IDEAS home Printed from https://ideas.repec.org/a/eee/ejores/v199y2009i3p702-705.html
   My bibliography  Save this article

Minimizing the number of machines for minimum length schedules

Author

Listed:
  • Finke, Gerd
  • Lemaire, Pierre
  • Proth, Jean-Marie
  • Queyranne, Maurice

Abstract

In this paper, we present a new objective function for scheduling on parallel machines: minimizing the number of machines for schedules of minimum length. We study its complexity and we prove the NP-completeness of this problem, even if there is no precedences or for unitary execution times. We propose several polynomial algorithms for various particular cases.

Suggested Citation

  • Finke, Gerd & Lemaire, Pierre & Proth, Jean-Marie & Queyranne, Maurice, 2009. "Minimizing the number of machines for minimum length schedules," European Journal of Operational Research, Elsevier, vol. 199(3), pages 702-705, December.
  • Handle: RePEc:eee:ejores:v:199:y:2009:i:3:p:702-705
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0377-2217(08)00459-1
    Download Restriction: Full text for ScienceDirect subscribers only
    ---><---

    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. Leo G. Kroon & Marc Salomon & Luk N. Van Wassenhove, 1997. "Exact and Approximation Algorithms for the Tactical Fixed Interval Scheduling Problem," Operations Research, INFORMS, vol. 45(4), pages 624-638, August.
    2. Aziz Moukrim, 2000. "Upper bound on the number of processors for scheduling with interprocessor communication delays," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 52(1), pages 99-113, September.
    3. Robert McNaughton, 1959. "Scheduling with Deadlines and Loss Functions," Management Science, INFORMS, vol. 6(1), pages 1-12, October.
    4. T. C. Hu, 1961. "Parallel Sequencing and Assembly Line Problems," Operations Research, INFORMS, vol. 9(6), pages 841-848, December.
    5. A. Moukrim, 1999. "On the minimum number of processors for scheduling problems with communicationdelays," Annals of Operations Research, Springer, vol. 86(0), pages 455-472, 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. Gerstl, Enrique & Mosheiov, Gur, 2013. "A two-stage flow shop batch-scheduling problem with the option of using Not-All-Machines," International Journal of Production Economics, Elsevier, vol. 146(1), pages 161-166.
    2. Shi, Yuhui & Reich, Daniel & Epelman, Marina & Klampfl, Erica & Cohn, Amy, 2017. "An analytical approach to prototype vehicle test scheduling," Omega, Elsevier, vol. 67(C), pages 168-176.

    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. Kravchenko, Svetlana A. & Werner, Frank, 2009. "Minimizing the number of machines for scheduling jobs with equal processing times," European Journal of Operational Research, Elsevier, vol. 199(2), pages 595-600, December.
    2. Jiang, Xiaojuan & Lee, Kangbok & Pinedo, Michael L., 2021. "Ideal schedules in parallel machine settings," European Journal of Operational Research, Elsevier, vol. 290(2), pages 422-434.
    3. Lenstra, J. K. & Rinnooy Kan, A. H. G., 1980. "An Introduction To Multiprocessor Scheduling," Econometric Institute Archives 272258, Erasmus University Rotterdam.
    4. Timkovsky, Vadim G., 2003. "Identical parallel machines vs. unit-time shops and preemptions vs. chains in scheduling complexity," European Journal of Operational Research, Elsevier, vol. 149(2), pages 355-376, September.
    5. Blazewicz, Jacek & Liu, Zhen, 2002. "Linear and quadratic algorithms for scheduling chains and opposite chains," European Journal of Operational Research, Elsevier, vol. 137(2), pages 248-264, March.
    6. Felix Happach, 2021. "Makespan minimization with OR-precedence constraints," Journal of Scheduling, Springer, vol. 24(3), pages 319-328, June.
    7. Tzafestas, Spyros & Triantafyllakis, Alekos, 1993. "Deterministic scheduling in computing and manufacturing systems: a survey of models and algorithms," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 35(5), pages 397-434.
    8. Nait Tahar, Djamel & Yalaoui, Farouk & Chu, Chengbin & Amodeo, Lionel, 2006. "A linear programming approach for identical parallel machine scheduling with job splitting and sequence-dependent setup times," International Journal of Production Economics, Elsevier, vol. 99(1-2), pages 63-73, February.
    9. Joseph Y.‐T. Leung & Michael Pinedo, 2004. "A note on scheduling parallel machines subject to breakdown and repair," Naval Research Logistics (NRL), John Wiley & Sons, vol. 51(1), pages 60-71, February.
    10. Blazwicz, Jacek & Liu, Zhen, 1996. "Scheduling multiprocessor tasks with chain constraints," European Journal of Operational Research, Elsevier, vol. 94(2), pages 231-241, October.
    11. Liu Guiqing & Li Kai & Cheng Bayi, 2015. "Preemptive Scheduling with Controllable Processing Times on Parallel Machines," Journal of Systems Science and Information, De Gruyter, vol. 3(1), pages 68-76, February.
    12. Anurag Agarwal & Varghese S. Jacob & Hasan Pirkul, 2006. "An Improved Augmented Neural-Network Approach for Scheduling Problems," INFORMS Journal on Computing, INFORMS, vol. 18(1), pages 119-128, February.
    13. Hoogeveen, J. A. & Lenstra, J. K. & Veltman, B., 1996. "Preemptive scheduling in a two-stage multiprocessor flow shop is NP-hard," European Journal of Operational Research, Elsevier, vol. 89(1), pages 172-175, February.
    14. Yung-Chia Chang & Kuei-Hu Chang & Ching-Ping Zheng, 2022. "Application of a Non-Dominated Sorting Genetic Algorithm to Solve a Bi-Objective Scheduling Problem Regarding Printed Circuit Boards," Mathematics, MDPI, vol. 10(13), pages 1-21, July.
    15. Nodari Vakhania, 2001. "Tight Performance Bounds of CP-Scheduling on Out-Trees," Journal of Combinatorial Optimization, Springer, vol. 5(4), pages 445-464, December.
    16. Ramachandra, Girish & Elmaghraby, Salah E., 2006. "Sequencing precedence-related jobs on two machines to minimize the weighted completion time," International Journal of Production Economics, Elsevier, vol. 100(1), pages 44-58, March.
    17. Scholl, Armin & Becker, Christian, 2006. "State-of-the-art exact and heuristic solution procedures for simple assembly line balancing," European Journal of Operational Research, Elsevier, vol. 168(3), pages 666-693, February.
    18. 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.
    19. Slotnick, Susan A., 2011. "Order acceptance and scheduling: A taxonomy and review," European Journal of Operational Research, Elsevier, vol. 212(1), pages 1-11, July.
    20. Leah Epstein, 2023. "Parallel solutions for preemptive makespan scheduling on two identical machines," Journal of Scheduling, Springer, vol. 26(1), pages 61-76, 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:eee:ejores:v:199:y:2009:i:3:p:702-705. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/eor .

    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.