A method for producing rod-shaped smoking products on a drum machine of the tobacco processing industry, wherein rod-shaped articles of the tobacco processing industry are arranged transversely axially behind one another in receiving troughs of rotating conveyor drums (12, 14, 16, 20, 22, 24, 26, 28, 30, 34) of a conveying arrangement for the transverse-axial conveyance of rod-shaped articles and are conveyed by rotating the conveyor drum in the transverse-axial conveying direction, and wherein the rod-shaped articles are transferred in the respective transfer region between two conveyor drums from an article-dispensing conveyor drum to an article-receiving conveyor drum, wherein the rod-shaped articles are conveyed in a first conveying section on at least one conveyor drum transversely axially with a first constant transverse-axial distance between the rod-shaped articles, wherein the rod-shaped articles conveyed transversely axially in the first conveying section are subsequently conveyed in a second conveying section configured with a first cutting device, wherein, during or following the transfer of the rod-shaped articles from the first conveying section to the second conveying section, the transverse-axial distance between the rod-shaped articles is enlarged or reduced, wherein, in the second conveying section, the rod-shaped articles are cut by means of the first cutting device of the second conveying section into multiple, in particular two or three, article rod segments (101, 102, 103) and, following the cutting of the rod-shaped articles into article rod segments (101, 102, 103), the article rod segments (101, 102, 103) in the second conveying section are formed into a sequence, preferably in a single row, of article rod segments (101, 102, 103) arranged transversely axially behind one another, wherein the transverse-axial constant distance of the article rod segments (101, 102, 103) of the sequence formed of article rod segments (101, 102, 103) corresponds to a part or fraction of the transverse-axial distance of the rod-shaped articles conveyed in the second conveying section, wherein the transverse-axial distance of the article rod segments (101, 102, 103) of the sequence formed in the second conveying section is determined by the product of the transverse-axial distance of the rod-shaped articles in the second conveying section, multiplied by the inverse of the number of the article rod segments (101, 102, 103) cut in each case from the rod-shaped articles, and wherein the article rod segments (101, 102, 103), arranged transversely axially behind one another, preferably in a single row, are subsequently transferred from the second conveying section to a third conveying section configured with a second cutting device, wherein, in the third conveying section, the article rod segments (101, 102, 103) are each cut, preferably centrally, into multiple, in particular two, article rod segment pieces, wherein, in the third conveying section, the article rod segments (101, 102, 103) and the article rod segment pieces are conveyed with a constant transverse-axial distance which corresponds to the transverse-axial distance of the article rod segments (101, 102, 103) of the sequence of article rod segments (101, 102, 103) formed, preferably in a single row, in the second conveying section, and the article rod segment pieces are subsequently conveyed with the same constant transverse-axial distance to a feed device for feeding smoking article components to the article rod segment pieces conveyed by the conveyor drums.