A Study of On-Line Scheduling Two-Stage Shops

  • Bo Chen
  • Gerhard J. Woeginger
Part of the Nonconvex Optimization and Its Applications book series (NOIA, volume 4)

Abstract

We investigate the problem of on-line scheduling two-stage shops with the objective of minimizing the maximum completion time. We show that for two-stage open shops, no on-line algorithm can have a worst-case performance ratio less than \(\tfrac{1}{2}(1 + \sqrt {5} ) \approx 1.618\) if preemption is not allowed. We provide an on-line heuristic algorithm with worst-case performance ratio 1.875. If preemption is allowed, however, we give an on-line algorithm with worst-case performance ratio 4/3, and show that it is a best possible on-line algorithm. On the other hand, for a two-stage flow shop or job shop, we prove that no on-line algorithm can outperform a simple one, which has a worst-case performance ratio of 2.

Keywords

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References

  1. 1.
    S. Ben-David, A. Borodin, R. Karp, G. Tardos and A. Widgerson, On the power of randomization in on-line algorithms, Proc. 22nd Annual Symp. on Theory of Computing, 1990, 379–386.Google Scholar
  2. 2.
    M. Garey, D.S. Johnson and R. Sethi, The complexity of flowshop and jobshop scheduling, Math. Oper. Res. 1, 1976, 117–129.MathSciNetMATHCrossRefGoogle Scholar
  3. 3.
    T. Gonzalez and S. Sahni, Open shop scheduling to minimize finish time, Journal ACM 23, 1976, 665–679.MathSciNetMATHCrossRefGoogle Scholar
  4. 4.
    T. Gonzalez and S. Sahni, Flowshop and jobshop schedules: complexity and approximation, Oper. Res. 26, 1978, 36–52.MathSciNetMATHCrossRefGoogle Scholar
  5. 5.
    E.L. Lawler, J.K. Lenstra, A.H.G. Rinnooy Kan and D.B. Shmoys, Sequencing and scheduling: algorithms and complexity, Handbooks in Operations Research and Management Science, Vol. 4: Logistics of Production and Inventory (S.C. Graves, A.H.G. Rinnooy Kan and P. Zipkin, Eds. ), North-Holland, 1993, 445–522.CrossRefGoogle Scholar
  6. 6.
    J.R. Jackson, An extension of Johnson’s results on job lot scheduling, Naval Res. Logist. Quart. 3, 1956, 201–203.CrossRefGoogle Scholar
  7. 7.
    S.M. Johnson, Optimal two- and three-stage production schedules with setup times included, Naval Res. Logist. Quart. 1, 1954, 61–68.CrossRefGoogle Scholar

Copyright information

© Kluwer Academic Publishers 1995

Authors and Affiliations

  • Bo Chen
    • 1
  • Gerhard J. Woeginger
    • 2
  1. 1.Warwick Business SchoolUniversity of WarwickCoventryUK
  2. 2.Institut für MathematikTU GrazGrazAustria

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