The cutting stock problem it is of great interest in relation with several real world problems. Basically it means that there are some smaller pieces that have to be cut from a greater stock piece, in such a way, that the remaining part of the stock piece should be minimal. The classical solution methods of this problem generally need a great amount of calculation. In order to reduce the comput...

We investigate the two-stage guillotine two-dimensional cutting stock problem. This problem commonly arises in the industry when small rectangular items need to be cut out of large stock sheets. We propose an integer programming formulation that extends the well-known Gilmore and Gomory model by explicitly considering solutions that are obtained by both slitting some stock sheets down their wid...

In this article we study a broad class of integer programming problems in variable dimension. We show that these so-termed n-fold integer programming problems are polynomial time solvable. Our proof involves two heavy ingredients discovered recently: the equivalence of linear optimization and so-called directed augmentation, and the stabilization of certain Graver bases. We discuss several appl...

We consider two integer linear programming models for the one-dimensional cutting stock problem that include various difficulties appearing in practical real problems. Our primary goals are the minimization of the trim loss or the minimization of the number of master rolls needed to satisfy the orders. In particular, we study an approach based on the classical column-generation procedure by Gil...

Cutting and packing problems occur in many real-world applications such as industrial glass, paper or steel cutting, container loading and VLSI design [1]. In this work we consider in particular the two-dimensional cutting stock problem with variable sheet size (2CSV) in which we are given a set of nE rectangular element types E = {1, . . . , nE}, each i ∈ E specified by a height hi ∈ N, a widt...