These reels are then cut into rolls or products of smaller widths and shorter lengths. This cutting stock problem is a classical optimization problem that can be solved using column generation and branch and bound. However, in practice there are a number of production specific restrictions e.g. certain products cannot be mixed and a maximum number of products on each cutting pattern. With these additional requirement it is not practical to use column generation. Furthermore, in modern paper mills there are web inspection systems available to detect defects on the reels produced.
Products have different quality restrictions expressed in terms of defects.
There are additional restrictions such as the number of knives and their closeness or various complicated possibilities to cut away waste sections. This gives an operative decision problem where cutting patterns have to be decided for each reel. We describe decision support systems that are capable of solving both planning problems. Numerical results from industrial applications are presented.