Побудова технологічної матриці варіантів лінійного розкрою

Abstract

Встатті розглянутий комбінаторний алгоритм розрахунку раціональних варіантів лінійного розкрою матеріалів для побудови технологічної матриці варіантів розкрою малої та середньої розмірності. Наведені приклади розрахунків за алгоритмом.The problem of linear cutting is found in many areas of industry: mechanical engineering, metallurgy, wood processing and garment industry, pulp and paper industry and others. Optimal cutting minimizes waste production, so this topic is relevant. The task of minimizing the waste production of cutting is preceded by the task of setting the maximum number of rational variants of cutting materials. The complexity of the problem, namely, the dimension of the cutting matrix and the number of variables for further optimization, is directly determined by the number of rational variants of cutting considered in the model. In the article a combinatorial algorithm for calculating rational variants of linear cutting of materials for constructing a technological matrix of small and medium dimension nesting variants is considered. The generating function for calculation the number of variants types of the cutting is used. The definition of all variants of cutting in the three-dimensional case is reduced to the search for all integer points of space near the plane constructed on the basis of the Diophantine equation. A block diagram of the algorithm for constructing the technological matrix of cutting in a general form is given. Numerical examples are considered. Carried out researches and computer calculations have shown that with a significant increase in the number of species parts that need to cut out the calculation card cutting increases geometrical progression law.