同时具有学习效应和退化效应的单机排序问题

本文给出了一种同时具有一般化学习效应和退化效应的单机排序模型。在此模型中,工件的实际加工时间既与工件所在位置又与其开工时间有关,且工件在加工之后具有一个配送时间。其中学习效应是工件所在位置的函数,退化效应是工件开工时间的函数。证明了极小化最大完工时间和极小化总完工时间问题是多项式可解的,在满足一定的条件下,极小化加权总完工时间和极小化最大延误问题也是多项式可解的。推广了一些已有文献中的结论。

Single-machine Scheduling Problems with General Effects of Learning and Deterioration

In this paper,we introduce a general single machine scheduling model with learning effect and deteriorating jobs simultaneously.In this model,the actual processing time of a job depends not only on its scheduling position but also on its starting time,and there is a past-sequence-dependent delivery time after each job is processed.The learning effect is a function of the scheduling position of the job in a schedule.The deterioration is a function of the starting time of the job in a schedule.We show that the makespan minimization problem and the total completion time minimization problem are polynomially solvable under the model.We also show that the total weighted completion time minimization problem and the maximum lateness minimization problem can be solved in polynomial time under certain conditions.We extend the conclusion in some of the existing literatures.