Abstract
In this paper, we study the constrained two-dimensional guillotine cutting problem with defects, which involves cutting a set of items from a large sheet containing defects while satisfying guillotine constraints. The goal is to maximise the value of the cut items. We propose an exact combinatorial Benders decomposition approach to solve this problem, decomposing it into a master problem and a subproblem. The master problem involves deciding which items to cut and determining the y-coordinates of the cut items. The subproblem is a feasibility problem that identifies a two-dimensional packing, ensuring no overlap and satisfying the guillotine constraints. Valid inequalities and enhanced Benders cuts are applied to strengthen the linear programming relaxation of the master problem. Numerical results on benchmark instances show that our algorithm proves 5,384 optimal solutions out of 5,400 instances. We also compare it with state-of-the-art algorithms in the literature to demonstrate the good performance of the proposed method.