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Proportionate flow shop: New complexity results and models with due date assignment

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  • S.S. Panwalkar
  • Christos Koulamas

Abstract

It is known that the proportionate flow shop minimum makespan F m / p r p t / C max problem is solved optimally by any permutation job sequence. We show that the F m / p r p t / C max problem is at least ordinary NP‐hard when missing operations are allowed and present some solvable cases. We then consider the standard proportionate flow shop problem (with no missing operations) and show that the solution algorithms for a class of single‐machine due date assignment problems can be extended/generalized to the corresponding proportionate flow shop problems. © 2015 Wiley Periodicals, Inc. Naval Research Logistics 62: 98–106, 2015

Suggested Citation

  • S.S. Panwalkar & Christos Koulamas, 2015. "Proportionate flow shop: New complexity results and models with due date assignment," Naval Research Logistics (NRL), John Wiley & Sons, vol. 62(2), pages 98-106, March.
    • Handle: RePEc:wly:navres:v:62:y:2015:i:2:p:98-106
    DOI: 10.1002/nav.21615
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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. Kyparisis, George J. & Koulamas, Christos, 2000. "Flow shop and open shop scheduling with a critical machine and two operations per job," European Journal of Operational Research, Elsevier, vol. 127(1), pages 120-125, November.
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    6. S. S. Panwalkar & M. L. Smith & C. R. Woollam, 1981. "Counterexamples to optimal permutation schedules for certain flow shop problems," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 28(2), pages 339-340, June.
    7. S. S. Panwalkar & M. L. Smith & A. Seidmann, 1982. "Common Due Date Assignment to Minimize Total Penalty for the One Machine Scheduling Problem," Operations Research, INFORMS, vol. 30(2), pages 391-399, April.
    8. Koulamas, Christos, 2011. "A unified solution approach for the due date assignment problem with tardy jobs," International Journal of Production Economics, Elsevier, vol. 132(2), pages 292-295, August.
    9. 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.
    10. N. Hefetz & I. Adiri, 1982. "A note on the influence of missing operations on scheduling problems," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 29(3), pages 535-539, September.
    11. Michael Pinedo, 1982. "Minimizing the Expected Makespan in Stochastic Flow Shops," Operations Research, INFORMS, vol. 30(1), pages 148-162, February.
    12. 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. Koulamas, Christos & Kyparisis, George J., 2023. "A classification of dynamic programming formulations for offline deterministic single-machine scheduling problems," European Journal of Operational Research, Elsevier, vol. 305(3), pages 999-1017.
    2. S.S. Panwalkar & Christos Koulamas, 2015. "On equivalence between the proportionate flow shop and single‐machine scheduling problems," Naval Research Logistics (NRL), John Wiley & Sons, vol. 62(7), pages 595-603, October.

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