IDEAS home Printed from https://ideas.repec.org/a/pal/jorsoc/v58y2007i7d10.1057_palgrave.jors.2602209.html
   My bibliography  Save this article

Minimizing makespan for two parallel machines with job limit on each availability interval

Author

Listed:
  • C-J Liao

    (National Taiwan University of Science and Technology)

  • C-M Chen

    (National Taiwan University of Science and Technology)

  • C-H Lin

    (Jin Wen Institute of Technology)

Abstract

We consider the problem of scheduling jobs on two parallel machines that are not continuously available for processing. The machine is not available after processing a fixed number of jobs in order to make precision adjustment of machines such as in wafer manufacturing, to reload the feeder in printed circuit board production, or to undertake any other maintenance works such as cleaning and safety inspections. The objective of the problem is to minimize the makespan. Two different scheduling horizons are investigated for this problem. For the short-term scheduling horizon, we consider only the time period before the unavailability interval, while for the long-term horizon, machines are allowed to restart processing after the unavailability interval. For both cases, which are strongly NP-hard, exact optimization algorithms based on the branch and bound method are proposed. Although the algorithms have exponential time complexities, computational results show that they can solve optimally the various-sized problems in reasonable computation time.

Suggested Citation

  • C-J Liao & C-M Chen & C-H Lin, 2007. "Minimizing makespan for two parallel machines with job limit on each availability interval," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 58(7), pages 938-947, July.
    • Handle: RePEc:pal:jorsoc:v:58:y:2007:i:7:d:10.1057_palgrave.jors.2602209
    DOI: 10.1057/palgrave.jors.2602209
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1057/palgrave.jors.2602209
    File Function: Abstract
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1057/palgrave.jors.2602209?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. Schmidt, Gunter, 2000. "Scheduling with limited machine availability," European Journal of Operational Research, Elsevier, vol. 121(1), pages 1-15, February.
    2. Johnny C. Ho & Johnny S. Wong, 1995. "Makespan minimization for m parallel identical processors," Naval Research Logistics (NRL), John Wiley & Sons, vol. 42(6), pages 935-948, September.
    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. Lee, Cheng-Hsiung & Liao, Ching-Jong & Chung, Tsui-Ping, 2014. "Scheduling with multi-attribute setup times on two identical parallel machines," International Journal of Production Economics, Elsevier, vol. 153(C), pages 130-138.
    2. A J Ruiz-Torres & F J López & P J Wojciechowski & J C Ho, 2010. "Parallel machine scheduling problems considering regular measures of performance and machine cost," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 61(5), pages 849-857, May.
    3. Sandeep Kumar & Bhupesh Kumar Lad, 2017. "Integrated production and maintenance planning for parallel machine system considering cost of rejection," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 68(7), pages 834-846, 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. Liao, Ching-Jong & Shyur, Der-Lin & Lin, Chien-Hung, 2005. "Makespan minimization for two parallel machines with an availability constraint," European Journal of Operational Research, Elsevier, vol. 160(2), pages 445-456, January.
    2. Navid Hashemian & Claver Diallo & Béla Vizvári, 2014. "Makespan minimization for parallel machines scheduling with multiple availability constraints," Annals of Operations Research, Springer, vol. 213(1), pages 173-186, February.
    3. Stanisław Gawiejnowicz, 2020. "A review of four decades of time-dependent scheduling: main results, new topics, and open problems," Journal of Scheduling, Springer, vol. 23(1), pages 3-47, February.
    4. Wang, Xiuli & Cheng, T.C.E., 2015. "A heuristic for scheduling jobs on two identical parallel machines with a machine availability constraint," International Journal of Production Economics, Elsevier, vol. 161(C), pages 74-82.
    5. Seyed Habib A. Rahmati & Abbas Ahmadi & Kannan Govindan, 2018. "A novel integrated condition-based maintenance and stochastic flexible job shop scheduling problem: simulation-based optimization approach," Annals of Operations Research, Springer, vol. 269(1), pages 583-621, October.
    6. Allaoui, H. & Lamouri, S. & Artiba, A. & Aghezzaf, E., 2008. "Simultaneously scheduling n jobs and the preventive maintenance on the two-machine flow shop to minimize the makespan," International Journal of Production Economics, Elsevier, vol. 112(1), pages 161-167, March.
    7. C N Potts & V A Strusevich, 2009. "Fifty years of scheduling: a survey of milestones," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 60(1), pages 41-68, May.
    8. Hongying Li & Chunjie Su, 2011. "An optimal semi-online algorithm for 2-machine scheduling with an availability constraint," Journal of Combinatorial Optimization, Springer, vol. 22(2), pages 153-165, August.
    9. Shabtay, Dvir, 2022. "Single-machine scheduling with machine unavailability periods and resource dependent processing times," European Journal of Operational Research, Elsevier, vol. 296(2), pages 423-439.
    10. Zhong, Xueling & Ou, Jinwen & Wang, Guoqing, 2014. "Order acceptance and scheduling with machine availability constraints," European Journal of Operational Research, Elsevier, vol. 232(3), pages 435-441.
    11. Guohua Wan & Xiangtong Qi, 2010. "Scheduling with variable time slot costs," Naval Research Logistics (NRL), John Wiley & Sons, vol. 57(2), pages 159-171, March.
    12. Huo, Yumei & Zhao, Hairong, 2015. "Total completion time minimization on multiple machines subject to machine availability and makespan constraints," European Journal of Operational Research, Elsevier, vol. 243(2), pages 547-554.
    13. Zribi, N. & El Kamel, A. & Borne, P., 2008. "Minimizing the makespan for the MPM job-shop with availability constraints," International Journal of Production Economics, Elsevier, vol. 112(1), pages 151-160, March.
    14. Hnaien, Faicel & Yalaoui, Farouk & Mhadhbi, Ahmed, 2015. "Makespan minimization on a two-machine flowshop with an availability constraint on the first machine," International Journal of Production Economics, Elsevier, vol. 164(C), pages 95-104.
    15. Jaykrishnan, G. & Levin, Asaf, 2024. "Scheduling with cardinality dependent unavailability periods," European Journal of Operational Research, Elsevier, vol. 316(2), pages 443-458.
    16. Geurtsen, M. & Didden, Jeroen B.H.C. & Adan, J. & Atan, Z. & Adan, I., 2023. "Production, maintenance and resource scheduling: A review," European Journal of Operational Research, Elsevier, vol. 305(2), pages 501-529.
    17. Shabtay, Dvir & Zofi, Moshe, 2018. "Single machine scheduling with controllable processing times and an unavailability period to minimize the makespan," International Journal of Production Economics, Elsevier, vol. 198(C), pages 191-200.
    18. Xu, Dehua & Wan, Long & Liu, Aihua & Yang, Dar-Li, 2015. "Single machine total completion time scheduling problem with workload-dependent maintenance duration," Omega, Elsevier, vol. 52(C), pages 101-106.
    19. Imed Kacem & Hans Kellerer & Yann Lanuel, 2015. "Approximation algorithms for maximizing the weighted number of early jobs on a single machine with non-availability intervals," Journal of Combinatorial Optimization, Springer, vol. 30(3), pages 403-412, October.
    20. Chatterjee A K & Mukherjee, Saral, 2006. "Unified Concept of Bottleneck," IIMA Working Papers WP2006-05-01, Indian Institute of Management Ahmedabad, Research and Publication Department.

    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:pal:jorsoc:v:58:y:2007:i:7:d:10.1057_palgrave.jors.2602209. 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.palgrave-journals.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.