with this level of waste is 10. It can also be computed that 19 different such solutions exist, each with 10 patterns and a waste of 0.401%, of which one such solution is shown below and in the picture: {| class="wikitable" !Repetition !align=center | Contents |- | align=center | 2 || 1820 + 1820 + 1820 |- | align=center | 3 || 1380 + 2150 + 1930 |- | align=center | 12 || 1380 + 2150 + 2050 |- | align=center | 7 || 1380 + 2100 + 2100 |- | align=center | 12 || 2200 + 1820 + 1560 |- | align=center | 8 || 2200 + 1520 + 1880 |- | align=center | 1 || 1520 + 1930 + 2150 |- | align=center | 16 || 1520 + 1930 + 2140 |- | align=center | 10 || 1710 + 2000 + 1880 |- | style="border-bottom:3px solid grey" align=center | 2 || 1710 + 1710 + 2150 |- | align=center | 73 |} Classification Cutting-stock problems can be classified in several ways. 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 containers (see e.g. containerization: the related sphere packing problem has been studied since the 17th century (Kepler conjecture)). Applications Industrial applications of cutting-stock problems for high production volumes arise especially when basic material is produced in large rolls that are further cut into smaller units (see roll slitting). This is done e.g. in paper and plastic film industries but also in production of flat metals like steel or brass. There are many variants and additional constraints arising from special production constraints due to machinery and process limits, customer requirements and quality issues; some examples are: Two-stage, where the rolls produced in the first stage are then processed a second time. For instance, all office stationery (e.g. A4 size in Europe, Letter size in US) is produced in such a process. The complication