| Cutting stock problems appear widely in various industries, such as fabricated metal, furniture, and sheet metal industries, etc. Currently, the wider application is two-dimensional rectangular cutting stock problem. Two-dimensional rectangular cutting stock problem is to cut the plates into rectangular blanks, on the premise of meeting the demand of blanks, and the objective is to minimize the total production cost. The solution of the two-dimensional rectangular cutting stock problem is a cutting plan that contains a set of cutting patterns. The objective is to minimize the total cost of the cutting plan. The space for improving material utilization is getting smaller with the advances of the research. Other factors should be considered to reduce the total cost further. So to solve the two-dimensional rectangular cutting stock problem, put forward a solution which considers the cutting costs. The main research works include the following:(1) Improving the pattern-generation algorithm for T-shape patterns. The algorithm is based on dynamic programming. It considers the cutting costs in generating each pattern, where the objective is to maximize the total value of the pattern. Experimental results show that the algorithm can decrease the number of cuts, simplify the cutting process, and increase the total value of the pattern.(2) Considering multiple objectives in generating the cutting plan. The reduction of cutting cost is taken as the auxiliary objective in using the linear programming approach to generate the cutting plan. Using the simplex method to call pattern-generation algorithm by iteration, according the needs of the lowest total cost of production to improving the objective function, and determining the present value of all blanks, finally choose the optimal patterns as the solution. Experimental results show that the cutting plan can reduce the number of cuts, simplify the cutting process, improve production efficiency, and reduce production costs. |
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