The Model was taken from The Man-Machine , which was the fourth studio album by Kraftwerk and
originally released in 1978.
The song was originally released as a B-side to Computer Love which reached #36 in 1981. However, DJ's decided to start playing The Model instead of the A-side Computer Love, and this led EMI to re-release the single in December 1981 with The Model as the A-side, which was, apparantly, against the band's wishes.
The Model reached #1 in February 1982 (four years after the original release of the Man Machine album!) and stayed inside the Top 75 for 21 weeks.