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On-Line Scheduling of Two-Machine Open Shops Where Jobs Arrive Over Time

Author

Listed:
  • Bo Chen

    (Warwick Business School, The University of Warwick, Coventry)

  • Arjen P.A. Vestjens

    (Eindhoven University of Technology)

  • Gerhard J. Woeginger

    (Institut füur Mathematik, Graz University of Technology)

Abstract

We investigate the problem of on-line scheduling two-machine open shops with the objective of minimizing the makespan.Jobs arrive independently over time, and the existence of a job is not known until its arrival. In the clairvoyant on-line model, the processing requirement of every job becomes fully known at the arrival of the job, while inthe non-clairvoyant on-line model, this processing requirement is notknown until the job is processed and completed.In both models, scheduling of a job is irrevocable. We study the two-machine open shop problem for both models in the preemptive and in the non-preemptive version. For each of the four variants, we provide an algorithm that is best possible with respect to the worst-case performance. In the clairvoyant on-line model, the best worst-case performance ratios are 5/4 (preemptive) and 3/2 (non-preemptive), and in the non-clairvoyant on-line model, they are 3/2 (preemptive and non-preemptive).

Suggested Citation

  • Bo Chen & Arjen P.A. Vestjens & Gerhard J. Woeginger, 1998. "On-Line Scheduling of Two-Machine Open Shops Where Jobs Arrive Over Time," Journal of Combinatorial Optimization, Springer, vol. 1(4), pages 355-365, December.
    • Handle: RePEc:spr:jcomop:v:1:y:1998:i:4:d:10.1023_a:1009786526733
    DOI: 10.1023/A:1009786526733
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    References listed on IDEAS

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    1. E. L. Lawler & J. K. Lenstra & A. H. G. Rinnooy Kan, 1981. "Minimizing Maximum Lateness in a Two-Machine Open Shop," Mathematics of Operations Research, INFORMS, vol. 6(1), pages 153-158, February.
    2. Bo Chen & Vitaly A. Strusevich, 1993. "Approximation Algorithms for Three-Machine Open Shop Scheduling," INFORMS Journal on Computing, INFORMS, vol. 5(3), pages 321-326, August.
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    Cited by:

    1. Ahmadian, Mohammad Mahdi & Khatami, Mostafa & Salehipour, Amir & Cheng, T.C.E., 2021. "Four decades of research on the open-shop scheduling problem to minimize the makespan," European Journal of Operational Research, Elsevier, vol. 295(2), pages 399-426.
    2. Zhang, Xiandong & van de Velde, Steef, 2010. "On-line two-machine open shop scheduling with time lags," European Journal of Operational Research, Elsevier, vol. 204(1), pages 14-19, July.

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