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Cutting stock problem
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===Solution=== [[File:CuttingStock.gif|thumb|430px|A minimum-waste solution, sequenced to minimise knife changes, shown as small white circles]] There are 308 possible patterns for this small instance. The optimal answer requires 73 master rolls and has 0.401% waste; it can be shown computationally that in this case the minimum number of patterns 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''' |}
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