Location via proxy:   [ UP ]  
[Report a bug]   [Manage cookies]                
Skip to main content
Springer Nature Link
Log in

Measuring the slack between lower bounds for scheduling on parallel machines

  • Original Research
  • Published:
Annals of Operations Research Aims and scope Submit manuscript

Abstract

This paper considers the problem of scheduling independent jobs with release dates and tails on m identical machines to minimize the makespan. The three main bounds are the preemptive bound, the energetic bound and the Jackson Pseudo Preemptive bound. It is known that they are very close in practice. The aim of this paper is to provide worst case instances where the slack between them is maximal and to prove tight bounds on the slack. We show that the slack is smaller than the maximal processing time.

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

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

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

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13

Similar content being viewed by others

References

  • Baptiste, P., Le Pape, C., & Nuijten, W. (1999). Satisfiability tests and time-bound adjustments for cumulative scheduling problems. Annals of Operations Research, 92, 305–333.

    Article  Google Scholar 

  • Baptiste, P., Le Pape, C., & Nuijten, W. (2001). Constraint-based scheduling: Applying constraint programming to scheduling problems (Vol. 39). Springer.

    Google Scholar 

  • Carlier, J. (1987). Scheduling jobs with release dates and tails on identical machines to minimize the makespan. European Journal of Operational Research, 29, 298–306.

    Article  Google Scholar 

  • Carlier, J., & Pinson, E. (1998). Jackson’s pseudo preemptive schedule for the \(pm\vert r_i, q_i \vert c_{\max }\) scheduling problem. Annals of Operations Research, 83, 41–58.

    Article  Google Scholar 

  • Carlier, J., & Pinson, E. (2004). Jackson’s pseudo-preemptive schedule and cumulative scheduling problems. Discrete Applied Mathematics, 145(1), 80–94.

    Article  Google Scholar 

  • Carlier, J., Pinson, E., Sahli, A., & Jouglet, A. (2021) Comparison of three classical lower bounds for the Cumulative Scheduling Problem. (submitted).

  • Carlier, J., Sahli, A., & Jouglet, A. (2023). Algorithms to compute the energetic lower bounds of the cumulative scheduling problem. Annals of Operations Research. https://doi.org/10.1007/s10479-023-05596-9

    Article  Google Scholar 

  • Carlier, J., Sahli, A., Jouglet, A., & Pinson, E. (2022). A faster checker of the energetic reasoning for the cumulative scheduling problem. International Journal of Production Research, 60(11), 3419–3434.

    Article  Google Scholar 

  • Erschler, J., & Lopez, C.T. P. (1989). Scheduling under time and resource constraints. In Proceedings of workshop on manufacturing scheduling, 11th IJCAI, Detroit, USA.

  • Erschler, J., & Lopez, P. (1990). Energy-based approach for task scheduling under time and resources constraints. In 2nd international workshop on project management and scheduling, Compiègne (France) (pp. 115–121).

  • Gale, D. (1957). A theorem on flows in networks. Pacific Journal of Mathematics, 7(2), 1073–1082. Publisher: Pacific Journal of Mathematics, A Non-profit Corporation.

    Article  Google Scholar 

  • Graham, R., Lawler, E. L., Lenstra, J. K., & Kan, A. H. G. R. (1977). Optimization and approximation in deterministic sequencing and scheduling: a survey. Annals of Discrete Mathematics, 5, 287–326.

    Article  Google Scholar 

  • Hanen, C., Munier Kordon, A., & Pedersen, T. (2021) Two deadline reduction algorithms for scheduling dependent tasks on parallel processors (extended version). hal-0320029.

  • Haouari, M., Kooli, A., & Néron, E. (2012). Enhanced energetic reasoning-based lower bounds for the resource constrained project scheduling problem. Computers and Operations Research, 39(5), 1187–1194.

    Article  Google Scholar 

  • Haouari, M., Kooli, A., Néron, E., & Carlier, J. (2014). A preemptive bound for the Resource Constrained Project Scheduling Problem. Journal of Scheduling, 17(3), 237–248.

    Article  Google Scholar 

  • Hartmann, S., & Briskorn, D. (2022). An updated survey of variants and extensions of the resource-constrained project scheduling problem. European Journal of Operational Research, 297(1), 1–14. https://doi.org/10.1016/j.ejor.2021.05.004

    Article  Google Scholar 

  • Hidri, L., Gharbi, A., & Haouari, M. (2008). Energetic reasoning revisited: Application to parallel machine scheduling. Journal of Scheduling, 11(4), 239–252. Publisher: Springer.

    Article  Google Scholar 

  • Laborie, P., & Nuijten, W. (2008). Constraint programming formulations and propagation algorithms. In Resource-constrained project scheduling (pp. 63–72). Wiley.

  • Lahrichi, A. (1982). Ordonnancements. La notion de "parties obligatoires" et son application aux problèmes cumulatifs. RAIRO - Operations Research - Recherche Opérationnelle, 16(3), 241–262

  • Martel, C. (1982). Preemptive scheduling with release times, deadlines, and due times. Journal of the Association of Computing Machinery, 29(3), 812–829. Place: New York, NY, USA Publisher: ACM.

    Article  Google Scholar 

  • McNaughton, R. (1959). Scheduling with deadlines and loss functions. Management Science, 6, 1–12.

    Article  Google Scholar 

  • Néron, E. (2008). Resource and precedence constraint relaxation. In Resource-constrained project scheduling (pp. 37–48). Wiley.

  • Ouellet, Y., & Quimper, C.-G. (2018). A \(\cal{O} {(n\log ^{2} n)}\) checker and \(\cal{O} {(n^{2}\log n)}\) filtering algorithm for the energetic reasoning. In W. J. van Hoeve (Ed.), CPAIOR 2018, June 26–29. Lecture notes in computer science (Vol. 10848, pp. 477–494). Springer.

  • Sanlaville, E. (1995). Nearly on line scheduling of preemptive independent tasks. Discrete Applied Mathematics, 57(2–3), 229–241.

    Article  Google Scholar 

  • Tercinet, F., Lenté, C., & Néron, E. (2004). Mixed satisfiability tests for multiprocessor scheduling with release dates and deadlines. Operations Research Letters, 32(4), 326–330.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. UTC, Heudiasyc, Compiègne, France

    Jacques Carlier

  2. Sorbonne Université, CNRS, LIP6, 75005, Paris, France

    Claire Hanen

  3. UPL, Université Paris Nanterre, 92000, Nanterre, France

    Claire Hanen

Authors
  1. Jacques Carlier
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Claire Hanen
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Claire Hanen.

Ethics declarations

Ethical approval

This article does not contain any studies with human participants or animals performed by any of the authors.

Conflict of interest

Author Claire Hanen declares that she has no conflict of interest. Author Jacques Carlier declares that he has no conflict of interest.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Carlier, J., Hanen, C. Measuring the slack between lower bounds for scheduling on parallel machines. Ann Oper Res 338, 347–377 (2024). https://doi.org/10.1007/s10479-023-05759-8

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10479-023-05759-8

Keywords

Search

Navigation