▁ 1 9 7 0 s ▁the ▁notation ▁has ▁been ▁constantly ▁extended , ▁sometimes ▁incons ist ently . ▁▁ ▁As ▁a ▁result , ▁today ▁there ▁are ▁some ▁problems ▁that ▁appear ▁with ▁distinct ▁not ations ▁in ▁several ▁papers . ▁ ▁Machine ▁environment ▁ ▁Single ▁stage ▁problems ▁ ▁Each ▁job ▁comes ▁with ▁a ▁given ▁processing ▁time . ▁▁▁ 1 ▁ ▁there ▁is ▁a ▁single ▁machine ▁ ▁P ▁ ▁there ▁are ▁ ▁parallel ▁identical ▁machines ▁ ▁Q ▁ ▁there ▁are ▁ ▁parallel ▁machines ▁with ▁different ▁given ▁spe eds , ▁length ▁of ▁job ▁ ▁on ▁machine ▁ ▁is ▁the ▁processing ▁time ▁ ▁divided ▁by ▁speed ▁. ▁ ▁R ▁ ▁there ▁are ▁ ▁parallel ▁un related ▁machines , ▁there ▁are ▁given ▁processing ▁times ▁ ▁for ▁job ▁ ▁on ▁machine ▁▁ ▁These ▁letters ▁might ▁be ▁followed ▁by ▁the ▁number ▁of ▁machines ▁which ▁is ▁then ▁fixed , ▁here ▁ ▁stands ▁then ▁for ▁a ▁fixed ▁number . ▁ ▁For ▁example , ▁ ▁is ▁the ▁problem ▁of ▁assigning ▁each ▁of ▁the ▁ ▁given ▁jobs ▁to ▁one ▁of ▁the ▁ 2 ▁given ▁machines ▁so ▁to ▁minim ize ▁the ▁maximum ▁total ▁processing ▁time ▁over ▁the ▁machines . ▁ ▁Multi - stage ▁problem ▁▁ ▁O ▁▁ ▁Open ▁shop ▁problem . ▁Every ▁job ▁ ▁consists ▁of ▁ ▁operations ▁ ▁for ▁. ▁ ▁The ▁operations ▁can ▁be ▁scheduled ▁in ▁any ▁order . ▁Operation ▁ ▁must ▁be ▁processed ▁for ▁ ▁units ▁on ▁machine ▁. ▁ ▁F ▁ ▁Flow ▁shop ▁problem . ▁Every ▁job ▁ ▁consists ▁of ▁ ▁operations ▁ ▁for ▁, ▁to ▁be ▁scheduled ▁in ▁that ▁order .