IDEAS home Printed from https://ideas.repec.org/a/eee/ejores/v282y2020i2p464-477.html
   My bibliography  Save this article

Shared processor scheduling of multiprocessor jobs

Author

Listed:
  • Dereniowski, Dariusz
  • Kubiak, Wiesław

Abstract

We study a problem of shared processor scheduling of multiprocessor weighted jobs. Each job can be executed on its private processor and simultaneously on possibly many processors shared by all jobs. This simultaneous execution reduces their completion times due to the processing time overlap. Each of the m shared processors may charge a different fee but otherwise the processors are identical. The goal is to maximize the total weighted overlap of all jobs. This is a key problem in subcontractor scheduling in extended enterprises and supply chains, and in divisible load scheduling in computing. We introduce synchronized schedules that complete each job that uses some shared processor at the same time on its private and on the shared processors. We prove that, quite surprisingly, the synchronized schedules include optimal ones. We obtain an α-approximation algorithm that runs in strongly polynomial time for the problem, where α=1/2+1/(4(m+1)). This improves the 1/2-approximation reported recently in the literature to 5/8-approximation for a single shared processor problem, m=1. The computational complexity of the problem, both in case of single and multi-shared processor, remains open. We show however an LP-based optimal algorithm for antithetical instances where for any pair of jobs j and i, if the processing time of j is smaller than or equal to the processing time of i, then the weight of j is greater than or equal to the weight of i.

Suggested Citation

  • Dereniowski, Dariusz & Kubiak, Wiesław, 2020. "Shared processor scheduling of multiprocessor jobs," European Journal of Operational Research, Elsevier, vol. 282(2), pages 464-477.
    • Handle: RePEc:eee:ejores:v:282:y:2020:i:2:p:464-477
    DOI: 10.1016/j.ejor.2019.09.033
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0377221719307908
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.ejor.2019.09.033?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. Dariusz Dereniowski & Wiesław Kubiak, 2018. "Shared processor scheduling," Journal of Scheduling, Springer, vol. 21(6), pages 583-593, December.
    2. George L. Vairaktarakis, 2013. "Noncooperative Games for Subcontracting Operations," Manufacturing & Service Operations Management, INFORMS, vol. 15(1), pages 148-158, September.
    3. Dereniowski, Dariusz & Kubiak, Wiesław, 2017. "Shared multi-processor scheduling," European Journal of Operational Research, Elsevier, vol. 261(2), pages 503-514.
    4. James B. Orlin, 1993. "A Faster Strongly Polynomial Minimum Cost Flow Algorithm," Operations Research, INFORMS, vol. 41(2), pages 338-350, April.
    Full references (including those not matched with items on IDEAS)

    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. Dariusz Dereniowski & Wiesław Kubiak, 2018. "Shared processor scheduling," Journal of Scheduling, Springer, vol. 21(6), pages 583-593, December.
    2. Wang, Gang, 2024. "Order assignment and two-stage integrated scheduling in fruit and vegetable supply chains," Omega, Elsevier, vol. 124(C).
    3. Shoshana Anily, 1996. "The vehicle‐routing problem with delivery and back‐haul options," Naval Research Logistics (NRL), John Wiley & Sons, vol. 43(3), pages 415-434, April.
    4. László A. Végh, 2017. "A Strongly Polynomial Algorithm for Generalized Flow Maximization," Mathematics of Operations Research, INFORMS, vol. 42(1), pages 179-211, January.
    5. Amirmahdi Tafreshian & Neda Masoud & Yafeng Yin, 2020. "Frontiers in Service Science: Ride Matching for Peer-to-Peer Ride Sharing: A Review and Future Directions," Service Science, INFORMS, vol. 12(2-3), pages 44-60, June.
    6. László A. Végh, 2014. "Concave Generalized Flows with Applications to Market Equilibria," Mathematics of Operations Research, INFORMS, vol. 39(2), pages 573-596, May.
    7. Ravindra K. Ahuja & Dorit S. Hochbaum, 2008. "TECHNICAL NOTE---Solving Linear Cost Dynamic Lot-Sizing Problems in O ( n log n ) Time," Operations Research, INFORMS, vol. 56(1), pages 255-261, February.
    8. Sharma, Anuj & Verma, Vanita & Kaur, Prabhjot & Dahiya, Kalpana, 2015. "An iterative algorithm for two level hierarchical time minimization transportation problem," European Journal of Operational Research, Elsevier, vol. 246(3), pages 700-707.
    9. Zsolt T. Kosztyán & István Szalkai, 2020. "Multimode resource-constrained project scheduling in flexible projects," Journal of Global Optimization, Springer, vol. 76(1), pages 211-241, January.
    10. I.N. Kamal Abadi & Nicholas G. Hall & Chelliah Sriskandarajah, 2000. "Minimizing Cycle Time in a Blocking Flowshop," Operations Research, INFORMS, vol. 48(1), pages 177-180, February.
    11. Adrian Marius Deaconu & Luciana Majercsik, 2021. "Flow Increment through Network Expansion," Mathematics, MDPI, vol. 9(18), pages 1-9, September.
    12. Ahmed Redha Mahlous, 2017. "SCMC: An Efficient Scheme for Minimizing Energy in WSNs Using a Set Cover Approach," Future Internet, MDPI, vol. 9(4), pages 1-18, December.
    13. Mehdi Ghiyasvand, 2019. "An $$O(n(m+n\log n)\log n)$$O(n(m+nlogn)logn) time algorithm to solve the minimum cost tension problem," Journal of Combinatorial Optimization, Springer, vol. 37(3), pages 957-969, April.
    14. Ding, Honglin & Li, Jianping & Lih, Ko-Wei, 2014. "Approximation algorithms for solving the constrained arc routing problem in mixed graphs," European Journal of Operational Research, Elsevier, vol. 239(1), pages 80-88.
    15. Elisa Letizia & Paolo Barucca & Fabrizio Lillo, 2018. "Resolution of ranking hierarchies in directed networks," PLOS ONE, Public Library of Science, vol. 13(2), pages 1-25, February.
    16. Niu, Yi-Feng & Song, Yi-Fan & Xu, Xiu-Zhen & Zhao, Xia, 2022. "Efficient reliability computation of a multi-state flow network with cost constraint," Reliability Engineering and System Safety, Elsevier, vol. 222(C).
    17. Hochbaum, Dorit S., 2002. "Solving integer programs over monotone inequalities in three variables: A framework for half integrality and good approximations," European Journal of Operational Research, Elsevier, vol. 140(2), pages 291-321, July.
    18. Maiko Shigeno & Satoru Iwata & S. Thomas McCormick, 2000. "Relaxed Most Negative Cycle and Most Positive Cut Canceling Algorithms for Minimum Cost Flow," Mathematics of Operations Research, INFORMS, vol. 25(1), pages 76-104, February.
    19. Laszlo A. Vegh, 2011. "Concave Generalized Flows with Applications to Market Equilibria," Papers 1109.3893, arXiv.org, revised Apr 2012.
    20. Mattia, Sara & Rossi, Fabrizio & Servilio, Mara & Smriglio, Stefano, 2017. "Staffing and scheduling flexible call centers by two-stage robust optimization," Omega, Elsevier, vol. 72(C), pages 25-37.

    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:282:y:2020:i:2:p:464-477. 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.