IDEAS home Printed from https://ideas.repec.org/a/spr/jcomop/v44y2022i1d10.1007_s10878-021-00842-x.html
   My bibliography  Save this article

Approximation algorithm for the parallel-machine scheduling problem with release dates and submodular rejection penalties

Author

Listed:
  • Hongye Zheng

    (Hebei Normal University)

  • Suogang Gao

    (Hebei Normal University)

  • Wen Liu

    (Hebei Normal University)

  • Weili Wu

    (University of Texas at Dallas)

  • Ding-Zhu Du

    (University of Texas at Dallas)

  • Bo Hou

    (Hebei Normal University)

Abstract

In this paper, we consider the parallel-machine scheduling problem with release dates and submodular rejection penalties. In this problem, we are given m identical parallel machines and n jobs. Each job has a processing time and a release date. A job is either rejected, in which case a rejection penalty has to be paid, or accepted and processed on one of the m identical parallel machines. The objective is to minimize the sum of the makespan of the accepted jobs and the rejection penalty of the rejected jobs which is determined by a submodular function. Our main work is to design a 2-approximation algorithm based on the primal-dual framework.

Suggested Citation

  • Hongye Zheng & Suogang Gao & Wen Liu & Weili Wu & Ding-Zhu Du & Bo Hou, 2022. "Approximation algorithm for the parallel-machine scheduling problem with release dates and submodular rejection penalties," Journal of Combinatorial Optimization, Springer, vol. 44(1), pages 343-353, August.
    • Handle: RePEc:spr:jcomop:v:44:y:2022:i:1:d:10.1007_s10878-021-00842-x
    DOI: 10.1007/s10878-021-00842-x
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10878-021-00842-x
    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/s10878-021-00842-x?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. E. L. Lawler, 1973. "Optimal Sequencing of a Single Machine Subject to Precedence Constraints," Management Science, INFORMS, vol. 19(5), pages 544-546, January.
    2. Liqi Zhang & Lingfa Lu, 2016. "Parallel-machine scheduling with release dates and rejection," 4OR, Springer, vol. 14(2), pages 165-172, June.
    3. Xianzhao Zhang & Dachuan Xu & Donglei Du & Chenchen Wu, 2018. "Approximation algorithms for precedence-constrained identical machine scheduling with rejection," Journal of Combinatorial Optimization, Springer, vol. 35(1), pages 318-330, January.
    4. Yuri N. Sotskov & Natalja G. Egorova, 2019. "The Optimality Region for a Single-Machine Scheduling Problem with Bounded Durations of the Jobs and the Total Completion Time Objective," Mathematics, MDPI, vol. 7(5), pages 1-21, April.
    5. Xiaofei Liu & Weidong Li, 2020. "Approximation Algorithm for the Single Machine Scheduling Problem with Release Dates and Submodular Rejection Penalty," Mathematics, MDPI, vol. 8(1), pages 1-11, January.
    6. Xueling Zhong & Zhangming Pan & Dakui Jiang, 2017. "Scheduling with release times and rejection on two parallel machines," Journal of Combinatorial Optimization, Springer, vol. 33(3), pages 934-944, April.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Guojun Hu & Pengxiang Pan & Suding Liu & Ping Yang & Runtao Xie, 2024. "The prize-collecting single machine scheduling with bounds and penalties," Journal of Combinatorial Optimization, Springer, vol. 48(2), pages 1-13, September.
    2. Bo Hou & Tianjiao Guo & Suogang Gao & Guanghua Wang & Weili Wu & Wen Liu, 2024. "W-prize-collecting scheduling problem on parallel machines," Journal of Combinatorial Optimization, Springer, vol. 48(3), pages 1-9, October.
    3. Xiaofei Liu & Man Xiao & Weidong Li & Yaoyu Zhu & Lei Ma, 2023. "Algorithms for single machine scheduling problem with release dates and submodular penalties," Journal of Combinatorial Optimization, Springer, vol. 45(4), pages 1-18, May.

    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. Xiaofei Liu & Man Xiao & Weidong Li & Yaoyu Zhu & Lei Ma, 2023. "Algorithms for single machine scheduling problem with release dates and submodular penalties," Journal of Combinatorial Optimization, Springer, vol. 45(4), pages 1-18, May.
    2. Xiaofei Liu & Weidong Li, 2020. "Approximation Algorithm for the Single Machine Scheduling Problem with Release Dates and Submodular Rejection Penalty," Mathematics, MDPI, vol. 8(1), pages 1-11, January.
    3. Ren-Xia Chen & Shi-Sheng Li, 2020. "Minimizing maximum delivery completion time for order scheduling with rejection," Journal of Combinatorial Optimization, Springer, vol. 40(4), pages 1044-1064, November.
    4. Baruch Mor & Gur Mosheiov & Dana Shapira, 2021. "Single machine lot scheduling with optional job-rejection," Journal of Combinatorial Optimization, Springer, vol. 41(1), pages 1-11, January.
    5. Xiaofei Liu & Weidong Li & Yaoyu Zhu, 2021. "Single Machine Vector Scheduling with General Penalties," Mathematics, MDPI, vol. 9(16), pages 1-16, August.
    6. Peihai Liu & Xiwen Lu, 2020. "New approximation algorithms for machine scheduling with rejection on single and parallel machine," Journal of Combinatorial Optimization, Springer, vol. 40(4), pages 929-952, November.
    7. Mosheiov, Gur & Oron, Daniel & Shabtay, Dvir, 2021. "Minimizing total late work on a single machine with generalized due-dates," European Journal of Operational Research, Elsevier, vol. 293(3), pages 837-846.
    8. Baruch Mor & Gur Mosheiov, 2021. "A note: flowshop scheduling with linear deterioration and job-rejection," 4OR, Springer, vol. 19(1), pages 103-111, March.
    9. Weidong Li & Qianna Cui, 2018. "Vector scheduling with rejection on a single machine," 4OR, Springer, vol. 16(1), pages 95-104, March.
    10. Enrique Gerstl & Gur Mosheiov, 2020. "Single machine scheduling to maximize the number of on-time jobs with generalized due-dates," Journal of Scheduling, Springer, vol. 23(3), pages 289-299, June.
    11. Ramachandra, Girish & Elmaghraby, Salah E., 2006. "Sequencing precedence-related jobs on two machines to minimize the weighted completion time," International Journal of Production Economics, Elsevier, vol. 100(1), pages 44-58, March.
    12. Bachtenkirch, David & Bock, Stefan, 2022. "Finding efficient make-to-order production and batch delivery schedules," European Journal of Operational Research, Elsevier, vol. 297(1), pages 133-152.
    13. Xiaofei Liu & Peiyin Xing & Weidong Li, 2020. "Approximation Algorithms for the Submodular Load Balancing with Submodular Penalties," Mathematics, MDPI, vol. 8(10), pages 1-12, October.
    14. Rubing Chen & Jinjiang Yuan, 2020. "Single-machine scheduling of proportional-linearly deteriorating jobs with positional due indices," 4OR, Springer, vol. 18(2), pages 177-196, June.
    15. Reha Uzsoy & Chung‐Yee Lee & Louis A. Martin‐Vega, 1992. "Scheduling semiconductor test operations: Minimizing maximum lateness and number of tardy jobs on a single machine," Naval Research Logistics (NRL), John Wiley & Sons, vol. 39(3), pages 369-388, April.
    16. Anna Arigliano & Gianpaolo Ghiani & Antonio Grieco & Emanuela Guerriero, 2017. "Single-machine time-dependent scheduling problems with fixed rate-modifying activities and resumable jobs," 4OR, Springer, vol. 15(2), pages 201-215, June.
    17. Matan Atsmony & Gur Mosheiov, 2023. "Scheduling to maximize the weighted number of on-time jobs on parallel machines with bounded job-rejection," Journal of Scheduling, Springer, vol. 26(2), pages 193-207, April.
    18. Chun-Lung Chen, 2023. "An Iterated Population-Based Metaheuristic for Order Acceptance and Scheduling in Unrelated Parallel Machines with Several Practical Constraints," Mathematics, MDPI, vol. 11(6), pages 1-14, March.
    19. Adam Kasperski & Paweł Zieliński, 2019. "Risk-averse single machine scheduling: complexity and approximation," Journal of Scheduling, Springer, vol. 22(5), pages 567-580, October.
    20. Lingfa Lu & Liqi Zhang, 2017. "Online Single Machine Scheduling to Minimize the Maximum Starting Time," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 34(05), pages 1-9, October.

    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:jcomop:v:44:y:2022:i:1:d:10.1007_s10878-021-00842-x. 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.