Antithetic sequences in flow shop scheduling

Sequencing or scheduling problems call for specifying an order in which a set of tasks can be performed to satisfy some operating criteria. One sequencing problem that has been thoroughly investigated over the past 2 decades is the n-job, m-machine static flowshop problem with minimization of the makespan criteria. No optimizing solution approach has been developed for solving the classic static flowshop problem within polynomial time. Researchers have recently explored the possibility of specifying a range within which there is a relatively high probability that reversing a sequence will yield an antithetic sequence with a lower makespan. The range was specified in terms of the mean and standard deviation of the makespan distribution. Empirical results of this work strongly suggest that a threshold value of the makespan exists beyond which reversing a sequence with a high makespan is generally beneficial. This value can be expressed as the number of standard deviations above the mean makespan.