Original scientific papers This paper mainly addresses a two-dimensional defective stocks guillotine cutting stock problem where stock of different sizes is available. Herein a new heuristic algorithm which is based on tree is proposed to discuss this problem. In particular, such an algorithm consists of two parts: the first part is an initial solution of the cutting stock problem where there a...

In a two-photon femtosecond laser system of three-dimensional micro-fabrication, a model of micro-device is fabricated layer by layer along its contours of cross-sections. So it is necessary to generate cutting path. In this paper, we present an efficient algorithm to generate cutting path which is a series of ordered contour points on each cross-section of a model. Keyword. Micro-fabrication, ...

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...

A review is presented of one-dimensional cutting lines that are utilized to obtain the physical properties of carbon nanotubes from the corresponding properties of graphite by the zone-folding scheme. Quantization effects in general low-dimensional systems are briefly discussed, followed by a more detailed consideration of one-dimensional single-wall carbon nanotubes. The geometrical structure ...

The two-dimensional Single Large Object Placement Problem (SLOPP) problem consists of determining a cutting pattern of a set of n small rectangular piece types (little object) on a rectangular stock plate (large object) of length L and width W, as to maximize the sum of the profits of the pieces to be cut. Each piece type i, i = 1, . . ., m, is characterized by a length li, a width wi, a profit...

A new ASTM method was developed for the analysis of trace methanol in crude oil samples. This method relies on the use of two-dimensional heart-cutting gas chromatography to separate methanol from the complex matrix. A new microfluidic Deans switch was developed for the Agilent 6890N GC system that improves the performance of heart-cutting two-dimensional gas chromatography. This system was use...

Practitioners of the geosciences, design, and engineering disciplines communicate complex ideas about shape by manipulating three-dimensional digital objects to match their conceptual model. However, the two-dimensional control interfaces, common in software applications, create a disconnect to three-dimensional manipulations. This research examines cutting, deforming, and painting manipulation...

The two-dimensional strip packing is a special case of “Cutting and Packing” problems that arises in many applications. The problem seeks to pack a given set of rectangles into a strip of given width in order to minimize its length. Some applications in which the strip packing problem arises are: Cutting pieces from wooden boards, cutting pieces from glass or steel sheets, optimal layout of ind...