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Two-stage proportionate flexible flow shop to minimize the makespan

Author

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  • Byung-Cheon Choi

    (Chungnam National University)

  • Kangbok Lee

    (The State University of New Jersey)

Abstract

We consider a two-stage flexible flow shop problem with a single machine at one stage and m identical machines at the other stage, where the processing times of each job at both stages are identical. The objective is to minimize the makespan. We describe some optimality conditions and show that the problem is NP-hard when m is fixed. Finally, we present an approximation algorithm that has a worst-case performance ratio of $\frac{5}{4}$ for m=2 and $\frac{\sqrt{1+m^{2}}+1+m}{2m}$ for m≥3.

Suggested Citation

  • Byung-Cheon Choi & Kangbok Lee, 2013. "Two-stage proportionate flexible flow shop to minimize the makespan," Journal of Combinatorial Optimization, Springer, vol. 25(1), pages 123-134, January.
    • Handle: RePEc:spr:jcomop:v:25:y:2013:i:1:d:10.1007_s10878-011-9423-1
    DOI: 10.1007/s10878-011-9423-1
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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.
    2. 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.
    3. Thornton, Henry W. & Hunsucker, John L., 2004. "A new heuristic for minimal makespan in flow shops with multiple processors and no intermediate storage," European Journal of Operational Research, Elsevier, vol. 152(1), pages 96-114, January.
    4. Peng Si Ow, 1985. "Focused Scheduling in Proportionate Flowshops," Management Science, INFORMS, vol. 31(7), pages 852-869, July.
    5. Riane, Fouad & Artiba, Abdelhakim & E. Elmaghraby, Salah, 1998. "A hybrid three-stage flowshop problem: Efficient heuristics to minimize makespan," European Journal of Operational Research, Elsevier, vol. 109(2), pages 321-329, September.
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    Cited by:

    1. Anzhen Peng & Longcheng Liu & Weifeng Lin, 2021. "Improved approximation algorithms for two-stage flexible flow shop scheduling," Journal of Combinatorial Optimization, Springer, vol. 41(1), pages 28-42, January.
    2. Gerstl, Enrique & Mosheiov, Gur, 2014. "A two-stage flexible flow shop problem with unit-execution-time jobs and batching," International Journal of Production Economics, Elsevier, vol. 158(C), pages 171-178.
    3. Minghui Zhang & Yan Lan & Xin Han, 2020. "Approximation algorithms for two-stage flexible flow shop scheduling," Journal of Combinatorial Optimization, Springer, vol. 39(1), pages 1-14, January.

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