Short shop schedules

D.P. Williamson, L.A. Hall, J.A. Hoogeveen, J.K. Lenstra, D.B. Shmoys

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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.
Original languageEnglish
Place of PublicationEindhoven
PublisherTechnische Universiteit Eindhoven
Number of pages15
Publication statusPublished - 1994

Publication series

NameMemorandum COSOR
ISSN (Print)0926-4493


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