带恶化效应的极小化总加权延误工件个数的单机双代理调度问题  

Single Machine Double-Agent Scheduling Problem for Minimizing Total Weighted Number of Delayed Artifacts With Deterioration Effect

作　　者：谢谢[1] 杨新茹 XIE Xie;YANG Xinru(Key Laboratory of Manufacturing Industrial and Integrated Automation,Shenyang University,Shenyang 110044,China;School of Information Engineering,Shenyang University,Shenyang 110044,China)

机构地区：[1]沈阳大学装备制造综合自动化重点实验室,辽宁沈阳110044 [2]沈阳大学信息工程学院,辽宁沈阳110044

出　　处：《沈阳大学学报(自然科学版)》2025年第1期34-43,共10页Journal of Shenyang University:Natural Science

基　　金：国家自然科学基金资助项目(71672117)。

摘　　要：针对钢铁企业的热轧实际生产流程,提出一类随工件加工位置呈一般线性恶化且工件正常加工时长为单位时间的单机双代理调度问题。在该问题中,热轧阶段进入冷轧厂进行冷轧的工件看作A代理商,直接销售给顾客的工件看作B代理商。A代理商的目标值为极小化最大完工时间,B代理商的目标值是极小化总加权延误工件个数,研究了在A代理商目标值不大于给定上界约束的条件下,寻找使B代理商的目标值最优的调度方案,设计了一个动态规划算法和两个时间复杂性不同的算法来求解代理商最优目标值的上下界,提出完全多项式时间近似方案,使所提的调度问题在多项式时间内可解。Aiming at the actual production process of hot rolling in iron and steel enterprises,a problem of single machine with double-agent scheduling was proposed with the general linear deterioration of workpiece processing position and the normal processing time of workpiece was unit time.In this problem,the workpiece entering the cold rolling plant for cold rolling was regarded as agent A,and the workpiece directly sold to customers was regarded as agent B.The target value of agent A was to minimize the maximum completion time,the target value of agent B was to minimize the total weighted delay of the target value of the agent.Under the condition that the target value of agent A was not greater than the given upper bound constraint,the scheduling scheme to make the target value of agent B optimal was studied.A dynamic programming algorithm and two algorithms with different time complexity were designed to solve the upper and lower bounds of the agent s optimal target value,and a complete polynomial time approximation scheme was proposed to solve the scheduling problem in polynomial time.

关 键 词：双代理调度 最大完工时间 延误 工件 恶化效应 完全多项式时间近似方案 

分 类 号：TP301.6[自动化与计算机技术—计算机系统结构]