project planning and control：arithmetical analysis

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1、15ArithmeticalanalysisThismethodistheclassicaltechniqueandcanbeperformedinanumberofways.Oneoftheeasiestmethodsistoaddupthevariousactivitydurationsonthenetworkitself,writingthesumofeachstageinasquareboxattheendofthatactivity,i.e.nexttotheendevent(Figure15.1).I

2、tisessentialthateachrouteisexaminedseparatelyandwheretheroutesmeet,thelargestsumtotalmustbeinsertedinthebox.Whenthecompletenetworkhasbeensummedinthisway,theearlieststartingwillhavebeenwrittenagainsteachevent.Nowthereverseprocessmustbecarriedout.Thelasteventsu

3、misnowusedasabasefromwhichtheactivitiesleadingintoitaresubtracted.Theresultofthesesubtractionsareenteredintriangularboxesagainsteachevent(Figure15.2).Aswiththeadditionprocessforcalculatingtheearlieststartingtimes,aproblemariseswhenanodeisreachedwheretworoutes

4、oractivitiesmeet.Sincethelateststartingtimesofanactivityarerequired,thesmallestresultiswrittenagainsttheevent.ThetwodiagramsarecombinedinFigure15.3.Thedifferencebetweentheearliestandlatesttimesgivesthe‘float’,andifthisdifferenceArithmeticalanalysisFigure15.1F

5、orwardpassFigure15.2BackwardpassFigure15.3iszero(i.e.ifthenumbersinthesquaresandtrianglesarethesame)theeventisonthecriticalpath.Theequivalentprecedence(AoN)diagramisshowninFigure15.6.Atablecannowbepreparedsettingouttheresultsinaconcisemanner(Table15.1).SlackT

6、hedifferencebetweenthelatestandearliesttimesofanyeventiscalled‘slack’.Sinceeachactivityhastwoevents,abeginningeventandanend105ProjectPlanningandControlTable15.1abcdefghLatestEarliestEarliesttimetimetimeTotalFreeDuration,endendbeginningfloatfloatTitleActivityD

7、eventeventevent(d-f-c)(e-f-c)A1–2333000B2–3588300DUMMY2–50113380C3–421010800E3–631311820F4–7414141000D5–621311386G6–7114141122Columna:activitiesbytheactivitytitles.Columnb:activitiesbytheeventnumbers.Columnc:activitydurations,D.Columnd:latesttimeoftheactiviti

8、es’endevent,TLE.Columne:earliesttimeoftheactivities’endevent,TEE.Columnf:earliesttimeoftheactivities’beginningevent,TEB.Columng:totalfloatoftheactivity.Columnh:freefloatoftheactivity.even