In this paper we present a heuristic method to generate constrained two-dimensional guillotine cutting patterns. This problem appears in different industrial processes of cutting rectangular plates to produce ordered items, such as in the glass, furniture and circuit board business. The method combines a state space relaxation of a dynamic programming formulation of the problem, an and/or-graph...

Abstract About 15 years ago, a paper proposed the first integer linear programming formulation for constrained two‐dimensional guillotine cutting problem (with unlimited stages). Since then, eight other formulations followed, seven of them in last four years. This spike interest gave no opportunity comprehensive comparison between formulations. We review each and compare their empirical results...

The paper deals with the purpose of one hybrid approach for solving the constrained two-dimensional cutting (2DC) problem. We study this hybrid approach that combines the genetic algorithm and the Tabu search method. For this problem, we assume a packing of a whole number of rectangular pieces to cut, and that all cuts are of guillotine type in one sheet of a fixed width and an infinite height....

T paper presents a parallel branch-and-bound method to address the two-dimensional rectangular guillotine strip cutting problem. Our paper focuses on a parallel branching schema. We present a series of computational experiments to evaluate the strength of the approach. Optimal solutions have been found for some benchmark instances that had unknown solutions until now. For many other instances, ...

The two-dimensional orthogonal non-guillotine cutting problem (NGCP) appears in many industries (like wood and steel industries) and consists in cutting a rectangular master surface into a number of rectangular pieces, each with a given size and value. The pieces must be cut with their edges always parallel or orthogonal to the edges of the master surface (orthogonal cuts). The objective is to ...

We present algorithms for the following three-dimensional (3D) guillotine cutting problems: Unbounded Knapsack, Cutting Stock and Strip Packing. We consider the case where the items have fixed orientation and the case where orthogonal rotations around all axes are allowed. For the Unbounded 3D Knapsack problem, we extend the recurrence formula proposed by Beasley for the Rectangular Knapsack Pr...

A guillotine partition of a d-dimensional axis-aligned box B is a recursive partition of B by axis-aligned hyperplane cuts. The size of a guillotine partition is the number of boxes it contains. Two guillotine partitions are box-equivalent if their boxes satisfy compatible order relations with respect to the axes. (In many works, box-equivalent guillotine partitions are considered identical.) I...

The paper deals with the purpose of one hybrid approach for solving the constrained two-dimensional cutting (2DC) problem. The authors study this hybrid approach that combines the genetic algorithm and the Tabu search method. For this problem, they assume a packing of a whole number of rectangular pieces to cut, and that all cuts are of guillotine type in one sheet of a fixed width and an infin...