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Short Shop Schedules
D. P. Williamson, L. A. Hall, J. A. Hoogeveen, C. A. J. Hurkens, J. K. Lenstra, S. V. Sevast'janov and D. B. Shmoys
Vol. 45, No. 2 (Mar. - Apr., 1997), pp. 288-294
Published by: INFORMS
Stable URL: http://www.jstor.org/stable/171745
Page Count: 7
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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 NP-complete. The latter result implies that, unless P=NP, 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.
Operations Research © 1997 INFORMS