OR Spectrum

, Volume 40, Issue 3, pp 809–829 | Cite as

Flow shop scheduling with flexible processing times

  • Matthias Bultmann
  • Sigrid Knust
  • Stefan Waldherr
Regular Article


In numerous flow shop variants, the processing times of the operations are not fixed in advance, but may be distributed with some flexibility among the machines. In this paper, we introduce a general model which is expressive enough to cover several models from the literature. While in most cases it is \(\mathcal {NP}\)-hard to find a job permutation and a corresponding distribution of processing times minimizing the makespan, we show that for a fixed job permutation a best processing time distribution can be calculated in polynomial time by linear programming. Based on this, we propose a tabu search procedure using the set of all job permutations as search space. In a computational study, we show the power of the new model. Besides the classical permutation flow shop environment, we study variants with blocking, no-wait and synchronous movement constraints.


Scheduling Flow shop Flexible processing times Processing time redistribution 



This work was supported by the Deutsche Forschungsgemeinschaft, KN 512/7-1. The work of Stefan Waldherr was supported by the TUM Institute for Advanced Study through a Hans Fischer Senior Fellowship. The authors would like to thank two anonymous referees for their constructive comments.


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Institute of Computer ScienceUniversity of OsnabrückOsnabrückGermany
  2. 2.Department of InformaticsTechnical University of MunichMunichGermany

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