Being able to limit the number of each piece appearing in one pattern is an important issue for applications of cutting stock procedures. When exact order fulfilment is a feature of the application, it is essential. Even when tolerances exist on order fulfilment, previous research has shown such limits may be beneficial. The means of achieving such limits in one-dimensional and n-stage two-dimensional pattern generation have appeared in the literature but no procedure for achieving such limits in three-stage two-dimensional patterns has been published, despite their predominance in reported applications. This article rectifies that omission. Modifications of the Gilmore-Gomory lexicographical search algorithm are proposed and the most computationally efficient form these modifications can take is determined empirically. The existing one-dimensional empirical results related to limiting the number of each piece per pattern in non-exact order fulfilment situations are also extended to the two-dimensional case. Reductions in both the number of setups and variation from order volumes after integerising solutions are apparent in all three classes of real-world based two-dimensional cutting stock problems simulated, although the impact is highly dependent upon the problem characteristics.
