Skip to main content
SpringerLink
Log in

Approximation Scheme for Scheduling Resumable Proportionally Deteriorating Jobs

  • Conference paper
Frontiers in Algorithmics and Algorithmic Aspects in Information and Management

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 6681))

Abstract

In this paper, we investigate the problem of scheduling resumable proportionally deteriorating jobs on a single machine with a non-availability constraint. The goal is to minimize the total completion time. We show the problem is NP-hard. Furthermore, we present a fully polynomial time approximation scheme (FPTAS).

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. Cheng, T.C.E., Ding, Q., Lin, B.M.T.: A concise survey of scheduling with time-dependent processing time. European Journal of Operation Research 152, 1–13 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  2. Garey, M.R., Johnson, D.S.: Computer and Intractability: A Guide to the Theory of NP-Completeness. Freeman, San Francisco (1979)

    MATH  Google Scholar 

  3. Graham, R.L., Lawler, E.L., Lenstra, J.K., Rinnooy Kan, A.H.G.: Optimization and approximation in deterministic sequencing and scheduling: A survey. Annals of Discrete Mathematics 5, 287–326 (1979)

    Article  MathSciNet  MATH  Google Scholar 

  4. Gawiejnowicz, S.: Scheduling deteriorating jobs subject to job or machine availability constraints. European Journal of Operational Research 180, 472–478 (2007)

    Article  MATH  Google Scholar 

  5. Gawiejnowicz, S., Kononov, A.: Complexity and approximability of scheduling resumable proportionally deteriorating jobs. European Journal of Operational Research 200, 305–308 (2010)

    Article  MATH  Google Scholar 

  6. Ji, M., He, Y., Cheng, T.C.E.: Scheduling linear deteriorating jobs with an availability constraint on a single machine. Theoretical Computer Science 362, 115–126 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  7. Ji, M., Cheng, T.C.E.: Scheduling resumable simple linear deteriorating jobs on a single machine with an availability constraint to minimize makespan. Computers & Industrial Engineering 59(4), 794–798 (2010)

    Article  Google Scholar 

  8. Mosheiov, G.: Scheduling jobs under simple linear deterioration. Computers & Operations Research 21, 653–659 (1994)

    Article  MATH  Google Scholar 

  9. Ma, Y., Chu, C., Zuo, C.: A survey of scheduling with deterministic machine availability constraints. Computers & Industrial Engineering 58, 199–211 (2010)

    Article  Google Scholar 

  10. Woeginger, G.J.: When does a dynamic programming formulation guarantee the existence of a fully polynomial time approximation scheme (FPTAS)? Informs Journal on Computing 12, 57–75 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  11. Wu, C.C., Lee, W.C.: Scheduling linear deteriorating jobs to minimize makespan with an availability constraint on a single machine. Information Processing Letters 87, 89–93 (2003)

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Faculty of Science, Ningbo University, Ningbo, 315211, China

    Wenchang Luo

  2. College of Computer Science, Zhejiang University, Hangzhou, 310027, China

    Lin Chen

Authors
  1. Wenchang Luo
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Lin Chen
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Department of Computer Science, Purdue University, 305 North University Street, 47907, West Lafayette, IN, USA

    Mikhail Atallah

  2. Department of Computer Science, Illinois Institute of Technology, 60616, Chicago, IL, USA

    Xiang-Yang Li

  3. Department of Computer Science, Montana State University, EPS 357, 59717, Bozeman, MT, USA

    Binhai Zhu

Rights and permissions

Reprints and permissions

Copyright information

© 2011 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Luo, W., Chen, L. (2011). Approximation Scheme for Scheduling Resumable Proportionally Deteriorating Jobs. In: Atallah, M., Li, XY., Zhu, B. (eds) Frontiers in Algorithmics and Algorithmic Aspects in Information and Management. Lecture Notes in Computer Science, vol 6681. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-21204-8_8

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-21204-8_8

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-21203-1

  • Online ISBN: 978-3-642-21204-8

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation