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Approximation algorithms for the parallel flow shop problem


  • Zhang, Xiandong
  • van de Velde, Steef


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.

Suggested Citation

  • Zhang, Xiandong & van de Velde, Steef, 2012. "Approximation algorithms for the parallel flow shop problem," European Journal of Operational Research, Elsevier, vol. 216(3), pages 544-552.
  • Handle: RePEc:eee:ejores:v:216:y:2012:i:3:p:544-552
    DOI: 10.1016/j.ejor.2011.08.007

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    References listed on IDEAS

    1. J.N.D. Gupta & A.M.A. Hariri & C.N. Potts, 1997. "Scheduling a two-stage hybrid flow shop with parallel machines at the first stage," Annals of Operations Research, Springer, vol. 69(0), pages 171-191, January.
    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.
    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.
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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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