Total flowtime in no-wait flowshops with separated setup times

An important class of scheduling problems is characterized by a no-wait constraint where the jobs have to be processed continuously without waiting between or on consecutive machines. This constraint of no-waiting arises from the characteristics of the processing technology itself. Considering setup times separate from processing times of the jobs forms another important class of scheduling problems. This is particularly important when the ratio of the setup time to the processing time is non-negligible. This paper addresses a scheduling problem which falls in the combined category of no-wait and separate setup times. The performance measure considered is the total flowtime. This paper addresses the two-machine no-wait flowshop problem where the setup time of a job is separated from its processing time. The performance measure considered is the total flowtime. An elimination criterion is developed and optimal solutions are obtained for two special cases. For the generic case, a heuristic algorithm is provided. Computational experience shows that the algorithm yields good solutions.