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Minimizing makespan in an ordered flow shop with machine-dependent processing times

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  • Byung-Cheon Choi

    (Chungnam National University)

  • Joseph Y.-T. Leung

    (New Jersey Institute of Technology)

  • Michael L. Pinedo

    (New York University)

Abstract

We consider a generalization of the proportionate flow shop problem with the makespan objective. Each job has a processing requirement and each machine has a characteristic value. In our case, we assume that the time a job occupies a machine is equal to the processing requirement of the job plus a setup time that is equal to the characteristic value of that machine. In this paper, we consider permutation schedules and show that the problem is solvable in polynomial time when the number of machines is fixed.

Suggested Citation

  • Byung-Cheon Choi & Joseph Y.-T. Leung & Michael L. Pinedo, 2011. "Minimizing makespan in an ordered flow shop with machine-dependent processing times," Journal of Combinatorial Optimization, Springer, vol. 22(4), pages 797-818, November.
    • Handle: RePEc:spr:jcomop:v:22:y:2011:i:4:d:10.1007_s10878-010-9330-x
    DOI: 10.1007/s10878-010-9330-x
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    References listed on IDEAS

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    1. M. L. Smith & S. S. Panwalkar & R. A. Dudek, 1975. "Flowshop Sequencing Problem with Ordered Processing Time Matrices," Management Science, INFORMS, vol. 21(5), pages 544-549, January.
    2. M. L. Smith & S. S. Panwalkar & R. A. Dudek, 1976. "Flowshop sequencing problem with ordered processing time matrices: A general case," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 23(3), pages 481-486, September.
    3. J. A. Hoogeveen & T. Kawaguchi, 1999. "Minimizing Total Completion Time in a Two-Machine Flowshop: Analysis of Special Cases," Mathematics of Operations Research, INFORMS, vol. 24(4), pages 887-910, November.
    4. Koulamas, Christos & Kyparisis, George J., 2009. "A note on the proportionate flow shop with a bottleneck machine," European Journal of Operational Research, Elsevier, vol. 193(2), pages 644-645, March.
    5. Biskup, Dirk, 2008. "A state-of-the-art review on scheduling with learning effects," European Journal of Operational Research, Elsevier, vol. 188(2), pages 315-329, July.
    6. Peng Si Ow, 1985. "Focused Scheduling in Proportionate Flowshops," Management Science, INFORMS, vol. 31(7), pages 852-869, July.
    7. S. M. Johnson, 1954. "Optimal two‐ and three‐stage production schedules with setup times included," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 1(1), pages 61-68, March.
    8. M. R. Garey & D. S. Johnson & Ravi Sethi, 1976. "The Complexity of Flowshop and Jobshop Scheduling," Mathematics of Operations Research, INFORMS, vol. 1(2), pages 117-129, May.
    9. Choi, Byung-Cheon & Yoon, Suk-Hun & Chung, Sung-Jin, 2007. "Minimizing maximum completion time in a proportionate flow shop with one machine of different speed," European Journal of Operational Research, Elsevier, vol. 176(2), pages 964-974, January.
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    Cited by:

    1. Yu, Tae-Sun & Han, Jun-Hee, 2021. "Scheduling proportionate flow shops with preventive machine maintenance," International Journal of Production Economics, Elsevier, vol. 231(C).
    2. Bing Wang & Xingbao Han & Xianxia Zhang & Shaohua Zhang, 2015. "Predictive-reactive scheduling for single surgical suite subject to random emergency surgery," Journal of Combinatorial Optimization, Springer, vol. 30(4), pages 949-966, November.
    3. Chung, Dae-Young & Choi, Byung-Cheon, 2013. "Outsourcing and scheduling for two-machine ordered flow shop scheduling problems," European Journal of Operational Research, Elsevier, vol. 226(1), pages 46-52.
    4. S.S. Panwalkar & Milton L. Smith & Christos Koulamas, 2013. "Review of the ordered and proportionate flow shop scheduling research," Naval Research Logistics (NRL), John Wiley & Sons, vol. 60(1), pages 46-55, February.

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