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Short Shop Schedules

Author

Listed:
  • D. P. Williamson

    (IBM Watson, Yorktown Heights, New York)

  • L. A. Hall

    (The Johns Hopkins University, Baltimore, Maryland)

  • J. A. Hoogeveen

    (Eindhoven University of Technology, Amsterdam, The Netherlands)

  • C. A. J. Hurkens

    (Eindhoven University of Technology, Amsterdam, The Netherlands)

  • J. K. Lenstra

    (Eindhoven University of Technology, Eindhoven, The Netherlands, and CWI, Amsterdam, The Netherlands)

  • S. V. Sevast'janov

    (Institute of Mathematics, Novosibirsk, Russia)

  • D. B. Shmoys

    (Cornell University, Ithaca, New York)

Abstract

We consider the open shop, job shop, and flow shop scheduling problems with integral processing times. We give polynomial-time algorithms to determine if an instance has a schedule of length at most 3, and show that deciding if there is a schedule of length at most 4 is (N-script)(P-script)-complete. The latter result implies that, unless (P-script) = (N-script)(P-script), there does not exist a polynomial-time approximation algorithm for any of these problems that constructs a schedule with length guaranteed to be strictly less than 5/4 times the optimal length. This work constitutes the first nontrivial theoretical evidence that shop scheduling problems are hard to solve even approximately.

Suggested Citation

  • 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.
    • Handle: RePEc:inm:oropre:v:45:y:1997:i:2:p:288-294
    DOI: 10.1287/opre.45.2.288
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