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One-Dimensional Cutting Stock

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Introduction to Cutting and Packing Optimization

Part of the book series: International Series in Operations Research & Management Science ((ISOR,volume 263))

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Abstract

In difference to one-dimensional Bin Packing Problems (1BPP) where each item is considered to be a unique one, in a one-dimensional Cutting Stock Problem (1CSP), the number of different piece types is rather small, but their order demands (or availability in case of packing problems) are mostly large. Another differentiator of bin packing and cutting stock problems could be the magnitude of the respective optimal value. If it is small in comparison to the total number of items, then the instance is of BPP type, otherwise the problem type depends on the number of different patterns in a solution.

In the beginning of this chapter, we consider the 1CSP with a single type of raw material. We present a solution strategy which is also applicable to higher-dimensional problems as, for instance, in the furniture industry when the production of rectangular pieces has to be optimized. Subsequently, we address generalizations and present alternative models. Finally, we investigate the relation between the standard ILP model and its LP relaxation and observe a small gap for any 1CSP instance.

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Authors and Affiliations

  1. Institute for Numerical Mathematics, TU Dresden, Dresden, Germany

    Guntram Scheithauer

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  1. Guntram Scheithauer
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Scheithauer, G. (2018). One-Dimensional Cutting Stock. In: Introduction to Cutting and Packing Optimization. International Series in Operations Research & Management Science, vol 263. Springer, Cham. https://doi.org/10.1007/978-3-319-64403-5_4

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