Skip to main content
SpringerLink
Log in

Job Shop Scheduling Problems with Controllable Processing Times

  • Conference paper
  • First Online:
Theoretical Computer Science (ICTCS 2001)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2202))

Included in the following conference series:

Abstract

Most scheduling models assume that the jobs have fixed processing times. However, in real-life applications the processing time of a job often depends on the amount of resources such as facilities, manpower, funds, etc. allocated to it, and so its processing time can be reduced when additional resources are assigned to the job. A scheduling problem in which the processing times of the jobs can be reduced at some expense is called a scheduling problem with controllable processing times. In this paper we study the job shop scheduling problem under the assumption that the jobs have controllable processing times. We consider two models of controllable processing times: continuous and discrete. For both models we present polynomial time approximation schemes when the number of machines and the number of operations per job are fixed.

Partially supported by EU project APPOL, “Approximation and Online Algorithms”, IST-1999-14084.

Supported by Swiss National Science Foundation project 20-63733.00/1, “Resource Allocation and Scheduling in Flexible Manufacturing Systems”, and by the “Metaheuristics Network”, grant HPRN-CT-1999-00106.

Partially supported by Natural Sciences and Engineering Research Council of Canada grant R3050A01.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. K. M. Anstreicher, Linear programming in \( O(\tfrac{{n^3 }} {{\ln n}}L) \) operations, SIAM Journal on Optimization, Vol. 9, No. 4, (1999), pp. 803–812.

    Article  MATH  MathSciNet  Google Scholar 

  2. Z. L. Chen, Q. Lu, G. Tang, Single machine scheduling with discretely controllable processing times, Operations Research Letters, 21 (1997), pp. 69–76.

    Article  MATH  MathSciNet  Google Scholar 

  3. T. C. E. Cheng, N. Shakhlevich, Proportionate flow shop with controllable processing times, Journal of Scheduling, Volume 2, Number 6, 1999, pp. 253–265.

    Article  MATH  MathSciNet  Google Scholar 

  4. M. Grigoriadis and L. Khachiyan, Coordination complexity of parallel pricedirective decomposition, Mathematics of Operations Research, 21(2), 1996, pp. 321–340.

    MATH  MathSciNet  Google Scholar 

  5. K. Jansen, R. Solis-Oba and M. I. Sviridenko, A linear time approximation scheme for the job shop scheduling problem, Proceedings of the Second International Workshop on Approximation Algorithms (APPROX 99), 177–188.

    Google Scholar 

  6. E. L. Lawler, (1977) “Fast Approximation Algorithms for Knapsack Problems”, 18th Annual Symposium on Foundations of Computer Science, 206–213.

    Google Scholar 

  7. E. L. Lawler, J. K. Lenstra, A. H. G. Rinnooy Kan, and D. B. Shmoys, Sequencing and scheduling: Algorithms and complexity, in: Handbook in Operations Research and Management Science, Vol. 4, North-Holland, 1993, 445–522.

    Article  Google Scholar 

  8. E. Nowicki and S. Zdrzalka, A survey of results for sequencing problems with controllable processing times, Discrete Applied Mathematics, 26, 1990, pp. 271–287.

    Article  MATH  MathSciNet  Google Scholar 

  9. E. Nowicki and S. Zdrzalka, A two-machine flow shop scheduling problem with controllable job processing times, European Journal of Operational Research, 34, 1988, pp. 208–220.

    Article  MATH  MathSciNet  Google Scholar 

  10. E. Nowicki, An approximation algorithm for the m-machine permutation flow shop scheduling problem with controllable processing time, European Journal of Operational Research, 70 (1993), pp. 342–349.

    Article  MATH  Google Scholar 

  11. S. V. Sevastianov, Bounding algorithms for the routing problem with arbitrary paths and alternative servers, Cybernetics (in Russian), 22, 1986, pp. 773–780.

    Article  Google Scholar 

  12. D. B. Shmoys and E. Tardos, An approximation algorithm for the generalized assignment problem, Mathematical Programming, 62, 1993, pp. 461–470.

    Article  MathSciNet  Google Scholar 

  13. M. Trick, Scheduling multiple variable-speed machines, Operations research, 42, 1994, pp.234–248.

    MATH  Google Scholar 

  14. R. G. Vickson, Two single machine sequencing problems involving controllable job processing times, AIIE Transactions, 12, 1980, pp. 258–262.

    MathSciNet  Google Scholar 

  15. R. G. Vickson, Choosing the job sequence and processing times to minimize total processing plus flow cost on a single machine, Operations Research, 28, 1980, pp. 1155–1167.

    MATH  MathSciNet  Google Scholar 

  16. D. Williamson, L. Hall, J. Hoogeveen, C. Hurkens, J. Lenstra, S. Sevastianov, and D. Shmoys, Short shop schedules, Operations Research 45 (1997), 288–294.

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institut für Informatik und Praktische Mathematik, Universität zu Kiel, Germany

    Klaus Jansen

  2. IDSIA, Switzerland

    Monaldo Mastrolilli

  3. Department of Computer Science, The University of Western Ontario, Canada

    Roberto Solis-Oba

Authors
  1. Klaus Jansen
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Monaldo Mastrolilli
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Roberto Solis-Oba
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

Copyright information

© 2001 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Jansen, K., Mastrolilli, M., Solis-Oba, R. (2001). Job Shop Scheduling Problems with Controllable Processing Times. In: Theoretical Computer Science. ICTCS 2001. Lecture Notes in Computer Science, vol 2202. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45446-2_7

Download citation

  • DOI: https://doi.org/10.1007/3-540-45446-2_7

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-42672-1

  • Online ISBN: 978-3-540-45446-5

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation