In this study we are concerned with the non-exact two-stage two-dimensional guillotine cutting problem considering usable leftovers, in which stock plates remainders of the cutting patterns (non-used material or trim loss) can be used in the future, if they are large enough to fulfill future demands of items (ordered smaller plates). This cutting problem can be characterized as a residual bin-p...

Two-dimensional bin packing problems are highly relevant combinatorial optimization problems. They find a large number of applications, for example, in the context of transportation or warehousing, and for the cutting of different materials such as glass, wood or metal. In this work we deal with the oriented two-dimensional bin packing problem under free guillotine cutting. In this specific pro...

An Iterated Local Search method for the constrained two-dimensional non-guillotine cutting problem is presented. This problem consists in cutting pieces from a large stock rectangle to maximize the total value of pieces cut. In this problem, we take into account restrictions on the number of pieces of each size required to be cut. It can be classified as 2D-SLOPP (two dimensional single large o...

This work presents a hybrid optimization framework for tackling cutting and packing problems, which is based upon a particular combination scheme between heuristic and exact methods. A metaheuristic engine works as a generator of reduced instances for the original optimization problem, which are formulated as mathematical programming models. These instances, in turn, are solved by an exact opti...

We consider a Two-Dimensional Cutting Stock Problem (2DCSP) where stock of different sizes is available, and a set of rectangular items has to be obtained through two-stage guillotine cuts. We propose and computationally compare three Mixed-Integer Programming models for the 2DCSP developing formulations from the literature. The first two models have a polynomial and pseudo-polynomial number of...

We consider two-dimensional cutting stock problems where single rectangular stocks have to be cut into some smaller rectangular so that the number of stocks needed to satisfy the demands is minimum. In this paper we focus our study to the problem where the stocks have to be cut with guillotine cutting type and fixed orientation of finals. We formulate the problem as an integer programming, wher...

The one-dimensional cutting stock problem (1D-CSP) and the twodimensional two-stage guillotine constrained cutting problem (2D-2CP) are considered in this paper. The Gilmore-Gomory model of these problems has a very strong continuous relaxation which provides a good bound in an LP-based solution approach. In recent years, there have been several efforts to attack the one-dimensional problem by ...

In this study we are concerned with the non-exact two-stage two-dimensional guillotine cutting problem considering usable leftovers, in which stock plates remainders of the cutting patterns (non-used material or trim loss) can be used in the future, if they are large enough to fulfill future demands of items (ordered smaller plates). This cutting problem can be characterized as a residual bin-p...

This paper addresses a constrained two-dimensional (2D) non-guillotine cutting problem, where a fixed set of small rectangles has to be cut from a larger stock rectangle so as to maximize the value of the rectangles cut. The algorithm we propose hybridizes a novel placement procedure with a genetic algorithm based on random keys. We propose also a new fitness function to drive the optimization....