Study On The Solution Of One-dimensional Cutting Stock For Multiple Stock Lengths With Variable Cross-section

Vehicles and construction machinery manufacturing industry to consume a large number of steel ingots for the production of various parts required each year,but the specificity of the raw materials provided by the ingot are mostly frustum of a cone shaped,so that the item section is different in cutting process at different positions,making the complexity of the problem higher than the equal section cutting problem.And because of the large annual consumption of steel ingot,it is worth to study the cutting problem,in order to improve material utilization,reduce production costs.In this paper,we introduce the single stock,unconstrained multiple stock and constrained multiple stock of one-dimensional cutting stock problem with variable cross-section,which are described in terms of problem description,mathematical model establishment,algorithm solving and experiment.This paper focuses on the solution of one-dimensional cutting stock problem for multiple stock lengths with variable cross-section,and uses different layout methods to cut the ingot of different sizes into items of the required weight and demand.The proposed approach combines the sequential value correction method and dynamic programming technique to solve the one-dimensional cutting stock problem for multiple stock lengths with variable cross-section.In the equal section of the cutting problem can be cut directly according to the length of the required item,and in the steel ingot cutting problem the weight of item will first be converted into its corresponding length.Therefore,it is necessary to find out the different weight of the item at any position in the cutting of the corresponding length.And then according to the above method,the cutting patterns in the cutting plan were generated sequentially,until all item demands are met.Multiple different cutting plans are generated by adjusting the item values.The best one among them is selected as the solution.Compared with a large number of random test questions,the experimental results show that the obtained solution is very close to the optimal solution.Computational testing is performed to compare the proposed approach with a published algorithm that generate cutting patterns by enumeration.Experimental results indicate that the proposed approach can generate cutting patterns quickly and improve material utilization.