We consider the two-dimensional strip packing problem with guillotine cuts. The problem consists in packing a set of rectangular items on one strip of width W and infinite height. The items packed without overlapping must be extracted by a series of cuts that go from one edge to the opposite edge guillotine constraint . To solve this problem, we use a dichotomic algorithm that uses a lower boun...

The MAXGAP problem of a linear integer optimization problem P consists in determining the maximum diierence (gap) (P) between the optimal value z (E) of an instance E 2 P and the LP bound z c (E) with respect to all E 2 P. In the case of the one-dimensional cutting stock problem (1D CSP) it is known that (1D CSP) 1 + 5 132 but there is also a conjecture that (1D CSP) 2. In this paper we show th...

We present a tree-search algorithm for two-dimensional cutting problems in which there is a constraint on the maximum number of each type of piece that is to be produced. The algorithm limits the size of the tree search by deriving and imposing necessary conditions for the cutting pattern to be optimal. A dynamic programming procedure for the solution of the unconstrained problem and a node eva...

The paper presents a tree search algorithm for the three-dimensional container loading problem (3D-CLP). The 3D-CLP is the problem of loading a subset of a given set of rectangular boxes into a rectangular container so that the packed volume is maximized. The method has two variants: the packing variant guarantees full support from below for all packed boxes, while this constraint is not taken ...