IDEAS home Printed from https://ideas.repec.org/a/spr/jsched/v22y2019i4d10.1007_s10951-018-0579-8.html
   My bibliography  Save this article

The single-processor scheduling problem with time restrictions: complexity and related problems

Author

Listed:
  • Rachid Benmansour

    (Institut National de Statistique et d’Économie Appliquée)

  • Oliver Braun

    (Trier University of Applied Sciences)

  • Saïd Hanafi

    (University of Valenciennes and Hainaut Cambrésis)

Abstract

We consider the single-processor scheduling problem with time restrictions (STR) in order to minimize the makespan, where a set of independent jobs has to be processed on a single processor, subject only to the following constraint: During any time period of length $$\alpha $$ α , the number of jobs being executed is less than or equal to a given integer value B. First, we prove that the STR problem is binary NP-hard even for $$B=2$$ B = 2 by pointing out an interesting analogy of this problem to the parallel machine scheduling problem with a single server with equal processing times. Next, we give a formal description of the STR problem by providing two mixed integer programming formulations to solve it optimally. The first is based on time-indexed variables and the second is based on assignment and positional date variables (APV). Both models were tested on randomly generated instances, and the experimental results show that the APV model performs very well and can solve problem instances of up to $$n=500$$ n = 500 jobs.

Suggested Citation

  • Rachid Benmansour & Oliver Braun & Saïd Hanafi, 2019. "The single-processor scheduling problem with time restrictions: complexity and related problems," Journal of Scheduling, Springer, vol. 22(4), pages 465-471, August.
    • Handle: RePEc:spr:jsched:v:22:y:2019:i:4:d:10.1007_s10951-018-0579-8
    DOI: 10.1007/s10951-018-0579-8
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10951-018-0579-8
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s10951-018-0579-8?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. DYER, Martin E. & WOLSEY, Laurence A., 1990. "Formulating the single machine sequencing problem with release dates as a mixed integer program," LIDAM Reprints CORE 878, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    2. Michael R. Garey & Robert E. Tarjan & Gordon T. Wilfong, 1988. "One-Processor Scheduling with Symmetric Earliness and Tardiness Penalties," Mathematics of Operations Research, INFORMS, vol. 13(2), pages 330-348, May.
    3. E. DYER, Martin & WOLSEY, Laurence A., 1990. "Formulating the single machine sequencing problem with release dates as a mixed integer program," LIDAM Reprints CORE 917, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    4. J.M. van den Akker & C.A.J. Hurkens & M.W.P. Savelsbergh, 2000. "Time-Indexed Formulations for Machine Scheduling Problems: Column Generation," INFORMS Journal on Computing, INFORMS, vol. 12(2), pages 111-124, May.
    5. Celia A. Glass & Yakov M. Shafransky & Vitaly A. Strusevich, 2000. "Scheduling for parallel dedicated machines with a single server," Naval Research Logistics (NRL), John Wiley & Sons, vol. 47(4), pages 304-328, June.
    6. Jacek Błażewicz & Klaus H. Ecker & Erwin Pesch & Günter Schmidt & Jan Węglarz, 2007. "Handbook on Scheduling," International Handbooks on Information Systems, Springer, number 978-3-540-32220-7, November.
    7. Oliver Braun & Fan Chung & Ron Graham, 2016. "Worst-case analysis of the LPT algorithm for single processor scheduling with time restrictions," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 38(2), pages 531-540, March.
    8. Francis Sourd, 2009. "New Exact Algorithms for One-Machine Earliness-Tardiness Scheduling," INFORMS Journal on Computing, INFORMS, vol. 21(1), pages 167-175, February.
    9. SOUSA, Jorge P. & WOLSEY, Laurence A., 1992. "A time indexed formulation of non-preemptive single machine scheduling problems," LIDAM Reprints CORE 984, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Natashia Boland & Riley Clement & Hamish Waterer, 2016. "A Bucket Indexed Formulation for Nonpreemptive Single Machine Scheduling Problems," INFORMS Journal on Computing, INFORMS, vol. 28(1), pages 14-30, February.
    2. Arthur Kramer & Anand Subramanian, 2019. "A unified heuristic and an annotated bibliography for a large class of earliness–tardiness scheduling problems," Journal of Scheduling, Springer, vol. 22(1), pages 21-57, February.
    3. Artur Alves Pessoa & Teobaldo Bulhões & Vitor Nesello & Anand Subramanian, 2022. "Exact Approaches for Single Machine Total Weighted Tardiness Batch Scheduling," INFORMS Journal on Computing, INFORMS, vol. 34(3), pages 1512-1530, May.
    4. Francis Sourd, 2009. "New Exact Algorithms for One-Machine Earliness-Tardiness Scheduling," INFORMS Journal on Computing, INFORMS, vol. 21(1), pages 167-175, February.
    5. Pasquale Avella & Maurizio Boccia & Bernardo D’Auria, 2005. "Near-Optimal Solutions of Large-Scale Single-Machine Scheduling Problems," INFORMS Journal on Computing, INFORMS, vol. 17(2), pages 183-191, May.
    6. Lotte Berghman & Roel Leus & Frits Spieksma, 2014. "Optimal solutions for a dock assignment problem with trailer transportation," Annals of Operations Research, Springer, vol. 213(1), pages 3-25, February.
    7. Martin W. P. Savelsbergh & R. N. Uma & Joel Wein, 2005. "An Experimental Study of LP-Based Approximation Algorithms for Scheduling Problems," INFORMS Journal on Computing, INFORMS, vol. 17(1), pages 123-136, February.
    8. Louis-Philippe Bigras & Michel Gamache & Gilles Savard, 2008. "Time-Indexed Formulations and the Total Weighted Tardiness Problem," INFORMS Journal on Computing, INFORMS, vol. 20(1), pages 133-142, February.
    9. Pereira, Jordi & Vásquez, Óscar C., 2017. "The single machine weighted mean squared deviation problem," European Journal of Operational Research, Elsevier, vol. 261(2), pages 515-529.
    10. Stéphane Dauzère-Pérès & Sigrid Lise Nonås, 2023. "An improved decision support model for scheduling production in an engineer-to-order manufacturer," 4OR, Springer, vol. 21(2), pages 247-300, June.
    11. Yunpeng Pan & Zhe Liang, 2017. "Dual relaxations of the time-indexed ILP formulation for min–sum scheduling problems," Annals of Operations Research, Springer, vol. 249(1), pages 197-213, February.
    12. Baptiste, Philippe & Sadykov, Ruslan, 2010. "Time-indexed formulations for scheduling chains on a single machine: An application to airborne radars," European Journal of Operational Research, Elsevier, vol. 203(2), pages 476-483, June.
    13. J.M. van den Akker & C.A.J. Hurkens & M.W.P. Savelsbergh, 2000. "Time-Indexed Formulations for Machine Scheduling Problems: Column Generation," INFORMS Journal on Computing, INFORMS, vol. 12(2), pages 111-124, May.
    14. Daniel Kowalczyk & Roel Leus, 2018. "A Branch-and-Price Algorithm for Parallel Machine Scheduling Using ZDDs and Generic Branching," INFORMS Journal on Computing, INFORMS, vol. 30(4), pages 768-782, November.
    15. Tjark Vredeveld & Cor Hurkens, 2002. "Experimental Comparison of Approximation Algorithms for Scheduling Unrelated Parallel Machines," INFORMS Journal on Computing, INFORMS, vol. 14(2), pages 175-189, May.
    16. Soric, Kristina, 2000. "A cutting plane algorithm for a single machine scheduling problem," European Journal of Operational Research, Elsevier, vol. 127(2), pages 383-393, December.
    17. Giuseppe Lancia & Franca Rinaldi & Paolo Serafini, 2011. "A time-indexed LP-based approach for min-sum job-shop problems," Annals of Operations Research, Springer, vol. 186(1), pages 175-198, June.
    18. José Manuel García-Sánchez & Plácido Moreno, 2024. "Novel Approaches to the Formulation of Scheduling Problems," Mathematics, MDPI, vol. 12(7), pages 1-15, March.
    19. Zhang, Hanxiao & Li, Yan-Fu, 2022. "Integrated optimization of test case selection and sequencing for reliability testing of the mainboard of Internet backbone routers," European Journal of Operational Research, Elsevier, vol. 299(1), pages 183-194.
    20. Kedad-Sidhoum, Safia & Solis, Yasmin Rios & Sourd, Francis, 2008. "Lower bounds for the earliness-tardiness scheduling problem on parallel machines with distinct due dates," European Journal of Operational Research, Elsevier, vol. 189(3), pages 1305-1316, September.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:jsched:v:22:y:2019:i:4:d:10.1007_s10951-018-0579-8. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.