▁that ▁each ▁node ▁is ▁represented ▁by ▁a ▁k - dimensional ▁point ▁and ▁there ▁is ▁a ▁preced ence ▁between ▁two ▁nodes ▁i ▁and ▁j ▁if f ▁for ▁any ▁dimension ▁the ▁coordinate ▁of ▁i ▁is ▁smaller ▁than ▁or ▁equal ▁to ▁the ▁one ▁of ▁j . ▁ ▁In ▁the ▁presence ▁of ▁a ▁preced ence ▁relation ▁one ▁might ▁in ▁addition ▁assume ▁time ▁l ags . ▁ ▁Let ▁ ▁denote ▁the ▁start ▁time ▁of ▁a ▁job ▁and ▁ ▁its ▁completion ▁time . ▁ ▁Then ▁the ▁preced ence ▁relation ▁ ▁implies ▁the ▁constraint ▁. ▁ ▁If ▁no ▁time ▁lag ▁ ▁is ▁specified ▁then ▁it ▁is ▁assumed ▁to ▁be ▁zero . ▁ ▁Time ▁l ags ▁can ▁be ▁positive ▁or ▁negative ▁numbers . ▁▁ ▁l ▁ ▁job ▁independent ▁time ▁l ags . ▁In ▁other ▁words ▁▁ ▁for ▁all ▁job ▁pairs ▁i , ▁j ▁and ▁a ▁given ▁number ▁l . ▁▁▁ ▁job ▁pair ▁dependent ▁arbitrary ▁time ▁l ags . ▁ ▁Transport ation ▁del ays ▁▁▁▁▁▁ ▁Between ▁the ▁completion ▁of ▁operation ▁ ▁of ▁job ▁ ▁on ▁machine ▁ ▁and ▁the ▁start ▁of ▁operation ▁ ▁of ▁job ▁ ▁on ▁machine ▁, ▁there ▁is ▁a ▁transport ation ▁delay ▁of ▁at ▁least ▁units . ▁▁▁▁ ▁Between ▁the ▁completion ▁of ▁operation ▁ ▁of ▁job ▁ ▁on ▁machine ▁ ▁and ▁the ▁start ▁of ▁operation ▁ ▁of ▁job ▁ ▁on ▁machine ▁, ▁there ▁is ▁a ▁transport ation ▁delay ▁of ▁at ▁least ▁ ▁units . ▁▁▁▁ ▁Machine ▁dependent ▁transport ation ▁delay . ▁Between ▁the ▁completion ▁of ▁operation ▁ ▁of ▁job ▁ ▁on ▁machine ▁ ▁and ▁the ▁start ▁of ▁operation ▁