網(wǎng)絡(luò)計(jì)劃技術(shù)講義

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1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.可信建筑公司項(xiàng)目ReliableConstructionCompanyProjectP285TheReliableConstructionCompanyhasjustmadethewinningbidof$5.4milliontoconstructanewplantforamajormanufacturer.可信建筑公司中標(biāo)540萬(wàn)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(wàn)美元。如果能在40周內(nèi)完成，將獲得15萬(wàn)美元的獎(jiǎng)勵(lì)A(yù)bonusof$150,000ifReliablehascompletedtheplantwithin40weeks.Questions:286Howcantheprojectbedisplayedgraphicallytobettervisualizetheactivities?如何用圖來(lái)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)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項(xiàng)目網(wǎng)絡(luò)

ProjectNetworks表示整個(gè)項(xiàng)目的網(wǎng)絡(luò)稱(chēng)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(dòng)名稱(chēng)編號(hào)工期最早開(kāi)始時(shí)間最早結(jié)束時(shí)間P290W1/1第一周第一天開(kāi)始W2/5第二周第五天完成二周AOAProjectNetwork1235ABCD6GEI4871011139H12FJKLNM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(chēng)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(lái)說(shuō)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(huà)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網(wǎng)絡(luò)圖中的節(jié)點(diǎn)表示一個(gè)事件件，是一個(gè)或或若干個(gè)工序序的開(kāi)始或結(jié)結(jié)束，是相鄰鄰工序在時(shí)間間上的分界點(diǎn)點(diǎn)，點(diǎn)圓圈表表示，數(shù)字表表示點(diǎn)的編號(hào)號(hào)?；”硎疽粋€(gè)工序序（或活動(dòng)）），弧的方向向是從工序開(kāi)開(kāi)始指向工序序的結(jié)束，弧弧上是各工序序的代號(hào)，下下面標(biāo)以完成成此工序所需需的時(shí)間（或或資源）等數(shù)數(shù)據(jù)，即為對(duì)對(duì)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(shí)間。畫(huà)網(wǎng)絡(luò)圖的規(guī)規(guī)則：兩節(jié)點(diǎn)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(gè)開(kāi)始節(jié)節(jié)點(diǎn)（事項(xiàng)））和一個(gè)終點(diǎn)點(diǎn)事項(xiàng)不允許有回路路，不能有缺缺口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繪制網(wǎng)絡(luò)圖分分3步：(1)任任務(wù)分解WBSWorkbreakdownStructure工作項(xiàng)目明細(xì)細(xì)表：工序名名稱(chēng)，代號(hào)；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(diǎn)統(tǒng)一編編號(hào)。采用平平行和交叉作作業(yè)技術(shù)例４、把例３３的工序進(jìn)度度表做一些擴(kuò)擴(kuò)充，如表12-9，請(qǐng)請(qǐng)畫(huà)出其統(tǒng)籌籌方法的網(wǎng)絡(luò)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解：我們把工工序ｆ擴(kuò)充到到圖12-4發(fā)生了問(wèn)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(kāi)始，，所以代表ｆｆ的弧的起點(diǎn)點(diǎn)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(gè)點(diǎn)點(diǎn)之間多于一一條弧，因此此增加了一個(gè)個(gè)點(diǎn)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(kāi)開(kāi)始始點(diǎn)點(diǎn)到到終終點(diǎn)點(diǎn)的的一一條條路路線線Thelengthofapathisthesumofthe(estimated)durationsoftheactivitiesonthepath.路長(zhǎng)長(zhǎng)度度為為路路上上所所有有活活動(dòng)動(dòng)時(shí)時(shí)間間總總和和The(estimated)projectdurationequalsthelengthofthelongestpaththroughtheprojectnetwork.項(xiàng)目目工工期期等等于于項(xiàng)項(xiàng)目目網(wǎng)網(wǎng)絡(luò)絡(luò)中中最最長(zhǎng)長(zhǎng)路路的的長(zhǎng)長(zhǎng)度度Thislongestpathiscalledthecriticalpath.(Ifmorethanonepathtieforthelongest,theyallarecriticalpaths.)項(xiàng)目目網(wǎng)網(wǎng)絡(luò)絡(luò)中中最最長(zhǎng)長(zhǎng)路路稱(chēng)稱(chēng)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(kāi)開(kāi)始始時(shí)時(shí)間間和和最最早早結(jié)結(jié)束束時(shí)時(shí)間間Thestartingandfinishingtimesofeachactivityifnodelaysoccuranywhereintheprojectarecalledtheearlieststarttimeandtheearliestfinishtime.用ES表表示示一一個(gè)個(gè)活活動(dòng)動(dòng)最最早早開(kāi)開(kāi)始始時(shí)時(shí)間間；；EF表表示示一一個(gè)個(gè)活活動(dòng)動(dòng)最最早早結(jié)結(jié)束束時(shí)時(shí)間間。。最最早早可可能能開(kāi)開(kāi)始始時(shí)時(shí)間間和和結(jié)結(jié)束束時(shí)時(shí)間間。。EarliestStartTimeRule:ES=LargestEFoftheimmediatepredecessors.最早早開(kāi)開(kāi)始始時(shí)時(shí)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(jì)算算所所有有活活動(dòng)動(dòng)的的ES時(shí)時(shí)間間:Foreachactivitythatstartstheproject(includingthestartnode),setitsES=0.項(xiàng)目目的的最最早早開(kāi)開(kāi)始始時(shí)時(shí)間間為為0最早早結(jié)結(jié)束束時(shí)時(shí)間間EF=ES+活活動(dòng)動(dòng)工工期期ForeachactivitywhoseEShasjustbeenobtained,calculateEF=ES+duration對(duì)于于每每個(gè)個(gè)新新活活動(dòng)動(dòng)，，用用最最早早開(kāi)開(kāi)始始時(shí)時(shí)間間法法則則求求ESForeachnewactivitywhoseimmediatepredecessorsnowhaveEFvalues,obtainitsESbyapplyingtheearlieststarttimerule.Applystep2tocalculateEF.重復(fù)復(fù)上上述述3個(gè)個(gè)步步驟驟Repeatstep3untilESandEFhavebeenobtainedforallactivities.最早早結(jié)結(jié)束束時(shí)時(shí)間間EF=最最早早開(kāi)開(kāi)始始時(shí)時(shí)間間ES+活活動(dòng)動(dòng)工工期期從開(kāi)開(kāi)始始(左左)向向后后計(jì)計(jì)算算ES只有有單單個(gè)個(gè)緊前前工工序序的的工工序序ES與與EF的的計(jì)計(jì)算算ESandEFTimesforReliableConstruction多個(gè)個(gè)緊緊前前工工序序的的ES與與EF的的計(jì)計(jì)算算ES=Max{25,23}=25ES=Max{29,20}=29最遲遲開(kāi)開(kāi)始始時(shí)時(shí)間間和和最最遲遲結(jié)結(jié)束束時(shí)時(shí)間間Thelateststarttimeforanactivityisthelatestpossibletimethatitcanstartwithoutdelayingthecompletionoftheproject(sothefinishnodestillisreachedatitsearliestfinishtime).在不不影影響響項(xiàng)項(xiàng)目目完完成成總總時(shí)時(shí)間間的的前前提提下下，，一一個(gè)個(gè)活活動(dòng)動(dòng)最晚晚必必須須開(kāi)開(kāi)始始的的時(shí)時(shí)間間。對(duì)于于終終點(diǎn)點(diǎn)，，最最晚晚時(shí)時(shí)間間仍仍然然是是最最早早結(jié)結(jié)束束時(shí)時(shí)間間,LF=EFLS=Lateststarttimeforaparticularactivity最最晚晚開(kāi)開(kāi)始始時(shí)時(shí)間間LF=Latestfinishtimeforaparticularactivity最最晚晚結(jié)結(jié)束束時(shí)時(shí)間間LatestFinishTimeRule:LF=SmallestLSoftheimmediatesuccessors.最晚晚時(shí)時(shí)間間等等于于其其所所有有緊緊后后活活動(dòng)動(dòng)最最晚晚開(kāi)開(kāi)始始時(shí)時(shí)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(dòng)動(dòng)（（工工序序））的的時(shí)時(shí)差差活動(dòng)LSESLFEF總時(shí)差(LS–ES)是否關(guān)鍵工序A00220YesB22440YesC4416160YesD201626224NoE161620200YesF202025250YesG262233294NoH332942384NoI181625232NoJ252533330YesK343338371NoL333338380YesM423844404NoN383844440Yes總時(shí)差差=最遲遲開(kāi)始始時(shí)間間－最最早開(kāi)開(kāi)始時(shí)時(shí)間=最遲遲結(jié)束束時(shí)間間－最最早結(jié)結(jié)束時(shí)時(shí)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(guò)程程如表表12-10,求：：完成成此工工程的的最少少時(shí)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(kāi)始始時(shí)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(shí)間間的前前提下下，其其開(kāi)始始時(shí)間間與結(jié)結(jié)束時(shí)時(shí)間可可以推推遲多多久。。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(shí)進(jìn)進(jìn)行，，所以以網(wǎng)絡(luò)絡(luò)中最最長(zhǎng)的的路線線就決決定了了完成成整個(gè)個(gè)工程程所需需的最最少時(shí)時(shí)間，，這條條路線線稱(chēng)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(diǎn)點(diǎn)開(kāi)始始計(jì)算算出在在不影影響整整個(gè)工工程最最早結(jié)結(jié)束時(shí)時(shí)間的的情況下各各個(gè)工工序的的最晚晚開(kāi)始始時(shí)間間(縮縮寫(xiě)為為L(zhǎng)S)和和最晚晚結(jié)束束時(shí)間間（縮縮寫(xiě)為為L(zhǎng)F),顯然對(duì)對(duì)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(yùn)用此此法則則，可可以從從首點(diǎn)點(diǎn)開(kāi)始始計(jì)算算出每每個(gè)工工序的的LF與LS，，如圖圖12-11所示。。接著，，可以以計(jì)算算出每每一個(gè)個(gè)工序序的時(shí)時(shí)差，，把在在不影影響工工程最最早結(jié)結(jié)束時(shí)時(shí)間的條件件下，，工序序最早早開(kāi)始始（或或結(jié)束束）的的時(shí)間間可以以推遲遲的時(shí)時(shí)間，，成為為該工工序的時(shí)差差，對(duì)對(duì)每個(gè)個(gè)工序序來(lái)說(shuō)說(shuō)其時(shí)時(shí)差記記為T(mén)s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(shí)差差，以以及其其他信信息構(gòu)構(gòu)成工工序時(shí)時(shí)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(diǎn)點(diǎn)到收收點(diǎn)的的關(guān)鍵鍵路線線。13ThePERT三三種種估計(jì)計(jì)方式式Mostlikelyestimate(m)=Estimateofmostlikelyvalueoftheduration最最大可可能估估計(jì)Optimisticestimate(o)=Estimateofdurationundermostfavorableconditions.樂(lè)樂(lè)觀估估計(jì)時(shí)時(shí)間Pessimisticestimate(p)=Estimateofdurationundermostunfavorableconditions.悲悲觀估估計(jì)時(shí)時(shí)間處理不不確定定活動(dòng)動(dòng)工期期分布時(shí)間均值和和標(biāo)準(zhǔn)準(zhǔn)差MeanandStandardDeviationAnapproximateformulaforthevariance活活動(dòng)時(shí)時(shí)間方方差(2)ofanactivityisAnapproximateformulaforthemean活活動(dòng)時(shí)時(shí)間的的均值值(m)ofanactivityis樂(lè)觀估估計(jì)P和悲觀觀估計(jì)計(jì)時(shí)間間O的差大大致為為6個(gè)個(gè)標(biāo)準(zhǔn)準(zhǔn)差可信公公司活活動(dòng)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(jì)計(jì)時(shí)間間的路路徑與與路徑徑長(zhǎng)度度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=63三個(gè)簡(jiǎn)簡(jiǎn)化的的近似似PERT/CPMP306Themeancriticalpathwillturnouttobethelongestpaththroughtheprojectnetwork.假設(shè)設(shè)均值值關(guān)鍵鍵路是是項(xiàng)目目中最最長(zhǎng)的的一條條路統(tǒng)計(jì)獨(dú)獨(dú)立性性Thedurationsoftheactivitiesonthemeancriticalpatharestatisticallyindependent.Thus,thethreeestimatesofthedurationofanactivitywouldneverchangeafterlearningthedurationsofsomeoftheotheractivities.正太分分布假假設(shè)Theformoftheprobabilitydistributionofprojectdurationisthenormaldistribution.Byusingsimplifyingapproximations1and2,thereissomestatisticaltheory(oneversionofthecentrallimittheorem)thatjustifiesthisasbeingareasonableapproximationifthenumberofactivitiesonthemeancriticalpathisnottoosmall（活活動(dòng)數(shù)數(shù)至少少5個(gè)個(gè)）.計(jì)算項(xiàng)項(xiàng)目的的均值值和方方差A(yù)ctivitiesonMeanCriticalPathMeanVarianceA21/9B41C104E44/9F51J81L51N64/9Projectdurationmp=44s2p=9ProbabilityofMeetingDeadlinez為d超過(guò)μμp的標(biāo)準(zhǔn)準(zhǔn)差個(gè)個(gè)數(shù)，，查統(tǒng)統(tǒng)計(jì)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(shí)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(xiàng)活活動(dòng)referstotakingspecialcostlymeasurestoreducethedurationofanactivitybelowitsnormalvalue.Specialmeasuresmightincludeovertime,hiringadditionaltemporaryhelp,usingspecialtime-savingmaterials,obtainingspecialequipment,etc.Crashingtheproject趕工完成項(xiàng)目目referstocrashinganumberofactivitiestoreducethedurationoftheprojectbelowitsnormalvalue.Time-CostGraphforanActivity趕工常規(guī)趕工成本本正常成本本活動(dòng)成本本常規(guī)常規(guī)時(shí)間間趕工時(shí)間間活動(dòng)時(shí)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(zhǎng)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(gè)活活動(dòng)的開(kāi)始時(shí)時(shí)間Thereductioninthedurationofeachactivityduetocrashing.每個(gè)活活動(dòng)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(