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Optimal Scheduling of a Two-stage Hybrid Flow Shop


  • Mohamed Haouari


  • Lotfi Hidri
  • Anis Gharbi


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

    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.
    2. 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.
    3. 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.
    4. 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.
    5. 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.
    6. 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.
    7. Brah, Shaukat A. & Hunsucker, John L., 1991. "Branch and bound algorithm for the flow shop with multiple processors," European Journal of Operational Research, Elsevier, vol. 51(1), pages 88-99, March.
    8. 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.
    9. 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.
    10. 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.
    11. 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.
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    Cited by:

    1. 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.
    2. 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.


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