中文摘要：

本文对具有相同工期的单机最小化加权总误工问题进行了讨论.利用强NP-困难问题1ΣwjTj的一个O（n2）时间的近似算法,把该算法得到的目标值作为问题1｜dj=d｜ΣwjTj的一个上界,对问题1｜dj=d｜ΣwjTj给出全多项式近似方案（FPTAS）.已知问题1｜dj=d｜ΣwjTj是一般意义下的NP-困难问题,并且已经有人对该问题给出了拟多项式时间算法,本文对已有结果进行了扩充.

英文摘要：

The article is about the single machine scheduling problem with common due date to minimize total weighted tardiness. It＇s also known that the problem1 ΣwjTjis strongly NP-hard and there is a O（n2） time approximation algorithm for this problem. The article took the objective value of this algorithm as the upper bound of our problem 1｜dj= d｜ΣwjTjand gave the problem 1｜dj= d｜ΣwjTja full polynomial time approximation scheme（FPTAS）. For the problem of 1｜dj= d｜ΣwjTj, it＇s known that it is NP-hard in the ordinary sense. And it has been provided a pseudo-polynomial algorithm. The results have been expanded by this article.