We describe an exact model for the two-dimensional Cutting Stock Problem with two stages and the guillotine constraint. It is a linear programming arc-flow model, formulated as a minimum flow problem, which is an extension of a model proposed by Valério de Carvalho for the one dimensional case. In this paper, we explore how this model behaves when it is solved with a commercial software, explic...

The MIRUP (Modified Integer Round-Up Property) leads to an upper bound for the gap between the optimal value of the integer problem and that of the corresponding continuous relaxation rounded up. This property is known to hold for many instances of the one-dimensional cutting stock problem but there are not known so far any results with respect to the two-dimensional case. In this paper we inve...

The MIRUP (Modiied Integer RoundUp Property) leads to an upper bound for the gap between the optimal value of the integer problem and that of the corresponding continuous relaxation rounded up. This property is known to hold for many instances of the one-dimensional cutting stock problem but there are not known so far any results with respect to the two-dimensional case. In this paper we invest...

In this paper we study the two-dimensional non-guillotine cutting problem, the problem of cutting rectangular pieces from a large stock rectangle so as to maximize the total value of the pieces cut. The problem has many industrial applications whenever small pieces have to be cut from or packed into a large stock sheet. We propose a tabu search algorithm. Several moves based on reducing and ins...

This paper provides an introduction to one-dimensional cutting stock problems and solution procedures. The first problem considered requires that both trim loss and pattern changes be controlled. Both linear programming and sequential heuristic procedures are discussed along with the ways they can be used jointly to generate the best possible solutions to this type of problem. Two other importa...

Consider the feasibility problem in higher-dimensional orthogonal packing. Given a set I of d-dimensional rectangles, we need to decide whether a feasible packing in a d-dimensional rectangular container is possible. No item rotation is allowed and item edges are parallel to the coordinate axes. Typically, solution methods employ some bounds to facilitate the decision. Various bounds are known,...