Two‐dimensional guillotine cutting problem for large objects with non‐rectangular shapes

Abstract In this paper, we address the two‐dimensional single large object placement problem with guillotine cutting constraints, focusing on non‐rectangular shapes. We consider objects with circular or convex polygonal geometries and study a variant that includes defective regions from which no items can be extracted. Rectangular items are cut using a two‐stage guillotine pattern, allowing items to be rotated orthogonally. To solve this problem, we adopt a recursive dynamic programming algorithm that handles geometric complexities arising from non‐rectangular shapes. For convex polygonal objects, we introduce a method that optimizes the starting angle of the cutting pattern to maximize utilization and profitability. Computational experiments show that our approach provides optimal solutions for circular objects with high computational efficiency. For polygonal objects, the method provides robust solutions by evaluating multiple rotation angles to determine the optimal cutting orientation. Our approach accommodates imperfections, maintaining high material utilization even in the presence of defects.