Skip to main content
SpringerLink
Log in

Efficient Approximation Schemes for Scheduling Problems with Release Dates and Delivery Times

  • Published:
Journal of Scheduling Aims and scope Submit manuscript

Abstract

We consider the problem of scheduling n independent jobs on m identical machines that operate in parallel. Each job must be processed without interruption for a given amount of time on any one of the m machines. In addition, each job has a release date, when it becomes available for processing, and, after completing its processing, requires an additional delivery time. The objective is to minimize the time by which all jobs are delivered. In the notation of Graham et al. (1979), this problem is noted P|r j|Lmax. We develop a polynomial time approximation scheme whose running time depends only linearly on n. This linear complexity bound gives a substantial improvement of the best previously known polynomial bound (Hall and Shmoys, 1989). Finally, we discuss the special case of this problem in which there is a single machine and present an improved approximation scheme.

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

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Similar content being viewed by others

REFERENCES

  • Alon, N., Y. Azar, G. J. Woeginger, and T. Yadid, “Approximation schemes for scheduling on parallel machines,” J. Sched., 1, 55–66 (1998).

    Google Scholar 

  • Cesati, M. and L. Trevisan, “On the efficiency of polynomial time approximation schemes,” Inform. Process. Lett., 64, 165–171 (1997).

    Google Scholar 

  • Garey, M. R. and D. S. Johnson, Computers and Intractability; A Guide to the Theory of NP-Completeness, W. H. Freeman, Freeman and Co., 1979.

  • Graham, R., E. Lawler, J. Lenstra, and A. R. Kan, “Optimization and approximation in deterministic sequencing and scheduling: A survey,” in Annals of Discrete Mathematics, Vol. 5, North-Holland, 1979, pp. 287–326.

  • Hall, L., and D. Shmoys, “Approximation algorithms for constrained scheduling problems,” in Proceedings of the 30th IEEE Symposium on Foundations of Computer Science, IEEE Computer Society Press, pp. 134–139, 1989.

  • Hall, L., and D. Shmoys, “Jackson's rule for single-machine scheduling: Making a good heuristic better,” MOR: Math. Oper. Res., 17, 22–35 (1992).

    Google Scholar 

  • D. Hochbaum (ed.) Approximation Algorithms for NP-hard Problems, ITP, PWS Publishing Company, 1995.

  • Lenstra, H. Jr., “Integer programming with a fixed number of variables,” Math. Oper. Res., 8, 538–548 (1983).

    Google Scholar 

  • Lenstra, J., A. R. Kan, and P. Brucker, “Complexity of machine scheduling problems,” Ann. Oper. Res., 1, 343–362 (1977).

    Google Scholar 

  • Potts, C., “Analysis of a heuristic for one machine sequencing with release dates and delivery times,” Oper. Res., 28, 1436–1441 (1980).

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. IDSIA, Galleria 2, 6928 Manno, Switzerland

    Monaldo Mastrolilli

Authors
  1. Monaldo Mastrolilli
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Mastrolilli, M. Efficient Approximation Schemes for Scheduling Problems with Release Dates and Delivery Times. Journal of Scheduling 6, 521–531 (2003). https://doi.org/10.1023/A:1026272526225

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/A:1026272526225

Search

Navigation