網(wǎng)絡(luò)計劃技術(shù)講義

Chapter12PERT/CPMModelsfor

ProjectManagement§1

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

網(wǎng)絡(luò)時間與關(guān)鍵路線§3DealingwithUncertainActivityDurations§4網(wǎng)絡(luò)優(yōu)化1項目管理ProjectManagement項目特征CharacteristicsofProjectsUnique,one-timeoperationsInvolvealargenumberofactivitiesthatmustbeplannedandcoordinatedLongtime-horizonGoalsofmeetingcompletiondeadlinesandbudgetsExamplesBuildingahousePlanningameetingIntroducinganewproductPERT—ProjectEvaluationandReviewTechnique計劃評審技術(shù)

CPM—CriticalPathMethod關(guān)鍵路線法Agraphicalornetworkapproachforplanningandcoordinatinglarge-scaleprojects.可信建筑公司項目ReliableConstructionCompanyProjectP285TheReliableConstructionCompanyhasjustmadethewinningbidof$5.4milliontoconstructanewplantforamajormanufacturer.可信建筑公司中標(biāo)540萬美元的項目Thecontractincludesthefollowingprovisions:Apenaltyof$300,000ifReliablehasnotcompletedconstructionwithin47weeks.如果不能在47周內(nèi)完成項目，將被罰款30萬美元。如果能在40周內(nèi)完成，將獲得15萬美元的獎勵A(yù)bonusof$150,000ifReliablehascompletedtheplantwithin40weeks.Questions:286Howcantheprojectbedisplayedgraphicallytobettervisualizetheactivities?如何用圖來表示項目中活動流程Whatisthetotaltimerequiredtocompletetheprojectifnodelaysoccur?Whendotheindividualactivitiesneedtostartandfinish?Whatarethecriticalbottleneckactivities?對于非關(guān)鍵的活動Forotheractivities,howmuchdelaycanbetolerated承受?Whatistheprobabilitytheprojectcanbecompletedin47weeks?Whatistheleastexpensivewaytocompletetheprojectwithin40weeks?Howshouldongoingcostsbemonitoredtotrytokeeptheprojectwithinbudget?如何對成本進行實時監(jiān)控，使項目成本控制在預(yù)算內(nèi)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(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項目網(wǎng)絡(luò)

ProjectNetworks表示整個項目的網(wǎng)絡(luò)稱為項目網(wǎng)絡(luò)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(gòu)建easiertounderstand易于理解easiertorevisewhentherearechanges更便于修改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(jié)束時間P290W1/1第一周第一天開始W2/5第二周第五天完成二周AOAProjectNetwork1235ABCD6GEI4871011139H12FJKLNM關(guān)于AOA計劃網(wǎng)絡(luò)圖

統(tǒng)籌方法的第一步工作就是繪制計劃網(wǎng)絡(luò)圖，也就是將工序（或稱為活動）進度表轉(zhuǎn)換為統(tǒng)籌方法的網(wǎng)絡(luò)圖。下面用一個例子來說明例3、某公司研制新產(chǎn)品的部分工序與所需時間以及它們之間的相互關(guān)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(luò)圖。

工序代號工序內(nèi)容所需時間（天)緊前工序abcde產(chǎn)品設(shè)計與工藝設(shè)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(luò)圖中的節(jié)點表示一個事件件，是一個或或若干個工序序的開始或結(jié)結(jié)束，是相鄰鄰工序在時間間上的分界點點，點圓圈表表示，數(shù)字表表示點的編號號?；”硎疽粋€工序序（或活動）），弧的方向向是從工序開開始指向工序序的結(jié)束，弧弧上是各工序序的代號，下下面標(biāo)以完成成此工序所需需的時間（或或資源）等數(shù)數(shù)據(jù)，即為對對此弧所賦的的權(quán)數(shù)．虛工序：只表示相鄰工工序的前后邏邏輯關(guān)系。需需要人力、物物力等資源與與時間。畫網(wǎng)絡(luò)圖的規(guī)規(guī)則：兩節(jié)點之間只只能有一條弧?。€）。。兩事件一工工序網(wǎng)絡(luò)圖只能有有一個開始節(jié)節(jié)點（事項））和一個終點點事項不允許有回路路，不能有缺缺口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(luò)圖分分3步：(1)任任務(wù)分解WBSWorkbreakdownStructure工作項目明細細表：工序名名稱，代號；前后邏輯關(guān)系系，消耗資源源。(2)按按表繪制網(wǎng)絡(luò)絡(luò)圖。（3））節(jié)點統(tǒng)一編編號。采用平平行和交叉作作業(yè)技術(shù)例４、把例３３的工序進度度表做一些擴擴充，如表12-9，請請畫出其統(tǒng)籌籌方法的網(wǎng)絡(luò)絡(luò)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：我們把工工序ｆ擴充到到圖12-4發(fā)生了問題題，由于ｆ的的緊前工序是是ｄ，故ｄ的的結(jié)束應(yīng)該是是ｆ的開始，，所以代表ｆｆ的弧的起點點應(yīng)該是④，，由于工序ｂｂ的結(jié)束也是是④，所以工工序ｂ也成了了工序ｆ的緊緊前工序，與與題意不符。。為此我們利用用虛工序。由由于e的緊前前工序是b和和ｄ，在④和和⑤之間加入入虛工序8e15243a60b151013dc38f圖12-55在網(wǎng)絡(luò)圖上添添加ｇ、ｈ工工序得網(wǎng)絡(luò)圖圖12-6。在統(tǒng)籌方法的的網(wǎng)絡(luò)圖中不不允許兩個點點之間多于一一條弧，因此此增加了一個個點和虛工序序如圖12-7。615243a60b158e1013dc38fg16h515243a60b158e1013dc38fg16h57681ActivityTime(Weeks)Immediate

PredecessorsActivityTime(Weeks)Immediate

PredecessorsABCDE241064－ABCCHIJKL97845E,GCF,IJJF5EM2HG7DN6K,L2A23B4C4105D67EI46G87F7510J89H9KLM542111312N6關(guān)鍵鍵路路線線TheCriticalPathApaththroughanetworkisoneoftheroutesfollowingthearrows(arcs)fromthestartnodetothefinishnode.路是是指指沿沿著著箭箭頭頭從從開開始始點點到到終終點點的的一一條條路路線線Thelengthofapathisthesumofthe(estimated)durationsoftheactivitiesonthepath.路長長度度為為路路上上所所有有活活動動時時間間總總和和The(estimated)projectdurationequalsthelengthofthelongestpaththroughtheprojectnetwork.項目目工工期期等等于于項項目目網(wǎng)網(wǎng)絡(luò)絡(luò)中中最最長長路路的的長長度度Thislongestpathiscalledthecriticalpath.(Ifmorethanonepathtieforthelongest,theyallarecriticalpaths.)項目目網(wǎng)網(wǎng)絡(luò)絡(luò)中中最最長長路路稱稱為為關(guān)關(guān)鍵鍵路路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關(guān)鍵鍵路路線線criticalpathP292最早早開開始始時時間間和和最最早早結(jié)結(jié)束束時時間間Thestartingandfinishingtimesofeachactivityifnodelaysoccuranywhereintheprojectarecalledtheearlieststarttimeandtheearliestfinishtime.用ES表表示示一一個個活活動動最最早早開開始始時時間間；；EF表表示示一一個個活活動動最最早早結(jié)結(jié)束束時時間間。。最最早早可可能能開開始始時時間間和和結(jié)結(jié)束束時時間間。。EarliestStartTimeRule:ES=LargestEFoftheimmediatepredecessors.最早早開開始始時時間間=所所有有緊緊前前工工序序EF的的最最大大者者ABCiES=Max{20,23,19}=23EF=20EF=23EF=19HCBAHEF=20EF=23EF=19ES=23計算算所所有有活活動動的的ES時時間間:Foreachactivitythatstartstheproject(includingthestartnode),setitsES=0.項目目的的最最早早開開始始時時間間為為0最早早結(jié)結(jié)束束時時間間EF=ES+活活動動工工期期ForeachactivitywhoseEShasjustbeenobtained,calculateEF=ES+duration對于于每每個個新新活活動動，，用用最最早早開開始始時時間間法法則則求求ESForeachnewactivitywhoseimmediatepredecessorsnowhaveEFvalues,obtainitsESbyapplyingtheearlieststarttimerule.Applystep2tocalculateEF.重復(fù)復(fù)上上述述3個個步步驟驟Repeatstep3untilESandEFhavebeenobtainedforallactivities.最早早結(jié)結(jié)束束時時間間EF=最最早早開開始始時時間間ES+活活動動工工期期從開開始始(左左)向向后后計計算算ES只有有單單個個緊前前工工序序的的工工序序ES與與EF的的計計算算ESandEFTimesforReliableConstruction多個個緊緊前前工工序序的的ES與與EF的的計計算算ES=Max{25,23}=25ES=Max{29,20}=29最遲遲開開始始時時間間和和最最遲遲結(jié)結(jié)束束時時間間Thelateststarttimeforanactivityisthelatestpossibletimethatitcanstartwithoutdelayingthecompletionoftheproject(sothefinishnodestillisreachedatitsearliestfinishtime).在不不影影響響項項目目完完成成總總時時間間的的前前提提下下，，一一個個活活動動最晚晚必必須須開開始始的的時時間間。對于于終終點點，，最最晚晚時時間間仍仍然然是是最最早早結(jié)結(jié)束束時時間間,LF=EFLS=Lateststarttimeforaparticularactivity最最晚晚開開始始時時間間LF=Latestfinishtimeforaparticularactivity最最晚晚結(jié)結(jié)束束時時間間LatestFinishTimeRule:LF=SmallestLSoftheimmediatesuccessors.最晚晚時時間間等等于于其其所所有有緊緊后后活活動動最最晚晚開開始始時時間間的的最最小小者者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活動動（（工工序序））的的時時差差活動LSESLFEF總時差(LS–ES)是否關(guān)鍵工序A00220YesB22440YesC4416160YesD201626224NoE161620200YesF202025250YesG262233294NoH332942384NoI181625232NoJ252533330YesK343338371NoL333338380YesM423844404NoN383844440Yes總時差差=最遲遲開始始時間間－最最早開開始時時間=最遲遲結(jié)束束時間間－最最早結(jié)結(jié)束時時間TS=LS－－ES=LF－EFTheslackofanactivity例、某公司司裝配配一條條新的的生產(chǎn)產(chǎn)線，，具體體過程程如表表12-10,求：：完成成此工工程的的最少少時間間，關(guān)關(guān)鍵路路線及及相應(yīng)應(yīng)的關(guān)關(guān)鍵工工序，，各工工序的的最早早開始始時間間和非非關(guān)鍵鍵工序序在不不影響響工程程完成成時間間的前前提下下，其其開始始時間間與結(jié)結(jié)束時時間可可以推推遲多多久。。7工序代號工序內(nèi)容所需時間（天）緊前工序abcdefghij生產(chǎn)線設(shè)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(diào)試60451020401830152535/aaaacdd,egb,i,f,h解：據(jù)據(jù)表12-10,繪繪制網(wǎng)網(wǎng)絡(luò)圖圖如圖圖12-8。圖12-8關(guān)鍵路路線：：如圖圖12-8,①-②-③-⑦-⑧就就是一一條關(guān)關(guān)鍵路路線，，我們們要干干完所所有的的工序序就必必須走走完所所有這這樣的的路線線，由由于很很多工工序可可以同同時進進行，，所以以網(wǎng)絡(luò)絡(luò)中最最長的的路線線就決決定了了完成成整個個工程程所需需的最最少時時間，，這條條路線線稱為為關(guān)鍵鍵路線線。12346785a60b45echj35ig1030d204025f18159圖12-10其次,從網(wǎng)網(wǎng)絡(luò)的的收點點開始始計算算出在在不影影響整整個工工程最最早結(jié)結(jié)束時時間的的情況下各各個工工序的的最晚晚開始始時間間(縮縮寫為為LS)和和最晚晚結(jié)束束時間間（縮縮寫為為LF),顯然對對同一一工序序有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運用此此法則則，可可以從從首點點開始始計算算出每每個工工序的的LF與LS，，如圖圖12-11所示。。接著，，可以以計算算出每每一個個工序序的時時差，，把在在不影影響工工程最最早結(jié)結(jié)束時時間的條件件下，，工序序最早早開始始（或或結(jié)束束）的的時間間可以以推遲遲的時時間，，成為為該工工序的時差差，對對每個個工序序來說說其時時差記記為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最后將將各工工序的的時差差，以以及其其他信信息構(gòu)構(gòu)成工工序時時間表表如表表12-11所所示。。這樣就就找到到了一一條由由關(guān)鍵鍵工序序a,d,g,i和和j依依次連連接成成的從從發(fā)點點到收收點的的關(guān)鍵鍵路線線。13ThePERT三三種種估計計方式式Mostlikelyestimate(m)=Estimateofmostlikelyvalueoftheduration最最大可可能估估計Optimisticestimate(o)=Estimateofdurationundermostfavorableconditions.樂樂觀估估計時時間Pessimisticestimate(p)=Estimateofdurationundermostunfavorableconditions.悲悲觀估估計時時間處理不不確定定活動動工期期分布時間均值和和標(biāo)準(zhǔn)準(zhǔn)差MeanandStandardDeviationAnapproximateformulaforthevariance活活動時時間方方差(2)ofanactivityisAnapproximateformulaforthemean活活動時時間的的均值值(m)ofanactivityis樂觀估估計P和悲觀觀估計計時間間O的差大大致為為6個個標(biāo)準(zhǔn)準(zhǔn)差可信公公司活活動的的均值值和方方差A(yù)ctivityompMeanVarianceA12321/9B23.5841C6918104D45.51061E14.5544/9F441051G56.51171H581794I37.5971J39981K44440L15.5751M12321/9N55.5964/9P306PessimisticPathLengthsforReliable’sProject悲觀觀估計計時間間的路路徑與與路徑徑長度度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=63三個簡簡化的的近似似PERT/CPMP306Themeancriticalpathwillturnouttobethelongestpaththroughtheprojectnetwork.假設(shè)設(shè)均值值關(guān)鍵鍵路是是項目目中最最長的的一條條路統(tǒng)計獨獨立性性Thedurationsoftheactivitiesonthemeancriticalpatharestatisticallyindependent.Thus,thethreeestimatesofthedurationofanactivitywouldneverchangeafterlearningthedurationsofsomeoftheotheractivities.正太分分布假假設(shè)Theformoftheprobabilitydistributionofprojectdurationisthenormaldistribution.Byusingsimplifyingapproximations1and2,thereissomestatisticaltheory(oneversionofthecentrallimittheorem)thatjustifiesthisasbeingareasonableapproximationifthenumberofactivitiesonthemeancriticalpathisnottoosmall（活活動數(shù)數(shù)至少少5個個）.計算項項目的的均值值和方方差A(yù)ctivitiesonMeanCriticalPathMeanVarianceA21/9B41C104E44/9F51J81L51N64/9Projectdurationmp=44s2p=9ProbabilityofMeetingDeadlinez為d超過μμp的標(biāo)準(zhǔn)準(zhǔn)差個個數(shù)，，查統(tǒng)統(tǒng)計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時間和和成本本權(quán)衡衡ConsideringTime-CostTrade-OffsQuestion:Ifextramoneyisspenttoexpeditetheproject,whatistheleastexpensivewayofattemptingtomeetthetargetcompletiontime(40weeks)?CPMMethodofTime-CostTrade-Offs:Crashinganactivity趕工完完成一一項活活動referstotakingspecialcostlymeasurestoreducethedurationofanactivitybelowitsnormalvalue.Specialmeasuresmightincludeovertime,hiringadditionaltemporaryhelp,usingspecialtime-savingmaterials,obtainingspecialequipment,etc.Crashingtheproject趕工完成項目目referstocrashinganumberofactivitiestoreducethedurationoftheprojectbelowitsnormalvalue.Time-CostGraphforanActivity趕工常規(guī)趕工成本本正常成本本活動成本本常規(guī)常規(guī)時間間趕工時間間活動時間間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’sProjectInitialTableLengthofPathActivity

to

CrashCrash

CostABCDGHMABCEHMABCEFJKNABCEFJLNABCIJKNABCIJLN403143444142最長路MarginalCostAnalysisforReliable’sProjectTableAfterCrashingOneWeekLengthofPathActivity

to

CrashCrash

CostABCDGHMABCEHMABCEFJKNABCEFJLNABCIJKNABCIJLN403143444142J$30,000403142434041MarginalCostAnalysisforReliable’sProjectTableAfterCrashingTwoWeeksLengthofPathActivity

to

CrashCrash

CostABCDGHMABCEHMABCEFJKNABCEFJLNABCIJKNABCIJLN403143444142J$30,000403142434041J$30,000403141423940J只大只能能趕工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.每一個活活動的開始時時間Thereductioninthedurationofeachactivityduetocrashing.每個活活動工期的減減少量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

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(