A new sufficient condition of optimality for the two-machine flowshop problem

This paper focuses on the characterization of a subset of optimal sequences for the famous two-machine flowshop problem. Based on the relative order of the job processing times, two particular interval structures are defined so that each job is associated with an interval. Then, using the Allen’s algebra, the interval relationships are analysed and a sufficient optimality condition is established providing a characterization of a large subset of optimal sequences. This set necessarily includes any Johnson’s sequences together with numerous other optimal job sequences.