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Definition.Thecriticaltimefortheprojectisthelargestforwardcriticaltimepresentamongthetasks 5! withintheproject. P" Thenicethinghereisthatthereisasimple,efficientprocedureforfindingtasksforwardcriticaltimes: $>! nc :*&b6 `  `@EH&H!` tt` `&") n HIHIH$H$ HIHIHIHI HIHIHIHI HIHIHIHI HIHIHIHI HIHIHIHI HIHIHIHI HIHIHIHI y.1+'HIHI Example:Inthefollowingprojectwith12tasks,findtheforwardcriticaltimeforeachtask,andthe H criticaltimefortheproject. c 33@*w`C 3/b~"  `.@EH~  3 w߈ ~6 33 WeseethatT6,T10,T11andT12aresinks,sotheirforwardcriticaltimes(wellabbreviatethis_FCT_)are5, }5  8,3and7respectively.Oncewevefoundthose,wecanfindthe_FCTs_ԀofT7,T8andT9.ForT7,weneed P  tolookatthe_FCTs_ԀofT10andT11.Thelargertimeis8atT10,sothe_FCT_ԀforT7is6+8,or14.ForT8, k  witharcsgoingtoT10,T11andT12,wecomparethe_FCTs_Ԁofallthree.Thelargestisagainthe8fromT10,  sothe_FCT_ԀforT8is4+8=12.FromT9,arcsgotoT11andT12,andT12hasthelarger_FCT_Ԁof7,sothe  _FCT_ԀofT9is9+7=16.Nowthatweknowthose,wecanfindthe_FCTs_ԀofT4andT5.ForT4,thearcs  pointtoT7andT8,andthemaximum_FCT_Ԁofthoseis14,sothe_FCT_ԀofT4is14+9=23.ForT5,the   maximum_FCT_Ԁattheverticesattheendofitsarcsisthe16atT9,sothe_FCT_ԀatT5is8+16=24.Finally, :  werereadytofindthe_FCTs_ԀofT1,T2andT3.AllthreeofthemhavearcsendingatT5wherethe_FCT_Ԁis U   24,T1andT2alsohavearcsendingatT4butT4's_FCT_Ԁislower,sotheyallusethe_FCT_ԀatT5plustheir p(  owntasktime.Thatmeansthe_FCT_ԀatT1is5+24=29,atT2its7+24=31,andatT3the_FCT_Ԁis C  3+24=27. ^ Sincethelargest_FCT_Ԁforanytaskis31atT2,theentireprojecthasacriticaltimeof31andacriticalpath  startingatT2.  _nc:*&b6  `@EH. H!tt` - "n_ HIHIH$H$ HIHIHIHI HIHIHIHI HIHIHIHI HIHIHIHI HIHIHIHI HIHIHIHI HIHIHIHI H$H$HIHIFollowingthisapproach,theonlycriticalpathfortheprojectaboveisT2T5T9T12. )% Incidentally,theaboveprojecthas32maximalpaths,requiring93additionsusingthebooksapproach.