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Approximation algorithms for the parallel flow shop problem

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  • Zhang, Xiandong
  • van de Velde, Steef
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    Abstract

    We consider the NP-hard problem of scheduling n jobs in m two-stage parallel flow shops so as to minimize the makespan. This problem decomposes into two subproblems: assigning the jobs to parallel flow shops; and scheduling the jobs assigned to the same flow shop by use of Johnson’s rule. For m=2, we present a 32-approximation algorithm, and for m=3, we present a 127-approximation algorithm. Both these algorithms run in O(nlogn) time. These are the first approximation algorithms with fixed worst-case performance guarantees for the parallel flow shop problem.

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    File URL: http://www.sciencedirect.com/science/article/pii/S0377221711007193
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    Bibliographic Info

    Article provided by Elsevier in its journal European Journal of Operational Research.

    Volume (Year): 216 (2012)
    Issue (Month): 3 ()
    Pages: 544-552

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    Handle: RePEc:eee:ejores:v:216:y:2012:i:3:p:544-552

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    Web page: http://www.elsevier.com/locate/eor

    Related research

    Keywords: Scheduling; Parallel flow shop; Hybrid flow shop; Approximation algorithms; Worst-case analysis;

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    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. 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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    Cited by:
    1. Mao, Kun & Pan, Quan-ke & Pang, Xinfu & Chai, Tianyou, 2014. "A novel Lagrangian relaxation approach for a hybrid flowshop scheduling problem in the steelmaking-continuous casting process," European Journal of Operational Research, Elsevier, vol. 236(1), pages 51-60.

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