The two-dimensional guillotine cutting problem for convex polygonal objects

In this paper, we address the two-dimensional single large object placement problem under guillotine cutting constraints for large objects with convex polygonal geometry. Rectangular items are cut from the object according to a two-stage guillotine cutting pattern with orthogonal rotations allowed. We also consider an extension with a defective region from which no items may be extracted. To solve the problem, we adopt a recursive dynamic programming algorithm capable of handling the geometric features of these shapes, including variable cut lengths. In addition, we propose a procedure to determine the initial angle of the cutting pattern in order to improve material utilization. Computational experiments show that the proposed approach yields effective and robust solutions, even in the presence of a defective region.