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. James B. Orlin, 1993. "A Faster Strongly Polynomial Minimum Cost Flow Algorithm," Operations Research, INFORMS, vol. 41(2), pages 338-350, April.
    2. Dariusz Dereniowski & Wiesław Kubiak, 2018. "Shared processor scheduling," Journal of Scheduling, Springer, vol. 21(6), pages 583-593, December.
    3. George L. Vairaktarakis, 2013. "Noncooperative Games for Subcontracting Operations," Manufacturing & Service Operations Management, INFORMS, vol. 15(1), pages 148-158, September.
    4. Dereniowski, Dariusz & Kubiak, Wiesław, 2017. "Shared multi-processor scheduling," European Journal of Operational Research, Elsevier, vol. 261(2), pages 503-514.
    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. Balaji Gopalakrishnan & Seunghyun Kong & Earl Barnes & Ellis Johnson & Joel Sokol, 2011. "A least-squares minimum-cost network flow algorithm," Annals of Operations Research, Springer, vol. 186(1), pages 119-140, June.
    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. Yosuke Hanawa & Yuya Higashikawa & Naoyuki Kamiyama & Naoki Katoh & Atsushi Takizawa, 2018. "The mixed evacuation problem," Journal of Combinatorial Optimization, Springer, vol. 36(4), pages 1299-1314, November.
    6. 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.
    7. Prabhjot Kaur & Anuj Sharma & Vanita Verma & Kalpana Dahiya, 2022. "An alternate approach to solve two-level hierarchical time minimization transportation problem," 4OR, Springer, vol. 20(1), pages 23-61, March.
    8. Adam N. Letchford, 2000. "Separating a Superclass of Comb Inequalities in Planar Graphs," Mathematics of Operations Research, INFORMS, vol. 25(3), pages 443-454, August.
    9. László A. Végh, 2014. "Concave Generalized Flows with Applications to Market Equilibria," Mathematics of Operations Research, INFORMS, vol. 39(2), pages 573-596, May.
    10. 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.
    11. Ons Sassi & Ammar Oulamara, 2017. "Electric vehicle scheduling and optimal charging problem: complexity, exact and heuristic approaches," International Journal of Production Research, Taylor & Francis Journals, vol. 55(2), pages 519-535, January.
    12. 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.
    13. P. Chardaire & A. Lisser, 2002. "Simplex and Interior Point Specialized Algorithms for Solving Nonoriented Multicommodity Flow Problems," Operations Research, INFORMS, vol. 50(2), pages 260-276, April.
    14. Yu Yokoi, 2017. "A Generalized Polymatroid Approach to Stable Matchings with Lower Quotas," Mathematics of Operations Research, INFORMS, vol. 42(1), pages 238-255, January.
    15. Bérczi, Kristóf & Mnich, Matthias & Vincze, Roland, 2023. "Approximations for many-visits multiple traveling salesman problems," Omega, Elsevier, vol. 116(C).
    16. 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.
    17. Herbert Hamers & Flip Klijn & Marco Slikker, 2013. "Price of Anarchy in Sequencing Situations and the Impossibility to Coordinate," Working Papers 709, Barcelona School of Economics.
    18. Costa, Marie-Christine & Letocart, Lucas & Roupin, Frederic, 2005. "Minimal multicut and maximal integer multiflow: A survey," European Journal of Operational Research, Elsevier, vol. 162(1), pages 55-69, April.
    19. 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.
    20. Sedeño-Noda, A. & de Pablo, D. Alcaide López & González-Martín, C., 2009. "A network flow-based method to solve performance cost and makespan open-shop scheduling problems with time-windows," European Journal of Operational Research, Elsevier, vol. 196(1), pages 140-154, July.

    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.