“…Johnson (1954) presented a seminal algorithm, referred to as Johnson's rule, that efficiently solves the problem of minimizing the makespan in a two-machine flow shop. Since the problem of minimizing the makespan in a flow shop with more than two machines is strongly NP-hard (Garey and Johnson, 1976), however, researchers have considered a flow shop with special structures for processing times, such as the ordered flow shop (Smith et al, 1975(Smith et al, , 1976 and the proportionate flow shop (Allahverdi, 1999;Hou and Hoogeveen, 2003;Ow, 1985). Smith et al (1975Smith et al ( , 1976 considered an m-machine ordered flow shop.…”