IDEAS home Printed from https://ideas.repec.org/a/spr/jsched/v24y2021i6d10.1007_s10951-021-00709-3.html
   My bibliography  Save this article

More on ordered open end bin packing

Author

Listed:
  • János Balogh

    (University of Szeged)

  • Leah Epstein

    (University of Haifa)

  • Asaf Levin

    (The Technion)

Abstract

We consider the Ordered Open End Bin Packing problem. Items of sizes in (0, 1] are presented one by one, to be assigned to bins in this order. An item can be assigned to any bin for which the current total size is strictly below 1. This means also that the bin can be overloaded by its last packed item. We improve lower and upper bounds on the asymptotic competitive ratio in the online case. Specifically, we design the first algorithm whose asymptotic competitive ratio is strictly below 2, and its value is close to the lower bound. This is in contrast to the best possible absolute competitive ratio, which is equal to 2. We also study the offline problem where the sequence of items is known in advance, while items are still assigned to bins based on their order in the sequence. For this scenario, we design an asymptotic polynomial time approximation scheme.

Suggested Citation

  • János Balogh & Leah Epstein & Asaf Levin, 2021. "More on ordered open end bin packing," Journal of Scheduling, Springer, vol. 24(6), pages 589-614, December.
    • Handle: RePEc:spr:jsched:v:24:y:2021:i:6:d:10.1007_s10951-021-00709-3
    DOI: 10.1007/s10951-021-00709-3
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10951-021-00709-3
    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/s10951-021-00709-3?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. Leah Epstein, 2009. "On online bin packing with LIB constraints," Naval Research Logistics (NRL), John Wiley & Sons, vol. 56(8), pages 780-786, December.
    2. Leah Epstein, 2019. "A lower bound for online rectangle packing," Journal of Combinatorial Optimization, Springer, vol. 38(3), pages 846-866, October.
    3. Gyorgy Dosa & Zsolt Tuza & Deshi Ye, 2013. "Bin packing with “Largest In Bottom” constraint: tighter bounds and generalizations," Journal of Combinatorial Optimization, Springer, vol. 26(3), pages 416-436, October.
    4. Jian Yang & Joseph Y.-T. Leung, 2003. "The Ordered Open-End Bin-Packing Problem," Operations Research, INFORMS, vol. 51(5), pages 759-770, October.
    5. H. W. Lenstra, 1983. "Integer Programming with a Fixed Number of Variables," Mathematics of Operations Research, INFORMS, vol. 8(4), pages 538-548, November.
    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. M. Köppe & M. Queyranne & C. T. Ryan, 2010. "Parametric Integer Programming Algorithm for Bilevel Mixed Integer Programs," Journal of Optimization Theory and Applications, Springer, vol. 146(1), pages 137-150, July.
    2. K. Aardal & R. E. Bixby & C. A. J. Hurkens & A. K. Lenstra & J. W. Smeltink, 2000. "Market Split and Basis Reduction: Towards a Solution of the Cornuéjols-Dawande Instances," INFORMS Journal on Computing, INFORMS, vol. 12(3), pages 192-202, August.
    3. Alberto Del Pia & Robert Hildebrand & Robert Weismantel & Kevin Zemmer, 2016. "Minimizing Cubic and Homogeneous Polynomials over Integers in the Plane," Mathematics of Operations Research, INFORMS, vol. 41(2), pages 511-530, May.
    4. Klaus Jansen & Roberto Solis-Oba, 2011. "A Polynomial Time OPT + 1 Algorithm for the Cutting Stock Problem with a Constant Number of Object Lengths," Mathematics of Operations Research, INFORMS, vol. 36(4), pages 743-753, November.
    5. Friedrich Eisenbrand & Gennady Shmonin, 2008. "Parametric Integer Programming in Fixed Dimension," Mathematics of Operations Research, INFORMS, vol. 33(4), pages 839-850, November.
    6. Elizabeth Baldwin & Paul Klemperer, 2019. "Understanding Preferences: “Demand Types”, and the Existence of Equilibrium With Indivisibilities," Econometrica, Econometric Society, vol. 87(3), pages 867-932, May.
    7. Masing, Berenike & Lindner, Niels & Borndörfer, Ralf, 2022. "The price of symmetric line plans in the Parametric City," Transportation Research Part B: Methodological, Elsevier, vol. 166(C), pages 419-443.
    8. Sanchari Deb & Kari Tammi & Karuna Kalita & Pinakeswar Mahanta, 2018. "Review of recent trends in charging infrastructure planning for electric vehicles," Wiley Interdisciplinary Reviews: Energy and Environment, Wiley Blackwell, vol. 7(6), November.
    9. Kenneth J. Arrow & Timothy J. Kehoe, 1994. "Distinguished Fellow: Herbert Scarf's Contributions to Economics," Journal of Economic Perspectives, American Economic Association, vol. 8(4), pages 161-181, Fall.
    10. Kubale, Marek, 1996. "Preemptive versus nonpreemptive scheduling of biprocessor tasks on dedicated processors," European Journal of Operational Research, Elsevier, vol. 94(2), pages 242-251, October.
    11. Matthias Bentert & Robert Bredereck & Péter Györgyi & Andrzej Kaczmarczyk & Rolf Niedermeier, 2023. "A multivariate complexity analysis of the material consumption scheduling problem," Journal of Scheduling, Springer, vol. 26(4), pages 369-382, August.
    12. Danny Nguyen & Igor Pak, 2020. "The Computational Complexity of Integer Programming with Alternations," Mathematics of Operations Research, INFORMS, vol. 45(1), pages 191-204, February.
    13. William Cook & Thomas Rutherford & Herbert E. Scarf & David F. Shallcross, 1991. "An Implementation of the Generalized Basis Reduction Algorithm for Integer Programming," Cowles Foundation Discussion Papers 990, Cowles Foundation for Research in Economics, Yale University.
    14. Egor Ianovski, 2022. "Electing a committee with dominance constraints," Annals of Operations Research, Springer, vol. 318(2), pages 985-1000, November.
    15. Sascha Kurz & Nikolas Tautenhahn, 2013. "On Dedekind’s problem for complete simple games," International Journal of Game Theory, Springer;Game Theory Society, vol. 42(2), pages 411-437, May.
    16. Alberto Caprara & Andrea Lodi & Michele Monaci, 2005. "Fast Approximation Schemes for Two-Stage, Two-Dimensional Bin Packing," Mathematics of Operations Research, INFORMS, vol. 30(1), pages 150-172, February.
    17. D. V. Gribanov & D. S. Malyshev & P. M. Pardalos & S. I. Veselov, 2018. "FPT-algorithms for some problems related to integer programming," Journal of Combinatorial Optimization, Springer, vol. 35(4), pages 1128-1146, May.
    18. Klaus Heeger & Danny Hermelin & George B. Mertzios & Hendrik Molter & Rolf Niedermeier & Dvir Shabtay, 2023. "Equitable scheduling on a single machine," Journal of Scheduling, Springer, vol. 26(2), pages 209-225, April.
    19. Karen Aardal & Arjen K. Lenstra, 2004. "Hard Equality Constrained Integer Knapsacks," Mathematics of Operations Research, INFORMS, vol. 29(3), pages 724-738, August.
    20. Herbert E. Scarf & David F. Shallcross, 2008. "The Frobenius Problem and Maximal Lattice Free Bodies," Palgrave Macmillan Books, in: Zaifu Yang (ed.), Herbert Scarf’s Contributions to Economics, Game Theory and Operations Research, chapter 7, pages 149-153, Palgrave Macmillan.

    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:6:d:10.1007_s10951-021-00709-3. 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.