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The Two Dimensional Bin Packing Problem with Side Constraints

In: Operations Research Proceedings 2017

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  • Markus Seizinger

    (University of Augsburg)

Abstract

We propose a new variant of Bin Packing Problem, where rectangular items of different types need to be placed on a two-dimensional surface. This new problem type is denoted as two-dimensional Bin Packing with side constraints. Each bin may consist of different two-dimensional sides, and items of different types may not overlap on different sides of the same bin. By different parameter settings, our model may be reduced to either a two- or three-dimensional Bin Packing Problem. We propose practical applications of this problem in production and logistics. We further introduce lower bounds, and heuristics for upper bounds. We can demonstrate for a variety of instance classes proposed in literature that the GAP between those bounds is rather low. Additionally, we introduce a Column-Generation based algorithm that is able to further improve the lower bounds and comes up with good solutions. For a total of 400 instances, extended from previous literature, the final relative gap was just 6.8%.

Suggested Citation

  • Markus Seizinger, 2018. "The Two Dimensional Bin Packing Problem with Side Constraints," Operations Research Proceedings, in: Natalia Kliewer & Jan Fabian Ehmke & Ralf Borndörfer (ed.), Operations Research Proceedings 2017, pages 45-50, Springer.
    • Handle: RePEc:spr:oprchp:978-3-319-89920-6_7
    DOI: 10.1007/978-3-319-89920-6_7
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