中文摘要：

在经典排序问题中,工件的加工时间往往是一个常数,但在现代生产过程中,工件的加工时间受许多因素的影响。因此,研究工件具有学习效应的单机可控加工时间排序问题,其中工件的加工时间是其所在位置的函数,且与加工时间的控制变量有关。目标是求出最优的加工时间控制变量和最优的排序使得目标函数最小,目标函数包括极小化时间表长与控制费用的和、极小化总完工时间与控制费用的和、极小化总完工时间偏差和与控制费用和。证明他们都能转化为指派问题,从而多项式时间可解。并给出数值例子来说明问题是如何求解的。

英文摘要：

In classical scheduling,the processing time of a job is a constant,but in modern production process,the processing time of a job is affected by many factors. Hence,in this paper we study scheduling problems jobs with learning effect and controllable processing times,where the processing time of a job is the function of its position in a sequence and its controllable variable. Our target is to find the optimal sequence and controllable variables so as to minimize the following objective functions：a cost containing makespan and total controllable cost,a cost containing total completion time and total controllable cost,a cost containing total absolute differences in completion times and total controllable cost. We prove that the problem is modeled as an assignment problem,and thus can be solved in polynomial time. We also give a numerical example.