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Approximation algorithms for the parallel flow shop problem

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  • Zhang, Xiandong
  • van de Velde, Steef

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.

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

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    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. Jianming Dong & Joshua Chang & Bing Su & Jueliang Hu & Guohui Lin, 2020. "Two-stage open-shop scheduling with a two-machine flow shop as a stage: approximation algorithms and empirical experiments," Journal of Scheduling, Springer, vol. 23(5), pages 595-608, October.
    2. Jianming Dong & Ruyan Jin & Jueliang Hu & Guohui Lin, 2019. "A fully polynomial time approximation scheme for scheduling on parallel identical two-stage openshops," Journal of Combinatorial Optimization, Springer, vol. 37(2), pages 668-684, February.
    3. 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.
    4. Perez-Gonzalez, Paz & Framinan, Jose M., 2024. "A review and classification on distributed permutation flowshop scheduling problems," European Journal of Operational Research, Elsevier, vol. 312(1), pages 1-21.

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