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...

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...

I N T R O D U C T I O N In a number of industries, such as paper and film, there is an important class of problems OVER THE past 20 years, a substantial amount that falls in between the well known one and of work has been done on one and two-dimentwo-dimensional problems. These are referred sional cutting stock problems. A number of to here as two-stage cutting stock problems early authors [1, ...

Cutting stock problems and bin packing problems are basically the same problems. They differ essentially on the variability of the input items. In the first, we have a set of items, each item with a given multiplicity; in the second, we have simply a list of items (each of which we may assume to have multiplicity 1). Many approximation algorithms have been designed for packing problems; a natur...

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...

This paper discusses some of the basic formulation issues and solution procedures for solving oneand twodimensional cutting stock problems. Linear programming, sequential heuristic and hybrid solution procedures are described. For two-dimensional cutting stock problems with rectangular shapes, we also propose an approach for solving large problems with limits on the number of times an ordered s...

In this paper, we develop a greedy randomized adaptive search procedure (GRASP) for the constrained two-dimensional two-staged cutting stock problem. This is a special cutting problem in which the cut is performed in two phases. In the first phase, the stock rectangle is slit down its width into different vertical strips and in the second phase, each of these strips is processed to obtain the f...