The Research And Application Of One-dimensional Multi-material Cutting Stock Problem

With the rapid development of national economy in recent years, the one-dimensional cutting stock problem occurs in many industry areas. Looking for an optimum cutting solution can not only save raw materials and decrease product cost, but also bring to immediate economic benefits for enterprises and accelerate the development of national economy. So research on the problem is of importance in theory and practice.Firstly, in this paper, we study one kind of one-dimensional cutting stock problems in great detail, put forward an algorithm that can generate cutting patterns automatically by the computer. And the mathematical model is established based on these patterns. Then two different algorithms are applied to solving one-dimensional cutting problems, and results of numerical examples are also given and discussed.1. Linear Programming. Simplex method of LP is a traditional method to solve this problem. This paper analyzed is advantages of this method, for instance: the solutions are not all integral numbers, or will get wrong even no solution because of great scale of the problem.2. Genetic Algorithm (short for GA) is an important intelligent algorithm. We use this algorithm to solve the one-dimensional cutting stock problem after analyzing GA from the view of application. At the same time, the coding method, fitness function definition, genetic operators and some key parameters are given. The results show that the algorithm is feasible and efficient.