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

Fennell Burns and John Rooker
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Fennell Burns: TRW Systems Group, Huntsville, Alabama
John Rooker: Science Applications, Inc., Huntsville, Alabama

Operations Research, 1976, vol. 24, issue 3, 578-580

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.

Date: 1976
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