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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
Operations Research
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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Short Shop Schedules
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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 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.

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