第九章網(wǎng)絡計劃技術(MBA講義)

Chapter12PERT/CPMModelsfor

ProjectManagement§1ProjectNetworks方案網(wǎng)絡圖§2SchedulingaProjectwithPERT/CPM網(wǎng)絡時間與關鍵道路§3DealingwithUncertainActivityDurations§4網(wǎng)絡優(yōu)化1工程管理ProjectManagement工程特征CharacteristicsofProjectsUnique,one-timeoperationsInvolvealargenumberofactivitiesthatmustbeplannedandcoordinatedLongtime-horizonGoalsofmeetingcompletiondeadlinesandbudgetsExamplesBuildingahousePlanningameetingIntroducinganewproductPERT—ProjectEvaluationandReviewTechnique方案評審技術

CPM—CriticalPathMethod關鍵道路法Agraphicalornetworkapproachforplanningandcoordinatinglarge-scaleprojects.可信建筑公司工程ReliableConstructionCompanyProjectP285TheReliableConstructionCompanyhasjustmadethewinningbidof$5.4milliontoconstructanewplantforamajormanufacturer.可信建筑公司中標540萬美圓的工程Thecontractincludesthefollowingprovisions:Apenaltyof$300,000ifReliablehasnotcompletedconstructionwithin47weeks.假設不能在47周內完成工程，將被罰款30萬美圓。假設能在40周內完成，將獲得15萬美圓的獎勵Abonusof$150,000ifReliablehascompletedtheplantwithin40weeks.Questions:286Howcantheprojectbedisplayedgraphicallytobettervisualizetheactivities?如何用圖來表示工程中活動流程Whatisthetotaltimerequiredtocompletetheprojectifnodelaysoccur?Whendotheindividualactivitiesneedtostartandfinish?Whatarethecriticalbottleneckactivities?對于非關鍵的活動Forotheractivities,howmuchdelaycanbetolerated接受?Whatistheprobabilitytheprojectcanbecompletedin47weeks?Whatistheleastexpensivewaytocompletetheprojectwithin40weeks?Howshouldongoingcostsbemonitoredtotrytokeeptheprojectwithinbudget?如何對本錢進展實時監(jiān)控，使工程本錢控制在預算內活動明細表ActivityListforReliableConstructionActivityActivityDescription緊前Immediate

Predecessors估計工期(Weeks)AExcavate挖掘—2BLaythefoundation打地基A4CPutuptheroughwall承重墻施工B10DPutuptheroof封頂C6EInstalltheexteriorplumbing安裝外部管道C4FInstalltheinteriorplumbing安裝內部管道E5GPutuptheexteriorsiding外墻施工D7HDotheexteriorpainting外部粉刷E,G9IDotheelectricalwork電路鋪設C7JPutupthewallboard豎墻板F,I8KInstalltheflooring鋪地板J4LDotheinteriorpainting內部粉刷J5MInstalltheexteriorfixtures設施H2NInstalltheinteriorfixtures安裝內部設備K,L6工程網(wǎng)絡ProjectNetworks表示整個工程的網(wǎng)絡稱為工程網(wǎng)絡Anetworkusedtorepresentaprojectiscalledaprojectnetwork.Aprojectnetworkconsistsofanumberof節(jié)點nodesandanumberofarcs.Twotypesofprojectnetworks:Activity-on-arc(AOA弧表示活動):eachactivityisrepresentedbyanarc.Anodeisusedtoseparateanactivityfromitspredecessors.Thesequencingofthearcsshowstheprecedencerelationships.Activity-on-node(AON節(jié)點表示活動):eachactivityisrepresentedbyanode.Thearcsareusedtoshowtheprecedence優(yōu)先relationships.AdvantagesofAON(usedinthistextbook):P288considerablyeasiertoconstruct易于構建easiertounderstand易于了解easiertorevisewhentherearechanges更便于修正ReliableConstruction

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

—ProjectNetwork活動名稱編號工期最早開始時間最早結束時間P290W1/1第一周第一天開場W2/5第二周第五天完成二周AOAProjectNetwork1235ABCD6GEI4871011139H12FJKLNM關于AOA方案網(wǎng)絡圖統(tǒng)籌方法的第一步任務就是繪制方案網(wǎng)絡圖，也就是將工序〔或稱為活動〕進度表轉換為統(tǒng)籌方法的網(wǎng)絡圖。下面用一個例子來闡明例3、某公司研制新產(chǎn)品的部分工序與所需時間以及它們之間的相互關系都顯示在其工序進度表如表12-8所示，請畫出其統(tǒng)籌方法網(wǎng)絡圖。工序代號工序內容所需時間（天)緊前工序abcde產(chǎn)品設計與工藝設計外購配套零件外購生產(chǎn)原料自制主件主配可靠性試驗601513388-aacb,d2表12-8網(wǎng)絡圖中的節(jié)點表示一個事件，是一個或假設干個工序的開場或終了，是相鄰工序在時間上的分界點，點圓圈表示，數(shù)字表示點的編號。弧表示一個工序〔或活動〕，弧的方向是從工序開場指向工序的終了，弧上是各工序的代號，下面標以完成此工序所需的時間〔或資源〕等數(shù)據(jù)，即為對此弧所賦的權數(shù)．虛工序：只表示相鄰工序的前后邏輯關系。需求人力、物力等資源與時間。畫網(wǎng)絡圖的規(guī)那么：兩節(jié)點之間只能有一條弧〔箭線〕。兩事件一工序網(wǎng)絡圖只能有一個開場節(jié)點〔事項〕和一個終點事項不允許有回路，不能有缺口

abcb,c的緊前工序為aabcdc,d的緊前工序為a,babcdc的緊前工序為a。d的緊前工序為a和b3繪制網(wǎng)絡圖分3步：(1)義務分解WBSWorkbreakdownStructure任務工程明細表：工序稱號，代號；前后邏輯關系，耗費資源。(2)按表繪制網(wǎng)絡圖?！?〕節(jié)點一致編號。采用平行和交叉作業(yè)技術例４、把例３的工序進度表做一些擴展，如表12-9，請畫出其統(tǒng)籌方法的網(wǎng)絡圖。表12-9工序代號所需時間（天）緊前工序工序代號所需時間（天）緊前工序abcd60151338－aacefgh810165b，ｄdde，ｆ，ｇ１２４５３abcde601383815圖12-44解：我們把工序ｆ擴展到圖12-4發(fā)生了問題，由于ｆ的緊前工序是ｄ，故ｄ的終了應該是ｆ的開場，所以代表ｆ的弧的起點應該是④，由于工序ｂ的終了也是④，所以工序ｂ也成了工序ｆ的緊前工序，與題意不符。為此我們利用虛工序。由于e的緊前工序是b和ｄ，在④和⑤之間參與虛工序

8e15243a60b151013dc38f圖12-55在網(wǎng)絡圖上添加ｇ、ｈ工序得網(wǎng)絡圖12-6。

在統(tǒng)籌方法的網(wǎng)絡圖中不允許兩個點之間多于一條弧，因此添加了一個點和虛工序如圖12-7。615243a60b158e1013dc38fg16h515243a60b158e1013dc38fg16h57681ActivityTime(Weeks)Immediate

PredecessorsActivityTime(Weeks)Immediate

PredecessorsABCDE241064－ABCCHIJKL97845E,GCF,IJJF5EM2HG7DN6K,L2A23B4C4105D67EI46G87F7510J89H9KLM542111312N6關鍵道路TheCriticalPathApaththroughanetworkisoneoftheroutesfollowingthearrows(arcs)fromthestartnodetothefinishnode.路是指沿著箭頭從開場點到終點的一條道路Thelengthofapath

isthesumofthe(estimated)durationsoftheactivitiesonthepath.路長度為路上一切活動時間總和The(estimated)projectdurationequalsthelengthofthelongestpaththroughtheprojectnetwork.工程工期等于工程網(wǎng)絡中最長路的長度Thislongestpathiscalledthecriticalpath.(Ifmorethanonepathtieforthelongest,theyallarecriticalpaths.)工程網(wǎng)絡中最長路稱為關鍵路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關鍵道路criticalpathP292最早開場時間和最早終了時間Thestartingandfinishingtimesofeachactivityifnodelaysoccuranywhereintheprojectarecalledtheearlieststarttimeandtheearliestfinishtime.用ES表示一個活動最早開場時間；EF表示一個活動最早終了時間。最早能夠開場時間和終了時間。EarliestStartTimeRule:ES=LargestEFoftheimmediatepredecessors.最早開場時間=一切緊前工序EF的最大者ABCiES=Max{20,23,19}=23EF=20EF=23EF=19HCBAHEF=20EF=23EF=19ES=23計算一切活動的ES時間:Foreachactivitythatstartstheproject(includingthestartnode),setitsES=0.工程的最早開場時間為0最早終了時間EF=ES+活開工期ForeachactivitywhoseEShasjustbeenobtained,calculateEF=ES+duration對于每個新活動，用最早開場時間法那么求ESForeachnewactivitywhoseimmediatepredecessorsnowhaveEFvalues,obtainitsESbyapplyingtheearlieststarttimerule.Applystep2tocalculateEF.反復上述3個步驟Repeatstep3untilESandEFhavebeenobtainedforallactivities.最早終了時間EF=最早開場時間ES+活開工期從開場(左)向后計算ES只需單個緊前工序的工序ES與EF的計算ESandEFTimesforReliableConstruction多個緊前工序的ES與EF的計算ES=Max{25,23}=25ES=Max{29,20}=29最遲開場時間和最遲終了時間Thelateststarttimeforanactivityisthelatestpossibletimethatitcanstartwithoutdelayingthecompletionoftheproject(sothefinishnodestillisreachedatitsearliestfinishtime).在不影響工程完成總時間的前提下，一個活動最晚必需開場的時間。對于終點，最晚時間依然是最早終了時間,LF=EFLS=Lateststarttimeforaparticularactivity最晚開場時間LF=Latestfinishtimeforaparticularactivity最晚終了時間LatestFinishTimeRule:LF=SmallestLSoftheimmediatesuccessors.最晚時間等于其一切緊后活動最晚開場時間的最小者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活動〔工序〕的時差活動LSESLFEF總時差(LS–ES)是否關鍵工序A00220YesB22440YesC4416160YesD201626224NoE161620200YesF202025250YesG262233294NoH332942384NoI181625232NoJ252533330YesK343338371NoL333338380YesM423844404NoN383844440Yes總時差=最遲開場時間－最早開場時間=最遲終了時間－最早終了時間TS=LS－ES=LF－EFTheslackofanactivity例、某公司裝配一條新的消費線，詳細過程如表12-10,求：完成此工程的最少時間，關鍵道路及相應的關鍵工序，各工序的最早開場時間和非關鍵工序在不影響工程完成時間的前提下，其開場時間與終了時間可以推遲多久。7工序代號工序內容所需時間（天）緊前工序abcdefghij生產(chǎn)線設計外購零配件下料、鍛件工裝制造1木模、鑄件機械加工1工裝制造2機械加工2機械加工3裝配調試60451020401830152535/aaaacdd,egb,i,f,h解：據(jù)表12-10,繪制網(wǎng)絡圖如圖12-8。圖12-8關鍵道路：如圖12-8,①-②-③-⑦-⑧就是一條關鍵道路，我們要干完一切的工序就必需走完一切這樣的道路，由于很多工序可以同時進展，所以網(wǎng)絡中最長的道路就決議了完成整個工程所需的最少時間，這條道路稱為關鍵道路。12346785a60b45echj35ig1030d204025f18159

圖12-10其次,從網(wǎng)絡的收點開場計算出在不影響整個工程最早終了時間的情況下各個工序的最晚開場時間(縮寫為LS)和最晚終了時間〔縮寫為LF),顯然對同一工序有LS=LF-t1236785a[0,60]60b[60,105]45e[60.100]c[60,70]h[100,115]j[,170]35i[110.]g[80,110]30d[60.80]204025f[70,88]184101511

運用此法那么，可以從首點開場計算出每個工序的LF與LS，如圖12-11所示。

接著，可以計算出每一個工序的時差，把在不影響工程最早終了時間的條件下，工序最早開場〔或終了〕的時間可以推遲的時間，成為該工序的時差，對每個工序來說其時差記為Ts有Ts=LS-ES=LF-EF1236785a[0,60]60[0,60]b[60,105]45[90,]e[60.100]c[60,70]h[100,115]j[,170]35[,170]i[110.]g[80,110]30[80,110]d[60.80]20[60,80]40[80,120]25[110,]f[70,88]18[117,]410[107,117]15[120,]12最后將各工序的時差，以及其他信息構成工序時間表如表12-11所示。這樣就找到了一條由關鍵工序a,d,g,i和j依次銜接成的從發(fā)點到收點的關鍵道路。13ThePERT三種估計方式Mostlikelyestimate(m)=Estimateofmostlikelyvalueoftheduration最大能夠估計

Optimisticestimate(o)=Estimateofdurationundermostfavorableconditions.樂觀估計時間

Pessimisticestimate(p)=Estimateofdurationundermostunfavorableconditions.悲觀估計時間處置不確定活開工期分布時間均值和規(guī)范差MeanandStandardDeviationAnapproximateformulaforthevariance活動時間方差(2)ofanactivityis Anapproximateformulaforthemean活動時間的均值(m)ofanactivityis

樂觀估計P和悲觀估計時間O的差大致為6個規(guī)范差可信公司活動的均值和方差ActivityompMeanVarianceA12321/9B23.5841C6918104D45.51061E14.5544/9F441051G56.51171H581794I37.5971J39981K44440L15.5751M12321/9N55.5964/9P306PessimisticPathLengthsforReliable’sProject悲觀估計時間的途徑與途徑長度PathPessimisticLength(Weeks)采用悲觀估計時間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=63三個簡化的近似PERT/CPMP306Themeancriticalpathwillturnouttobethelongestpaththroughtheprojectnetwork.假設均值關鍵路是工程中最長的一條路統(tǒng)計獨立性Thedurationsoftheactivitiesonthemeancriticalpatharestatisticallyindependent.Thus,thethreeestimatesofthedurationofanactivitywouldneverchangeafterlearningthedurationsofsomeoftheotheractivities.正太分布假設Theformoftheprobabilitydistributionofprojectdurationisthenormaldistribution.Byusingsimplifyingapproximations1and2,thereissomestatisticaltheory(oneversionofthecentrallimittheorem)thatjustifiesthisasbeingareasonableapproximationifthenumberofactivitiesonthemeancriticalpathisnottoosmall〔活動數(shù)至少5個〕.計算工程的均值和方差ActivitiesonMeanCriticalPathMeanVarianceA21/9B41C104E44/9F51J81L51N64/9Projectdurationmp=44s2p=9ProbabilityofMeetingDeadlinez為d超越μp的規(guī)范差個數(shù)，查統(tǒng)計表可得概率值ProbabilityofMeetingaDeadlineP(T≤

d)P(T≤d)–3.00.001400.50–2.50.00620.250.60–2.00.0230.50.69–1.750.0400.750.77–1.50.0671.00.84–1.250.111.250.89–1.00.161.50.933–0.750.231.750.960–0.50.312.00.977–0.250.402.50.993800.503.00.9986SpreadsheetforPERTThree-EstimateApproach時間和本錢權衡ConsideringTime-CostTrade-OffsQuestion:Ifextramoneyisspenttoexpeditetheproject,whatistheleastexpensivewayofattemptingtomeetthetargetcompletiontime(40weeks)?CPMMethodofTime-CostTrade-Offs:Crashinganactivity趕工完成一項活動referstotakingspecialcostlymeasurestoreducethedurationofanactivitybelowitsnormalvalue.Specialmeasuresmightincludeovertime,hiringadditionaltemporaryhelp,usingspecialtime-savingmaterials,obtainingspecialequipment,etc.Crashingtheproject趕工完成工程referstocrashinganumberofactivitiestoreducethedurationoftheprojectbelowitsnormalvalue.Time-CostGraphforanActivity趕工常規(guī)趕工本錢正常本錢活動本錢常規(guī)常規(guī)時間趕工時間活動時間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’sProject

InitialTableLengthofPathActivity

to

CrashCrash

CostABCDGHMABCEHMABCEFJKNABCEFJLNABCIJKNABCIJLN403143444142最長路MarginalCostAnalysisforReliable’sProject

TableAfterCrashingOneWeekLengthofPathActivity

to

CrashCrash

CostABCDGHMABCEHMABCEFJKNABCEFJLNABCIJKNABCIJLN403143444142J$30,000403142434041MarginalCostAnalysisforReliable’sProject

TableAfterCrashingTwoWeeksLengthofPathActivity

to

CrashCrash

CostABCDGHMABCEHMABCEFJKNABCEFJLNABCIJKNABCIJLN403143444142J$30,000403142434041J$30,000403141423940J只大只能趕工2天MarginalCostAnalysisforReliable’sProject

TableAfterCrashingThreeWeeksLengthofPathActivity

to

CrashCrash

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

FinalTableAfterCrashingFourWeeksLengthofPathActivity

to

CrashCrash

CostABCDGHMABCEHMABCEFJKNABCEFJLNABCIJKNABCIJLN403143444142J$30,000403142434041J$30,000403141423940F$40,000403140413940F$40,000403139403940ProjectNetworkAfterCrashingUsingLPtoMakeCrashingDecisionsRestatmentoftheproblem:Considerthetotalcostoftheproject,includingtheextracostofcrashingactivities.Theproblemthenistominimizethistotalcost,subjecttotheconstraintthatprojectdurationmustbelessthanorequaltothetimedesiredbytheprojectmanager.Thedecisionstobemadearethefollowing:Thestarttimeofeachactivity.每一個活動的開場時間Thereductioninthedurationofeachactivityduetocrashing.每個活開工期的減少量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

o