
About  Description  Cutting Stock Problem  Circle Optimization Problem 
Cutting Rectangles  Cutting Triangles  Cutting Circles  Contact Us 
A triangle is a 3sided polygon. Every triangle has three sides and three angles, some of which may be the same. All triangles are convex. Triangles can be classified according to the number of their equal sides. A triangle with 3 equal sides is called equilateral, a triangle with 2 equal sides is called isosceles, and a triangle with no equal sides is called scalene. The portion of the area enclosed by the triangle is called the triangle interior. The sum of angles in a triangle is pi radians or 180 degrees. If a line is drawn parallel to one side of a triangle so that it intersects the other two sides, it divides them proportionally. The term nesting is used to describe a wide variety of twodimensional cutting problems. They all involve a nonoverlapping placement of a set of triangles within some region of 2d area. The basic requirement is to produce a solution with no overlap between the triangles. This means that the items must be placed without creating overlap between the triangles. The generation of a cutting pattern depends on the order of handling the triangles, and the way of fitting these triangles into the sheet with respect to the sheet boundaries. The twodimensional cutting stock problem may be applied in a number of industries, including clothing industry, shoeleather cutting, furniture industry, etc. The problem is as follows: a set of triangles is to be placed on a given area of a stockmaterial with minimum of trimloss. Permissible placement of wanted triangles on stockmaterial is called cutting pattern. The cutting pattern has no overlaps of the triangles and meets all technological requirements. The quality of a cutting pattern is determined by the cutting ratio, which is defined as the ratio between the total area of the placed triangles and the total area of the stockmaterial. Nesting software is used to generate optimized layouts and reduced scrap for both Rectangular and Triangular cutting processes. The nesting technology is based on algorithms designed to optimize the cutting layouts. It provides high utilization layouts, significantly reducing the waste and maximizing productivity. In the cutting problems one or more pieces of material or space must be divided into smaller triangles. The minimization of the waste is usually the main objective of these combinatorial optimization problems. In nesting problems the combinatorial problem coexists with a geometric problem, since solutions must be geometrically feasible and triangles may not overlap and must completely fit inside the plate. Packing problems are optimization problems that are concerned with searching a good arrangement of multiple items in a 2d regions. The usual objective of the allocation is to maximize the material utilization and to minimize the wasted area. This is of particular interest to industries involved with massproduction as small improvements in the layout can result in savings of material and a considerable reduction in production costs. The goal in the cutting stock problem is to determine the optimal plan to cut a 2 dimensional sheet to satisfy a set of customers demands. Cutting triangle problems may involve a variety of objectives, minimizing trim loss, minimizing the number of cutting lines, maximizing profit, and so on. In order to solve the cutting triangle problem, we use a cutting pattern optimizer and mathematical programming. In general, the cutting triangle problem is reduce to an integer programming application. Because of its complexity, solutions to the 2 dimensional cutting stock problem have often been generated using genetic algorithms. This is due, in part, to the fact that the 2 dimensional cutting stock problem may also be reduced to a binpacking problem. The rectangular cutting stock problem is to determine how to cut a number of rectangular pieces out of a given stock of rectangular sheets. Most variants of the nesting problem is the problem of packing shapes within some regions without overlap. The cutting stock problem asks for a minimization of the area of a rectangular region. In the cutting industry a multitude of additional constraints are very often necessary. The shapes or regions can have different quality zones or even holes. The nesting problem occurs in a number of industries and it seems to have many names. In the clothing industry it is called marker making, while the metal industry call it simply nesting. In a theoretical context the problem is most often called the twodimensional irregular cutting stock problem. The 2 dimensional cutting stock problem is a classic combinatorial optimization problem in which a number of parts of various lengths must be cut from an inventory of 2d material. The twodimensional cutting stock problem may be applied in a number of industries, glass, shoeleather cutting, furniture, machinebuilding, etc. The problem is as follows : a set of rectangular pieces is to be placed on a given area of a stock material with minimum of trimloss. The cutting pattern has no overlaps of the pieces and meets all technological requirements. The stock cutting problem has gained a lot of attention in many industrial sectors. Stock Cutting Problems is essential in many industries. These problems are treated in different fields. The reduction of scrap may not only affects cost of materials used but may also reduce the costs of handling and labor. A great number of problems are essentially based on the same logical structure of the Cutting and Packing problems. The stock cutting problem is an example of a large scale optimization problem. This means that this problem requires a computing effort that increases exponentially with the problem size. Since the stock cutting problem is an efficient approximation algorithms, namely, algorithms that do not produce optimal but rather closetooptimal solutions, Cutting and packing problems are encountered in many industries. The wood, glass and paper industry are mainly concerned with the cutting of regular figures, whereas in the textile and leather industry irregular, arbitrary items are to be packed. 