IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v7y2019i10p960-d275974.html
   My bibliography  Save this article

Online Bi-Criteria Scheduling on Batch Machines with Machine Costs

Author

Listed:
  • Wenhua Li

    (School of Mathematics and Statistics, Zhengzhou University, Zhengzhou 450001, China)

  • Weina Zhai

    (School of Mathematics and Statistics, Zhengzhou University, Zhengzhou 450001, China)

  • Xing Chai

    (School of Mathematics and Statistics, Zhengzhou University, Zhengzhou 450001, China)

Abstract

We consider online scheduling with bi-criteria on parallel batch machines, where the batch capacity is unbounded. In this paper, online means that jobs’ arrival is over time. The objective is to minimize the maximum machine cost subject to the makespan being at its minimum. In unbounded parallel batch scheduling, a machine can process several jobs simultaneously as a batch. The processing time of a job and a batch is equal to 1. When job J j is processed on machine M i , it results cost c i j . We only consider two types of cost functions: c i j = a + c j and c i j = a · c j , where a is the fixed cost of machines and c j is the cost of job J j . The number of jobs is n and the number of machines is m . For this problem, we provide two online algorithms, which are showed to be the best possible with a competitive ratio of ( 1 + β m , ⌈ n m ⌉ ) , where β m is the positive root of the equation ( 1 + β m ) m + 1 = β m + 2 .

Suggested Citation

  • Wenhua Li & Weina Zhai & Xing Chai, 2019. "Online Bi-Criteria Scheduling on Batch Machines with Machine Costs," Mathematics, MDPI, vol. 7(10), pages 1-11, October.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:10:p:960-:d:275974
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/7/10/960/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/7/10/960/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Lee, Kangbok & Leung, Joseph Y-T. & Jia, Zhao-hong & Li, Wenhua & Pinedo, Michael L. & Lin, Bertrand M.T., 2014. "Fast approximation algorithms for bi-criteria scheduling with machine assignment costs," European Journal of Operational Research, Elsevier, vol. 238(1), pages 54-64.
    2. Jianfa Cao & Jinjiang Yuan & Wenjie Li & Hailin Bu, 2011. "Online scheduling on batching machines to minimise the total weighted completion time of jobs with precedence constraints and identical processing times," International Journal of Systems Science, Taylor & Francis Journals, vol. 42(1), pages 51-55.
    3. Wenhua Li & Jinjiang Yuan & Yixun Lin, 2007. "A note on special optimal batching structures to minimize total weighted completion time," Journal of Combinatorial Optimization, Springer, vol. 14(4), pages 475-480, November.
    4. Wenjie Li, 2015. "A Best Possible Online Algorithm for the Parallel-Machine Scheduling to Minimize the Maximum Weighted Completion Time," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 32(04), pages 1-10.
    5. Qijia Liu & Jinjiang Yuan, 2016. "Online tradeoff scheduling on a single machine to minimize makespan and maximum lateness," Journal of Combinatorial Optimization, Springer, vol. 32(2), pages 385-395, August.
    6. Yang Fang & Peihai Liu & Xiwen Lu, 2011. "Optimal on-line algorithms for one batch machine with grouped processing times," Journal of Combinatorial Optimization, Springer, vol. 22(4), pages 509-516, November.
    7. Wenhua Li & Xing Chai, 2019. "The medical laboratory scheduling for weighted flow-time," Journal of Combinatorial Optimization, Springer, vol. 37(1), pages 83-94, January.
    8. Ma, Ran & Yuan, Jinjiang, 2014. "Online tradeoff scheduling on a single machine to minimize makespan and total weighted completion time," International Journal of Production Economics, Elsevier, vol. 158(C), pages 114-119.
    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. Xing Chai & Wenhua Li & Yuejuan Zhu, 2021. "Online scheduling to minimize maximum weighted flow-time on a bounded parallel-batch machine," Annals of Operations Research, Springer, vol. 298(1), pages 79-93, March.
    2. Christoph Hertrich & Christian Weiß & Heiner Ackermann & Sandy Heydrich & Sven O. Krumke, 2022. "Online algorithms to schedule a proportionate flexible flow shop of batching machines," Journal of Scheduling, Springer, vol. 25(6), pages 643-657, December.
    3. Wenjie Li & Jinjiang Yuan, 2021. "Single-machine online scheduling of jobs with non-delayed processing constraint," Journal of Combinatorial Optimization, Springer, vol. 41(4), pages 830-843, May.
    4. Xing Chai & Lingfa Lu & Wenhua Li & Liqi Zhang, 2018. "Best-Possible Online Algorithms for Single Machine Scheduling to Minimize the Maximum Weighted Completion Time," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 35(06), pages 1-11, December.
    5. Jing Fan & Hui Shi, 0. "A three-stage supply chain scheduling problem based on the nursing assistants’ daily work in a hospital," Journal of Combinatorial Optimization, Springer, vol. 0, pages 1-13.
    6. Li, Guo & Liu, Mengqi & Sethi, Suresh P. & Xu, Dehua, 2017. "Parallel-machine scheduling with machine-dependent maintenance periodic recycles," International Journal of Production Economics, Elsevier, vol. 186(C), pages 1-7.
    7. Ma, Ran & Tao, Jiping & Yuan, Jinjiang, 2016. "Online scheduling with linear deteriorating jobs to minimize the total weighted completion time," Applied Mathematics and Computation, Elsevier, vol. 273(C), pages 570-583.
    8. Zhang, Jun & Liu, Feng & Tang, Jiafu & Li, Yanhui, 2019. "The online integrated order picking and delivery considering Pickers’ learning effects for an O2O community supermarket," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 123(C), pages 180-199.
    9. Wenhua Li & Xing Chai, 2019. "The medical laboratory scheduling for weighted flow-time," Journal of Combinatorial Optimization, Springer, vol. 37(1), pages 83-94, January.
    10. Qijia Liu & Jinjiang Yuan, 2016. "Online tradeoff scheduling on a single machine to minimize makespan and maximum lateness," Journal of Combinatorial Optimization, Springer, vol. 32(2), pages 385-395, August.
    11. Jiang, Xiaojuan & Lee, Kangbok & Pinedo, Michael L., 2023. "Approximation algorithms for bicriteria scheduling problems on identical parallel machines for makespan and total completion time," European Journal of Operational Research, Elsevier, vol. 305(2), pages 594-607.
    12. Hui-Chih Hung & Bertrand M. T. Lin & Marc E. Posner & Jun-Min Wei, 2019. "Preemptive parallel-machine scheduling problem of maximizing the number of on-time jobs," Journal of Scheduling, Springer, vol. 22(4), pages 413-431, August.
    13. Jing Fan & Hui Shi, 2022. "Non-resumable scheduling on a single bounded parallel-batch machine with periodic maintenance," Journal of Combinatorial Optimization, Springer, vol. 43(5), pages 1645-1654, July.
    14. Jing Fan & Hui Shi, 2021. "A three-stage supply chain scheduling problem based on the nursing assistants’ daily work in a hospital," Journal of Combinatorial Optimization, Springer, vol. 42(4), pages 896-908, November.
    15. Wan, Long & Ding, Zhihao & Li, Yunpeng & Chen, Qianqian & Tan, Zhiyi, 2015. "Scheduling to minimize the maximum total completion time per machine," European Journal of Operational Research, Elsevier, vol. 242(1), pages 45-50.
    16. Jiawei Zhang & Ling Wang & Lining Xing, 2019. "Large-scale medical examination scheduling technology based on intelligent optimization," Journal of Combinatorial Optimization, Springer, vol. 37(1), pages 385-404, January.
    17. Ran Ma & Jinjiang Yuan, 2017. "Online scheduling to minimize the total weighted completion time plus the rejection cost," Journal of Combinatorial Optimization, Springer, vol. 34(2), pages 483-503, 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:7:y:2019:i:10:p:960-:d:275974. 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.