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Packing Rectangles into a Strip

In: Introduction to Cutting and Packing Optimization

Author

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  • Guntram Scheithauer

    (TU Dresden)

Abstract

Within this chapter we consider the following problem of minimizing material consumption in the two-dimensional case: there are given a list of rectangles and a strip of fixed width and unlimited height. The task is to pack all rectangles orthogonally into the strip such that the minimal needed height is used. The Strip Packing Problem (SPP) belongs, like many other cutting and packing problems, to the class of NP-hard optimization problems. It is polynomially equivalent to the Orthogonal Packing (Feasibility) Problem. Due to the NP-hardness, efficient heuristics are considered in the majority of related literature. Besides an appropriate modeling of the SPP, we describe and analyze some heuristic and metaheuristic approaches. Moreover, based on lower bounds, we present a branch-and-bound algorithm which packs the pieces sequentially. The Guillotine Strip Packing Problem is considered as well.

Suggested Citation

  • Guntram Scheithauer, 2018. "Packing Rectangles into a Strip," International Series in Operations Research & Management Science, in: Introduction to Cutting and Packing Optimization, chapter 0, pages 183-226, Springer.
    • Handle: RePEc:spr:isochp:978-3-319-64403-5_7
    DOI: 10.1007/978-3-319-64403-5_7
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