Advertisement

Grouping Techniques for One Machine Scheduling Subject to Precedence Constraints

  • Monaldo Mastrolilli
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2245)

Abstract

We consider the problem of scheduling n jobs on a single machine. Each job has a release date, when it becomes available for processing, and, after completing its processing, requires an additional delivery time. Feasible schedules are further restricted by job precedence constraints, and the objective is to minimize the time by which all jobs are delivered. In the notation of Graham et al. [2], this problem is noted 1∣r j, prec∣Lmax. We develop a polynomial time approximation scheme whose running time depends only linearly on the input size. This linear complexity bound gives a substantial improvement of the best previously known polynomial bound [4].

Keywords

Release Date Delivery Time Precedence Constraint Precedence Relation Feasible Schedule 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    M. R. Garey and D. S. Johnson. Computers and intractability; a guide to the theory of NP-completeness. W.H. Freeman, 1979.Google Scholar
  2. 2.
    R. Graham, E. Lawler, J. Lenstra, and A. R. Kan. Optimization and approximation in deterministic sequencing and scheduling: A survey. volume 5, pages 287–326. North-Holland, 1979.zbMATHGoogle Scholar
  3. 3.
    L. A. Hall and D. B. Shmoys. Approximation algorithms for constrained schedulingproblems. In Proceedings of the 30th IEEE Symposium on Foundations of Computer Science (FOCS 1989), pages 134–139, 1989.Google Scholar
  4. 4.
    L. A. Hall and D. B. Shmoys. Near-optimal sequencingwith precedence constraints. In Proceedings of the 1st Integer Programming and Combinatorial Optimization Conference (IPCO1990), pages 249–260. University of Waterloo Press, 1990.Google Scholar
  5. 5.
    L. A. Hall and D. B. Shmoys. Jackson’s rule for single-machine scheduling: Making a good heuristic better. MOR: Mathematics of Operations Research, 17:22–35, 1992.zbMATHMathSciNetCrossRefGoogle Scholar
  6. 6.
    J. R. Jackson. Schedulinga production line to minimize maximum tardiness. Technical Report Research Report 43, Management Science Research Project, UCLA, 1955.Google Scholar
  7. 7.
    B. J. Lageweg, J. K. Lenstra, and A. H. G. R. Kan. Minimizing maximum lateness on one machine: Computational experience and some applications. Statist. Neerlandica, 30:25–41, 1976.zbMATHGoogle Scholar
  8. 8.
    J. K. Lenstra, A. H. G. R. Kan, and P. Brucker. Complexity of machine scheduling problems. Annals of Operations Research, 1:343–362, 1977.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2001

Authors and Affiliations

  • Monaldo Mastrolilli
    • 1
  1. 1.IDSIAMannoSwitzerland

Personalised recommendations