IDEAS home Printed from https://ideas.repec.org/a/spr/annopr/v146y2006i1p91-10410.1007-s10479-006-0048-1.html
   My bibliography  Save this article

LP based heuristics for the multiple knapsack problem with assignment restrictions

Author

Listed:
  • Geir Dahl
  • Njål Foldnes

Abstract

Starting with a problem in wireless telecommunication, we are led to study the multiple knapsack problem with assignment restrictions. This problem is NP-hard. We consider special cases and their computational complexity. We present both randomized and deterministic LP based algorithms, and show both theoretically and computationally their usefulness for large-scale problems. Copyright Springer Science+Business Media, LLC 2006

Suggested Citation

  • Geir Dahl & Njål Foldnes, 2006. "LP based heuristics for the multiple knapsack problem with assignment restrictions," Annals of Operations Research, Springer, vol. 146(1), pages 91-104, September.
    • Handle: RePEc:spr:annopr:v:146:y:2006:i:1:p:91-104:10.1007/s10479-006-0048-1
    DOI: 10.1007/s10479-006-0048-1
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s10479-006-0048-1
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s10479-006-0048-1?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. Fred Glover, 1967. "Maximum matching in a convex bipartite graph," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 14(3), pages 313-316.
    2. Pisinger, David, 1999. "An exact algorithm for large multiple knapsack problems," European Journal of Operational Research, Elsevier, vol. 114(3), pages 528-541, May.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Hans Kellerer & Joseph Y.‐T. Leung & Chung‐Lun Li, 2011. "Multiple subset sum with inclusive assignment set restrictions," Naval Research Logistics (NRL), John Wiley & Sons, vol. 58(6), pages 546-563, September.
    2. Yiting Xing & Ling Li & Zhuming Bi & Marzena Wilamowska‐Korsak & Li Zhang, 2013. "Operations Research (OR) in Service Industries: A Comprehensive Review," Systems Research and Behavioral Science, Wiley Blackwell, vol. 30(3), pages 300-353, May.
    3. Martello, Silvano & Monaci, Michele, 2020. "Algorithmic approaches to the multiple knapsack assignment problem," Omega, Elsevier, vol. 90(C).
    4. J. Álvaro Gómez-Pantoja & M. Angélica Salazar-Aguilar & José Luis González-Velarde, 2021. "The food bank resource allocation problem," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 29(1), pages 266-286, April.
    5. Homsi, Gabriel & Jordan, Jeremy & Martello, Silvano & Monaci, Michele, 2021. "The assignment and loading transportation problem," European Journal of Operational Research, Elsevier, vol. 289(3), pages 999-1007.
    6. Stefka Fidanova & Krassimir Todorov Atanassov, 2021. "ACO with Intuitionistic Fuzzy Pheromone Updating Applied on Multiple-Constraint Knapsack Problem," Mathematics, MDPI, vol. 9(13), pages 1-7, June.

    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. Tomohiko Mizutani & Makoto Yamashita, 2013. "Correlative sparsity structures and semidefinite relaxations for concave cost transportation problems with change of variables," Journal of Global Optimization, Springer, vol. 56(3), pages 1073-1100, July.
    2. 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.
    3. Mancini, Simona & Ciavotta, Michele & Meloni, Carlo, 2021. "The Multiple Multidimensional Knapsack with Family-Split Penalties," European Journal of Operational Research, Elsevier, vol. 289(3), pages 987-998.
    4. Stefan Hajkowicz & Andrew Higgins & Kristen Williams & Daniel P. Faith & Michael Burton, 2007. "Optimisation and the selection of conservation contracts," Australian Journal of Agricultural and Resource Economics, Australian Agricultural and Resource Economics Society, vol. 51(1), pages 39-56, March.
    5. Yamada, Takeo & Takeoka, Takahiro, 2009. "An exact algorithm for the fixed-charge multiple knapsack problem," European Journal of Operational Research, Elsevier, vol. 192(2), pages 700-705, January.
    6. Martello, Silvano & Monaci, Michele, 2020. "Algorithmic approaches to the multiple knapsack assignment problem," Omega, Elsevier, vol. 90(C).
    7. Ang, James S.K. & Cao, Chengxuan & Ye, Heng-Qing, 2007. "Model and algorithms for multi-period sea cargo mix problem," European Journal of Operational Research, Elsevier, vol. 180(3), pages 1381-1393, August.
    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. Olivier Lalonde & Jean-François Côté & Bernard Gendron, 2022. "A Branch-and-Price Algorithm for the Multiple Knapsack Problem," INFORMS Journal on Computing, INFORMS, vol. 34(6), pages 3134-3150, November.
    10. Zhenbo Wang & Wenxun Xing, 2009. "A successive approximation algorithm for the multiple knapsack problem," Journal of Combinatorial Optimization, Springer, vol. 17(4), pages 347-366, May.
    11. Kubat, Peter & Smith, J. MacGregor, 2001. "A multi-period network design problem for cellular telecommunication systems," European Journal of Operational Research, Elsevier, vol. 134(2), pages 439-456, October.
    12. Kataoka, Seiji & Yamada, Takeo, 2014. "Upper and lower bounding procedures for the multiple knapsack assignment problem," European Journal of Operational Research, Elsevier, vol. 237(2), pages 440-447.
    13. Wascher, Gerhard & Hau[ss]ner, Heike & Schumann, Holger, 2007. "An improved typology of cutting and packing problems," European Journal of Operational Research, Elsevier, vol. 183(3), pages 1109-1130, December.
    14. Karel Ječmen & Denisa Mocková & Dušan Teichmann, 2024. "Solving Transport Infrastructure Investment Project Selection and Scheduling Using Genetic Algorithms," Mathematics, MDPI, vol. 12(19), pages 1-28, September.
    15. 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.
    16. Yang, Zhen & Chen, Haoxun & Chu, Feng & Wang, Nengmin, 2019. "An effective hybrid approach to the two-stage capacitated facility location problem," European Journal of Operational Research, Elsevier, vol. 275(2), pages 467-480.
    17. Peng Wu & Junheng Cheng & Feng Chu, 2021. "Large-scale energy-conscious bi-objective single-machine batch scheduling under time-of-use electricity tariffs via effective iterative heuristics," Annals of Operations Research, Springer, vol. 296(1), pages 471-494, January.
    18. Zheng Wang & Wei Xu & Xiangpei Hu & Yong Wang, 2022. "Inventory allocation to robotic mobile-rack and picker-to-part warehouses at minimum order-splitting and replenishment costs," Annals of Operations Research, Springer, vol. 316(1), pages 467-491, September.
    19. Tolga Çezik & Oktay Günlük, 2004. "Reformulating linear programs with transportation constraints—With applications to workforce scheduling," Naval Research Logistics (NRL), John Wiley & Sons, vol. 51(2), pages 275-296, March.
    20. Alex Fukunaga, 2011. "A branch-and-bound algorithm for hard multiple knapsack problems," Annals of Operations Research, Springer, vol. 184(1), pages 97-119, April.

    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:annopr:v:146:y:2006:i:1:p:91-104:10.1007/s10479-006-0048-1. 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.