木板最优切割问题

Optimal Cutting of Wood

摘要: 本文以整数线性规划和多目标规划为理论基础，针对二维矩形切割优化问题，建立了以木板利用率最大为目标的多阶段分析模型。考虑了产品类型由单一到多元，产品生产任务以及木板原料的限定，由浅到深，一步步编写程序结合LINGO求解得到系统的最优切割方案。与商业切割软件对比结果表明，该模型可以有效地解决木板切割问题，模型稳定且寻优能力较好。

Abstract: In this paper, based on integer linear programming and multi-objective programming, a multi-stage analysis model with the goal of maximizing the utilization rate of wood board is established for the optimization of two-dimensional rectangular cutting. Considering the product type from single to multiple, the product production task and the limit of wood material, from the shallow to the deep, program is written step by step, and then combined with LINGO solution, the system’s optimal cutting program is gotten. Compared with commercial cutting software, the results show that the model can effectively solve the problem of wood cutting, and the model is stable and has good optimization ability.