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Packing small boxes into a big box

Author

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  • Manfred Padberg

Abstract

The three-dimensional orthogonal packing problem consists of filling a big rectangular box with as many small rectangular boxes as possible. In a recent paper G. Fasano (Alenia Aerospazio, Turin) has given a mixed-integer programming formulation of this problem. Here we extend Fasano's formulation and subject it to polyhedral analysis. The result is a more general formulation whose linear programming relaxation is a tighter approximation of the convex hull of the mixed-integer solutions to the problem than the original model. Copyright Springer-Verlag Berlin Heidelberg 2000

Suggested Citation

  • Manfred Padberg, 2000. "Packing small boxes into a big box," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 52(1), pages 1-21, September.
    • Handle: RePEc:spr:mathme:v:52:y:2000:i:1:p:1-21
    DOI: 10.1007/s001860000066
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    Citations

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    Cited by:

    1. Sándor P. Fekete & Jörg Schepers, 2004. "A Combinatorial Characterization of Higher-Dimensional Orthogonal Packing," Mathematics of Operations Research, INFORMS, vol. 29(2), pages 353-368, May.
    2. Felix Prause & Kai Hoppmann-Baum & Boris Defourny & Thorsten Koch, 2021. "The maximum diversity assortment selection problem," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 93(3), pages 521-554, June.
    3. Araya, Ignacio & Moyano, Mauricio & Sanchez, Cristobal, 2020. "A beam search algorithm for the biobjective container loading problem," European Journal of Operational Research, Elsevier, vol. 286(2), pages 417-431.
    4. Baldacci, Roberto & Boschetti, Marco A., 2007. "A cutting-plane approach for the two-dimensional orthogonal non-guillotine cutting problem," European Journal of Operational Research, Elsevier, vol. 183(3), pages 1136-1149, December.
    5. Lorenzo Brunetta & Philippe Grégoire, 2005. "A General Purpose Algorithm for Three-Dimensional Packing," INFORMS Journal on Computing, INFORMS, vol. 17(3), pages 328-338, August.
    6. Gleb Belov & Heide Rohling, 2013. "LP Bounds in an Interval-Graph Algorithm for Orthogonal-Packing Feasibility," Operations Research, INFORMS, vol. 61(2), pages 483-497, April.
    7. Sam D. Allen & Edmund K. Burke, 2012. "Data Structures for Higher-Dimensional Rectilinear Packing," INFORMS Journal on Computing, INFORMS, vol. 24(3), pages 457-470, August.
    8. Sándor P. Fekete & Jörg Schepers & Jan C. van der Veen, 2007. "An Exact Algorithm for Higher-Dimensional Orthogonal Packing," Operations Research, INFORMS, vol. 55(3), pages 569-587, June.
    9. Xiangling Zhao & Yun Dong & Lei Zuo, 2023. "A Combinatorial Optimization Approach for Air Cargo Palletization and Aircraft Loading," Mathematics, MDPI, vol. 11(13), pages 1-16, June.
    10. Bortfeldt, Andreas & Wäscher, Gerhard, 2013. "Constraints in container loading – A state-of-the-art review," European Journal of Operational Research, Elsevier, vol. 229(1), pages 1-20.
    11. David Pisinger & Mikkel Sigurd, 2007. "Using Decomposition Techniques and Constraint Programming for Solving the Two-Dimensional Bin-Packing Problem," INFORMS Journal on Computing, INFORMS, vol. 19(1), pages 36-51, February.
    12. Galrão Ramos, A. & Oliveira, José F. & Gonçalves, José F. & Lopes, Manuel P., 2016. "A container loading algorithm with static mechanical equilibrium stability constraints," Transportation Research Part B: Methodological, Elsevier, vol. 91(C), pages 565-581.

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