IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v8y2020i2p258-d321211.html
   My bibliography  Save this article

Single-Machine Parallel-Batch Scheduling with Nonidentical Job Sizes and Rejection

Author

Listed:
  • Miaomiao Jin

    (School of Mathematics and Statistics, Ningbo University, Ningbo 315211, China)

  • Xiaoxia Liu

    (School of Mathematics and Statistics, Ningbo University, Ningbo 315211, China)

  • Wenchang Luo

    (School of Mathematics and Statistics, Ningbo University, Ningbo 315211, China)

Abstract

We investigate the single-machine parallel-batch scheduling problem with nonidentical job sizes and rejection. In this problem, a set of jobs with different processing times and nonidentical sizes is given to be possibly processed on a parallel-batch processing machine. Each job is either accepted and then processed on the machine or rejected by paying its rejection penalty. Preemption is not allowed. Our task is to choose the accepted jobs and schedule them as batches on the machine to minimize the makespan of the accepted jobs plus the total rejection penalty of the rejected jobs. We provide an integer programming formulation to exactly solve our problem. Then, we propose three fast heuristic algorithms to solve the problem and evaluate their performances by using a small numerical example.

Suggested Citation

  • Miaomiao Jin & Xiaoxia Liu & Wenchang Luo, 2020. "Single-Machine Parallel-Batch Scheduling with Nonidentical Job Sizes and Rejection," Mathematics, MDPI, vol. 8(2), pages 1-8, February.
  • Handle: RePEc:gam:jmathe:v:8:y:2020:i:2:p:258-:d:321211
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/8/2/258/pdf
    Download Restriction: no

    File URL: https://www.mdpi.com/2227-7390/8/2/258/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Guochuan Zhang & Xiaoqiang Cai & C.‐Y Lee & C.K Wong, 2001. "Minimizing makespan on a single batch processing machine with nonidentical job sizes," Naval Research Logistics (NRL), John Wiley & Sons, vol. 48(3), pages 226-240, April.
    2. Zhang, Liqi & Lu, Lingfa & Yuan, Jinjiang, 2009. "Single machine scheduling with release dates and rejection," European Journal of Operational Research, Elsevier, vol. 198(3), pages 975-978, November.
    3. Potts, Chris N. & Kovalyov, Mikhail Y., 2000. "Scheduling with batching: A review," European Journal of Operational Research, Elsevier, vol. 120(2), pages 228-249, January.
    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. Tarhan, İstenç & Oğuz, Ceyda, 2022. "A matheuristic for the generalized order acceptance and scheduling problem," European Journal of Operational Research, Elsevier, vol. 299(1), pages 87-103.
    2. Xu, Jun & Wang, Jun-Qiang & Liu, Zhixin, 2022. "Parallel batch scheduling: Impact of increasing machine capacity," Omega, Elsevier, vol. 108(C).
    3. Jun-Qiang Wang & Guo-Qiang Fan & Zhixin Liu, 2020. "Mixed batch scheduling on identical machines," Journal of Scheduling, Springer, vol. 23(4), pages 487-496, August.
    4. Min Kong & Xinbao Liu & Jun Pei & Panos M. Pardalos & Nenad Mladenovic, 2020. "Parallel-batching scheduling with nonlinear processing times on a single and unrelated parallel machines," Journal of Global Optimization, Springer, vol. 78(4), pages 693-715, December.
    5. Jinwen Ou, 2020. "Near-linear-time approximation algorithms for scheduling a batch-processing machine with setups and job rejection," Journal of Scheduling, Springer, vol. 23(5), pages 525-538, October.
    6. Zhang, Hongbin & Yang, Yu & Wu, Feng, 2024. "Scheduling a set of jobs with convex piecewise linear cost functions on a single-batch-processing machine," Omega, Elsevier, vol. 122(C).
    7. Yuzhong Zhang & Zhigang Cao, 2008. "An asymptotic PTAS for batch scheduling with nonidentical job sizes to minimize makespan," Journal of Combinatorial Optimization, Springer, vol. 16(2), pages 119-126, August.
    8. Gyorgy Dosa & Zhiyi Tan & Zsolt Tuza & Yujie Yan & Cecília Sik Lányi, 2014. "Improved bounds for batch scheduling with nonidentical job sizes," Naval Research Logistics (NRL), John Wiley & Sons, vol. 61(5), pages 351-358, August.
    9. Jason Pan & Chi-Shiang Su, 2015. "Two parallel machines problem with job delivery coordination and availability constraint," Annals of Operations Research, Springer, vol. 235(1), pages 653-664, December.
    10. Altekin, F. Tevhide & Bukchin, Yossi, 2022. "A multi-objective optimization approach for exploring the cost and makespan trade-off in additive manufacturing," European Journal of Operational Research, Elsevier, vol. 301(1), pages 235-253.
    11. Elisabeth Lübbecke & Marco E. Lübbecke & Rolf H. Möhring, 2019. "Ship Traffic Optimization for the Kiel Canal," Operations Research, INFORMS, vol. 67(3), pages 791-812, May.
    12. Gahm, Christian & Uzunoglu, Aykut & Wahl, Stefan & Ganschinietz, Chantal & Tuma, Axel, 2022. "Applying machine learning for the anticipation of complex nesting solutions in hierarchical production planning," European Journal of Operational Research, Elsevier, vol. 296(3), pages 819-836.
    13. Biber Nurit & Mor Baruch & Schlissel Yitzhak & Shapira Dana, 2023. "Lot scheduling involving completion time problems on identical parallel machines," Operational Research, Springer, vol. 23(1), pages 1-29, March.
    14. Shen, Liji & Buscher, Udo, 2012. "Solving the serial batching problem in job shop manufacturing systems," European Journal of Operational Research, Elsevier, vol. 221(1), pages 14-26.
    15. Derya Deliktaş, 2022. "Self-adaptive memetic algorithms for multi-objective single machine learning-effect scheduling problems with release times," Flexible Services and Manufacturing Journal, Springer, vol. 34(3), pages 748-784, September.
    16. Shi-Sheng Li & Ren-Xia Chen & Qi Feng, 2016. "Scheduling two job families on a single machine with two competitive agents," Journal of Combinatorial Optimization, Springer, vol. 32(3), pages 784-799, October.
    17. Jun Pei & Xinbao Liu & Panos M. Pardalos & Wenjuan Fan & Shanlin Yang, 2017. "Scheduling deteriorating jobs on a single serial-batching machine with multiple job types and sequence-dependent setup times," Annals of Operations Research, Springer, vol. 249(1), pages 175-195, February.
    18. Shisheng Li & T.C.E. Cheng & C.T. Ng & Jinjiang Yuan, 2017. "Two‐agent scheduling on a single sequential and compatible batching machine," Naval Research Logistics (NRL), John Wiley & Sons, vol. 64(8), pages 628-641, December.
    19. Anurag Agarwal & Varghese S. Jacob & Hasan Pirkul, 2006. "An Improved Augmented Neural-Network Approach for Scheduling Problems," INFORMS Journal on Computing, INFORMS, vol. 18(1), pages 119-128, February.
    20. Lingfa Lu & Liqi Zhang, 2023. "Scheduling problems with rejection to minimize the k-th power of the makespan plus the total rejection cost," Journal of Combinatorial Optimization, Springer, vol. 46(1), pages 1-17, August.

    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:gam:jmathe:v:8:y:2020:i:2:p:258-:d:321211. 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: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.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.