▁be ▁scheduled ▁on ▁one ▁machine ▁out ▁of ▁a ▁given ▁set ▁. ▁ ▁Sometimes ▁also ▁denoted ▁by ▁' M _ j '. ▁ ▁Object ive ▁functions ▁▁ ▁Usually ▁the ▁goal ▁is ▁to ▁minim ize ▁some ▁objective ▁value . ▁One ▁difference ▁is ▁the ▁notation ▁ ▁where ▁the ▁goal ▁is ▁to ▁maxim ize ▁the ▁number ▁of ▁jobs ▁that ▁complete ▁before ▁their ▁dead line . ▁This ▁is ▁also ▁called ▁the ▁through put . ▁ ▁The ▁objective ▁value ▁can ▁be ▁sum , ▁possibly ▁weight ed ▁by ▁some ▁given ▁priority ▁weights ▁ ▁per ▁job . ▁▁ ▁- ▁ ▁The ▁absence ▁of ▁an ▁objective ▁value ▁is ▁denoted ▁by ▁a ▁single ▁dash . ▁This ▁means ▁that ▁the ▁problem ▁consists ▁simply ▁in ▁producing ▁a ▁feas ible ▁sched uling , ▁satisfying ▁all ▁given ▁constraints . ▁▁▁ ▁This ▁denotes ▁the ▁completion ▁time ▁of ▁job ▁. ▁▁▁ ▁The ▁flow ▁time ▁of ▁a ▁job ▁is ▁difference ▁between ▁its ▁completion ▁time ▁and ▁its ▁release ▁time , ▁i . e . ▁. ▁▁▁▁ ▁L aten ess . ▁Every ▁job ▁ ▁is ▁given ▁a ▁due ▁date ▁. ▁The ▁laten ess ▁of ▁job ▁ ▁is ▁defined ▁as ▁. ▁ ▁Sometimes ▁ ▁is ▁used ▁to ▁denote ▁feas ibility ▁for ▁a ▁problem ▁with ▁dead lines . ▁Indeed ▁using ▁binary ▁search , ▁the ▁complexity ▁of ▁the ▁feas ibility ▁version ▁is ▁equivalent ▁to ▁the ▁minim ization ▁of ▁. ▁▁▁ ▁Through put . ▁Every ▁job ▁is ▁given ▁a ▁due ▁date ▁. ▁ ▁There ▁is ▁a ▁unit ▁profit ▁for ▁jobs ▁that ▁complete ▁one ▁time , ▁i . e . ▁ ▁if ▁ ▁and ▁▁ ▁otherwise .