网络计划技术讲义

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1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.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ReliableConstruction

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

—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AOAProjectNetwork1235ABCD6GEI4871011139H12FJKLNM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网络图中的节点表示一个事件件，是一个或或若干个工序序的开始或结结束，是相邻邻工序在时间间上的分界点点，点圆圈表表示，数字表表示点的编号号。弧表示一个工序序（或活动）），弧的方向向是从工序开开始指向工序序的结束，弧弧上是各工序序的代号，下下面标以完成成此工序所需需的时间（或或资源）等数数据，即为对对此弧所赋的的权数．虚工序：只表示相邻工工序的前后逻逻辑关系。需需要人力、物物力等资源与与时间。画网络图的规规则：两节点之间只只能有一条弧弧（箭线）。。两事件一工工序网络图只能有有一个开始节节点（事项））和一个终点点事项不允许有回路路，不能有缺缺口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绘制网络图分分3步：(1)任任务分解WBSWorkbreakdownStructure工作项目明细细表：工序名名称，代号；前后逻辑关系系，消耗资源源。(2)按按表绘制网络络图。（3））节点统一编编号。采用平平行和交叉作作业技术例４、把例３３的工序进度度表做一些扩扩充，如表12-9，请请画出其统筹筹方法的网络络图。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解：我们把工工序ｆ扩充到到图12-4发生了问题题，由于ｆ的的紧前工序是是ｄ，故ｄ的的结束应该是是ｆ的开始，，所以代表ｆｆ的弧的起点点应该是④，，由于工序ｂｂ的结束也是是④，所以工工序ｂ也成了了工序ｆ的紧紧前工序，与与题意不符。。为此我们利用用虚工序。由由于e的紧前前工序是b和和ｄ，在④和和⑤之间加入入虚工序8e15243a60b151013dc38f图12-55在网络图上添添加ｇ、ｈ工工序得网络图图12-6。在统筹方法的的网络图中不不允许两个点点之间多于一一条弧，因此此增加了一个个点和虚工序序如图12-7。615243a60b158e1013dc38fg16h515243a60b158e1013dc38fg16h57681ActivityTime(Weeks)Immediate

PredecessorsActivityTime(Weeks)Immediate

PredecessorsABCDE241064－ABCCHIJKL97845E,GCF,IJJF5EM2HG7DN6K,L2A23B4C4105D67EI46G87F7510J89H9KLM542111312N6关键键路路线线TheCriticalPathApaththroughanetworkisoneoftheroutesfollowingthearrows(arcs)fromthestartnodetothefinishnode.路是是指指沿沿着着箭箭头头从从开开始始点点到到终终点点的的一一条条路路线线Thelengthofapathisthesumofthe(estimated)durationsoftheactivitiesonthepath.路长长度度为为路路上上所所有有活活动动时时间间总总和和The(estimated)projectdurationequalsthelengthofthelongestpaththroughtheprojectnetwork.项目目工工期期等等于于项项目目网网络络中中最最长长路路的的长长度度Thislongestpathiscalledthecriticalpath.(Ifmorethanonepathtieforthelongest,theyallarecriticalpaths.)项目目网网络络中中最最长长路路称称为为关关键键路路ThePathsforReliable’’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关键键路路线线criticalpathP292最早早开开始始时时间间和和最最早早结结束束时时间间Thestartingandfinishingtimesofeachactivityifnodelaysoccuranywhereintheprojectarecalledtheearlieststarttimeandtheearliestfinishtime.用ES表表示示一一个个活活动动最最早早开开始始时时间间；；EF表表示示一一个个活活动动最最早早结结束束时时间间。。最最早早可可能能开开始始时时间间和和结结束束时时间间。。EarliestStartTimeRule:ES=LargestEFoftheimmediatepredecessors.最早早开开始始时时间间=所所有有紧紧前前工工序序EF的的最最大大者者ABCiES=Max{20,23,19}=23EF=20EF=23EF=19HCBAHEF=20EF=23EF=19ES=23计算算所所有有活活动动的的ES时时间间:Foreachactivitythatstartstheproject(includingthestartnode),setitsES=0.项目目的的最最早早开开始始时时间间为为0最早早结结束束时时间间EF=ES+活活动动工工期期ForeachactivitywhoseEShasjustbeenobtained,calculateEF=ES+duration对于于每每个个新新活活动动，，用用最最早早开开始始时时间间法法则则求求ESForeachnewactivitywhoseimmediatepredecessorsnowhaveEFvalues,obtainitsESbyapplyingtheearlieststarttimerule.Applystep2tocalculateEF.重复复上上述述3个个步步骤骤Repeatstep3untilESandEFhavebeenobtainedforallactivities.最早早结结束束时时间间EF=最最早早开开始始时时间间ES+活活动动工工期期从开开始始(左左)向向后后计计算算ES只有有单单个个紧前前工工序序的的工工序序ES与与EF的的计计算算ESandEFTimesforReliableConstruction多个个紧紧前前工工序序的的ES与与EF的的计计算算ES=Max{25,23}=25ES=Max{29,20}=29最迟迟开开始始时时间间和和最最迟迟结结束束时时间间Thelateststarttimeforanactivityisthelatestpossibletimethatitcanstartwithoutdelayingthecompletionoftheproject(sothefinishnodestillisreachedatitsearliestfinishtime).在不不影影响响项项目目完完成成总总时时间间的的前前提提下下，，一一个个活活动动最晚晚必必须须开开始始的的时时间间。对于于终终点点，，最最晚晚时时间间仍仍然然是是最最早早结结束束时时间间,LF=EFLS=Lateststarttimeforaparticularactivity最最晚晚开开始始时时间间LF=Latestfinishtimeforaparticularactivity最最晚晚结结束束时时间间LatestFinishTimeRule:LF=SmallestLSoftheimmediatesuccessors.最晚晚时时间间等等于于其其所所有有紧紧后后活活动动最最晚晚开开始始时时间间的的最最小小者者ABCLF=Min{30,28,27}=27LS=30LS=28LS=27HCBAHLS=30LS=28LS=27LF=27LSandLFTimesforReliable’’sProjectMin{20,33}=20F[20,25][20,25]EFLSLFESH[29,38][33,42]EFLSLFESTheCompleteProjectNetworkCriticalpath:StartABCEFJLNFinish{ES，，LS}{EF，，LF}TimesforReliable’’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]SlackforReliable’’sActivities活动动（（工工序序））的的时时差差活动LSESLFEF总时差(LS–ES)是否关键工序A00220YesB22440YesC4416160YesD201626224NoE161620200YesF202025250YesG262233294NoH332942384NoI181625232NoJ252533330YesK343338371NoL333338380YesM423844404NoN383844440Yes总时差差=最迟迟开始始时间间－最最早开开始时时间=最迟迟结束束时间间－最最早结结束时时间TS=LS－－ES=LF－EFTheslackofanactivity例、某公司司装配配一条条新的的生产产线，，具体体过程程如表表12-10,求：：完成成此工工程的的最少少时间间，关关键路路线及及相应应的关关键工工序，，各工工序的的最早早开始始时间间和非非关键键工序序在不不影响响工程程完成成时间间的前前提下下，其其开始始时间间与结结束时时间可可以推推迟多多久。。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解：据据表12-10,绘绘制网网络图图如图图12-8。图12-8关键路路线：：如图图12-8,①-②-③-⑦-⑧就就是一一条关关键路路线，，我们们要干干完所所有的的工序序就必必须走走完所所有这这样的的路线线，由由于很很多工工序可可以同同时进进行，，所以以网络络中最最长的的路线线就决决定了了完成成整个个工程程所需需的最最少时时间，，这条条路线线称为为关键键路线线。12346785a60b45echj35ig1030d204025f18159图12-10其次,从网网络的的收点点开始始计算算出在在不影影响整整个工工程最最早结结束时时间的的情况下各各个工工序的的最晚晚开始始时间间(缩缩写为为LS)和和最晚晚结束束时间间（缩缩写为为LF),显然对对同一一工序序有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]184101511运用此此法则则，可可以从从首点点开始始计算算出每每个工工序的的LF与LS，，如图图12-11所示。。接着，，可以以计算算出每每一个个工序序的时时差，，把在在不影影响工工程最最早结结束时时间的条件件下，，工序序最早早开始始（或或结束束）的的时间间可以以推迟迟的时时间，，成为为该工工序的时差差，对对每个个工序序来说说其时时差记记为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最后将将各工工序的的时差差，以以及其其他信信息构构成工工序时时间表表如表表12-11所所示。。这样就就找到到了一一条由由关键键工序序a,d,g,i和和j依依次连连接成成的从从发点点到收收点的的关键键路线线。13ThePERT三三种种估计计方式式Mostlikelyestimate(m)=Estimateofmostlikelyvalueoftheduration最最大可可能估估计Optimisticestimate(o)=Estimateofdurationundermostfavorableconditions.乐乐观估估计时时间Pessimisticestimate(p)=Estimateofdurationundermostunfavorableconditions.悲悲观估估计时时间处理不不确定定活动动工期期分布时间均值和和标准准差MeanandStandardDeviationAnapproximateformulaforthevariance活活动时时间方方差(2)ofanactivityisAnapproximateformulaforthemean活活动时时间的的均值值(m)ofanactivityis乐观估估计P和悲观观估计计时间间O的差大大致为为6个个标准准差可信公公司活活动的的均值值和方方差ActivityompMeanVarianceA12321/9B23.5841C6918104D45.51061E14.5544/9F441051G56.51171H581794I37.5971J39981K44440L15.5751M12321/9N55.5964/9P306PessimisticPathLengthsforReliable’sProject悲观观估计计时间间的路路径与与路径径长度度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=63三个简简化的的近似似PERT/CPMP306Themeancriticalpathwillturnouttobethelongestpaththroughtheprojectnetwork.假设设均值值关键键路是是项目目中最最长的的一条条路统计独独立性性Thedurationsoftheactivitiesonthemeancriticalpatharestatisticallyindependent.Thus,thethreeestimatesofthedurationofanactivitywouldneverchangeafterlearningthedurationsofsomeoftheotheractivities.正太分分布假假设Theformoftheprobabilitydistributionofprojectdurationisthenormaldistribution.Byusingsimplifyingapproximations1and2,thereissomestatisticaltheory(oneversionofthecentrallimittheorem)thatjustifiesthisasbeingareasonableapproximationifthenumberofactivitiesonthemeancriticalpathisnottoosmall（活活动数数至少少5个个）.计算项项目的的均值值和方方差ActivitiesonMeanCriticalPathMeanVarianceA21/9B41C104E44/9F51J81L51N64/9Projectdurationmp=44s2p=9ProbabilityofMeetingDeadlinez为d超过μμp的标准准差个个数，，查统统计表表可得得概率率值ProbabilityofMeetingaDeadlineP(T≤

d)P(T≤d)–3.00.001400.50–2.50.00620.250.60–2.00.0230.50.69–1.750.0400.750.77–1.50.0671.00.84–50.89–1.033–0.750.231.750.960–0.50.312.00.977–0.250.402.50.993800.503.00.9986SpreadsheetforPERTThree-EstimateApproach时间和和成本本权衡衡ConsideringTime-CostTrade-OffsQuestion:Ifextramoneyisspenttoexpeditetheproject,whatistheleastexpensivewayofattemptingtomeetthetargetcompletiontime(40weeks)?CPMMethodofTime-CostTrade-Offs:Crashinganactivity赶工完完成一一项活活动referstotakingspecialcostlymeasurestoreducethedurationofanactivitybelowitsnormalvalue.Specialmeasuresmightincludeovertime,hiringadditionaltemporaryhelp,usingspecialtime-savingmaterials,obtainingspecialequipment,etc.Crashingtheproject赶工完成项目目referstocrashinganumberofactivitiestoreducethedurationoftheprojectbelowitsnormalvalue.Time-CostGraphforanActivity赶工常规赶工成本本正常成本本活动成本本常规常规时间间赶工时间间活动时间间Time-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=6150,000P400MarginalCostAnalysisforReliable’sProjectInitialTableLengthofPathActivity

to

CrashCrash

CostABCDGHMABCEHMABCEFJKNABCEFJLNABCIJKNABCIJLN403143444142最长路MarginalCostAnalysisforReliable’sProjectTableAfterCrashingOneWeekLengthofPathActivity

to

CrashCrash

CostABCDGHMABCEHMABCEFJKNABCEFJLNABCIJKNABCIJLN403143444142J$30,000403142434041MarginalCostAnalysisforReliable’sProjectTableAfterCrashingTwoWeeksLengthofPathActivity

to

CrashCrash

CostABCDGHMABCEHMABCEFJKNABCEFJLNABCIJKNABCIJLN403143444142J$30,000403142434041J$30,000403141423940J只大只能能赶工2天MarginalCostAnalysisforReliable’sProjectTableAfterCrashingThreeWeeksLengthofPathActivity

to

CrashCrash

CostABCDGHMABCEHMABCEFJKNABCEFJLNABCIJKNABCIJLN403143444142J$30,000403142434041J$30,000403141423940F$40,000403140413940MarginalCostAnalysisforReliable’sProjectFinalTableAfterCrashingFourWeeksLengthofPathActivity

to

CrashCrash

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

Duration(weeks)Estimated

CostCostperWeek

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