Chapter12PERT/CPMModelsfor

ProjectManagement§1

ProjectNetworks計(jì)劃網(wǎng)絡(luò)圖§2SchedulingaProjectwithPERT/CPM

網(wǎng)絡(luò)時(shí)間與關(guān)鍵路線§3DealingwithUncertainActivityDurations§4網(wǎng)絡(luò)優(yōu)化1Chapter12PERT/CPMModelsfo1項(xiàng)目管理ProjectManagement項(xiàng)目特征CharacteristicsofProjectsUnique,one-timeoperationsInvolvealargenumberofactivitiesthatmustbeplannedandcoordinatedLongtime-horizonGoalsofmeetingcompletiondeadlinesandbudgetsExamplesBuildingahousePlanningameetingIntroducinganewproductPERT—ProjectEvaluationandReviewTechnique計(jì)劃評(píng)審技術(shù)

CPM—CriticalPathMethod關(guān)鍵路線法Agraphicalornetworkapproachforplanningandcoordinatinglarge-scaleprojects.項(xiàng)目管理ProjectManagement項(xiàng)目特征Cha2可信建筑公司項(xiàng)目ReliableConstructionCompanyProjectP285TheReliableConstructionCompanyhasjustmadethewinningbidof$5.4milliontoconstructanewplantforamajormanufacturer.可信建筑公司中標(biāo)540萬美元的項(xiàng)目Thecontractincludesthefollowingprovisions:Apenaltyof$300,000ifReliablehasnotcompletedconstructionwithin47weeks.如果不能在47周內(nèi)完成項(xiàng)目，將被罰款30萬美元。如果能在40周內(nèi)完成，將獲得15萬美元的獎(jiǎng)勵(lì)A(yù)bonusof$150,000ifReliablehascompletedtheplantwithin40weeks.Questions:286Howcantheprojectbedisplayedgraphicallytobettervisualizetheactivities?如何用圖來表示項(xiàng)目中活動(dòng)流程Whatisthetotaltimerequiredtocompletetheprojectifnodelaysoccur?Whendotheindividualactivitiesneedtostartandfinish?Whatarethecriticalbottleneckactivities?對(duì)于非關(guān)鍵的活動(dòng)Forotheractivities,howmuchdelaycanbetolerated承受?Whatistheprobabilitytheprojectcanbecompletedin47weeks?Whatistheleastexpensivewaytocompletetheprojectwithin40weeks?Howshouldongoingcostsbemonitoredtotrytokeeptheprojectwithinbudget?如何對(duì)成本進(jìn)行實(shí)時(shí)監(jiān)控，使項(xiàng)目成本控制在預(yù)算內(nèi)可信建筑公司項(xiàng)目ReliableConstruction3活動(dòng)明細(xì)表

ActivityListforReliableConstructionActivityActivityDescription緊前Immediate

Predecessors估計(jì)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(nèi)部管道E5GPutuptheexteriorsiding外墻施工D7HDotheexteriorpainting外部粉刷E,G9IDotheelectricalwork電路鋪設(shè)C7JPutupthewallboard豎墻板F,I8KInstalltheflooring鋪地板J4LDotheinteriorpainting內(nèi)部粉刷J5MInstalltheexteriorfixtures設(shè)施H2NInstalltheinteriorfixtures安裝內(nèi)部設(shè)備K,L6活動(dòng)明細(xì)表ActivityListforReliab4項(xiàng)目網(wǎng)絡(luò)

ProjectNetworks表示整個(gè)項(xiàng)目的網(wǎng)絡(luò)稱為項(xiàng)目網(wǎng)絡(luò)Anetworkusedtorepresentaprojectiscalledaprojectnetwork.Aprojectnetworkconsistsofanumberof節(jié)點(diǎn)nodesandanumberofarcs.Twotypesofprojectnetworks:Activity-on-arc(AOA弧表示活動(dòng)):eachactivityisrepresentedbyanarc.Anodeisusedtoseparateanactivityfromitspredecessors.Thesequencingofthearcsshowstheprecedencerelationships.Activity-on-node(AON節(jié)點(diǎn)表示活動(dòng)):eachactivityisrepresentedbyanode.Thearcsareusedtoshowtheprecedence優(yōu)先relationships.AdvantagesofAON(usedinthistextbook):P288considerablyeasiertoconstruct易于構(gòu)建easiertounderstand易于理解easiertorevisewhentherearechanges更便于修改項(xiàng)目網(wǎng)絡(luò)ProjectNetworks表示整個(gè)項(xiàng)目的網(wǎng)絡(luò)5ReliableConstruction

ProjectNetworkReliableConstruction

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

—ProjectNetwork活動(dòng)名稱編號(hào)工期最早開始時(shí)間最早結(jié)束時(shí)間P290W1/1第一周第一天開始W2/5第二周第五天完成二周MicrosoftProject

—ProjectNet8AOAProjectNetwork1235ABCD6GEI4871011139H12FJKLNMAOAProjectNetwork1235ABCD6G9關(guān)于AOA計(jì)劃網(wǎng)絡(luò)圖

統(tǒng)籌方法的第一步工作就是繪制計(jì)劃網(wǎng)絡(luò)圖，也就是將工序（或稱為活動(dòng)）進(jìn)度表轉(zhuǎn)換為統(tǒng)籌方法的網(wǎng)絡(luò)圖。下面用一個(gè)例子來說明例3、某公司研制新產(chǎn)品的部分工序與所需時(shí)間以及它們之間的相互關(guān)系都顯示在其工序進(jìn)度表如表12-8所示，請(qǐng)畫出其統(tǒng)籌方法網(wǎng)絡(luò)圖。

工序代號(hào)工序內(nèi)容所需時(shí)間（天)緊前工序abcde產(chǎn)品設(shè)計(jì)與工藝設(shè)計(jì)外購(gòu)配套零件外購(gòu)生產(chǎn)原料自制主件主配可靠性試驗(yàn)601513388-aacb,d2表12-8關(guān)于AOA計(jì)劃網(wǎng)絡(luò)圖工序代號(hào)工序內(nèi)容所需時(shí)間（天)緊10網(wǎng)絡(luò)圖中的節(jié)點(diǎn)表示一個(gè)事件，是一個(gè)或若干個(gè)工序的開始或結(jié)束，是相鄰工序在時(shí)間上的分界點(diǎn)，點(diǎn)圓圈表示，數(shù)字表示點(diǎn)的編號(hào)。弧表示一個(gè)工序（或活動(dòng)），弧的方向是從工序開始指向工序的結(jié)束，弧上是各工序的代號(hào)，下面標(biāo)以完成此工序所需的時(shí)間（或資源）等數(shù)據(jù)，即為對(duì)此弧所賦的權(quán)數(shù)．虛工序：只表示相鄰工序的前后邏輯關(guān)系。需要人力、物力等資源與時(shí)間。畫網(wǎng)絡(luò)圖的規(guī)則：兩節(jié)點(diǎn)之間只能有一條?。€）。兩事件一工序網(wǎng)絡(luò)圖只能有一個(gè)開始節(jié)點(diǎn)（事項(xiàng)）和一個(gè)終點(diǎn)事項(xiàng)不允許有回路，不能有缺口

abcb,c的緊前工序?yàn)閍abcdc,d的緊前工序?yàn)閍,babcdc的緊前工序?yàn)閍。d的緊前工序?yàn)閍和b3網(wǎng)絡(luò)圖中的節(jié)點(diǎn)表示一個(gè)事件，是一個(gè)或若干個(gè)工序的開始或結(jié)束11繪制網(wǎng)絡(luò)圖分3步：(1)任務(wù)分解WBS

WorkbreakdownStructure

工作項(xiàng)目明細(xì)表：工序名稱，代號(hào)；前后邏輯關(guān)系，消耗資源。(2)按表繪制網(wǎng)絡(luò)圖。（3）節(jié)點(diǎn)統(tǒng)一編號(hào)。采用平行和交叉作業(yè)技術(shù)

例４、把例３的工序進(jìn)度表做一些擴(kuò)充，如表12-9，請(qǐng)畫出其統(tǒng)籌方法的網(wǎng)絡(luò)圖。

表12-9工序代號(hào)所需時(shí)間（天）緊前工序工序代號(hào)所需時(shí)間（天）緊前工序abcd60151338－aacefgh810165b，ｄdde，ｆ，ｇ１２４５３abcde601383815圖12-44繪制網(wǎng)絡(luò)圖分3步：(1)任務(wù)分解WBSWorkbr12

解：我們把工序ｆ擴(kuò)充到圖12-4發(fā)生了問題，由于ｆ的緊前工序是ｄ，故ｄ的結(jié)束應(yīng)該是ｆ的開始，所以代表ｆ的弧的起點(diǎn)應(yīng)該是④，由于工序ｂ的結(jié)束也是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之間加入虛工序

8e15243a60b151013dc38f圖12-55解：我們把工序ｆ擴(kuò)充到圖12-4發(fā)生了問題，由于ｆ的緊前工13

在網(wǎng)絡(luò)圖上添加ｇ、ｈ工序得網(wǎng)絡(luò)圖12-6。

在統(tǒng)籌方法的網(wǎng)絡(luò)圖中不允許兩個(gè)點(diǎn)之間多于一條弧，因此增加了一個(gè)點(diǎn)和虛工序如圖12-7。615243a60b158e1013dc38fg16h515243a60b158e1013dc38fg16h5768在網(wǎng)絡(luò)圖上添加ｇ、ｈ工序得網(wǎng)絡(luò)圖12-6。615243a141ActivityTime(Weeks)Immediate

PredecessorsActivityTime(Weeks)Immediate

PredecessorsABCDE241064－ABCCHIJKL97845E,GCF,IJJF5EM2HG7DN6K,L2A23B4C4105D67EI46G87F7510J89H9KLM542111312N61ActivityTime(Weeks)Immediate15關(guān)鍵路線TheCriticalPathApaththroughanetworkisoneoftheroutesfollowingthearrows(arcs)fromthestartnodetothefinishnode.路是指沿著箭頭從開始點(diǎn)到終點(diǎn)的一條路線Thelengthofapath

isthesumofthe(estimated)durationsoftheactivitiesonthepath.路長(zhǎng)度為路上所有活動(dòng)時(shí)間總和The(estimated)projectdurationequalsthelengthofthelongestpaththroughtheprojectnetwork.項(xiàng)目工期等于項(xiàng)目網(wǎng)絡(luò)中最長(zhǎng)路的長(zhǎng)度Thislongestpathiscalledthecriticalpath.(Ifmorethanonepathtieforthelongest,theyallarecriticalpaths.)項(xiàng)目網(wǎng)絡(luò)中最長(zhǎng)路稱為關(guān)鍵路關(guān)鍵路線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關(guān)鍵路線criticalpathP292ThePathsforReliable’sProje17最早開始時(shí)間和最早結(jié)束時(shí)間Thestartingandfinishingtimesofeachactivityifnodelaysoccuranywhereintheprojectarecalledtheearlieststarttimeandtheearliestfinishtime.用ES表示一個(gè)活動(dòng)最早開始時(shí)間；EF表示一個(gè)活動(dòng)最早結(jié)束時(shí)間。最早可能開始時(shí)間和結(jié)束時(shí)間。

EarliestStartTimeRule:ES=LargestEFoftheimmediatepredecessors.最早開始時(shí)間=所有緊前工序EF的最大者ABCiES=Max{20,23,19}=23EF=20EF=23EF=19HCBAHEF=20EF=23EF=19ES=23最早開始時(shí)間和最早結(jié)束時(shí)間Thestartingand18計(jì)算所有活動(dòng)的ES時(shí)間:Foreachactivitythatstartstheproject(includingthestartnode),setitsES=0.項(xiàng)目的最早開始時(shí)間為0最早結(jié)束時(shí)間EF=ES+活動(dòng)工期ForeachactivitywhoseEShasjustbeenobtained,calculateEF=ES+duration對(duì)于每個(gè)新活動(dòng)，用最早開始時(shí)間法則求ESForeachnewactivitywhoseimmediatepredecessorsnowhaveEFvalues,obtainitsESbyapplyingtheearlieststarttimerule.Applystep2tocalculateEF.重復(fù)上述3個(gè)步驟Repeatstep3untilESandEFhavebeenobtainedforallactivities.最早結(jié)束時(shí)間EF=最早開始時(shí)間ES+活動(dòng)工期從開始(左)向后計(jì)算ES計(jì)算所有活動(dòng)的ES時(shí)間:最早結(jié)束時(shí)間EF=最早開始時(shí)間E19只有單個(gè)緊前工序的工序ES與EF的計(jì)算只有單個(gè)緊前工序的工序ES與EF的計(jì)算20ESandEFTimesforReliableConstruction多個(gè)緊前工序的ES與EF的計(jì)算ES=Max{25,23}=25ES=Max{29,20}=29ESandEFTimesforReliableC21最遲開始時(shí)間和最遲結(jié)束時(shí)間Thelateststarttimeforanactivityisthelatestpossibletimethatitcanstartwithoutdelayingthecompletionoftheproject(sothefinishnodestillisreachedatitsearliestfinishtime).在不影響項(xiàng)目完成總時(shí)間的前提下，一個(gè)活動(dòng)最晚必須開始的時(shí)間。對(duì)于終點(diǎn)，最晚時(shí)間仍然是最早結(jié)束時(shí)間,LF=EFLS=Lateststarttimeforaparticularactivity最晚開始時(shí)間LF=Latestfinishtimeforaparticularactivity最晚結(jié)束時(shí)間LatestFinishTimeRule:

LF=SmallestLSoftheimmediatesuccessors.最晚時(shí)間等于其所有緊后活動(dòng)最晚開始時(shí)間的最小者ABCLF=Min{30,28,27}=27LS=30LS=28LS=27HCBAHLS=30LS=28LS=27LF=27最遲開始時(shí)間和最遲結(jié)束時(shí)間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活動(dòng)（工序）的時(shí)差活動(dòng)LSESLFEF總時(shí)差(LS–ES)是否關(guān)鍵工序A00220YesB22440YesC4416160YesD201626224NoE161620200YesF202025250YesG262233294NoH332942384NoI181625232NoJ252533330YesK343338371NoL333338380YesM423844404NoN383844440Yes總時(shí)差=最遲開始時(shí)間－最早開始時(shí)間=最遲結(jié)束時(shí)間－最早結(jié)束時(shí)間TS=LS－

ES=LF－EFTheslackofanactivitySlackforReliable’sActivitie26

例、某公司裝配一條新的生產(chǎn)線，具體過程如表12-10,求：完成此工程的最少時(shí)間，關(guān)鍵路線及相應(yīng)的關(guān)鍵工序，各工序的最早開始時(shí)間和非關(guān)鍵工序在不影響工程完成時(shí)間的前提下，其開始時(shí)間與結(jié)束時(shí)間可以推遲多久。7工序代號(hào)工序內(nèi)容所需時(shí)間（天）緊前工序abcdefghij生產(chǎn)線設(shè)計(jì)外購(gòu)零配件下料、鍛件工裝制造1木模、鑄件機(jī)械加工1工裝制造2機(jī)械加工2機(jī)械加工3裝配調(diào)試60451020401830152535/aaaacdd,egb,i,f,h例、某公司裝配一條新的生產(chǎn)線，具體過程如表12-10,求27解：據(jù)表12-10,繪制網(wǎng)絡(luò)圖如圖12-8。圖12-8關(guān)鍵路線：如圖12-8,①-②-③-⑦-⑧就是一條關(guān)鍵路線，我們要干完所有的工序就必須走完所有這樣的路線，由于很多工序可以同時(shí)進(jìn)行，所以網(wǎng)絡(luò)中最長(zhǎng)的路線就決定了完成整個(gè)工程所需的最少時(shí)間，這條路線稱為關(guān)鍵路線。12346785a60b45echj35ig1030d204025f18159解：據(jù)表12-10,繪制網(wǎng)絡(luò)圖如圖12-8。1234678528

圖12-10其次,從網(wǎng)絡(luò)的收點(diǎn)開始計(jì)算出在不影響整個(gè)工程最早結(jié)束時(shí)間的情況下各個(gè)工序的最晚開始時(shí)間(縮寫為L(zhǎng)S)和最晚結(jié)束時(shí)間（縮寫為L(zhǎng)F),顯然對(duì)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

運(yùn)用此法則，可以從首點(diǎn)開始計(jì)算出每個(gè)工序的LF與LS，如圖12-11所示。

接著，可以計(jì)算出每一個(gè)工序的時(shí)差，把在不影響工程最早結(jié)束時(shí)間的條件下，工序最早開始（或結(jié)束）的時(shí)間可以推遲的時(shí)間，成為該工序的時(shí)差，對(duì)每個(gè)工序來說其時(shí)差記為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運(yùn)用此法則，可以從首點(diǎn)開始計(jì)算出每個(gè)工序的L30最后將各工序的時(shí)差，以及其他信息構(gòu)成工序時(shí)間表如表12-11所示。這樣就找到了一條由關(guān)鍵工序a,d,g,i和j依次連接成的從發(fā)點(diǎn)到收點(diǎn)的關(guān)鍵路線。13最后將各工序的時(shí)差，以及其他信息構(gòu)成工序時(shí)間表如表12-1131ThePERT三種估計(jì)方式Mostlikelyestimate(m)=Estimateofmostlikelyvalueoftheduration最大可能估計(jì)

Optimisticestimate(o)=Estimateofdurationundermostfavorableconditions.樂觀估計(jì)時(shí)間

Pessimisticestimate(p)=Estimateofdurationundermostunfavorableconditions.悲觀估計(jì)時(shí)間處理不確定活動(dòng)工期分布時(shí)間ThePERT三種估計(jì)方式Mostlikelyest32均值和標(biāo)準(zhǔn)差MeanandStandardDeviationAnapproximateformulaforthevariance活動(dòng)時(shí)間方差(2)ofanactivityis Anapproximateformulaforthemean活動(dòng)時(shí)間的均值(m)ofanactivityis

樂觀估計(jì)P和悲觀估計(jì)時(shí)間O的差大致為6個(gè)標(biāo)準(zhǔn)差均值和標(biāo)準(zhǔn)差MeanandStandardDeviat33可信公司活動(dòng)的均值和方差A(yù)ctivityompMeanVarianceA12321/9B23.5841C6918104D45.51061E14.5544/9F441051G56.51171H581794I37.5971J39981K44440L15.5751M12321/9N55.5964/9P306可信公司活動(dòng)的均值和方差A(yù)ctivityompMeanVar34PessimisticPathLengthsforReliable’sProject悲觀估計(jì)時(shí)間的路徑與路徑長(zhǎng)度PathPessimisticLength(Weeks)采用悲觀估計(jì)時(shí)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=63PessimisticPathLengthsforR35三個(gè)簡(jiǎn)化的近似PERT/CPMP306Themeancriticalpathwillturnouttobethelongestpaththroughtheprojectnetwork.假設(shè)均值關(guān)鍵路是項(xiàng)目中最長(zhǎng)的一條路統(tǒng)計(jì)獨(dú)立性Thedurationsoftheactivitiesonthemeancriticalpatharestatisticallyindependent.Thus,thethreeestimatesofthedurationofanactivitywouldneverchangeafterlearningthedurationsofsomeoftheotheractivities.正太分布假設(shè)Theformoftheprobabilitydistributionofprojectdurationisthenormaldistribution.Byusingsimplifyingapproximations1and2,thereissomestatisticaltheory(oneversionofthecentrallimittheorem)thatjustifiesthisasbeingareasonableapproximationifthenumberofactivitiesonthemeancriticalpathisnottoosmall（活動(dòng)數(shù)至少5個(gè)）.三個(gè)簡(jiǎn)化的近似PERT/CPMP306The36計(jì)算項(xiàng)目的均值和方差A(yù)ctivitiesonMeanCriticalPathMeanVarianceA21/9B41C104E44/9F51J81L51N64/9Projectdurationmp=44s2p=9計(jì)算項(xiàng)目的均值和方差A(yù)ctivitiesonMeanC37ProbabilityofMeetingDeadlinez為d超過μp的標(biāo)準(zhǔn)差個(gè)數(shù)，查統(tǒng)計(jì)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時(shí)間和成本權(quán)衡ConsideringTime-CostTrade-OffsQuestion:Ifextramoneyisspenttoexpeditetheproject,whatistheleastexpensivewayofattemptingtomeetthetargetcompletiontime(40weeks)?CPMMethodofTime-CostTrade-Offs:Crashinganactivity趕工完成一項(xiàng)活動(dòng)referstotakingspecialcostlymeasurestoreducethedurationofanactivitybelowitsnormalvalue.Specialmeasuresmightincludeovertime,hiringadditionaltemporaryhelp,usingspecialtime-savingmaterials,obtainingspecialequipment,etc.Crashingtheproject趕工完成項(xiàng)目referstocrashinganumberofactivitiestoreducethedurationoftheprojectbelowitsnormalvalue.時(shí)間和成本權(quán)衡ConsideringTime-CostT41Time-CostGraphforanActivity趕工常規(guī)趕工成本正常成本活動(dòng)成本常規(guī)常規(guī)時(shí)間趕工時(shí)間活動(dòng)時(shí)間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最長(zhǎng)路MarginalCostAnalysisforRel44MarginalCostAnalysisforReliable’sProject

TableAfterCrashingOneWeekLengthofPathActivity

to

CrashCrash

CostABCDGHMABCEHMABCEFJKNABCEFJLNABCIJKNABCIJLN403143444142J$30,000403142434041MarginalCostAnalysisforRel45MarginalCostAnalysisforReliable’sProject

TableAfterCrashingTwoWeeksLengthofPathActivity

to

CrashCrash

CostABCDGHMABCEHMABCEFJKNABCEFJLNABCIJKNABCIJLN403143444142J$30,000403142434041J$30,000403141423940J只大只能趕工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.每一個(gè)活動(dòng)的開始時(shí)間Thereductioninthedurationofeachactivityduetocrashing.每個(gè)活動(dòng)工期的減少量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、網(wǎng)絡(luò)優(yōu)化得到初始的計(jì)劃方案，但通常要對(duì)初始方案進(jìn)行調(diào)整與完善。根據(jù)計(jì)劃目標(biāo)，綜合考慮資源和降低成本等目標(biāo)，進(jìn)行網(wǎng)絡(luò)優(yōu)化，確定最優(yōu)的計(jì)劃方案。1.時(shí)間-資源優(yōu)化做法：1）優(yōu)先安排關(guān)鍵工序所需的資源。2）利用非關(guān)鍵工序的時(shí)差，錯(cuò)開各工序的開始時(shí)間。3）統(tǒng)籌兼顧工程進(jìn)度的要求和現(xiàn)有資源的限制，多次綜合平衡。下面列舉一個(gè)拉平資源需要量最高峰的實(shí)例。在例5中，若加工工人為65人，并假定這些工人可完成這5個(gè)工序任一個(gè)，下面來尋求一個(gè)時(shí)間-資源最優(yōu)方案。如表12-16所示：四、網(wǎng)絡(luò)優(yōu)化61表12-16工序需要人數(shù)最早開始時(shí)間所需時(shí)間時(shí)差d5860200f22701847g428030h391001520i26110250若上述工序都按最早開始時(shí)間安排，那么從第60天至第135天的75天里，所需的機(jī)械加工工人人數(shù)如圖12-17所示。表12-16工序需要人數(shù)最早開始時(shí)間所需時(shí)間時(shí)差d5860262在圖的上半部中，工序代號(hào)后的數(shù)字是人數(shù)，線下面的數(shù)字是非關(guān)鍵工序時(shí)差長(zhǎng)度。圖的下半部表示從第60天至135天內(nèi)的75天里，所需機(jī)械加工工人數(shù)，這樣的圖稱為資源負(fù)荷圖。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圖12-17在圖的上半部中，工序代號(hào)后的數(shù)字是人數(shù)，線下63同時(shí)我們應(yīng)優(yōu)先安排關(guān)鍵工序所需的工人，再利用非關(guān)鍵工序的時(shí)差，錯(cuò)開各工序的開始時(shí)間，從而拉平工人需要量的高峰。經(jīng)過調(diào)整，我們讓非關(guān)鍵工序f從第80天開始，工序h從第110天開始。找到了時(shí)間-資源優(yōu)化的方案，如圖12-18所示，在不增加工人的情況下保證了工程按期完成。246753f(22人）h(39人）d(58人）i(26人）g(42人）工人數(shù)65人608010012013058人42人64人26人65人圖12-18同時(shí)我們應(yīng)優(yōu)先安排關(guān)鍵工序所需的工人，再利用64Chapter12PERT/CPMModelsfor

ProjectManagement§1

ProjectNetworks計(jì)劃網(wǎng)絡(luò)圖§2SchedulingaProjectwithPERT/CPM

網(wǎng)絡(luò)時(shí)間與關(guān)鍵路線§3DealingwithUncertainActivityDurations§4網(wǎng)絡(luò)優(yōu)化1Chapter12PERT/CPMModelsfo65項(xiàng)目管理ProjectManagement項(xiàng)目特征CharacteristicsofProjectsUnique,one-timeoperationsInvolvealargenumberofactivitiesthatmustbeplannedandcoordinatedLongtime-horizonGoalsofmeetingcompletiondeadlinesandbudgetsExamplesBuildingahousePlanningameetingIntroducinganewproductPERT—ProjectEvaluationandReviewTechnique計(jì)劃評(píng)審技術(shù)

CPM—CriticalPathMethod關(guān)鍵路線法Agraphicalornetworkapproachforplanningandcoordinatinglarge-scaleprojects.項(xiàng)目管理ProjectManagement項(xiàng)目特征Cha66可信建筑公司項(xiàng)目ReliableConstructionCompanyProjectP285TheReliableConstructionCompanyhasjustmadethewinningbidof$5.4milliontoconstructanewplantforamajormanufacturer.可信建筑公司中標(biāo)540萬美元的項(xiàng)目Thecontractincludesthefollowingprovisions:Apenaltyof$300,000ifReliablehasnotcompletedconstructionwithin47weeks.如果不能在47周內(nèi)完成項(xiàng)目，將被罰款30萬美元。如果能在40周內(nèi)完成，將獲得15萬美元的獎(jiǎng)勵(lì)A(yù)bonusof$150,000ifReliablehascompletedtheplantwithin40weeks.Questions:286Howcantheprojectbedisplayedgraphicallytobettervisualizetheactivities?如何用圖來表示項(xiàng)目中活動(dòng)流程Whatisthetotaltimerequiredtocompletetheprojectifnodelaysoccur?Whendotheindividualactivitiesneedtostartandfinish?Whatarethecriticalbottleneckactivities?對(duì)于非關(guān)鍵的活動(dòng)Forotheractivities,howmuchdelaycanbetolerated承受?Whatistheprobabilitytheprojectcanbecompletedin47weeks?Whatistheleastexpensivewaytocompletetheprojectwithin40weeks?Howshouldongoingcostsbemonitoredtotrytokeeptheprojectwithinbudget?如何對(duì)成本進(jìn)行實(shí)時(shí)監(jiān)控，使項(xiàng)目成本控制在預(yù)算內(nèi)可信建筑公司項(xiàng)目ReliableConstruction67活動(dòng)明細(xì)表

ActivityListforReliableConstructionActivityActivityDescription緊前Immediate

Predecessors估計(jì)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(nèi)部管道E5GPutuptheexteriorsiding外墻施工D7HDotheexteriorpainting外部粉刷E,G9IDotheelectricalwork電路鋪設(shè)C7JPutupthewallboard豎墻板F,I8KInstalltheflooring鋪地板J4LDotheinteriorpainting內(nèi)部粉刷J5MInstalltheexteriorfixtures設(shè)施H2NInstalltheinteriorfixtures安裝內(nèi)部設(shè)備K,L6活動(dòng)明細(xì)表ActivityListforReliab68項(xiàng)目網(wǎng)絡(luò)

ProjectNetworks表示整個(gè)項(xiàng)目的網(wǎng)絡(luò)稱為項(xiàng)目網(wǎng)絡(luò)Anetworkusedtorepresentaprojectiscalledaprojectnetwork.Aprojectnetworkconsistsofanumberof節(jié)點(diǎn)nodesandanumberofarcs.Twotypesofprojectnetworks:Activity-on-arc(AOA弧表示活動(dòng)):eachactivityisrepresentedbyanarc.Anodeisusedtoseparateanactivityfromitspredecessors.Thesequencingofthearcsshowstheprecedencerelationships.Activity-on-node(AON節(jié)點(diǎn)表示活動(dòng)):eachactivityisrepresentedbyanode.Thearcsareusedtoshowtheprecedence優(yōu)先relationships.AdvantagesofAON(usedinthistextbook):P288considerablyeasiertoconstruct易于構(gòu)建easiertounderstand易于理解easiertorevisewhentherearechanges更便于修改項(xiàng)目網(wǎng)絡(luò)ProjectNetworks表示整個(gè)項(xiàng)目的網(wǎng)絡(luò)69ReliableConstruction

ProjectNetworkReliableConstruction

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

—ProjectNetwork活動(dòng)名稱編號(hào)工期最早開始時(shí)間最早結(jié)束時(shí)間P290W1/1第一周第一天開始W2/5第二周第五天完成二周MicrosoftProject

—ProjectNet72AOAProjectNetwork1235ABCD6GEI4871011139H12FJKLNMAOAProjectNetwork1235ABCD6G73關(guān)于AOA計(jì)劃網(wǎng)絡(luò)圖

統(tǒng)籌方法的第一步工作就是繪制計(jì)劃網(wǎng)絡(luò)圖，也就是將工序（或稱為活動(dòng)）進(jìn)度表轉(zhuǎn)換為統(tǒng)籌方法的網(wǎng)絡(luò)圖。下面用一個(gè)例子來說明例3、某公司研制新產(chǎn)品的部分工序與所需時(shí)間以及它們之間的相互關(guān)系都顯示在其工序進(jìn)度表如表12-8所示，請(qǐng)畫出其統(tǒng)籌方法網(wǎng)絡(luò)圖。

工序代號(hào)工序內(nèi)容所需時(shí)間（天)緊前工序abcde產(chǎn)品設(shè)計(jì)與工藝設(shè)計(jì)外購(gòu)配套零件外購(gòu)生產(chǎn)原料自制主件主配可靠性試驗(yàn)601513388-aacb,d2表12-8關(guān)于AOA計(jì)劃網(wǎng)絡(luò)圖工序代號(hào)工序內(nèi)容所需時(shí)間（天)緊74網(wǎng)絡(luò)圖中的節(jié)點(diǎn)表示一個(gè)事件，是一個(gè)或若干個(gè)工序的開始或結(jié)束，是相鄰工序在時(shí)間上的分界點(diǎn)，點(diǎn)圓圈表示，數(shù)字表示點(diǎn)的編號(hào)?；”硎疽粋€(gè)工序（或活動(dòng)），弧的方向是從工序開始指向工序的結(jié)束，弧上是各工序的代號(hào)，下面標(biāo)以完成此工序所需的時(shí)間（或資源）等數(shù)據(jù)，即為對(duì)此弧所賦的權(quán)數(shù)．虛工序：只表示相鄰工序的前后邏輯關(guān)系。需要人力、物力等資源與時(shí)間。畫網(wǎng)絡(luò)圖的規(guī)則：兩節(jié)點(diǎn)之間只能有一條?。€）。兩事件一工序網(wǎng)絡(luò)圖只能有一個(gè)開始節(jié)點(diǎn)（事項(xiàng)）和一個(gè)終點(diǎn)事項(xiàng)不允許有回路，不能有缺口

abcb,c的緊前工序?yàn)閍abcdc,d的緊前工序?yàn)閍,babcdc的緊前工序?yàn)閍。d的緊前工序?yàn)閍和b3網(wǎng)絡(luò)圖中的節(jié)點(diǎn)表示一個(gè)事件，是一個(gè)或若干個(gè)工序的開始或結(jié)束75繪制網(wǎng)絡(luò)圖分3步：(1)任務(wù)分解WBS

WorkbreakdownStructure

工作項(xiàng)目明細(xì)表：工序名稱，代號(hào)；前后邏輯關(guān)系，消耗資源。(2)按表繪制網(wǎng)絡(luò)圖。（3）節(jié)點(diǎn)統(tǒng)一編號(hào)。采用平行和交叉作業(yè)技術(shù)

例４、把例３的工序進(jìn)度表做一些擴(kuò)充，如表12-9，請(qǐng)畫出其統(tǒng)籌方法的網(wǎng)絡(luò)圖。

表12-9工序代號(hào)所需時(shí)間（天）緊前工序工序代號(hào)所需時(shí)間（天）緊前工序abcd60151338－aacefgh810165b，ｄdde，ｆ，ｇ１２４５３abcde601383815圖12-44繪制網(wǎng)絡(luò)圖分3步：(1)任務(wù)分解WBSWorkbr76

解：我們把工序ｆ擴(kuò)充到圖12-4發(fā)生了問題，由于ｆ的緊前工序是ｄ，故ｄ的結(jié)束應(yīng)該是ｆ的開始，所以代表ｆ的弧的起點(diǎn)應(yīng)該是④，由于工序ｂ的結(jié)束也是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之間加入虛工序

8e15243a60b151013dc38f圖12-55解：我們把工序ｆ擴(kuò)充到圖12-4發(fā)生了問題，由于ｆ的緊前工77

在網(wǎng)絡(luò)圖上添加ｇ、ｈ工序得網(wǎng)絡(luò)圖12-6。

在統(tǒng)籌方法的網(wǎng)絡(luò)圖中不允許兩個(gè)點(diǎn)之間多于一條弧，因此增加了一個(gè)點(diǎn)和虛工序如圖12-7。615243a60b158e1013dc38fg16h515243a60b158e1013dc38fg16h5768在網(wǎng)絡(luò)圖上添加ｇ、ｈ工序得網(wǎng)絡(luò)圖12-6。615243a781ActivityTime(Weeks)Immediate

PredecessorsActivityTime(Weeks)Immediate

PredecessorsABCDE241064－ABCCHIJKL97845E,GCF,IJJF5EM