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A fully polynomial time approximation scheme for scheduling on parallel identical two-stage openshops

Author

Listed:
  • Jianming Dong

    (Zhejiang Sci-Tech University
    University of Alberta)

  • Ruyan Jin

    (Zhejiang Sci-Tech University)

  • Jueliang Hu

    (Zhejiang Sci-Tech University
    University of Alberta)

  • Guohui Lin

    (University of Alberta)

Abstract

A two-stage openshop consists of a machine in the first stage and a machine in the second stage; a job processed on the two-stage openshop means it is processed non-preemptively by each of the two machines, in whichever order. We consider the scheduling problem at the availability of multiple parallel identical two-stage openshops, with the goal to minimize the makespan. By uncovering the important role of the critical job in the optimal schedule on a two-stage openshop, we propose to sort the jobs in the novel critical-job order, and use this order to design a pseudo-polynomial time dynamic programming exact algorithm to solve our scheduling problem with any fixed number of two-stage openshops. Afterwards, using the standard scaling technique, we develop the dynamic programming algorithm into a fully polynomial-time approximation scheme. These results improve previously proposed constant ratio approximation algorithms.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:jcomop:v:37:y:2019:i:2:d:10.1007_s10878-018-0314-6
    DOI: 10.1007/s10878-018-0314-6
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    References listed on IDEAS

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    1. Chen, Bo & Strusevich, Vitaly A., 1993. "Worst-case analysis of heuristics for open shops with parallel machines," European Journal of Operational Research, Elsevier, vol. 70(3), pages 379-390, November.
    2. Teofilo Gonzalez & Sartaj Sahni, 1978. "Flowshop and Jobshop Schedules: Complexity and Approximation," Operations Research, INFORMS, vol. 26(1), pages 36-52, February.
    3. 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.
    4. 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.
    5. D. P. Williamson & L. A. Hall & J. A. Hoogeveen & C. A. J. Hurkens & J. K. Lenstra & S. V. Sevast'janov & D. B. Shmoys, 1997. "Short Shop Schedules," Operations Research, INFORMS, vol. 45(2), pages 288-294, April.
    6. 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.
    7. Bo Chen & Celia A. Glass & Chris N. Potts & Vitaly A. Strusevich, 1996. "A New Heuristic for Three-Machine Flow Shop Scheduling," Operations Research, INFORMS, vol. 44(6), pages 891-898, December.
    8. M. R. Garey & D. S. Johnson & Ravi Sethi, 1976. "The Complexity of Flowshop and Jobshop Scheduling," Mathematics of Operations Research, INFORMS, vol. 1(2), pages 117-129, May.
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    Cited by:

    1. Zeynep Adak & Mahmure Övül Arıoğlu Akan & Serol Bulkan, 0. "Multiprocessor open shop problem: literature review and future directions," Journal of Combinatorial Optimization, Springer, vol. 0, pages 1-23.
    2. Zeynep Adak & Mahmure Övül Arıoğlu Akan & Serol Bulkan, 2020. "Multiprocessor open shop problem: literature review and future directions," Journal of Combinatorial Optimization, Springer, vol. 40(2), pages 547-569, August.

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