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The Loading Problem

Author

Listed:
  • Samuel Eilon

    (Imperial College of Science and Technology, London)

  • Nicos Christofides

    (Imperial College of Science and Technology, London)

Abstract

The loading problem is defined as the allocation of given items with known magnitude to boxes with constrained capacity, so as to minimize the number of boxes required. Two methods of solution are considered: The first is by a zero-one programming model, for which the solution procedure is described; the second is by a heuristic algorithm. Fifty problems were solved by the two methods and in all but two the second method yielded the optimal solution with significantly less computing time than that needed by the first method.

Suggested Citation

  • Samuel Eilon & Nicos Christofides, 1971. "The Loading Problem," Management Science, INFORMS, vol. 17(5), pages 259-268, January.
    • Handle: RePEc:inm:ormnsc:v:17:y:1971:i:5:p:259-268
    DOI: 10.1287/mnsc.17.5.259
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    Cited by:

    1. Simon, Jay & Apte, Aruna & Regnier, Eva, 2017. "An application of the multiple knapsack problem: The self-sufficient marine," European Journal of Operational Research, Elsevier, vol. 256(3), pages 868-876.
    2. G, Young-Gun & Kang, Maing-Kyu, 2001. "A fast algorithm for two-dimensional pallet loading problems of large size," European Journal of Operational Research, Elsevier, vol. 134(1), pages 193-202, October.
    3. Yu Fu & Amarnath Banerjee, 2020. "Heuristic/meta-heuristic methods for restricted bin packing problem," Journal of Heuristics, Springer, vol. 26(5), pages 637-662, October.
    4. Delorme, Maxence & Iori, Manuel & Martello, Silvano, 2016. "Bin packing and cutting stock problems: Mathematical models and exact algorithms," European Journal of Operational Research, Elsevier, vol. 255(1), pages 1-20.
    5. Cherri, Adriana Cristina & Arenales, Marcos Nereu & Yanasse, Horacio Hideki & Poldi, Kelly Cristina & Gonçalves Vianna, Andréa Carla, 2014. "The one-dimensional cutting stock problem with usable leftovers – A survey," European Journal of Operational Research, Elsevier, vol. 236(2), pages 395-402.
    6. Muñoz, Susana & Teresa Ortuño, M. & Ramírez, Javier & Yáñez, Javier, 2005. "Coloring fuzzy graphs," Omega, Elsevier, vol. 33(3), pages 211-221, June.
    7. Lijun Wei & Zhixing Luo, & Roberto Baldacci & Andrew Lim, 2020. "A New Branch-and-Price-and-Cut Algorithm for One-Dimensional Bin-Packing Problems," INFORMS Journal on Computing, INFORMS, vol. 32(2), pages 428-443, April.
    8. Sarin, Subhash C. & Aggarwal, Sanjay, 2001. "Modeling and algorithmic development of a staff scheduling problem," European Journal of Operational Research, Elsevier, vol. 128(3), pages 558-569, February.
    9. Kumar Satyendra & Venkata Rao, V. & Tirupati Devanath, 2003. "A heuristic procedure for one dimensional bin packing problem with additional constraints," IIMA Working Papers WP2003-11-02, Indian Institute of Management Ahmedabad, Research and Publication Department.
    10. 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.
    11. Toth, Paolo, 2000. "Optimization engineering techniques for the exact solution of NP-hard combinatorial optimization problems," European Journal of Operational Research, Elsevier, vol. 125(2), pages 222-238, September.
    12. Nicos Christofides, 2022. "Worst-Case Analysis of a New Heuristic for the Travelling Salesman Problem," SN Operations Research Forum, Springer, vol. 3(1), pages 1-4, March.

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