This paper studies the problem of scheduling three-operation jobs in a two-machine flowshop subject to a predetermined job processing sequence. Each job has two preassigned operations, which are to be performed on their respective dedicated machines, and a flexible operation, which may be processed on either of the two machines subject to the processing order as specified. Five standard objective functions, including the makespan, the maximum lateness, the total weighted completion time, the total weighted tardiness, and the weighted number of tardy jobs are considered. We show that the studied problem for either of the five considered objective functions is ordinary NP-hard, even if the processing times of the preassigned operations are zero for all jobs. A pseudo-polynomial time dynamic programming framework, coupled with brief numerical experiments, is then developed for all the addressed performance metrics with different run times.
Flowshop Three-operation job Fixed job sequence NP-hardness Dynamic program
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The authors are grateful to the editors and the anonymous reviewers for their constructive comments that have improved earlier versions of this paper. Lin was partially supported by the Ministry of Science and Technology of Taiwan under the Grant MOST 104-2410-H-009-029-MY2.
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