IDEAS home Printed from https://ideas.repec.org/a/spr/aqjoor/v21y2023i3d10.1007_s10288-022-00514-4.html
   My bibliography  Save this article

Integer knapsack problems with profit functions of the same value range

Author

Listed:
  • Evgeny Gurevsky

    (LS2N, Université de Nantes)

  • Dmitry Kopelevich

    (Belarusian State University)

  • Sergey Kovalev

    (INSEEC Business School)

  • Mikhail Y. Kovalyov

    (United Institute of Informatics Problems, NASB)

Abstract

Integer knapsack problems with profit functions of the same value range are studied. Linear time algorithms are presented for the case of convex non-decreasing profit functions, and an NP-hardness proof and a fully polynomial-time approximation scheme are provided for the case of arbitrary non-negative non-decreasing profit functions. Fast solution procedures are also devised for the bottleneck counterparts of these problems. Computational complexity of the case with concave profit functions remains open.

Suggested Citation

  • Evgeny Gurevsky & Dmitry Kopelevich & Sergey Kovalev & Mikhail Y. Kovalyov, 2023. "Integer knapsack problems with profit functions of the same value range," 4OR, Springer, vol. 21(3), pages 405-419, September.
    • Handle: RePEc:spr:aqjoor:v:21:y:2023:i:3:d:10.1007_s10288-022-00514-4
    DOI: 10.1007/s10288-022-00514-4
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10288-022-00514-4
    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/s10288-022-00514-4?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. Malaguti, Enrico & Monaci, Michele & Paronuzzi, Paolo & Pferschy, Ulrich, 2019. "Integer optimization with penalized fractional values: The Knapsack case," European Journal of Operational Research, Elsevier, vol. 273(3), pages 874-888.
    2. Bin Zhang & Bo Chen, 2012. "Heuristic And Exact Solution Method For Convex Nonlinear Knapsack Problem," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 29(05), pages 1-14.
    3. George B. Dantzig, 1957. "Discrete-Variable Extremum Problems," Operations Research, INFORMS, vol. 5(2), pages 266-288, April.
    4. Egon Balas & Eitan Zemel, 1980. "An Algorithm for Large Zero-One Knapsack Problems," Operations Research, INFORMS, vol. 28(5), pages 1130-1154, October.
    5. Sartaj Sahni, 1977. "General Techniques for Combinatorial Approximation," Operations Research, INFORMS, vol. 25(6), pages 920-936, 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. 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.
    2. 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.
    3. Michel, S. & Perrot, N. & Vanderbeck, F., 2009. "Knapsack problems with setups," European Journal of Operational Research, Elsevier, vol. 196(3), pages 909-918, August.
    4. 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.
    5. 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.
    6. Wishon, Christopher & Villalobos, J. Rene, 2016. "Robust efficiency measures for linear knapsack problem variants," European Journal of Operational Research, Elsevier, vol. 254(2), pages 398-409.
    7. Jooken, Jorik & Leyman, Pieter & De Causmaecker, Patrick, 2022. "A new class of hard problem instances for the 0–1 knapsack problem," European Journal of Operational Research, Elsevier, vol. 301(3), pages 841-854.
    8. M Hifi & M Michrafy & A Sbihi, 2004. "Heuristic algorithms for the multiple-choice multidimensional knapsack problem," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 55(12), pages 1323-1332, December.
    9. Mavrotas, George & Florios, Kostas & Figueira, José Rui, 2015. "An improved version of a core based algorithm for the multi-objective multi-dimensional knapsack problem: A computational study and comparison with meta-heuristics," Applied Mathematics and Computation, Elsevier, vol. 270(C), pages 25-43.
    10. Tobias Achterberg & Robert E. Bixby & Zonghao Gu & Edward Rothberg & Dieter Weninger, 2020. "Presolve Reductions in Mixed Integer Programming," INFORMS Journal on Computing, INFORMS, vol. 32(2), pages 473-506, April.
    11. 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.
    12. 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.
    13. Pisinger, David, 1995. "A minimal algorithm for the multiple-choice knapsack problem," European Journal of Operational Research, Elsevier, vol. 83(2), pages 394-410, June.
    14. Franklin Djeumou Fomeni & Adam N. Letchford, 2014. "A Dynamic Programming Heuristic for the Quadratic Knapsack Problem," INFORMS Journal on Computing, INFORMS, vol. 26(1), pages 173-182, February.
    15. Martello, Silvano & Pisinger, David & Toth, Paolo, 2000. "New trends in exact algorithms for the 0-1 knapsack problem," European Journal of Operational Research, Elsevier, vol. 123(2), pages 325-332, June.
    16. B. Golany & N. Goldberg & U. Rothblum, 2015. "Allocating multiple defensive resources in a zero-sum game setting," Annals of Operations Research, Springer, vol. 225(1), pages 91-109, February.
    17. Teresa Estañ & Natividad Llorca & Ricardo Martínez & Joaquín Sánchez-Soriano, 2020. "On the difficulty of budget allocation in claims problems with indivisible items of different prices," ThE Papers 20/09, Department of Economic Theory and Economic History of the University of Granada..
    18. Teresa Estañ & Natividad Llorca & Ricardo Martínez & Joaquín Sánchez-Soriano, 2021. "On the Difficulty of Budget Allocation in Claims Problems with Indivisible Items and Prices," Group Decision and Negotiation, Springer, vol. 30(5), pages 1133-1159, October.
    19. 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.
    20. 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.

    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:aqjoor:v:21:y:2023:i:3:d:10.1007_s10288-022-00514-4. 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.