Abstract
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.
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References
Crama, Y., & Gultekin, H. (2010). Throughput optimization in two-machine flowshops with flexible operations. Journal of Scheduling, 13(3), 227–243.
Gupta, J. N., Koulamas, C. P., Kyparisis, G. J., Potts, C. N., & Strusevich, V. A. (2004). Scheduling three-operation jobs in a two-machine flow shop to minimize makespan. Annals of Operations Research, 129(1), 171–185.
Gultekin, H. (2012). Scheduling in flowshops with flexible operations: Throughput optimization and benefits of flexibility. International Journal of Production Economics, 140(2), 900–911.
Hwang, F. J., Kovalyov, M. Y., & Lin, B. M. T. (2012). Total completion time minimization in two-machine flow shop scheduling problems with a fixed job sequence. Discrete Optimization, 9(1), 29–39.
Hwang, F. J., Kovalyov, M. Y., & Lin, B. M. T. (2014). Scheduling for fabrication and assembly in a two-machine flowshop with a fixed job sequence. Annals of Operations Research, 217(1), 263–279.
Johnson, S. M. (1954). Optimal two- and three-stage production schedules with setup times included. Naval Research Logistics Quarterly, 1(1), 61–68.
Lin, B. M. T., & Hwang, F. J. (2011). Total completion time minimization in a 2-stage differentiation flowshop with fixed sequences per job type. Information Processing Letters, 111(5), 208–212.
Lin, B. M. T., Hwang, F. J., & Kononov, A. V. (2016). Relocation scheduling subject to fixed processing sequences. Journal of Scheduling, 19(2), 153–163.
Shafransky, Y. M., & Strusevich, V. A. (1998). The open shop scheduling problem with a given sequence of jobs on one machine. Naval Research Logistics, 45(7), 705–731.
Uruk, Z., Gultekin, H., & Akturk, M. S. (2013). Two-machine flowshop scheduling with flexible operations and controllable processing times. Computers & Operations Research, 40(2), 639–653.
Acknowledgments
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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Lin, B.M.T., Hwang, F.J. & Gupta, J.N.D. Two-machine flowshop scheduling with three-operation jobs subject to a fixed job sequence. J Sched 20, 293–302 (2017). https://doi.org/10.1007/s10951-016-0493-x
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DOI: https://doi.org/10.1007/s10951-016-0493-x