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Algorithmic approaches to the multiple knapsack assignment problem

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  • Martello, Silvano
  • Monaci, Michele

Abstract

We consider a variant of the multiple knapsack problem in which some assignment-type side constraints have to be satisfied. The problem finds applications in logistics sectors related, e.g., to transportation and maritime shipping. We derive upper bounds from Lagrangian and surrogate relaxations of a mathematical model of the problem. We introduce a constructive heuristic and a metaheuristic refinement. We study the computational complexity of the proposed methods and evaluate their practical performance through extensive computational experiments on benchmarks from the literature and on new sets of randomly generated instances.

Suggested Citation

  • Martello, Silvano & Monaci, Michele, 2020. "Algorithmic approaches to the multiple knapsack assignment problem," Omega, Elsevier, vol. 90(C).
    • Handle: RePEc:eee:jomega:v:90:y:2020:i:c:s030504831830149x
    DOI: 10.1016/j.omega.2018.11.013
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    References listed on IDEAS

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    1. Diaz, Juan Esteban & Handl, Julia & Xu, Dong-Ling, 2018. "Integrating meta-heuristics, simulation and exact techniques for production planning of a failure-prone manufacturing system," European Journal of Operational Research, Elsevier, vol. 266(3), pages 976-989.
    2. 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.
    3. 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.
    4. Pisinger, David, 1999. "An exact algorithm for large multiple knapsack problems," European Journal of Operational Research, Elsevier, vol. 114(3), pages 528-541, May.
    5. Zhen, Lu & Wang, Kai & Wang, Shuaian & Qu, Xiaobo, 2018. "Tug scheduling for hinterland barge transport: A branch-and-price approach," European Journal of Operational Research, Elsevier, vol. 265(1), pages 119-132.
    6. Mohamed Esseghir Lalami & Moussa Elkihel & Didier El Baz & Vincent Boyer, 2012. "A procedure-based heuristic for 0-1 Multiple Knapsack Problems," International Journal of Mathematics in Operational Research, Inderscience Enterprises Ltd, vol. 4(3), pages 214-224.
    7. 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.
    8. 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.
    9. Dimitrov, Nedialko B. & Solow, Daniel & Szmerekovsky, Joseph & Guo, Jia, 2017. "Emergency relocation of items using single trips: Special cases of the Multiple Knapsack Assignment Problem," European Journal of Operational Research, Elsevier, vol. 258(3), pages 938-942.
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    Cited by:

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