IDEAS home Printed from https://ideas.repec.org/a/spr/jcomop/v34y2017i4d10.1007_s10878-017-0139-8.html
   My bibliography  Save this article

An optimal online algorithm for the parallel-batch scheduling with job processing time compatibilities

Author

Listed:
  • Ruyan Fu

    (China University of Mining and Technology)

  • Ji Tian

    (China University of Mining and Technology)

  • Shisheng Li

    (Zhongyuan University of Technology)

  • Jinjiang Yuan

    (Zhengzhou University)

Abstract

We consider the online (over time) scheduling on a single unbounded parallel-batch machine with job processing time compatibilities to minimize makespan. In the problem, a constant $$\alpha >0$$ α > 0 is given in advance. Each job $$J_{j}$$ J j has a normal processing time $$p_j$$ p j . Two jobs $$J_i$$ J i and $$J_j$$ J j are compatible if $$\max \{p_i, p_j\} \le (1+\alpha )\cdot \min \{p_i, p_j\}$$ max { p i , p j } ≤ ( 1 + α ) · min { p i , p j } . In the problem, mutually compatible jobs can form a batch being processed on the machine. The processing time of a batch is equal to the maximum normal processing time of the jobs in this batch. For this problem, we provide an optimal online algorithm with a competitive ratio of $$1+\beta _\alpha $$ 1 + β α , where $$\beta _\alpha $$ β α is the positive root of the equation $$(1+\alpha )x^{2}+\alpha x=1+\alpha $$ ( 1 + α ) x 2 + α x = 1 + α .

Suggested Citation

  • Ruyan Fu & Ji Tian & Shisheng Li & Jinjiang Yuan, 2017. "An optimal online algorithm for the parallel-batch scheduling with job processing time compatibilities," Journal of Combinatorial Optimization, Springer, vol. 34(4), pages 1187-1197, November.
    • Handle: RePEc:spr:jcomop:v:34:y:2017:i:4:d:10.1007_s10878-017-0139-8
    DOI: 10.1007/s10878-017-0139-8
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10878-017-0139-8
    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/s10878-017-0139-8?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. Gregory Dobson & Ramakrishnan S. Nambimadom, 2001. "The Batch Loading and Scheduling Problem," Operations Research, INFORMS, vol. 49(1), pages 52-65, February.
    2. Nong, Qingqin & Yuan, Jinjiang & Fu, Ruyan & Lin, Lin & Tian, Ji, 2008. "The single-machine parallel-batching on-line scheduling problem with family jobs to minimize makespan," International Journal of Production Economics, Elsevier, vol. 111(2), pages 435-440, February.
    3. Chung-Yee Lee & Reha Uzsoy & Louis A. Martin-Vega, 1992. "Efficient Algorithms for Scheduling Semiconductor Burn-In Operations," Operations Research, INFORMS, vol. 40(4), pages 764-775, August.
    4. Jolai, Fariborz, 2005. "Minimizing number of tardy jobs on a batch processing machine with incompatible job families," European Journal of Operational Research, Elsevier, vol. 162(1), pages 184-190, April.
    5. Xiaotie Deng & Chung Keung Poon & Yuzhong Zhang, 2003. "Approximation Algorithms in Batch Processing," Journal of Combinatorial Optimization, Springer, vol. 7(3), pages 247-257, September.
    6. Gouchuan Zhang & Xiaoqiang Cai & C.K. Wong, 2001. "On‐line algorithms for minimizing makespan on batch processing machines," Naval Research Logistics (NRL), John Wiley & Sons, vol. 48(3), pages 241-258, April.
    7. Chung Poon & Wenci Yu, 2005. "A Flexible On-line Scheduling Algorithm for Batch Machine with Infinite Capacity," Annals of Operations Research, Springer, vol. 133(1), pages 175-181, January.
    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. Jae Won Jang & Yong Jae Kim & Byung Soo Kim, 2022. "A Three-Stage ACO-Based Algorithm for Parallel Batch Loading and Scheduling Problem with Batch Deterioration and Rate-Modifying Activities," Mathematics, MDPI, vol. 10(4), pages 1-26, February.

    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. 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.
    2. Chakhlevitch, Konstantin & Glass, Celia A. & Kellerer, Hans, 2011. "Batch machine production with perishability time windows and limited batch size," European Journal of Operational Research, Elsevier, vol. 210(1), pages 39-47, April.
    3. Fowler, John W. & Mönch, Lars, 2022. "A survey of scheduling with parallel batch (p-batch) processing," European Journal of Operational Research, Elsevier, vol. 298(1), pages 1-24.
    4. Beat Gfeller & Leon Peeters & Birgitta Weber & Peter Widmayer, 2009. "Single machine batch scheduling with release times," Journal of Combinatorial Optimization, Springer, vol. 17(3), pages 323-338, April.
    5. A H Kashan & B Karimi, 2008. "Scheduling a single batch-processing machine with arbitrary job sizes and incompatible job families: An ant colony framework," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 59(9), pages 1269-1280, September.
    6. Jinjiang Yuan & Shisheng Li & Ji Tian & Ruyan Fu, 2009. "A best on-line algorithm for the single machine parallel-batch scheduling with restricted delivery times," Journal of Combinatorial Optimization, Springer, vol. 17(2), pages 206-213, February.
    7. Chengwen Jiao & Jinjiang Yuan & Qi Feng, 2019. "Online Algorithms for Scheduling Unit Length Jobs on Unbounded Parallel-Batch Machines with Linearly Lookahead," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 36(05), pages 1-8, October.
    8. Chung Keung Poon & Wenci Yu, 2005. "On-Line Scheduling Algorithms for a Batch Machine with Finite Capacity," Journal of Combinatorial Optimization, Springer, vol. 9(2), pages 167-186, March.
    9. Hailing Liu & Jinjiang Yuan & Wenjie Li, 2016. "Online scheduling of equal length jobs on unbounded parallel batch processing machines with limited restart," Journal of Combinatorial Optimization, Springer, vol. 31(4), pages 1609-1622, May.
    10. Shisheng Li & Jinjiang Yuan, 2010. "Parallel-machine parallel-batching scheduling with family jobs and release dates to minimize makespan," Journal of Combinatorial Optimization, Springer, vol. 19(1), pages 84-93, January.
    11. Li, Dongni & Jiang, Yuzhou & Zhang, Jinhui & Cui, Zihua & Yin, Yong, 2023. "An on-line seru scheduling algorithm with proactive waiting considering resource conflicts," European Journal of Operational Research, Elsevier, vol. 309(2), pages 506-515.
    12. Koh, Shie-Gheun & Koo, Pyung-Hoi & Kim, Dong-Chun & Hur, Won-Suk, 2005. "Scheduling a single batch processing machine with arbitrary job sizes and incompatible job families," International Journal of Production Economics, Elsevier, vol. 98(1), pages 81-96, October.
    13. 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.
    14. Xu, Jun & Wang, Jun-Qiang & Liu, Zhixin, 2022. "Parallel batch scheduling: Impact of increasing machine capacity," Omega, Elsevier, vol. 108(C).
    15. Lin, Ran & Wang, Jun-Qiang & Liu, Zhixin & Xu, Jun, 2023. "Best possible algorithms for online scheduling on identical batch machines with periodic pulse interruptions," European Journal of Operational Research, Elsevier, vol. 309(1), pages 53-64.
    16. Lin, Ran & Wang, Jun-Qiang & Oulamara, Ammar, 2023. "Online scheduling on parallel-batch machines with periodic availability constraints and job delivery," Omega, Elsevier, vol. 116(C).
    17. Bin Ji & Xin Xiao & Samson S. Yu & Guohua Wu, 2023. "A Hybrid Large Neighborhood Search Method for Minimizing Makespan on Unrelated Parallel Batch Processing Machines with Incompatible Job Families," Sustainability, MDPI, vol. 15(5), pages 1-25, February.
    18. Payman Jula & Robert C. Leachman, 2010. "Coordinated Multistage Scheduling of Parallel Batch-Processing Machines Under Multiresource Constraints," Operations Research, INFORMS, vol. 58(4-part-1), pages 933-947, August.
    19. Yuan Gao & Jinjiang Yuan, 2019. "Unbounded parallel-batch scheduling under agreeable release and processing to minimize total weighted number of tardy jobs," Journal of Combinatorial Optimization, Springer, vol. 38(3), pages 698-711, October.
    20. Yuan Gao & Jinjiang Yuan & Zhigang Wei, 2019. "Unbounded parallel-batch scheduling with drop-line tasks," Journal of Scheduling, Springer, vol. 22(4), pages 449-463, 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:spr:jcomop:v:34:y:2017:i:4:d:10.1007_s10878-017-0139-8. 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.