IDEAS home Printed from https://ideas.repec.org/a/eee/ejores/v268y2018i1p101-112.html
   My bibliography  Save this article

Parallel machine scheduling with speed-up resources

Author

Listed:
  • Chen, Lin
  • Ye, Deshi
  • Zhang, Guochuan

Abstract

We consider the problem of scheduling with renewable speed-up resources. Given m identical machines, n jobs and c different discrete resources, the task is to process each job non-preemptively on one of the machines so as to minimize the makespan. In our problem, a job has its original processing time, which could be reduced by utilizing one of the resources. As resources are different, the amount of the time reduced for each job is different depending on the resource it uses. Once a resource is being used by one job, it cannot be used simultaneously by any other job until this job is finished, hence the scheduler should take into account the job-to-machine assignment together with the resource-to-job assignment. We observe that, the classical unrelated machine scheduling problem is actually a special case of our problem when m=c, i.e., the number of resources equals the number of machines. Extending the techniques for the unrelated machine scheduling, we give a 2-approximation algorithm when both m and c are part of the input. We then consider two special cases for the problem, with either m or c being a constant, and derive PTASes (Polynomial Time Approximation Schemes) respectively. We also establish the relationship between the two parameters m and c, through which we are able to transform the PTAS for the case when m is constant to the case when c is a constant. The relationship between the two parameters reveals the structure within the problem, and may be of independent interest.

Suggested Citation

  • Chen, Lin & Ye, Deshi & Zhang, Guochuan, 2018. "Parallel machine scheduling with speed-up resources," European Journal of Operational Research, Elsevier, vol. 268(1), pages 101-112.
    • Handle: RePEc:eee:ejores:v:268:y:2018:i:1:p:101-112
    DOI: 10.1016/j.ejor.2018.01.037
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0377221718300730
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.ejor.2018.01.037?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. Robert McNaughton, 1959. "Scheduling with Deadlines and Loss Functions," Management Science, INFORMS, vol. 6(1), pages 1-12, October.
    2. Ravi Kannan, 1987. "Minkowski's Convex Body Theorem and Integer Programming," Mathematics of Operations Research, INFORMS, vol. 12(3), pages 415-440, August.
    3. Klaus Jansen & Lorant Porkolab, 2001. "Improved Approximation Schemes for Scheduling Unrelated Parallel Machines," Mathematics of Operations Research, INFORMS, vol. 26(2), pages 324-338, May.
    4. Jansen, Klaus & Mastrolilli, Monaldo & Solis-Oba, Roberto, 2005. "Approximation schemes for job shop scheduling problems with controllable processing times," European Journal of Operational Research, Elsevier, vol. 167(2), pages 297-319, December.
    5. Nip, Kameng & Wang, Zhenbo & Wang, Zizhuo, 2016. "Scheduling under linear constraints," European Journal of Operational Research, Elsevier, vol. 253(2), pages 290-297.
    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. 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.
    2. Jartnillaphand, Ponpot & Mardaneh, Elham & Bui, Hoa T., 2025. "Bilinear branch and check for unspecified parallel machine scheduling with shift consideration," European Journal of Operational Research, Elsevier, vol. 320(1), pages 35-56.
    3. Bentao Su & Naiming Xie & Yingjie Yang, 2021. "Hybrid genetic algorithm based on bin packing strategy for the unrelated parallel workgroup scheduling problem," Journal of Intelligent Manufacturing, Springer, vol. 32(4), pages 957-969, April.
    4. Jianzhong Qiu & Jun Wu & Xi Chen & Bingyan Zhao & Yan Fang, 2024. "Production scheduling decision-making technology for multiple CNC machining centers with constraints on serviceable time," Journal of Scheduling, Springer, vol. 27(5), pages 441-459, October.

    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. 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.
    2. Siyun Zhang & Kameng Nip & Zhenbo Wang, 0. "Related machine scheduling with machine speeds satisfying linear constraints," Journal of Combinatorial Optimization, Springer, vol. 0, pages 1-17.
    3. 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.
    4. 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.
    5. Jacomine Grobler & Andries Engelbrecht & Schalk Kok & Sarma Yadavalli, 2010. "Metaheuristics for the multi-objective FJSP with sequence-dependent set-up times, auxiliary resources and machine down time," Annals of Operations Research, Springer, vol. 180(1), pages 165-196, November.
    6. 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.
    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. Klaus Jansen & Roberto Solis-Oba, 2011. "A Polynomial Time OPT + 1 Algorithm for the Cutting Stock Problem with a Constant Number of Object Lengths," Mathematics of Operations Research, INFORMS, vol. 36(4), pages 743-753, November.
    9. Xiaofei Liu & Peiyin Xing & Weidong Li, 2020. "Approximation Algorithms for the Submodular Load Balancing with Submodular Penalties," Mathematics, MDPI, vol. 8(10), pages 1-12, October.
    10. Leah Epstein, 2023. "Parallel solutions for preemptive makespan scheduling on two identical machines," Journal of Scheduling, Springer, vol. 26(1), pages 61-76, February.
    11. Djellab, Housni & Djellab, Khaled, 2002. "Preemptive Hybrid Flowshop Scheduling problem of interval orders," European Journal of Operational Research, Elsevier, vol. 137(1), pages 37-49, February.
    12. Han, Bin & Zhang, Wenjun & Lu, Xiwen & Lin, Yingzi, 2015. "On-line supply chain scheduling for single-machine and parallel-machine configurations with a single customer: Minimizing the makespan and delivery cost," European Journal of Operational Research, Elsevier, vol. 244(3), pages 704-714.
    13. 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.
    14. Xu, Jun & Wang, Jun-Qiang & Liu, Zhixin, 2022. "Parallel batch scheduling: Impact of increasing machine capacity," Omega, Elsevier, vol. 108(C).
    15. Zeynep Adak & Mahmure Övül Arıoğlu Akan & Serol Bulkan, 0. "Multiprocessor open shop problem: literature review and future directions," Journal of Combinatorial Optimization, Springer, vol. 0, pages 1-23.
    16. Matthias Bentert & Robert Bredereck & Péter Györgyi & Andrzej Kaczmarczyk & Rolf Niedermeier, 2023. "A multivariate complexity analysis of the material consumption scheduling problem," Journal of Scheduling, Springer, vol. 26(4), pages 369-382, August.
    17. Jacques Carlier & Claire Hanen, 2024. "Measuring the slack between lower bounds for scheduling on parallel machines," Annals of Operations Research, Springer, vol. 338(1), pages 347-377, July.
    18. William Cook & Thomas Rutherford & Herbert E. Scarf & David F. Shallcross, 1991. "An Implementation of the Generalized Basis Reduction Algorithm for Integer Programming," Cowles Foundation Discussion Papers 990, Cowles Foundation for Research in Economics, Yale University.
    19. Mehdi Rajabi Asadabadi, 2017. "A developed slope order index (SOI) for bottlenecks in projects and production lines," Computational Management Science, Springer, vol. 14(2), pages 281-291, April.
    20. D. V. Gribanov & D. S. Malyshev & P. M. Pardalos & S. I. Veselov, 2018. "FPT-algorithms for some problems related to integer programming," Journal of Combinatorial Optimization, Springer, vol. 35(4), pages 1128-1146, May.

    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:268:y:2018:i:1:p:101-112. 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.