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LP based heuristics for the multiple knapsack problem with assignment restrictions

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  • 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
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    References listed on IDEAS

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    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.
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    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. 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.
    3. 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.
    4. 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.
    5. Martello, Silvano & Monaci, Michele, 2020. "Algorithmic approaches to the multiple knapsack assignment problem," Omega, Elsevier, vol. 90(C).
    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.

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