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Optimal Scheduling of a Two-stage Hybrid Flow Shop

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  • Mohamed Haouari
  • Lotfi Hidri
  • Anis Gharbi

Abstract

We present an exact branch-and-bound algorithm for the two-stage hybrid flow shop problem with multiple identical machines in each stage. The objective is to schedule a set of jobs so as to minimize the makespan. This is the first exact procedure which has been specifically designed for this strongly $$\mathcal{NP}$$ -hard problem. Among other features, our algorithm is based on the exact solution of identical parallel machine scheduling problems with heads and tails. We report the results of extensive computational experiments on instances which show that the proposed algorithm solves large-scale instances in moderate CPU time. Copyright Springer-Verlag 2006

Suggested Citation

  • Mohamed Haouari & Lotfi Hidri & Anis Gharbi, 2006. "Optimal Scheduling of a Two-stage Hybrid Flow Shop," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 64(1), pages 107-124, August.
    • Handle: RePEc:spr:mathme:v:64:y:2006:i:1:p:107-124
    DOI: 10.1007/s00186-006-0066-4
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    References listed on IDEAS

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    1. Hoogeveen, J. A. & Lenstra, J. K. & Veltman, B., 1996. "Preemptive scheduling in a two-stage multiprocessor flow shop is NP-hard," European Journal of Operational Research, Elsevier, vol. 89(1), pages 172-175, February.
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    3. Portmann, M. -C. & Vignier, A. & Dardilhac, D. & Dezalay, D., 1998. "Branch and bound crossed with GA to solve hybrid flowshops," European Journal of Operational Research, Elsevier, vol. 107(2), pages 389-400, June.
    4. Rajendran, Chandrasekharan & Chaudhuri, Dipak, 1992. "Scheduling in n-job, m-stage flowshop with parallel processors to minimize makespan," International Journal of Production Economics, Elsevier, vol. 27(2), pages 137-143, May.
    5. Carlier, J. & Pinson, E., 1994. "Adjustment of heads and tails for the job-shop problem," European Journal of Operational Research, Elsevier, vol. 78(2), pages 146-161, October.
    6. Joseph Adams & Egon Balas & Daniel Zawack, 1988. "The Shifting Bottleneck Procedure for Job Shop Scheduling," Management Science, INFORMS, vol. 34(3), pages 391-401, March.
    7. Sriskandarajah, C. & Sethi, S. P., 1989. "Scheduling algorithms for flexible flowshops: Worst and average case performance," European Journal of Operational Research, Elsevier, vol. 43(2), pages 143-160, November.
    8. Mohamed Haouari & Anis Gharbi, 2004. "Lower Bounds for Scheduling on Identical Parallel Machines with Heads and Tails," Annals of Operations Research, Springer, vol. 129(1), pages 187-204, July.
    9. Moursli, O. & Pochet, Y., 2000. "A branch-and-bound algorithm for the hybrid flowshop," International Journal of Production Economics, Elsevier, vol. 64(1-3), pages 113-125, March.
    10. Lin, Hung-Tso & Liao, Ching-Jong, 2003. "A case study in a two-stage hybrid flow shop with setup time and dedicated machines," International Journal of Production Economics, Elsevier, vol. 86(2), pages 133-143, November.
    11. Carlier, Jacques, 1987. "Scheduling jobs with release dates and tails on identical machines to minimize the makespan," European Journal of Operational Research, Elsevier, vol. 29(3), pages 298-306, June.
    12. Néron, Emmanuel & Baptiste, Philippe & Gupta, Jatinder N. D., 2001. "Solving hybrid flow shop problem using energetic reasoning and global operations," Omega, Elsevier, vol. 29(6), pages 501-511, December.
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    Cited by:

    1. Fan Yang & Roel Leus, 2021. "Scheduling hybrid flow shops with time windows," Journal of Heuristics, Springer, vol. 27(1), pages 133-158, April.
    2. Haouari, Mohamed & Hidri, Lotfi, 2008. "On the hybrid flowshop scheduling problem," International Journal of Production Economics, Elsevier, vol. 113(1), pages 495-497, May.
    3. Ruiz, Rubén & Vázquez-Rodríguez, José Antonio, 2010. "The hybrid flow shop scheduling problem," European Journal of Operational Research, Elsevier, vol. 205(1), pages 1-18, August.
    4. R. Hansmann & T. Rieger & U. Zimmermann, 2014. "Flexible job shop scheduling with blockages," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 79(2), pages 135-161, April.
    5. Berghman, Lotte & Leus, Roel, 2015. "Practical solutions for a dock assignment problem with trailer transportation," European Journal of Operational Research, Elsevier, vol. 246(3), pages 787-799.
    6. Lotte Berghman & Roel Leus & Frits Spieksma, 2014. "Optimal solutions for a dock assignment problem with trailer transportation," Annals of Operations Research, Springer, vol. 213(1), pages 3-25, February.

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