IDEAS home Printed from https://ideas.repec.org/a/spr/jcomop/v40y2020i4d10.1007_s10878-020-00634-9.html
   My bibliography  Save this article

A characterization of optimal multiprocessor schedules and new dominance rules

Author

Listed:
  • Rico Walter

    (Friedrich Schiller University Jena)

  • Alexander Lawrinenko

    (Friedrich Schiller University Jena)

Abstract

The paper on hand approaches the classical makespan minimization problem on identical parallel machines from a rather theoretical point of view. Using an approach similar to the idea behind inverse optimization, we identify a general structural pattern of optimal multiprocessor schedules. We also show how to derive new dominance rules from the characteristics of optimal solutions. Results of our computational study attest to the efficacy of the new rules. They are particularly useful in limiting the search space when each machine processes only a few jobs on average.

Suggested Citation

  • Rico Walter & Alexander Lawrinenko, 2020. "A characterization of optimal multiprocessor schedules and new dominance rules," Journal of Combinatorial Optimization, Springer, vol. 40(4), pages 876-900, November.
    • Handle: RePEc:spr:jcomop:v:40:y:2020:i:4:d:10.1007_s10878-020-00634-9
    DOI: 10.1007/s10878-020-00634-9
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10878-020-00634-9
    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/s10878-020-00634-9?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. Walter, Rico & Wirth, Martin & Lawrinenko, Alexander, 2017. "Improved approaches to the exact solution of the machine covering problem," Publications of Darmstadt Technical University, Institute for Business Studies (BWL) 80530, Darmstadt Technical University, Department of Business Administration, Economics and Law, Institute for Business Studies (BWL).
    2. Federico Della Croce & Rosario Scatamacchia & Vincent T’kindt, 2019. "A tight linear time $$\frac{13}{12}$$ 13 12 -approximation algorithm for the $$P2 || C_{\max }$$ P 2 | | C max problem," Journal of Combinatorial Optimization, Springer, vol. 38(2), pages 608-617, August.
    3. Rico Walter & Martin Wirth & Alexander Lawrinenko, 2017. "Improved approaches to the exact solution of the machine covering problem," Journal of Scheduling, Springer, vol. 20(2), pages 147-164, April.
    4. Mokotoff, Ethel, 2004. "An exact algorithm for the identical parallel machine scheduling problem," European Journal of Operational Research, Elsevier, vol. 152(3), pages 758-769, February.
    5. Christos Koulamas, 2005. "Inverse scheduling with controllable job parameters," International Journal of Services and Operations Management, Inderscience Enterprises Ltd, vol. 1(1), pages 35-43.
    6. Mauro Dell'Amico & Manuel Iori & Silvano Martello & Michele Monaci, 2008. "Heuristic and Exact Algorithms for the Identical Parallel Machine Scheduling Problem," INFORMS Journal on Computing, INFORMS, vol. 20(3), pages 333-344, August.
    7. Mauro Dell’Amico & Silvano Martello, 1995. "Optimal Scheduling of Tasks on Identical Parallel Processors," INFORMS Journal on Computing, INFORMS, vol. 7(2), pages 191-200, May.
    8. Antonio Frangioni & Emiliano Necciari & Maria Grazia Scutellà, 2004. "A Multi-Exchange Neighborhood for Minimum Makespan Parallel Machine Scheduling Problems," Journal of Combinatorial Optimization, Springer, vol. 8(2), pages 195-220, June.
    9. Jouglet, Antoine & Carlier, Jacques, 2011. "Dominance rules in combinatorial optimization problems," European Journal of Operational Research, Elsevier, vol. 212(3), pages 433-444, August.
    10. Clemens Heuberger, 2004. "Inverse Combinatorial Optimization: A Survey on Problems, Methods, and Results," Journal of Combinatorial Optimization, Springer, vol. 8(3), pages 329-361, September.
    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. Rico Walter & Martin Wirth & Alexander Lawrinenko, 2017. "Improved approaches to the exact solution of the machine covering problem," Journal of Scheduling, Springer, vol. 20(2), pages 147-164, April.
    2. Kris Boudt & Edgars Jakobsons & Steven Vanduffel, 2018. "Block rearranging elements within matrix columns to minimize the variability of the row sums," 4OR, Springer, vol. 16(1), pages 31-50, March.
    3. Alexander Lawrinenko & Stefan Schwerdfeger & Rico Walter, 2018. "Reduction criteria, upper bounds, and a dynamic programming based heuristic for the max–min $$k_i$$ k i -partitioning problem," Journal of Heuristics, Springer, vol. 24(2), pages 173-203, April.
    4. Guopeng Song & Roel Leus, 2022. "Parallel Machine Scheduling Under Uncertainty: Models and Exact Algorithms," INFORMS Journal on Computing, INFORMS, vol. 34(6), pages 3059-3079, November.
    5. Daniel Kowalczyk & Roel Leus, 2017. "An exact algorithm for parallel machine scheduling with conflicts," Journal of Scheduling, Springer, vol. 20(4), pages 355-372, August.
    6. Absalom E Ezugwu & Olawale J Adeleke & Serestina Viriri, 2018. "Symbiotic organisms search algorithm for the unrelated parallel machines scheduling with sequence-dependent setup times," PLOS ONE, Public Library of Science, vol. 13(7), pages 1-23, July.
    7. Mauro Dell'Amico & Manuel Iori & Silvano Martello & Michele Monaci, 2008. "Heuristic and Exact Algorithms for the Identical Parallel Machine Scheduling Problem," INFORMS Journal on Computing, INFORMS, vol. 20(3), pages 333-344, August.
    8. Fröhlich von Elmbach, Alexander & Scholl, Armin & Walter, Rico, 2019. "Minimizing the maximal ergonomic burden in intra-hospital patient transportation," European Journal of Operational Research, Elsevier, vol. 276(3), pages 840-854.
    9. Silvano Martello & David Pisinger & Daniele Vigo, 2000. "The Three-Dimensional Bin Packing Problem," Operations Research, INFORMS, vol. 48(2), pages 256-267, April.
    10. Johnny C. Ho & Ivar Massabò & Giuseppe Paletta & Alex J. Ruiz-Torres, 2019. "A note on posterior tight worst-case bounds for longest processing time schedules," 4OR, Springer, vol. 17(1), pages 97-107, March.
    11. Antonio Frangioni & Emiliano Necciari & Maria Grazia Scutellà, 2004. "A Multi-Exchange Neighborhood for Minimum Makespan Parallel Machine Scheduling Problems," Journal of Combinatorial Optimization, Springer, vol. 8(2), pages 195-220, June.
    12. Mecler, Davi & Abu-Marrul, Victor & Martinelli, Rafael & Hoff, Arild, 2022. "Iterated greedy algorithms for a complex parallel machine scheduling problem," European Journal of Operational Research, Elsevier, vol. 300(2), pages 545-560.
    13. Bassem Jarboui & Saber Ibrahim & Abdelwaheb Rebai, 2010. "A new destructive bounding scheme for the bin packing problem," Annals of Operations Research, Springer, vol. 179(1), pages 187-202, September.
    14. Iori, Manuel & de Lima, Vinícius L. & Martello, Silvano & Miyazawa, Flávio K. & Monaci, Michele, 2021. "Exact solution techniques for two-dimensional cutting and packing," European Journal of Operational Research, Elsevier, vol. 289(2), pages 399-415.
    15. Mauro Dell'Amico & Silvano Martello, 1999. "Reduction of the Three-Partition Problem," Journal of Combinatorial Optimization, Springer, vol. 3(1), pages 17-30, July.
    16. Michael Brusco & Hans Köhn & Douglas Steinley, 2013. "Exact and approximate methods for a one-dimensional minimax bin-packing problem," Annals of Operations Research, Springer, vol. 206(1), pages 611-626, July.
    17. Oluf Faroe & David Pisinger & Martin Zachariasen, 2003. "Guided Local Search for the Three-Dimensional Bin-Packing Problem," INFORMS Journal on Computing, INFORMS, vol. 15(3), pages 267-283, August.
    18. Libura, Marek, 2007. "On the adjustment problem for linear programs," European Journal of Operational Research, Elsevier, vol. 183(1), pages 125-134, November.
    19. Burkard, Rainer E. & Galavii, Mohammadreza & Gassner, Elisabeth, 2010. "The inverse Fermat-Weber problem," European Journal of Operational Research, Elsevier, vol. 206(1), pages 11-17, October.
    20. Abumoslem Mohammadi & Javad Tayyebi, 2019. "Maximum Capacity Path Interdiction Problem with Fixed Costs," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 36(04), pages 1-21, August.

    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:jcomop:v:40:y:2020:i:4:d:10.1007_s10878-020-00634-9. 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.