Editing Cutting stock problem (section)

== Classification ==
Cutting-stock problems can be classified in several ways.<ref name="Wäscher2007">Wäscher, G.; Haußner, H.; Schumann, H. ''[http://prolog.univie.ac.at/teaching/LVAs/KFK-Seminar/SS15/2007%20W%E4scherHaussnerSchuhmann%20An%20improved%20typology%20of%20cutting%20and%20packing%20problems.pdf An Improved Typology of Cutting and Packing Problems] {{Webarchive|url=https://web.archive.org/web/20200424185417/https://prolog.univie.ac.at/teaching/LVAs/KFK-Seminar/SS15/2007%20W%E4scherHaussnerSchuhmann%20An%20improved%20typology%20of%20cutting%20and%20packing%20problems.pdf |date=2020-04-24 }}''. European Journal of Operational Research Volume 183, Issue 3, 1109-1130</ref> One way is the dimensionality of the cutting: the above example illustrates a one-dimensional (1D) problem; other industrial applications of 1D occur when cutting pipes, cables, and steel bars. Two-dimensional (2D) problems are encountered in furniture, clothing and glass production. When either the master item or the required parts are irregular-shaped (a situation often encountered in the leather, textile, metals industries) this is referred to as the ''nesting'' problem.

Not many three-dimensional (3D) applications involving cutting are known; however the closely related 3D [[packing problem]] has many industrial applications, such as packing objects into [[shipping container]]s (see e.g. [[containerization]]: the related [[sphere packing]] problem has been studied since the 17th century ([[Kepler conjecture]])).