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Technical Note—Johnson's Three-Machine Flow-Shop Conjecture

Author

Listed:
  • Fennell Burns

    (TRW Systems Group, Huntsville, Alabama)

  • John Rooker

    (Science Applications, Inc., Huntsville, Alabama)

Abstract

In an epoch-setting paper on scheduling theory, Johnson determined an efficient algorithm for solving the two-stage flow-shop problem and two special cases of the three-stage problem. In his concluding remarks he suggested another special condition in which one would obtain a three-stage solution. We give an example to show that this conjecture is not quite true. A true statement is obtained, however, by only a slight strengthening of the original. The primary issue concerns the impact of the two-stage no-preference precedent rules on the three-stage problem.

Suggested Citation

  • Fennell Burns & John Rooker, 1976. "Technical Note—Johnson's Three-Machine Flow-Shop Conjecture," Operations Research, INFORMS, vol. 24(3), pages 578-580, June.
    • Handle: RePEc:inm:oropre:v:24:y:1976:i:3:p:578-580
    DOI: 10.1287/opre.24.3.578
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    Cited by:

    1. J M Framinan & J N D Gupta & R Leisten, 2004. "A review and classification of heuristics for permutation flow-shop scheduling with makespan objective," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 55(12), pages 1243-1255, December.

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