The irregular cutting-stock problem - a new procedure for deriving the no-fit polygon

The no"t polygon is a powerful and e!ective tool for handling the geometry required for a range of solution approaches to two-dimensional irregular cutting-stock problems. However, unless all the pieces are convex, it is widely perceived as being di$cult to implement, and its use has therefore been somewhat limited. The primary purpose of this paper is to correct this misconception by introducing a new method of calculating the no"t polygon. Although it is based on previous approaches which use the mathematical concept of Minkowski sums, this new method can be stated as a set of simple rules that can be implemented without an indepth understanding of the underlying mathematics. The result is an approach that is both very general and easy to use.