单一尺寸圆坯的无缝钢管坯料设计模型与算法  

Model and algorithm of the billet design problem in the production of seamless steel tubes with a single billet size

作　　者：李铁克[1] 刘玉琢[1] 王柏琳[1] 栾治伟 

机构地区：[1]北京科技大学东陵经济管理学院,北京100083

出　　处：《工程科学学报》2017年第4期634-641,共8页Chinese Journal of Engineering

基　　金：中央高校基本科研业务费资助项目(FRF-BD-16-006A);国家自然科学基金资助项目(71231001);北京市自然科学基金资助项目(9174038)

摘　　要：无缝钢管坯料设计是在满足生产工艺要求下,将客户订单钢管合理地分配到生产原料圆坯的过程.实际生产中的批量原则使得每个钢管订单在圆坯中有最小分配重量要求;由于无缝钢管分配支数必须取整,导致钢管订单在圆坯中的分配重量并非连续取值.因此,比起相关的板坯设计问题和装箱问题,无缝钢管坯料设计的求解更为复杂.本文给出了无缝钢管坯料设计问题的一般性描述,并建立了混合整数规划模型.针对库存中只有单一尺寸圆坯的情况,简化了问题模型并且求得了问题的下界.结合问题特点,提出了基于贪婪策略的两阶段启发式算法,并用实际生产数据和仿真数据验证了算法求解此类问题具有很好的有效性和稳定性.The billet design problem（ BDP） in seamless steel tube production is to assign order tubes to billets under process constraints. Because of the batch rule in practical production,each order has a minimum weight of tubes assigned to any billet. Meanwhile,as the number of tubes assigned to a billet must be an integer,the weight of tubes assigned to any billet is not continuous in its domain. Thus,the BDP discussed herein is more difficult to solve than the slab design and bin packing problems. In this study,a multi-objective mix-integer programming model was built based on a generalized description of the BDP,which is proved to be non-deterministic polynomial（ NP） hard. For the case with single billet size wherein two objectives in the model are equivalent,a simplified model was set up and the lower bound of the objective could be found. Further,a two-stage heuristic algorithm based on greedy strategy was proposed to solve the problem. Finally,using computational results,it was proved that the algorithm is effective and efficient in solving the BDP.

关 键 词：坯料设计 无缝钢管 贪婪策略 启发式算法 

分 类 号：O221.4[理学—运筹学与控制论] TG335.7[理学—数学]