Advertisement

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
  • 41 Downloads

Abstract

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.

Keywords

Flowshop Coupled-operations Complexity Polynomial time algorithms 

Notes

Acknowledgements

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.

References

  1. Ageev, A. (2008). A \(\frac{3}{2}\)-approximation for the proportionate two-machine flow shop scheduling with minimum delays. In Lecture Notes in Computer Science (Vol. 4927, pp. 55–66).Google Scholar
  2. Ageev, A. A., & Baburin, A. E. (2007). Approximation algorithms for UET scheduling problems with exact delays. Operations Research Letters, 35, 533–540.CrossRefGoogle Scholar
  3. Ageev, A. A., & Kononov, A. V. (2007). Approximation algorithms for scheduling problems with exact delays. In WAOA 2006, LNCS (Vol. 4368, pp. 1–14).Google Scholar
  4. Ahr, D., Békési, J., Galambos, G., Oswald, M., & Reinelt, G. (2004). An exact algorithm for scheduling identical coupled tasks. Mathematical Methods of Operational Research, 59, 193–203.CrossRefGoogle Scholar
  5. Blazewicz, J., Ecker, K., Kis, T., Potts, C. N., Tanas, M., & Whitehead, J. (2010). Scheduling of coupled tasks with unit processing times. Journal of Scheduling, 13, 453–461.CrossRefGoogle Scholar
  6. Blazewicz, J., Pawlak, G., Tanas, M., & Wojciechowicz, W. (2012). New algorithms for coupled tasks scheduling—A survey. RAIRO - Operations Research, 46(04), 335–353.CrossRefGoogle Scholar
  7. Brauner, N., Finke, G., Lehoux-Lebacque, V., Potts, C., & Whitehead, J. (2009). Scheduling of coupled tasks and one-machine no-wait robotic cells. Computers and Operational Research, 36(2), 301–307.CrossRefGoogle Scholar
  8. Chu C., & Proth, J.-M. (1994). Sequencing with chain structured precedence constraints and minimal and maximal separation times. In Proceedings of the fourth international conference on computer integrated manufacturing and automation technology (pp. 333–338).Google Scholar
  9. Dell’Amico, M. (1996). Shop problems with two machines and time lags. Operations Research, 44(5), 777–787.CrossRefGoogle Scholar
  10. Fondrevelle, J., Oulamara, A., & Portmann, M. C. (2006). Permutation flowshop scheduling problem with maximal and minimal time lags. Computers and Operations Research, 33, 1540–1556.CrossRefGoogle Scholar
  11. Fondrevelle, J., Oulamara, A., & Portmann, M. C. (2008). Permutation flow shop scheduling problems with time lags to minimize the weighted sum of machine completion times. International Journal of Production Economics, 112, 168–176.CrossRefGoogle Scholar
  12. Garey M. R., & Johnson D. S. (1979). Computers and intractability: A guide to the theory of NP-completeness, V. Klee (Ed.). A series of books in the mathematical sciences. San Francisco, CA: W.H. Freeman and Co.Google Scholar
  13. Johnson, S. M. (1954). Optimal two and three stage production schedules with setup time included. Naval Research Logistics Quarterly, 1, 61–67.CrossRefGoogle Scholar
  14. Karuno, Y., & Nagamochi, H. (2003). A better approximation for the two-machine flowshop scheduling problem with time lags. In Algorithms and computation: 14th international symposium, ISAAC 2003, Kyoto, Japan, December 15–17, 2003.Google Scholar
  15. Mitten, L. G. (1958). Sequencing \(n\) jobs on two jobs with arbitrary time lags. Management Science, 5(3), 293–298.CrossRefGoogle Scholar
  16. Orman, A. J., & Potts, C. N. (1997). On the complexity of coupled-task scheduling. Discrete Applied Mathematics, 72, 141–154.CrossRefGoogle Scholar
  17. Shapiro, R. D. (1980). Scheduling coupled tasks. Naval Research Logistics Quarterly, 20, 489–498.CrossRefGoogle Scholar
  18. Simonin, G., Giroudeau, R., & Konig, J. C. (2010). Polynomial-time algorithms for scheduling problem for coupled-tasks in presence of treatment tasks. Electronic Notes in Discrete Mathematics, 36, 647–654.CrossRefGoogle Scholar
  19. Yu, W., Hoogeveen, H., & Lenstra, J. K. (2004). Minimizing makespan in a two-machine flow shop with delays and unit-time operations is NP-hard. Journal of Scheduling, 7, 333–348.CrossRefGoogle Scholar

Copyright information

© 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

Personalised recommendations