Skip to main content
Log in

Parallel-machine scheduling with release dates and rejection

  • Research paper
  • Published:
4OR Aims and scope Submit manuscript

Abstract

In this paper, we consider the parallel-machine scheduling problem with release dates and rejection. A job is either rejected, in which case a rejection penalty has to be paid, or accepted and processed on one of the m identical parallel machines. The objective is to minimize the sum of the makespan of the accepted jobs and the total rejection penalty of the rejected jobs. When m is a fixed constant, we provide a pseudo-polynomial-time algorithm and a fully polynomial-time approximation scheme for the problem. When m is arbitrary, we present a 2-approximation algorithm for the problem.

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

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1

Similar content being viewed by others

References

  • Bartal Y, Leonardi S, Spaccamela AM, Sgall J, Stougie L (2000) Multi-processor scheduling with rejection. SIAM J Discret Math 13:64–78

    Article  Google Scholar 

  • Cheng YS, Sun SJ (2009) Scheduling linear deteriorating jobs with rejection on a single machine. Eur J Oper Res 194:18–27

    Article  Google Scholar 

  • Dosa G, He Y (2006) Scheduling with machine cost and rejection. J Comb Optim 12:337–350

    Article  Google Scholar 

  • Engels DW, Karger DR, Kolliopoulos SG, Sengupta S, Uma RN, Wein J (2003) Techniques for scheduling with rejection. J Algorithms 49:175–191

    Article  Google Scholar 

  • Epstein L, Noga J, Woeginger GJ (2002) On-line scheduling of unit time jobs with rejection: minimizing the total completion time. Oper Res Lett 30:415–420

    Article  Google Scholar 

  • Hoogeveen H, Skutella M, Woeginger GJ (2003) Preemptive scheduling with rejection. Math Program 94:361–374

    Article  Google Scholar 

  • Lawler EL (1973) Optimal sequencing a single machine subject to precedence constraints. Manag Sci 19:544–546

    Article  Google Scholar 

  • Lu LF, Ng CT, Zhang LQ (2011) Optimal algorithms for single-machine scheduling with rejection to minimize the makespan. Int J Prod Econ 130:153–158

    Article  Google Scholar 

  • Ma R, Yuan JJ (2013) On-line scheduling on a single machine with rejection under an agreeable condition to minimize the total completion time plus the total rejection cost. Inf Process Lett 113:593–598

    Article  Google Scholar 

  • Seiden S (2001) Preemptive multiprocessor scheduling with rejection. Theor Comput Sci 262:437–458

    Article  Google Scholar 

  • Shabtay D, Gaspar N, Kaspi M (2013) A survey on off-line scheduling with rejection. J Sched 16:3–28

    Article  Google Scholar 

  • Steiner G, Zhang R (2011) Revised delivery-time quotation in scheduling with tardiness penalties. Oper Res 59:1504–1511

    Article  Google Scholar 

  • Zhang LQ, Lu LF, Yuan JJ (2009) Single machine scheduling with release dates and rejection. Eur J Oper Res 198:975–978

    Article  Google Scholar 

Download references

Acknowledgments

This research was supported in part by NSFC (11571321), NSFC (U1504103) and NSF-Henan (15IRTSTHN006).

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Lingfa Lu.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Zhang, L., Lu, L. Parallel-machine scheduling with release dates and rejection. 4OR-Q J Oper Res 14, 165–172 (2016). https://doi.org/10.1007/s10288-016-0304-4

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10288-016-0304-4

Keywords

Mathematics Subject Classification

Navigation