市政工程施工组织与管理课件 模块3 任务五 优化网络计划（费用优化2）-（原译双语）

第四节网络计划优化

Section4:NetworkPlanOptimization案例：Case:

巳知某工程双代号网络计划如图4.34所示,图中箭线下方括号外数字为工作的正常时间,括号内数字为最短持续时间；箭线上方号外数字工作按正常持续时间完成时所需的直接费；括号内数字为工作按最短持续时间完成时所需的直接费。该工程的间接费用率为0.8万元/d,试对其进行费用优化。Theactivity-on-arrownetworkplanofacertainprojectisshowninFigure4.34.Thenumbersoutsidethebracketsbelowthearrowsrepresentthenormaldurationofthetasks,andthenumbersinsidethebracketsrepresenttheshortestduration.Thenumbersabovethearrowsrepresentthedirectcostwhenthetaskiscompletedinthenormalduration,andthenumbersinthebracketsrepresentthedirectcostwhenthetaskiscompletedintheshortestduration.TheindirectcostrateforthisprojectisRMB8,000perday.Thetaskistooptimizethecost.(解)：该网络计划的费用优化可按以下步骤进行:

①根据各项工作的正常持续时间,用标号法确定网络计划的计算工期和关键线路,如图4.35所示。计算工期为19d,关键线路有两条：①③④⑥和①③④⑤⑥(Solution):Thecostoptimizationofthisnetworkplancanbecarriedoutinthefollowingsteps:

①Basedonthenormaldurationofeachtask,usethenumberingmethodtodeterminethecalculationdurationandcriticalpathofthenetworkplan,asshowninFigure4.35.Thecalculatedprojectdurationis19days,andtherearetwocriticalpaths:①③④⑥and①③④⑤⑥.②计算各项工作的直接费用率:②Calculatethedirectcostrateforeachtask:③计算工程总费用:

a.直接费总和:Cd=7.0+90+57+55+8.0+80+5+7.5+65=62.2(万元),

b.间接费总和:Ci=0.8x19=15.2(万元),

c.工程总费用:Ct=Cd+Ci=62.2+15.2=77.4(万元)

④通过压缩关键工作的持续时间进行费用优化(优化过程见表4.3)③Calculatethetotalcostoftheproject:

a.Totaldirectcost:Cd=7.0+9.0+5.7+5.5+8.0+8.0+5.0+7.5+6.5=62.2(RMB10,000),

b.Totalindirectcost:Ci=0.8×19=15.2(RMB10,000),

c.Totalprojectcost:Ct=Cd+Ci=62.2+15.2=77.4(RMB10,000).

④Performcostoptimizationbyshorteningthedurationofcriticaltasks(optimizationprocessshowninTable4.3).A.第一次压缩。

由图4.35可知,该网络计划中有两条关键线路,为了同时缩短两条关键线路的总持续时间,有以下4个压缩方案:

a.压缩工作B,直接费用率为1.0万元/d,

b.压缩工作E,直接费用率为0.2万元/d:,

c.同时压缩工作H和工作l,组合直接费用率为0.7+0.5=l.2(万元/d),

d.同时压缩工作I和工作J,组合直接费用率为0.5+0.2=0.7(万元/d)

在上述压缩方案中,由于工作的直接费用率最小,故应选择工作E作为压缩对象。工作E的直接费用率0.2万元/,小于间接费用率0.8万元/d,说明压缩工作E可使工程总费用降低。将工作E的持续时间压缩至最短持续时间3天，利用标号法重新确定计算工期和关键线路,如图4.36所示A.Firstshortening.

AsseeninFigure4.35,thenetworkplanhastwocriticalpaths.Tosimultaneouslyshortenthetotaldurationofbothcriticalpaths,therearethefollowingfourshorteningoptions:

a.ShorteningthedurationoftaskB,directcostrateisRMB10,000perday,

b.ShorteningthedurationoftaskE,directcostrateisRMB2,000perday,

c.SimultaneouslyshorteningthedurationoftasksHandI,combineddirectcostrateis0.7+0.5=1.2(RMB10,000perday),d.

SimultaneouslyshorteningthedurationoftasksIandJ,combineddirectcostrateis0.5+0.2=0.7(RMB10,000perday).

Amongtheaboveshorteningoptions,sincethedirectcostrateisthesmallestfortaskE,itshouldbeselectedforshortening.ThedirectcostrateoftaskEisRMB2,000perday,whichislowerthantheindirectcostrateofRMB8,000perday,indicatingthatshorteningthedurationoftaskEcanreducethetotalprojectcost.ReducethedurationoftaskEtoitsminimumof3days,andusethelabelingmethodtorecalculatetheconstructionperiodandcriticalpath,asshowninFig.4.36.图4.36Fig.4.36此时,关键工作E被压缩成非关键工作,故将其持续时间延长为4d,使成为关键工作。

第一次压缩后的网络计划如图4.37所示。图中箭线上方括号内数字为工作的直接费用率。Aftertheshortening,criticaltaskEbecomesanon-criticaltask,soitsdurationisextendedto4daystomakeitacriticaltask.

ThenetworkplanafterthefirstshorteningisshowninFig.4.37.Thenumbersinthebracketsabovethearrowsinthefigurerepresentthedirectcostrateofthetasks.B.第二次压缩。由图4.37可知,该络计划中有3条关键线路,即①③④⑥和①③④⑤⑥及①③⑤⑥。

为了同时缩短3条关键线路的总持续时间,有以下5个压缩方案:B.Secondshortening.AsseeninFigure4.37,therearethreecriticalpathsinthisnetworkplan:①③④⑥,①③④⑤⑥,and①③⑤⑥.

Thereare5schemesavailableforsimultaneouslyshorteningthetotaldurationofthethreecriticalpaths:

a.压缩工作B,直接费用率为1.0万元/d,

b.同时压缩工作E和工作G,组合直接费用率为:0.2+0.8=1.0(万元/d):

c.同时压缩工作E和工作J,组合直接费用率为:0.2+0.2=0.4(万元/d):

d.同时压缩工作G、工作H和工作I,组合直接费用率为:08.+0.7+0.5=2.0(万元/d),

e.同时压缩工作I和工作J,组合直接费用率为0.5+0.2=0.7(万元0)

在上述压缩方案中,由于工作E和工作J的组合直接费用率最小,故应选择工作E和工作J作为压缩对象。工作E和工作J的组合直接费用率0.4万元/d,小于间接费用率0.8万元/d,说明同时压缩工作E和工作J可使工程总费用降低。a.ShorteningthedurationoftaskB,directcostrateisRMB10,000perday,

b.SimultaneouslyshorteningthedurationoftasksEandG,combineddirectcostrateis0.2+0.8=1.0(RMB10,000perday),

c.SimultaneouslyshorteningthedurationoftasksEandJ,combineddirectcostrateis0.2+0.2=0.4(RMB10,000perday),

d.SimultaneouslyshorteningthedurationoftasksG,H,andI,combineddirectcostrateis0.8+0.7+0.5=2.0(RMB10,000perday),

e.SimultaneouslyshorteningthedurationoftasksIandJ,combineddirectcostrateis0.5+0.2=0.7(RMB10,000perday).

Amongtheseshorteningoptions,sincethecombineddirectcostrateoftasksEandJisthelowest,theyshouldbeselectedforshortening.ThecombineddirectcostrateoftasksEandJisRMB4,000perday,whichislowerthantheindirectcostrateofRMB8,000perday,indicatingthatsimultaneouslyshorteningthedurationoftasksEandJcanreducethetotalprojectcost.由于工作E的持续时间只能压缩1d,工作J的持续时间也只能随之压缩1d。工作E和工作J的持续时间同时压缩1d后,利用标号法重新确定计算工期和关键线路。此时,关键线路由压缩前的3条变为2条,即①③④⑥和①③⑤⑥。原来的关键工作H未经压缩而被动地变成了非关键工作。第二次压缩后的网络计划如图4.38所示。此时,关键工作E的持续时间已达最短,不能再压缩,故其直接费用率变为无穷大。SincethedurationoftaskEcanonlybeshortenedby1day,thedurationoftaskJmustalsobeshortenedby1dayaccordingly.AftersimultaneouslyshorteningthedurationoftasksEandJby1day,usethelabelingmethodtorecalculatetheconstructionperiodandcriticalpath.Thethreecriticalpathsbeforeshorteningarereducedtotwo,①③④⑥and①③⑤⑥.ThepreviouslycriticaltaskH,whosedurationisnotshortened,passivelyturnedintoanon-criticaltask.ThenetworkplanafterthesecondshorteningisshowninFig.4.38.Atthispoint,thedurationofcriticaltaskEhasalsoreachedtheminimumandcan'tbefurthershortened,sothedirectcostrateoftaskJbecomesinfinite.C.第三次压缩。由图4.38可知,由于工作E不能再压缩,而为了同时缩短两条关键线路①③④⑥和①③⑤⑥的总持续时间，只有以下3个压缩方案:

a.压缩工作B,直接费用率为1.0万元/d,

b.同时压缩工作G和工作I组合直接费用率为:0.8+0.5=1.3(万元d)

C.同时压缩工作I和工作J,组合直接费率为:0.5+0.2=0.7(万元/d)C.Thirdshortening.AsseeninFigure4.38,sincetaskEcannotbefurthershortened,andinordertosimultaneouslyshortenthetotaldurationoftwocriticalpaths,①③④⑥and①③⑤⑥,thereareonlythefollowingthreeshorteningoptions:

a.ShorteningthedurationoftaskB,directcostrateisRMB10,000perday,

b.SimultaneouslyshorteningthedurationoftasksGandI,combineddirectcostrateis0.8+0.5=1.3(RMB10,000perday),

c.SimultaneouslyshorteningthedurationoftasksIandJ,combineddirectcostrateis0.5+0.2=0.7(RMB10,000perday).上述压缩方案中,由于工作I和工作J的组合直接费用率最小,故应选择工作I和工作J作为压缩对象。工作I和工作J的组合直接费用率0.7万元/d,小于间接费用率0.8万元/d,说明同时压缩工作I和工作J可使工程总费用降低。由于工作J的持续时间只能压缩1d,工作I的持续时间也只能随之压缩1d。工作I和工作J的持续时间同时压缩1d后,利用标号法重新确定计算工期和关键线路。此时,关键线路仍然为两条,即①③④⑥和①③⑤⑥。Amongthecompressionschemesabove,sinceactivityIandactivityJhasthelowestcombineddirectcostrate,activityIandactivityJshouldbeselectedasthecompressiontargets.Thecombineddirectcostrateof0.7(10,000yuan/d)foractivitiesIandJislowerthantheindirectcostrateof0.8(10,000yuan/d),indicatingthatcompressingbothactivitiescanlowertotalprojectcost.AsthedurationofactivityJcanonlybecompressedby1day,thedurationofactivityImustcorrespondinglybecompressedby1day.Aftercompressingbothactivities'durationsby1day,thelabelingmethodisappliedtoredeterminethecalculatedconstructionperiodandthecriticalpath.Atthispoint,therearestilltwocriticalpaths,namely①③④⑥and①③⑤⑥.第三次压缩后的网络计划如图4.39所示。此时,关键工作J的持续时间也已达最短,不能再压缩,故其直接费用率变为无穷大。ThenetworkplanafterthethirdshorteningisshowninFig.4.39.Atthispoint,thedurationofcriticaltaskJhasalsoreachedtheminimumandcan'tbefurthershortened,sothedirectcostrateoftaskJbecomesinfinite.D.第四次压缩。从图4.39可知,由于工作E和工作J不能再压缩,而为了同时缩短两条关键线路①③④⑥和①③⑤⑥的总持续时间，只有以下2个压缩方案:

a.压缩工作B,直接费用率为1.0万元/d,

b.同时压缩工作G和工作l,组合直接费用率为:0.8+0.5=1.3(万元/d)D.Fourthshortening.AsseeninFigure4.39,sincetasksEandJcannotbefurthershortened,andinordertosimultaneouslyshortenthetotaldurationoftwocriticalpaths,①③④⑥and①③⑤⑥,thereareonlythefollowingtwoshorteningoptions:

a.ShorteningthedurationoftaskB,directcostrateisRMB10,000perday,

b.SimultaneouslyshorteningthedurationoftasksGandI,combineddirectcostrateis0.8+0.5=1.3(RMB10,000perday).

在上述压缩方案中,由于工作B的直接费用率最小,故应选择工作B作为压缩对象。但是，由于工作B的直接费用率1.0万元/d,大于间接费用率0.8万元/d,说明压缩工作B会使工程总费用增加。因此,不需要压缩工作B,优化方案已得到，优化后的网络计划如图4.40所示。图中箭线上方括号内数字为工作的直接费。

Amongtheaboveshorteningplans,sincetaskBhasthelowestdirectcostrate,itshouldbeselectedforshortening.HoweverHowever,thedirectcostratefortaskBisRMB10,000perday,whichismorethantheindirectcostrateofRMB8,000perday.Therefore,shorteningthedurationoftaskBwillincreasethetotalprojectcosts.Therefore,itisunnecessarytoshortenthedurationoftaskB,andtheoptimizedplanhasbeenobtained.TheoptimizednetworkplanisshowninFig.4.40.Thenumbersinbracketsabovethearrowsinthefigurerepresent