Dynamic Rules Rectangular Single Row Of Samples

Optimal layout of rectangle pieces refers to that the necessary rectangle pieces could be arranged as many as possible on a plate with given length and width for the purpose of reducing the amount of the plates as few as possible. This work is widely applied to machining, light industry, furniture and glass cutting etc. The problem of two-dimensional layout of the irregular blanks on the rectangular stocks can be transformed to that of blanking of rectangle pieces by computer graphics technology. Optimal layout of rectangle pieces belongs to NP-complete problem ,so it is usually impossible to find its optimal solution .According to whether various-sized blanks could be arranged on the same plate, the corresponding cutting patterns are termed as rectangular object optimal embed placement or cutting patterns for rectangular blanks of a single size from a rectangular. The former is good for improving utilization ratio of materials, but since the latter is accepted easily by the clients because of its simple technology and convenient management in the process of blanking. At present, the common algorithms of cutting patterns for rectangular blanks of a single size from a rectangular sheet generally include dynamic program, branch and bound algorithm, time-based polynomial algorithm, continue fraction algorithm. The degree of difficulty in algorithms is gradually enhanced in proper order from dynamic programming to continue fraction algorithm. Dynamic programming is often employed due to its simplicity and easy realization; besides, it has its superiority over others. In productive practice, the length of the plates that the enterprises purchase may be longer than the maximum length that the shear machining can be cut. When blanking, the long rectangular sheet should be divided into several sections by the cutting line which parallels the rim of the width. Each section's length is shorter than or equal to length of blade. Then, cutting blanks off from those sections. Here, we term this problem as limitation of blade. The proposed dynamic programming demands the length of blade should not be shorter than that of the plate; otherwise, the layouts which can not be cut may be made. As a result, the above-stated problem can not be effectively resolved. This thesis, from the perspective of realization, explores how to improve dynamic programmin by the feature of it, thus solving the problem of limitation of blade. Moreover, what the proposed dynamic programming solves is actually the problem of no restraint layout, that is, how to produce blanks as many as possible on a single plate. In real production, there is a limited demand for blanks. Therefore, restrained layouts are necessary, namely, minimizing the usable space of the plates under the condition that the demands for blanks are satisfied. From the angle of realization, this paper expounds how to improve dynamic programming for the purpose of restrained layouts. In addition, this thesis also discusses how to apply the optimum cutting patterns for rectangular blanks of a single size from a rectangular sheet to the stock optimum decision-making. The plates with various sizes can be provided in markets. This paper deals with how to combine dynamic programming and the stock cost calculation to improve the scientificity of stock decision-making. When an enterprise can not purchase the suitable-sized plates, it may directly order custom-made plates from the factory by pay a certain amount of ordering regular size expenses. This paper discusses how to optimize decision-making by adopting dynamic programming.