IDEAS home Printed from https://ideas.repec.org/a/spr/jcomop/v30y2015i2d10.1007_s10878-014-9760-y.html
   My bibliography  Save this article

Online scheduling on two parallel machines with release dates and delivery times

Author

Listed:
  • Peihai Liu

    (East China University of Science and Technology)

  • Xiwen Lu

    (East China University of Science and Technology)

Abstract

We consider an online scheduling problem where jobs arrive over time. A set of independent jobs has to be scheduled on two parallel machines, where preemption is not allowed and the number of jobs is unknown in advance. The characteristics of each job, i.e., processing time and delivery time, become known at its release date. Each job is delivered to the destination independently and immediately at its completion time on the machines. The objective is to minimize the time by which all jobs have been delivered. We present an online algorithm which has a competitive ratio of $$(1+\sqrt{5})/2\approx 1.618$$ ( 1 + 5 ) / 2 ≈ 1.618 . Finally, our experimental results show that, in practice, the worst case error ratio is much better than the theoretical bound.

Suggested Citation

  • Peihai Liu & Xiwen Lu, 2015. "Online scheduling on two parallel machines with release dates and delivery times," Journal of Combinatorial Optimization, Springer, vol. 30(2), pages 347-359, August.
    • Handle: RePEc:spr:jcomop:v:30:y:2015:i:2:d:10.1007_s10878-014-9760-y
    DOI: 10.1007/s10878-014-9760-y
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10878-014-9760-y
    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/s10878-014-9760-y?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. C. N. Potts, 1980. "Technical Note—Analysis of a Heuristic for One Machine Sequencing with Release Dates and Delivery Times," Operations Research, INFORMS, vol. 28(6), pages 1436-1441, December.
    2. Steve Seiden, 1999. "Randomized Online Scheduling with Delivery Times," Journal of Combinatorial Optimization, Springer, vol. 3(4), pages 399-416, December.
    3. Leslie A. Hall & David B. Shmoys, 1992. "Jackson's Rule for Single-Machine Scheduling: Making a Good Heuristic Better," Mathematics of Operations Research, INFORMS, vol. 17(1), pages 22-35, February.
    4. 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.
    5. Imed Kacem, 2009. "Approximation algorithms for the makespan minimization with positive tails on a single machine with a fixed non-availability interval," Journal of Combinatorial Optimization, Springer, vol. 17(2), pages 117-133, February.
    6. Liu, Ming & Chu, Chengbin & Xu, Yinfeng & Zheng, Feifeng, 2010. "An optimal online algorithm for single machine scheduling with bounded delivery times," European Journal of Operational Research, Elsevier, vol. 201(3), pages 693-700, March.
    7. Mohamed Haouari & Anis Gharbi, 2004. "Lower Bounds for Scheduling on Identical Parallel Machines with Heads and Tails," Annals of Operations Research, Springer, vol. 129(1), pages 187-204, July.
    8. Carlier, Jacques, 1987. "Scheduling jobs with release dates and tails on identical machines to minimize the makespan," European Journal of Operational Research, Elsevier, vol. 29(3), pages 298-306, June.
    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. Söhnke Maecker & Liji Shen, 2020. "Solving parallel machine problems with delivery times and tardiness objectives," Annals of Operations Research, Springer, vol. 285(1), pages 315-334, February.
    2. 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.
    3. Ji Tian & Yan Zhou & Ruyan Fu, 2020. "An improved semi-online algorithm for scheduling on a single machine with unexpected breakdown," Journal of Combinatorial Optimization, Springer, vol. 40(1), pages 170-180, July.

    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. Ji Tian & Yan Zhou & Ruyan Fu, 2020. "An improved semi-online algorithm for scheduling on a single machine with unexpected breakdown," Journal of Combinatorial Optimization, Springer, vol. 40(1), pages 170-180, July.
    2. Zhi-Long Chen, 2010. "Integrated Production and Outbound Distribution Scheduling: Review and Extensions," Operations Research, INFORMS, vol. 58(1), pages 130-148, February.
    3. Söhnke Maecker & Liji Shen, 2020. "Solving parallel machine problems with delivery times and tardiness objectives," Annals of Operations Research, Springer, vol. 285(1), pages 315-334, February.
    4. Chang, Yung-Chia & Lee, Chung-Yee, 2004. "Machine scheduling with job delivery coordination," European Journal of Operational Research, Elsevier, vol. 158(2), pages 470-487, October.
    5. Imed Kacem, 2009. "Approximation algorithms for the makespan minimization with positive tails on a single machine with a fixed non-availability interval," Journal of Combinatorial Optimization, Springer, vol. 17(2), pages 117-133, February.
    6. Guruprasad Pundoor & Zhi‐Long Chen, 2005. "Scheduling a production–distribution system to optimize the tradeoff between delivery tardiness and distribution cost," Naval Research Logistics (NRL), John Wiley & Sons, vol. 52(6), pages 571-589, September.
    7. Alejandro Reynoso & Nodari Vakhania, 2021. "Theoretical and practical issues in single-machine scheduling with two job release and delivery times," Journal of Scheduling, Springer, vol. 24(6), pages 615-647, December.
    8. Lixin Tang & Feng Li & Jiyin Liu, 2015. "Integrated scheduling of loading and transportation with tractors and semitrailers separated," Naval Research Logistics (NRL), John Wiley & Sons, vol. 62(5), pages 416-433, August.
    9. Koulamas, Christos & Kyparisis, George J., 2023. "A classification of dynamic programming formulations for offline deterministic single-machine scheduling problems," European Journal of Operational Research, Elsevier, vol. 305(3), pages 999-1017.
    10. Li Kai & Li Hui & Cheng Bayi & Luo Qing, 2015. "Uniform Parallel Machine Scheduling Problem with Controllable Delivery Times," Journal of Systems Science and Information, De Gruyter, vol. 3(6), pages 525-537, December.
    11. Liang-Liang Fu & Mohamed Ali Aloulou & Christian Artigues, 2018. "Integrated production and outbound distribution scheduling problems with job release dates and deadlines," Journal of Scheduling, Springer, vol. 21(4), pages 443-460, August.
    12. Blazewicz, Jacek & Domschke, Wolfgang & Pesch, Erwin, 1996. "The job shop scheduling problem: Conventional and new solution techniques," European Journal of Operational Research, Elsevier, vol. 93(1), pages 1-33, August.
    13. Li, Chung-Lun & Vairaktarakis, George & Lee, Chung-Yee, 2005. "Machine scheduling with deliveries to multiple customer locations," European Journal of Operational Research, Elsevier, vol. 164(1), pages 39-51, July.
    14. Zhi-Long Chen & Guruprasad Pundoor, 2006. "Order Assignment and Scheduling in a Supply Chain," Operations Research, INFORMS, vol. 54(3), pages 555-572, June.
    15. Yinling Wang & Yan Lan & Xin Chen & Xin Han & Yong Piao, 2022. "A tight approximation algorithm for problem $$P2\rightarrow D|v=1,c=1|C_{\max }$$ P 2 → D | v = 1 , c = 1 | C max," Journal of Combinatorial Optimization, Springer, vol. 44(4), pages 2195-2206, November.
    16. Sun Lee, Ik & Yoon, S.H., 2010. "Coordinated scheduling of production and delivery stages with stage-dependent inventory holding costs," Omega, Elsevier, vol. 38(6), pages 509-521, December.
    17. Federico Alonso-Pecina & José Alberto Hernández & José Maria Sigarreta & Nodari Vakhania, 2020. "Fast Approximation for Scheduling One Machine," Mathematics, MDPI, vol. 8(9), pages 1-18, September.
    18. Mohamed Haouari & Lotfi Hidri & Anis Gharbi, 2006. "Optimal Scheduling of a Two-stage Hybrid Flow Shop," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 64(1), pages 107-124, August.
    19. Zhi-Long Chen & George L. Vairaktarakis, 2005. "Integrated Scheduling of Production and Distribution Operations," Management Science, INFORMS, vol. 51(4), pages 614-628, April.
    20. Yinling Wang & Yan Lan & Xin Chen & Xin Han & Yong Piao, 0. "A tight approximation algorithm for problem $$P2\rightarrow D|v=1,c=1|C_{\max }$$P2→D|v=1,c=1|Cmax," Journal of Combinatorial Optimization, Springer, vol. 0, pages 1-12.

    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:30:y:2015:i:2:d:10.1007_s10878-014-9760-y. 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.