What software is there for cutting or packing problems?
The cutting (or “cutting stock”) problem involves cutting large pieces of something into specified numbers of smaller pieces in the most economical way. In the one-dimensional version, cutting only reduces a single measurement, usually referred to as the length or width of the pieces; examples include cutting wide rolls of paper or sheet steel into specified numbers of smaller widths (also called the “roll trim” problem), and cutting long pieces of wood or pipe into specified specified numbers of shorter pieces. In the two-dimensional version, both a length and width may be specified for both the large pieces you start with and the smaller ones to be cut, or the shapes to be cut may be more general. The material may again be wood or metal, or paper or fabric, or even cookie dough. The packing problem can be regarded as a kind of cutting in reverse, where the goal is to fill large spaces with specified smaller pieces in the most economical (or profitable) way. As with cutting, there are
