云制造中带学习效应平行机排序问题的最优可中断算法  

Optimal preemptive algorithm for parallel machine scheduling with learning effect in cloud manufacturing

作　　者：蒋义伟 张振宇 魏麒 季敏 JIANG Yi-wei;ZHANG Zhen-yu;WEI Qi;JI Min(School of Management and E-Business,Zhejiang Gongshang University,Hangzhou 310018,China;College of International Finance and Trade,Ningbo Institute of Finance and Economics,Ningbo 315100,China)

机构地区：[1]浙江工商大学管理工程与电子商务学院,浙江杭州310018 [2]宁波财经学院国际经济贸易学院,浙江宁波315100

出　　处：《高校应用数学学报（A辑）》2020年第4期487-494,共8页Applied Mathematics A Journal of Chinese Universities(Ser.A)

基　　金：国家自然科学基金(11971434);浙江省哲社规划项目成果(19NDJC093YB);浙江省自然科学基金(LY21G010002);宁波市自然科学基金(2019A610048)。

摘　　要：研究了云制造环境下一类带有学习效应的m台平行机排序问题.每台机器都有一个不同的单位时间加工费用,目标是在不超过给定的总费用情况下,从m台机器中选取若干机器加工工件,极小化最大完工时间.考虑了机器加工费用依赖于时间变化的学习效应函数.分别针对基于指数函数和幂函数的两类学习效应函数,分析了最优排序的性质并给出了最优可中断算法.This paper considers preemptive scheduling on m parallel machines with learning effect in cloud manufacturing.Each machine has a unit processing cost.The objective is to select a number of machines from the given m machines such that the makespan is minimized under the constraint that the total cost is not greater than the given cost budget.The learning effect of the machine cost function is considered.A uniform optimal preemptive algorithm is provided for two learning effect functions based on exponential function and power function,respectively.

关 键 词：学习效应 平行机 最优算法 最大完工时间 

分 类 号：O223[理学—运筹学与控制论]