Higher-dimensional orthogonal packing problems have a wide range of practical applications, including packing, cutting, and scheduling. Previous efforts for exact algorithms have been unable to avoid structural problems that appear for instances in twoor higher-dimensional space. We present a new approach for modeling packings, using a graph-theoretical characterization of feasible packings. Ou...

We report on an experimental study of the Gilmore-Gomory cutting-stock heuristic and related LP-based approaches to bin packing, as applied to instances generated according to discrete distributions. No polynomial running time bound is known to hold for the Gilmore-Gomory approach, and empirical operation counts suggest that no straightforward implementation can have average running time O(m), ...

The two dimensional strip packing problem occurs in industries such as metal, wood, glass, paper, and textiles. The problem involves cutting shapes from a larger stock sheet or roll of material, while minimising waste. This is a well studied problem for which many heuristic methodologies are available in the literature, ranging from the basic ‘one-pass’ best-fit heuristic, to the state of the a...

This paper is concerned with the development of a customized circle packing algorithm for a manufacturer of sprockets for the motor cycle industry. Practical constraints mean that the problem differs somewhat from those tackled elsewhere in the literature. In particular, the layouts need to conform to a given structure. This is achieved by using a local search algorithm with an appropriate star...

The problem of planning the layout of containers on board supply vessels can be reformulated as the problem of packing a given set of rectangles into a larger rectangle, subject to constraints. A method combining the use of guillotine cuts with forward checking is proposed, and compared to standard forward checking on finite domains. The initial results show that the method has potential for im...

The cutting stock problem with binary patterns (0-1 CSP) is a variant of CSP that usually appears as a relaxation of 2D and 3D packing problems. We present an exact method, based on an arc-flow formulation with side constraints, for solving 0-1 CSP by simply representing all the patterns in a very compact graph. Gilmore-Gomory’s column generation approach is usually used to compute strong lower...

We introduce two improvements in the numerical scheme to simulate collision and slow shearing of irregular particles. First, we propose an alternative approach based on simple relations to compute the frictional contact forces. The approach improves efficiency and accuracy of the Discrete Element Method (DEM) when modeling the dynamics of the granular packing. We determine the proper upper limi...

Irregular nesting is a subgroup of cutting and packing problems in which a set of irregular items must be inserted in a rectangular container with a variable width. It is often found in industries such as textile, wood and shipbuilding and an efficient solution usually renders an economical and environmental positive impact. Due to the complex geometry of items, the no overlapping rule is hard ...

The cutting stock problem with binary patterns (0-1 CSP) is a variant of CSP that usually appears as a relaxation of 2D and 3D packing problems. We present an exact method, based on an arc-flow formulation with side constraints, for solving 0-1 CSP by simply representing all the patterns in a very compact graph. Gilmore-Gomory’s column generation approach is usually used to compute strong lower...