the one-dimensional cutting stock problem, has so many applications in lots of industrial processes and during the past few years has attracted so many researchers’ attention all over the world. in this paper a meta-heuristic method based on aco is presented to solve this problem. in this algorithm, based on designed probabilistic laws, artificial ants do select various cuts and then select the...

Abstract Two-dimensional cutting and packing problems model a large number of relevant industrial applications.The literature on practical algorithms for such is very large. We introduce the , library two-dimensional orthogonal problems. The makes available, in unified format, 25 benchmarks from total over 3000 instances, provides direct links to surveys typologies, includes list links.

The dynamics of the cutting process are investigated. Using the increase of cutting depth as a control parameter, two diierent cutting regimes are observed. In the rst regime, which is observed at small cutting depths, complex, high-dimensional dynamics occur. In the second cutting regime, observed for deeper cuts, low dimensional dynamics are typical. The second cutting regime is usually ident...

In this study we are concerned with the non-exact two-stage two-dimensional guillotine cutting problem considering usable leftovers, in which stock plates remainders of the cutting patterns (non-used material or trim loss) can be used in the future, if they are large enough to fulfill future demands of items (ordered smaller plates). This cutting problem can be characterized as a residual bin-p...

Starting from a two-dimensional rectangular Cutting-Stock pattern with gaps, this paper is focuses on the problem of determination if the pattern is with guillotine restrictions or not and proposes an algorithm for solving it. First we present two new graph representations of the cutting pattern, weighted graph of downward adjacency and weighted graph of rightward adjacency. Using these represe...

We consider a two-dimensional rectangular Cutting-Stock problem in case of a cutting pattern with gaps. First we present two new graph representations of the cutting pattern, weighted graph of downward adjacency and weighted graph of rightward adjacency. Using this kind of representation we propose a method to verify guillotine restrictions of the pattern which can be applied for cutting-stock ...

The one-dimensional cutting stock problem (1D-CSP) and the twodimensional two-stage guillotine constrained cutting problem (2D-2CP) are considered in this paper. The Gilmore-Gomory model of these problems has a very strong continuous relaxation which provides a good bound in an LP-based solution approach. In recent years, there have been several efforts to attack the one-dimensional problem by ...

We survey the main formulations and solution methods for two-dimensional orthogonal cutting packing problems, where both items bins are rectangles. focus on exact relaxations four problems from literature: finding a with minimum height, into number of bins, maximum value, determining existence feasible packing.