In case of the one-dimensional cutting stock problem (CSP) one can observe for any instance a very small gap between the integer optimal value and the continuous relaxation bound. These observations have initiated a series of investigations. An instance possesses the integer roundup property (IRUP) if its gap is smaller than 1. It is well-known that there exist instances of the CSP having a gap...

This work presents a hybrid approach based on the use of genetic algorithms to solve efficiently the problem of cutting structural beams arising in a local metalwork company. The problem belongs to the class of onedimensional multiple stock sizes cutting stock problem, namely 1dimensional multiple stock sizes cutting stock problem. The proposed approach handles overproduction and underproductio...

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 propose a framework to model general guillotine restrictions in two-dimensional cutting problems formulated as Mixed Integer Linear Programs (MIP). The modeling framework requires a pseudo-polynomial number of variables and constraints, which can be effectively enumerated for medium-size instances. Our modeling of general guillotine cuts is the first one that, once it is implemented within a...

The cutting stock problem is an important problem in the field of combinational optimization. In classic versions of this problem, the aim is to find a solution for cutting some equalwidth mother rolls into smaller parts with given width so that the amount of trim-loss become as small as possible. There are plenty of works which addressed the classic cutting stock problem. However in real world...

Despite its great applicability in several industries, the combined cutting stock and lot-sizing problem has not been sufficiently studied because of its great complexity. This paper analyses the trade-off that arises when we solve the cutting stock problem by taking into account the production planning for various periods. An optimal solution for the combined problem probably contains non-opti...

The constrained 2-D cutting stock problem is an irregular problem with dynamic data structures, highly variable amounts of computation per task, and unpredictable amounts and patterns of communication. This paper describes the design and implementation of a parallel solution to this problem on a cluster of workstations and a distributed memory multicomputer. The key element of our parallel solu...