Tandem repeated regions are closely related to some genetic diseases in human beings. Once a region containing pseudo-periodic repeats is found, it is interesting to study the history of creating the repeats. It is important to reveal the relationship between repeats and genetic diseases. The duplication model has been proposed to describe the history [3, 9, 4]. We design a polynomial-time approximation scheme (PTAS) for the case where the size of the duplication