Advertisement

Journal of Scheduling

, Volume 18, Issue 3, pp 311–314 | Cite as

A cyclical search for the two machine flow shop and open shop to minimise finishing time

  • Alan J. SoperEmail author
Article

Abstract

This paper considers scheduling problems on two machines to minimise the makespan. It shows that a simple cyclical search can find a flow shop schedule with one job omitted with makespan less than or equal to the maximum of the total processing time of all jobs on either machine. This flow shop schedule is used as the basis for constructing a number of schedules with minimum makespan for the two machine open shop. The search may be applied unchanged to batches of jobs to provide more optimal schedules.

Keywords

Flow shop Open shop Minimum makespan 

Notes

Acknowledgments

The author is grateful for the comments of the reviewer for helping to improve the presentation of this manuscript.

References

  1. de Werra, D. (1989). Graph-theoretical models for preemptive scheduling. In R. Slowinski & J. Weglarz (Eds.), Advances in project scheduling (pp. 171–185). Amsterdam: Elsevier.Google Scholar
  2. Gonzalez, T., & Sahni, S. (1976). Open shop scheduling to minimize finish time. J Assoc Comput Mach, 23, 665–679. Google Scholar
  3. Gribkovskaia, I. V., Lee, C.-Y., Strusevich, V. A., & de Werra, D. (2006). Three is easy, two is hard: open shop sum-batch scheduling problem refined. Oper Res Lett, 34, 459–464.Google Scholar
  4. Johnson, S. M. (1954). Optimal two- and three-stage production schedules with setup times included. Naval Res Logist Quart, 1, 61–68.CrossRefGoogle Scholar
  5. Pinedo, M., & Schrage, L. (1982). Stochastic shop scheduling a survey. In M. A. H. Dempster, E. L. Lawler, J. K. Lenstra, & A. H. G. Rinnooy Kan (Eds.), Deterministic and stochastic scheduling (pp. 181–196). Dordrecht: Riedel.CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  1. 1.School of Computing and Mathematical SciencesUniversity of GreenwichLondonUK

Personalised recommendations