In this paper, we address the constrained two‐dimensional rectangular guillotine single large placement problem (2D_R_CG_SLOPP). This problem involves cutting a rectangular object to produce smaller rectangular items from orthogonal guillotine cuts. In addition, there is an upper limit on the number of copies that can be produced of each item type. To model this problem, we propose a new pseudopolynomial integer nonlinear programming (INLP) formulation and obtain an equivalent integer linear programming (ILP) formulation from it. Additionally, we developed a procedure to reduce the numbers of variables and constraints of the integer linear programming (ILP) formulation, without loss of optimality. From the ILP formulation, we derive two new pseudopolynomial models for particular cases of the 2D_R_CG_SLOPP, which consider only two‐staged or one‐group patterns. Finally, as a specific solution method for the 2D_R_CG_SLOPP, we apply Benders decomposition to the proposed ILP formulation and develop a branch‐and‐Benders‐cut algorithm. All proposed approaches are evaluated through computational experiments using benchmark instances and compared with other formulations available in the literature. The results show that the new formulations are appropriate in scenarios characterized by few item types that are large with respect to the object's dimensions.

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Paper and steel industries store large amounts of raw material to be cut to manufacture products, because (i) the cost of transport, storage, and handling of large objects is smaller than the cost of the items, when they are considered separately throughout the manufacturing process, and (ii) the uncertainty of the demand for items. The determination of how the stored master rolls (objects) are supposed to be cut to manufacture the reels (items) required by the customers is known as the One-Dimensional Cutting Stock Problem. This classic problem in Operational Research represents a key process in these production chains. To minimize the trim loss or the number of rolls is a straightforward strategy. The first approach in this field was carried out by Kantorovich (1960)-and followed by Metzger (1958), Eilon (1960) and others. However, it was Gilmore and Gomory's approach in the 1960s that extended the application to real size problems (Gilmore & Gomory, 1961; 1963).

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