IDEAS home Printed from https://ideas.repec.org/a/spr/jsched/v24y2021i5d10.1007_s10951-019-00626-6.html
   My bibliography  Save this article

Scheduling divisible loads with time and cost constraints

Author

Listed:
  • M. Drozdowski

    (Poznań University of Technology)

  • N. V. Shakhlevich

    (University of Leeds)

Abstract

In distributed computing, divisible load theory provides an important system model for allocation of data-intensive computations to processing units working in parallel. The main task is to define how a computation job should be split into parts, to which processors those parts should be allocated and in which sequence. The model is characterized by multiple parameters describing processor availability in time, transfer times of job parts to processors, their computation times and processor usage costs. The main criteria are usually the schedule length and cost minimization. In this paper, we provide the generalized formulation of the problem, combining key features of divisible load models studied in the literature, and prove its NP-hardness even for unrestricted processor availability windows. We formulate a linear program for the version of the problem with a fixed number of processors. For the case with an arbitrary number of processors, we close the gaps in the study of special cases, developing efficient algorithms for single criterion and bicriteria versions of the problem, when transfer times are negligible.

Suggested Citation

  • M. Drozdowski & N. V. Shakhlevich, 2021. "Scheduling divisible loads with time and cost constraints," Journal of Scheduling, Springer, vol. 24(5), pages 507-521, October.
    • Handle: RePEc:spr:jsched:v:24:y:2021:i:5:d:10.1007_s10951-019-00626-6
    DOI: 10.1007/s10951-019-00626-6
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10951-019-00626-6
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s10951-019-00626-6?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. Egon Balas & Eitan Zemel, 1980. "An Algorithm for Large Zero-One Knapsack Problems," Operations Research, INFORMS, vol. 28(5), pages 1130-1154, October.
    2. Maciej Drozdowski & Florian Jaehn & Radosław Paszkowski, 2017. "Scheduling Position-Dependent Maintenance Operations," Operations Research, INFORMS, vol. 65(6), pages 1657-1677, December.
    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. Esmaeil Afrashteh & Behrooz Alizadeh & Fahimeh Baroughi, 2020. "Optimal approaches for upgrading selective obnoxious p-median location problems on tree networks," Annals of Operations Research, Springer, vol. 289(2), pages 153-172, June.
    2. David Pisinger, 1999. "Core Problems in Knapsack Algorithms," Operations Research, INFORMS, vol. 47(4), pages 570-575, August.
    3. M Hifi & M Michrafy, 2006. "A reactive local search-based algorithm for the disjunctively constrained knapsack problem," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 57(6), pages 718-726, June.
    4. Renata Mansini & M. Grazia Speranza, 2012. "CORAL: An Exact Algorithm for the Multidimensional Knapsack Problem," INFORMS Journal on Computing, INFORMS, vol. 24(3), pages 399-415, August.
    5. Altay, Nezih & Robinson Jr., Powell E. & Bretthauer, Kurt M., 2008. "Exact and heuristic solution approaches for the mixed integer setup knapsack problem," European Journal of Operational Research, Elsevier, vol. 190(3), pages 598-609, November.
    6. Jakob Puchinger & Günther R. Raidl & Ulrich Pferschy, 2010. "The Multidimensional Knapsack Problem: Structure and Algorithms," INFORMS Journal on Computing, INFORMS, vol. 22(2), pages 250-265, May.
    7. Dell’Amico, Mauro & Delorme, Maxence & Iori, Manuel & Martello, Silvano, 2019. "Mathematical models and decomposition methods for the multiple knapsack problem," European Journal of Operational Research, Elsevier, vol. 274(3), pages 886-899.
    8. Kerem Bülbül & Safia Kedad-Sidhoum & Halil Şen, 2019. "Single-machine common due date total earliness/tardiness scheduling with machine unavailability," Journal of Scheduling, Springer, vol. 22(5), pages 543-565, October.
    9. Mhand Hifi & Hedi Mhalla & Slim Sadfi, 2005. "Sensitivity of the Optimum to Perturbations of the Profit or Weight of an Item in the Binary Knapsack Problem," Journal of Combinatorial Optimization, Springer, vol. 10(3), pages 239-260, November.
    10. Binh Thanh Dang & Tung Khac Truong, 2022. "Binary salp swarm algorithm for discounted {0-1} knapsack problem," PLOS ONE, Public Library of Science, vol. 17(4), pages 1-28, April.
    11. Pisinger, David, 1995. "An expanding-core algorithm for the exact 0-1 knapsack problem," European Journal of Operational Research, Elsevier, vol. 87(1), pages 175-187, November.
    12. W. David Pisinger & Anders Bo Rasmussen & Rune Sandvik, 2007. "Solution of Large Quadratic Knapsack Problems Through Aggressive Reduction," INFORMS Journal on Computing, INFORMS, vol. 19(2), pages 280-290, May.
    13. Emilio Carrizosa & Frank Plastria, 2008. "Optimal Expected-Distance Separating Halfspace," Mathematics of Operations Research, INFORMS, vol. 33(3), pages 662-677, August.
    14. Michel, S. & Perrot, N. & Vanderbeck, F., 2009. "Knapsack problems with setups," European Journal of Operational Research, Elsevier, vol. 196(3), pages 909-918, August.
    15. T. Kuno, 1999. "Solving a Class of Multiplicative Programs with 0–1 Knapsack Constraints," Journal of Optimization Theory and Applications, Springer, vol. 103(1), pages 121-135, October.
    16. Bjorndal, M. H. & Caprara, A. & Cowling, P. I. & Della Croce, F. & Lourenco, H. & Malucelli, F. & Orman, A. J. & Pisinger, D. & Rego, C. & Salazar, J. J., 1995. "Some thoughts on combinatorial optimisation," European Journal of Operational Research, Elsevier, vol. 83(2), pages 253-270, June.
    17. Alizadeh, Behrooz & Afrashteh, Esmaeil, 2020. "Budget-constrained inverse median facility location problem on tree networks," Applied Mathematics and Computation, Elsevier, vol. 375(C).
    18. Patrick Gemander & Wei-Kun Chen & Dieter Weninger & Leona Gottwald & Ambros Gleixner & Alexander Martin, 2020. "Two-row and two-column mixed-integer presolve using hashing-based pairing methods," EURO Journal on Computational Optimization, Springer;EURO - The Association of European Operational Research Societies, vol. 8(3), pages 205-240, October.
    19. Silvano Martello & Paolo Toth, 2003. "An Exact Algorithm for the Two-Constraint 0--1 Knapsack Problem," Operations Research, INFORMS, vol. 51(5), pages 826-835, October.
    20. Tsesmetzis, Dimitrios & Roussaki, Ioanna & Sykas, Efstathios, 2008. "QoS-aware service evaluation and selection," European Journal of Operational Research, Elsevier, vol. 191(3), pages 1101-1112, December.

    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:spr:jsched:v:24:y:2021:i:5:d:10.1007_s10951-019-00626-6. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    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.