IDEAS home Printed from https://ideas.repec.org/a/spr/jcomop/v7y2003i3d10.1023_a1027316504440.html
   My bibliography  Save this article

Approximation Algorithms in Batch Processing

Author

Listed:
  • Xiaotie Deng

    (City University of Hong Kong)

  • Chung Keung Poon

    (City University of Hong Kong)

  • Yuzhong Zhang

    (Qufu Normal University)

Abstract

A polynomial approximation scheme for minimizing makespan in a batch processing system under dynamic job arrivals is presented. A lower bound of $${{(\sqrt 5 + 2)} \mathord{\left/ {\vphantom {{(\sqrt 5 + 2)} 2}} \right. \kern-\nulldelimiterspace} 2}$$ on the competitive ratio of any on-line algorithm is proved. This is matched by an on-line algorithm for the special case of unbounded machine capacity.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:jcomop:v:7:y:2003:i:3:d:10.1023_a:1027316504440
    DOI: 10.1023/A:1027316504440
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1023/A:1027316504440
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1023/A:1027316504440?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. 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.
    2. Chung-Lun Li & Chung-Yee Lee, 1997. "Scheduling with agreeable release times and due dates on a batch processing machine," European Journal of Operational Research, Elsevier, vol. 96(3), pages 564-569, February.
    3. Javad H. Ahmadi & Reza H. Ahmadi & Sriram Dasu & Christopher S. Tang, 1992. "Batching and Scheduling Jobs on Batch and Discrete Processors," Operations Research, INFORMS, vol. 40(4), pages 750-763, August.
    4. Unknown, 1986. "Letters," Choices: The Magazine of Food, Farm, and Resource Issues, Agricultural and Applied Economics Association, vol. 1(4), pages 1-9.
    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. 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.
    2. 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.
    3. 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.
    4. 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.
    5. 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.
    6. Ou, Jinwen & Lu, Lingfa & Zhong, Xueling, 2023. "Parallel-batch scheduling with rejection: Structural properties and approximation algorithms," European Journal of Operational Research, Elsevier, vol. 310(3), pages 1017-1032.
    7. Li, Shisheng & Ng, C.T. & Cheng, T.C.E. & Yuan, Jinjiang, 2011. "Parallel-batch scheduling of deteriorating jobs with release dates to minimize the makespan," European Journal of Operational Research, Elsevier, vol. 210(3), pages 482-488, May.
    8. 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.
    9. 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.
    10. 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.
    11. Peihai Liu & Xiwen Lu, 2015. "Online unbounded batch scheduling on parallel machines with delivery times," Journal of Combinatorial Optimization, Springer, vol. 29(1), pages 228-236, January.
    12. 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.
    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. Li, Shuguang, 2017. "Approximation algorithms for scheduling jobs with release times and arbitrary sizes on batch machines with non-identical capacities," European Journal of Operational Research, Elsevier, vol. 263(3), pages 815-826.
    15. Li, Shuguang, 2017. "Parallel batch scheduling with inclusive processing set restrictions and non-identical capacities to minimize makespan," European Journal of Operational Research, Elsevier, vol. 260(1), pages 12-20.

    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. 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.
    2. Sung, Chang Sup & Kim, Young Hwan & Yoon, Sang Hum, 2000. "A problem reduction and decomposition approach for scheduling for a flowshop of batch processing machines," European Journal of Operational Research, Elsevier, vol. 121(1), pages 179-192, February.
    3. Sup Sung, Chang & Hwan Kim, Young, 2003. "Minimizing due date related performance measures on two batch processing machines," European Journal of Operational Research, Elsevier, vol. 147(3), pages 644-656, June.
    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. Jolai Ghazvini, Fariborz & Dupont, Lionel, 1998. "Minimizing mean flow times criteria on a single batch processing machine with non-identical jobs sizes," International Journal of Production Economics, Elsevier, vol. 55(3), pages 273-280, August.
    6. Melouk, Sharif & Damodaran, Purushothaman & Chang, Ping-Yu, 2004. "Minimizing makespan for single machine batch processing with non-identical job sizes using simulated annealing," International Journal of Production Economics, Elsevier, vol. 87(2), pages 141-147, January.
    7. 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.
    8. 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.
    9. Tang, Lixin & Zhao, Yufang, 2008. "Scheduling a single semi-continuous batching machine," Omega, Elsevier, vol. 36(6), pages 992-1004, December.
    10. Christoph Hertrich & Christian Weiß & Heiner Ackermann & Sandy Heydrich & Sven O. Krumke, 2020. "Scheduling a proportionate flow shop of batching machines," Journal of Scheduling, Springer, vol. 23(5), pages 575-593, October.
    11. 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.
    12. Chung-Lun Li & Chung-Yee Lee, 1997. "Scheduling with agreeable release times and due dates on a batch processing machine," European Journal of Operational Research, Elsevier, vol. 96(3), pages 564-569, February.
    13. John Tajan & Appa Sivakumar & Stanley Gershwin, 2011. "Controlling job arrivals with processing time windows into Batch Processor Buffer," Annals of Operations Research, Springer, vol. 191(1), pages 193-218, November.
    14. Damodaran, Purushothaman & Kumar Manjeshwar, Praveen & Srihari, Krishnaswami, 2006. "Minimizing makespan on a batch-processing machine with non-identical job sizes using genetic algorithms," International Journal of Production Economics, Elsevier, vol. 103(2), pages 882-891, October.
    15. Sung, C. S. & Choung, Y. I., 2000. "Minimizing makespan on a single burn-in oven in semiconductor manufacturing," European Journal of Operational Research, Elsevier, vol. 120(3), pages 559-574, February.
    16. 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.
    17. 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.
    18. Bo Chen & Xiaotie Deng & Wenan Zang, 2004. "On-Line Scheduling a Batch Processing System to Minimize Total Weighted Job Completion Time," Journal of Combinatorial Optimization, Springer, vol. 8(1), pages 85-95, March.
    19. Ciftci, B.B. & Borm, P.E.M. & Hamers, H.J.M. & Slikker, M., 2008. "Batch Sequencing and Cooperation," Other publications TiSEM ed1f8fce-da76-41a6-9a9e-9, Tilburg University, School of Economics and Management.
    20. Gregory Dobson & Ramakrishnan S. Nambimadom, 2001. "The Batch Loading and Scheduling Problem," Operations Research, INFORMS, vol. 49(1), pages 52-65, February.

    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:7:y:2003:i:3:d:10.1023_a:1027316504440. 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.