IDEAS home Printed from https://ideas.repec.org/a/inm/oropre/v61y2013i5p1243-1257.html
   My bibliography  Save this article

Parallel Machine Scheduling: Impact of Adding Extra Machines

Author

Listed:
  • Kabir Rustogi

    (School of Computing and Mathematical Sciences, Old Royal Naval College, University of Greenwich, London SE10 9LS, United Kingdom)

  • Vitaly A. Strusevich

    (School of Computing and Mathematical Sciences, Old Royal Naval College, University of Greenwich, London SE10 9LS, United Kingdom)

Abstract

We consider the classical scheduling problems of processing jobs on identical parallel machines to minimize (i) the makespan (the maximum completion time) or (ii) the total flow time (the sum of the completion times). The focus of this study is on the impact that additional machines may have, if added to the system. We measure such a machine impact by the ratio of the value of the objective function computed with the original number of machines to the one computed with extra machines. We give tight bounds on the machine impact for the problem of minimizing the makespan, for both the preemptive and non-preemptive versions, as well as for the problem of minimizing the total flow time. We also present polynomial-time exact and approximation algorithms to make a cost-effective choice of the number of machines, provided that each machine incurs a cost and the objective function captures the trade-off between the cost of the used machines and a scheduling objective.

Suggested Citation

  • Kabir Rustogi & Vitaly A. Strusevich, 2013. "Parallel Machine Scheduling: Impact of Adding Extra Machines," Operations Research, INFORMS, vol. 61(5), pages 1243-1257, October.
    • Handle: RePEc:inm:oropre:v:61:y:2013:i:5:p:1243-1257
    DOI: 10.1287/opre.2013.1208
    as

    Download full text from publisher

    File URL: http://dx.doi.org/10.1287/opre.2013.1208
    Download Restriction: no
    File URL: https://libkey.io/10.1287/opre.2013.1208?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
    ---><---

    References listed on IDEAS

    as
    1. Rustogi, Kabir & Strusevich, Vitaly A., 2012. "Single machine scheduling with general positional deterioration and rate-modifying maintenance," Omega, Elsevier, vol. 40(6), pages 791-804.
    2. Robert McNaughton, 1959. "Scheduling with Deadlines and Loss Functions," Management Science, INFORMS, vol. 6(1), pages 1-12, October.
    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. Rachid Benmansour & Oliver Braun, 2023. "On the minimum number of resources for a perfect schedule," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 31(1), pages 191-204, March.
    2. Halman, Nir & Kellerer, Hans & Strusevich, Vitaly A., 2018. "Approximation schemes for non-separable non-linear boolean programming problems under nested knapsack constraints," European Journal of Operational Research, Elsevier, vol. 270(2), pages 435-447.
    3. Alan J. Soper & Vitaly A. Strusevich, 2022. "Preemptive and non-preemptive scheduling on two unrelated parallel machines," Journal of Scheduling, Springer, vol. 25(6), pages 659-674, December.
    4. Xu, Jun & Wang, Jun-Qiang & Liu, Zhixin, 2022. "Parallel batch scheduling: Impact of increasing machine capacity," Omega, Elsevier, vol. 108(C).
    5. Alan J. Soper & Vitaly A. Strusevich, 2021. "Parametric analysis of the quality of single preemption schedules on three uniform parallel machines," Annals of Operations Research, Springer, vol. 298(1), pages 469-495, March.
    6. Chen, Jianfu & Chu, Chengbin & Sahli, Abderrahim & Li, Kai, 2024. "A branch-and-price algorithm for unrelated parallel machine scheduling with machine usage costs," European Journal of Operational Research, Elsevier, vol. 316(3), pages 856-872.
    7. Abdelhak Elidrissi & Rachid Benmansour & Nicolas Zufferey & Mohammed Benbrahim & David Duvivier, 2024. "Minimization of maximum lateness on parallel machines with a single server and job release dates," 4OR, Springer, vol. 22(3), pages 351-385, September.

    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. 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.
    3. 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.
    4. 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.
    5. 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.
    6. Finke, Gerd & Gara-Ali, Ahmed & Espinouse, Marie-Laure & Jost, Vincent & Moncel, Julien, 2017. "Unified matrix approach to solve production-maintenance problems on a single machine," Omega, Elsevier, vol. 66(PA), pages 140-146.
    7. Leah Epstein, 2023. "Parallel solutions for preemptive makespan scheduling on two identical machines," Journal of Scheduling, Springer, vol. 26(1), pages 61-76, February.
    8. 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.
    9. 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.
    10. 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.
    11. Anna Arigliano & Gianpaolo Ghiani & Antonio Grieco & Emanuela Guerriero, 2017. "Single-machine time-dependent scheduling problems with fixed rate-modifying activities and resumable jobs," 4OR, Springer, vol. 15(2), pages 201-215, June.
    12. 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.
    13. Xu, Jun & Wang, Jun-Qiang & Liu, Zhixin, 2022. "Parallel batch scheduling: Impact of increasing machine capacity," Omega, Elsevier, vol. 108(C).
    14. 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.
    15. 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.
    16. 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.
    17. Norelhouda Sekkal & Fayçal Belkaid, 0. "A multi-objective simulated annealing to solve an identical parallel machine scheduling problem with deterioration effect and resources consumption constraints," Journal of Combinatorial Optimization, Springer, vol. 0, pages 1-37.
    18. 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.
    19. 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.
    20. Yiwei Jiang & Zewei Weng & Jueliang Hu, 2014. "Algorithms with limited number of preemptions for scheduling on parallel machines," Journal of Combinatorial Optimization, Springer, vol. 27(4), pages 711-723, 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:inm:oropre:v:61:y:2013:i:5:p:1243-1257. 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: Chris Asher (email available below). General contact details of provider: https://edirc.repec.org/data/inforea.html .

    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.