具有学习效应的两个单机排序问题(英文)

摘要

Two single machine scheduling problems with a learning effect are considered. The learning effect of a job is assumed to be a function of its position. For the following two objective functions: the weighted sum of completion times and the maximum lateness, it is shown that the weighted shortest processing time first (WSPT) rule and the earliest due date first (EDD) rule can construct the optimal sequence for some special cases, respectively. The worst case error bounds for these two rules in general cases are also given.%研究工件具有学习效应的两个单机排序问题.工件的学习效应指的是工件的加工时间为所排位置的函数. 对以下两个目标函数:加权总完工时间与最大延误, 证明在某些特殊情况下加权最小加工时间优先(WSPT)规则和最早工期优先(EDD)规则可以分别给出最优算法. 也给出了这两个规则在一般条件下的最坏情况界.