Annals of Operations Research

, Volume 275, Issue 2, pp 511–530 | Cite as

Two-machine flowshop scheduling problem with coupled-operations

  • Nadjat Meziani
  • Ammar OulamaraEmail author
  • Mourad Boudhar
Original Research


This paper addresses a generalization of the coupled-operations scheduling problem in the context of a flow shop environment. We consider the two-machine scheduling problem with the objective of minimizing the makespan. Each job consists of a coupled-operation to be processed first on the first machine and a single operation to be then processed on the second machine. A coupled-operation contains two operations separated by an exact time delay. The single operation can start on the second machine only when the coupled-operation on the first machine is completed. We prove the NP-completeness of two restricted versions of the general problem, whereas we also exhibit several other well solvable cases.


Flowshop Coupled-operations Complexity Polynomial time algorithms 



The authors gratefully wish to thank the anonymous reviewers for their careful reading of this paper and for their valuable and useful comments. Their contributions greatly helped to improve the paper.


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© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  • Nadjat Meziani
    • 1
    • 3
  • Ammar Oulamara
    • 2
    Email author
  • Mourad Boudhar
    • 3
  1. 1.Abderrahmane Mira UniversityBejaiaAlgeria
  2. 2.LORIA Laboratory, UMR CNRS 75003University of LorraineVandoeuvre-lès-NancyFrance
  3. 3.RECITS Laboratory, Faculty of MathematicsUniversity of Sciences and Technology Houari Boumediene (USTHB)Bab-Ezzouar, AlgiersAlgeria

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