Abstract: This paper deals with single-machine scheduling with rate-modify activities and position-dependent deteriorated job. The machine can be performed multiple rate-modify activities to change the processing times of the jobs scheduled after the activity. The objective is to find a common due window for all the jobs and a location of the rate-modifying activities for each job to minimize the sum of earliness, tardiness and the cost and the starting time of common due window. The common due window is divided into two cases：in maintenance interval or out maintenance interval. Some properties of the optimal schedule are provided for the problem and present polynomial algorithms, respectively.

Key words: scheduling, single-machine, rate-modify activities, common due window

摘要： 针对工件具有位置退化效应，机器具有多个维修区间的单机调度问题。工件的加工时间为位置相关的函数。每次机器维修后回到初始的水平。目标函数为总的提前费用，误工费用，共同交货期的窗时费用和开始时间费用。对于共同交货期分为包括维修区间和不包括维修区间两种情形进行讨论，采用线性规划建立指派问题的数学模型，并分别提出最优序列的一些最优性质和相应的多项式时间算法。

关键词: 调度, 单台机器, 速率改变行为, 共同交货期