Document Open Access Logo

Single Machine Scheduling with Few Deadlines

Authors Klaus Heeger , Danny Hermelin , Dvir Shabtay

PDF

File

Thumbnail PDF
PDF
LIPIcs.IPEC.2023.24.pdf
  • Filesize: 0.65 MB
  • 15 pages

Document Identifiers

Subject Classification

ACM Subject Classification
  • Mathematics of computing → Discrete mathematics
  • Theory of computation → W hierarchy
  • Theory of computation → Dynamic programming
  • Theory of computation → Scheduling algorithms
Keywords
  • Single-machine scheduling
  • weighted completion time
  • tardy jobs
  • pseudopolynomial algorithms
  • parameterized complexity

Metrics

  • Access Statistics
  • Total Accesses (updated on a weekly basis)
    0
    PDF Downloads
    0
    Metadata Views

Abstract

We study single-machine scheduling problems with few deadlines. We focus on two classical objectives, namely minimizing the weighted number of tardy jobs and the total weighted completion time. For both problems, we give a pseudopolynomial-time algorithm for a constant number of different deadlines. This algorithm is complemented with an ETH-based, almost tight lower bound. Furthermore, we study the case where the number of jobs with a nontrivial deadline is taken as parameter. For this case, the complexity of our two problems differ: Minimizing the total number of tardy jobs becomes fixed-parameter tractable, while minimizing the total weighted completion time is W[1]-hard.

Cite As Get BibTex

Klaus Heeger, Danny Hermelin, and Dvir Shabtay. Single Machine Scheduling with Few Deadlines. In 18th International Symposium on Parameterized and Exact Computation (IPEC 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 285, pp. 24:1-24:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023) https://doi.org/10.4230/LIPIcs.IPEC.2023.24

Author Details

Klaus Heeger
  • Department of Industrial Engineering and Management, Ben-Gurion University of the Negev, Beer-Sheva, Israel
Danny Hermelin
  • Department of Industrial Engineering and Management, Ben-Gurion University of the Negev, Beer-Sheva, Israel
Dvir Shabtay
  • Department of Industrial Engineering and Management, Ben-Gurion University of the Negev, Beer-Sheva, Israel

Funding

Supported by the ISF, grant No. 1070/20.

References

  1. Philippe Baptiste, Federico Della Croce, Andrea Grosso, and Vincent T'kindt. Sequencing a single machine with due dates and deadlines: an ILP-based approach to solve very large instances. Journal of Scheduling, 13(1):39-47, 2010. Google Scholar
  2. Peter Brucker. Scheduling algorithms (4. ed.). Springer, 2004. Google Scholar
  3. Rubing Chen and Jinjiang Yuan. Unary NP-hardness of single-machine scheduling to minimize the total tardiness with deadlines. Journal of Scheduling, 22(5):595-601, 2019. Google Scholar
  4. Rubing Chen and Jinjiang Yuan. Unary NP-hardness of preemptive scheduling to minimize total completion time with release times and deadlines. Discrete Applied Mathematics, 304:45-54, 2021. Google Scholar
  5. Rubing Chen, Jinjiang Yuan, C.T. Ng, and T.C.E. Cheng. Single-machine scheduling with deadlines to minimize the total weighted late work. Naval Research Logistics, 66(7):582-595, 2019. Google Scholar
  6. Michael R. Garey and David S. Johnson. Complexity results for multiprocessor scheduling under resource constraints. SIAM J. Comput., 4(4):397-411, 1975. Google Scholar
  7. Michael R. Garey and David S. Johnson. Computers and Intractability: A Guide to the Theory of NP-Completeness. W. H. Freeman, 1979. Google Scholar
  8. Ronald L. Graham, Eugene L. Lawler, Jan K. Lenstra, and Alexander H. G. Rinnooy Kan. Optimization and approximation in deterministic sequencing and scheduling: a survey. In Discrete Optimization II, volume 5 of Annals of Discrete Mathematics, pages 287-326. Elsevier, 1979. Google Scholar
  9. A. M. A. Hariri and Chris N. Potts. Single machine scheduling with deadlines to minimize the weighted number of tardy jobs. Management Science, 40(12):1712-1719, 1994. Google Scholar
  10. Cheng He, Hao Lin, Yixun Lin, and Junmei Dou. Minimizing total completion time for preemptive scheduling with release dates and deadline constraints. Foundations of Computing and Decision Sciences, 39(1):17-26, 2014. Google Scholar
  11. Cheng He, Yixun Lin, and Jinjiang Yuan. A note on the single machine scheduling to minimize the number of tardy jobs with deadlines. European Journal of Operational Research, 201(3):966-970, 2010. Google Scholar
  12. Yumei Huo, Joseph Y.-T. Leung, and Hairong Zhao. Bi-criteria scheduling problems: Number of tardy jobs and maximum weighted tardiness. European Journal of Operational Research, 177(1):116-134, 2007. Google Scholar
  13. Klaus Jansen, Stefan Kratsch, Dániel Marx, and Ildikó Schlotter. Bin packing with fixed number of bins revisited. Journal of Computer and System Sciences, 79(1):39-49, 2013. Google Scholar
  14. Richard M. Karp. Reducibility among combinatorial problems. In Proceedings of a symposium on the Complexity of Computer Computations, held March 20-22, 1972, at the IBM Thomas J. Watson Research Center, The IBM Research Symposia Series, pages 85-103. Plenum Press, 1972. Google Scholar
  15. Eugene L. Lawler. Scheduling a single machine to minimize the number of late jobs. Technical Report UCB/CSD-83-139, EECS Department, University of California, Berkeley, 1983. Google Scholar
  16. Eugene L. Lawler and J. Michael Moore. A functional equation and its application to resource allocation and sequencing problems. Management Science, 16(1):77-84, 1969. Google Scholar
  17. Jan K. Lenstra, Alexander H.G. Rinnooy Kan, and Peter Brucker. Complexity of machine scheduling problems. In Studies in Integer Programming, volume 1 of Annals of Discrete Mathematics, pages 343-362. Elsevier, 1977. Google Scholar
  18. J. Michael Moore. An n job, one machine sequencing algorithm for minimizing the number of late jobs. Management Science, 15(1):102-109, 1968. Google Scholar
  19. Michael Pinedo. Scheduling: Theory, Algorithms, and Systems (5. ed.). Springer, 2016. Google Scholar
  20. Sartaj Sahni. Algorithms for scheduling independent tasks. Journal of the ACM, 23(1):116-127, 1976. Google Scholar
  21. Jeffrey B. Sidney. An extension of Moore’s due date algotithm. In Symposium on the Theory of Scheduling and Its Applications, pages 393-398. Springer Berlin Heidelberg, 1973. Google Scholar
  22. Wayne E. Smith. Various optimizers for single-stage production. Naval Research Logistics Quarterly, 3:59-66, 1956. Google Scholar
  23. Long Wan, Jinjiang Yuan, and Zhichao Geng. A note on the preemptive scheduling to minimize total completion time with release time and deadline constraints. Journal of Scheduling, 18(3):315-323, 2015. Google Scholar
  24. Jinjiang Yuan. Unary NP-hardness of minimizing the number of tardy jobs with deadlines. Journal of Scheduling, 20(2):211-218, 2017. Google Scholar
Questions / Remarks / Feedback
X

Feedback for Dagstuhl Publishing


Thanks for your feedback!

Feedback submitted

Could not send message

Please try again later or send an E-mail
© 2023-2025 Schloss Dagstuhl – LZI GmbH About DROPS Imprint Privacy Contact