPutuptheroughwall承重墙施工B10DPutuptheroof封顶C6EInstalltheexteriorplumbing安装外部管道C4FInstalltheinteriorplumbing安装内部管道E5GPutuptheexteriorsiding外墙施工D7HDotheexteriorpainting外部粉刷E,G9IDotheelectricalwork电路铺设C7JPutupthewallboard竖墙板F,I8KInstalltheflooring铺地板J4LDotheinteriorpainting内部粉刷J5MInstalltheexteriorfixtures设施H2NInstalltheinteriorfixtures安装内部设备K,L6活动明细表ActivityListforReliab68项目网络

ProjectNetworks表示整个项目的网络称为项目网络Anetworkusedtorepresentaprojectiscalledaprojectnetwork.Aprojectnetworkconsistsofanumberof节点nodesandanumberofarcs.Twotypesofprojectnetworks:Activity-on-arc(AOA弧表示活动):eachactivityisrepresentedbyanarc.Anodeisusedtoseparateanactivityfromitspredecessors.Thesequencingofthearcsshowstheprecedencerelationships.Activity-on-node(AON节点表示活动):eachactivityisrepresentedbyanode.Thearcsareusedtoshowtheprecedence优先relationships.AdvantagesofAON(usedinthistextbook):P288considerablyeasiertoconstruct易于构建easiertounderstand易于理解easiertorevisewhentherearechanges更便于修改项目网络ProjectNetworks表示整个项目的网络69ReliableConstruction

ProjectNetworkReliableConstruction

Project70MicrosoftProjectGanttChart甘特图W1/1表示第一周第一天；W2/5表示第二周第五天；MicrosoftProjectGanttChart71MicrosoftProject

—ProjectNetwork活动名称编号工期最早开始时间最早结束时间P290W1/1第一周第一天开始W2/5第二周第五天完成二周MicrosoftProject

—ProjectNet72AOAProjectNetwork1235ABCD6GEI4871011139H12FJKLNMAOAProjectNetwork1235ABCD6G73关于AOA计划网络图

统筹方法的第一步工作就是绘制计划网络图，也就是将工序（或称为活动）进度表转换为统筹方法的网络图。下面用一个例子来说明例3、某公司研制新产品的部分工序与所需时间以及它们之间的相互关系都显示在其工序进度表如表12-8所示，请画出其统筹方法网络图。

工序代号工序内容所需时间（天)紧前工序abcde产品设计与工艺设计外购配套零件外购生产原料自制主件主配可靠性试验601513388-aacb,d2表12-8关于AOA计划网络图工序代号工序内容所需时间（天)紧74网络图中的节点表示一个事件，是一个或若干个工序的开始或结束，是相邻工序在时间上的分界点，点圆圈表示，数字表示点的编号。弧表示一个工序（或活动），弧的方向是从工序开始指向工序的结束，弧上是各工序的代号，下面标以完成此工序所需的时间（或资源）等数据，即为对此弧所赋的权数．虚工序：只表示相邻工序的前后逻辑关系。需要人力、物力等资源与时间。画网络图的规则：两节点之间只能有一条弧（箭线）。两事件一工序网络图只能有一个开始节点（事项）和一个终点事项不允许有回路，不能有缺口

abcb,c的紧前工序为aabcdc,d的紧前工序为a,babcdc的紧前工序为a。d的紧前工序为a和b3网络图中的节点表示一个事件，是一个或若干个工序的开始或结束75绘制网络图分3步：(1)任务分解WBS

WorkbreakdownStructure

工作项目明细表：工序名称，代号；前后逻辑关系，消耗资源。(2)按表绘制网络图。（3）节点统一编号。采用平行和交叉作业技术

例４、把例３的工序进度表做一些扩充，如表12-9，请画出其统筹方法的网络图。

表12-9工序代号所需时间（天）紧前工序工序代号所需时间（天）紧前工序abcd60151338－aacefgh810165b，ｄdde，ｆ，ｇ１２４５３abcde601383815图12-44绘制网络图分3步：(1)任务分解WBSWorkbr76

解：我们把工序ｆ扩充到图12-4发生了问题，由于ｆ的紧前工序是ｄ，故ｄ的结束应该是ｆ的开始，所以代表ｆ的弧的起点应该是④，由于工序ｂ的结束也是④，所以工序ｂ也成了工序ｆ的紧前工序，与题意不符。为此我们利用虚工序。由于e的紧前工序是b和ｄ，在④和⑤之间加入虚工序

8e15243a60b151013dc38f图12-55解：我们把工序ｆ扩充到图12-4发生了问题，由于ｆ的紧前工77

在网络图上添加ｇ、ｈ工序得网络图12-6。

在统筹方法的网络图中不允许两个点之间多于一条弧，因此增加了一个点和虚工序如图12-7。615243a60b158e1013dc38fg16h515243a60b158e1013dc38fg16h5768在网络图上添加ｇ、ｈ工序得网络图12-6。615243a781ActivityTime(Weeks)Immediate

PredecessorsActivityTime(Weeks)Immediate

PredecessorsABCDE241064－ABCCHIJKL97845E,GCF,IJJF5EM