Advertisement

Journal of Scheduling

, Volume 13, Issue 5, pp 463–477 | Cite as

Parallel batch scheduling of equal-length jobs with release and due dates

  • Alessandro Condotta
  • Sigrid Knust
  • Natalia V. ShakhlevichEmail author
Article

Abstract

In this paper we study parallel batch scheduling problems with bounded batch capacity and equal-length jobs in a single and parallel machine environment. It is shown that the feasibility problem 1|p-batch,b<n,r j ,p j =p,C j d j |− can be solved in O(n 2) time and that the problem of minimizing the maximum lateness can be solved in O(n 2log n) time. For the parallel machine problem P|p-batch,b<n,r j ,p j =p,C j d j |− an O(n 3log n)-time algorithm is provided, which can also be used to solve the problem of minimizing the maximum lateness in O(n 3log 2 n) time.

Keywords

Single machine scheduling Parallel machine scheduling Parallel batching Complexity 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Baptiste, P. (2000). Batching identical jobs. Mathematical Methods of Operations Research, 52, 355–367. CrossRefGoogle Scholar
  2. Brucker, P. (2007). Scheduling algorithms. Berlin: Springer. Google Scholar
  3. Cheng, T. C. E., Yuan, J. J., & Yang, A. F. (2005). Scheduling a batch-processing machine subject to precedence constraints, release dates and identical processing times. Computers and Operations Research, 32, 849–859. CrossRefGoogle Scholar
  4. Garey, M. R., Johnson, D. S., Simons, B. B., & Tarjan, R. E. (1981). Scheduling unit-time tasks with arbitrary release times and deadlines. SIAM Journal on Computing, 10, 256–269. CrossRefGoogle Scholar
  5. Ikura, Y., & Gimple, M. (1986). Efficient scheduling algorithms for a single batch processing machine. Operations Research Letters, 5, 61–65. CrossRefGoogle Scholar
  6. Lageweg, B. J., Lenstra, J. K., & Rinnooy Kan, A. H. G. (1976). Minimizing maximum lateness on one machine: computational experience and some applications. Statistica Neerlandica, 30, 25–41. CrossRefGoogle Scholar
  7. Lawler, E. L., Lenstra, J. K., Rinnooy Kan, A. H. G., & Shmoys, D. B. (1993). Sequencing and scheduling: algorithms and complexity. In Graves, S. C., Rinnooy Kan, A. H. G., & Zipkin, P. H. (Eds.) Handbooks in operations research and management science, logistics of production and inventory (Vol. 4, pp. 445–522). Amsterdam: North-Holland. CrossRefGoogle Scholar
  8. Lee, C. Y., Uzsoy, R., & Martin-Vega, L. A. (1992). Efficient algorithms for scheduling semiconductor burn-in operations. Operations Research, 40, 764–775. CrossRefGoogle Scholar
  9. Simons, B. B. (1978). A fast algorithm for multiprocessor scheduling of unit-length jobs. In IEEE 19th annual symposium on foundations of computer science (pp. 246–252). Google Scholar
  10. Simons, B. B. (1983). Multiprocessor scheduling of unit-time jobs with arbitrary release times and deadlines. SIAM Journal on Computing, 12, 294–299. CrossRefGoogle Scholar
  11. Simons, B. B., & Warmuth, M. K. (1989). A fast algorithm for multiprocessor scheduling of unit-length jobs. SIAM Journal on Computing, 18, 690–710. CrossRefGoogle Scholar
  12. Ullman, J. D. (1975). NP-complete scheduling problems. Journal of Computer and System Sciences, 10, 384–393. CrossRefGoogle Scholar
  13. Vakhania, N. (2003). A better algorithm for sequencing with release and delivery times on identical machines. Journal of Algorithms, 48, 273–293. CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  • Alessandro Condotta
    • 1
  • Sigrid Knust
    • 2
  • Natalia V. Shakhlevich
    • 1
    Email author
  1. 1.School of ComputingUniversity of LeedsLeedsUK
  2. 2.Institute of MathematicsTechnical University of ClausthalClausthal-ZellerfeldGermany

Personalised recommendations