Large-scale optimization methods applied to the cutting stock problem of irregular shapes

This paper describes a real feasibility study of applying large-scale optimization methods to the cutting stock problem of irregular shapes. We identify two approaches for minimizing waste in the cutting stock problem of irregular shapes: better packing and better scheduling of cuts. This paper is concerned with the scheduling problem only. By scheduling of cuts we mean deciding which combination of parts to group together on the cutting table so that overall material needed by all cuts is minimized. Such a problem usually requires considering many combinations. However, with the development of various feasibility requirements imposed on the column generation process this number can be reduced considerably. Furthermore, the introduction of interior-point algorithms for linear programming by Karmarkar in 1984, allows the consideration of much larger linear programming problems than was possible just a few years ago.