This project addresses the Constrained Two-Dimensional Guillotine Cutting Problems (C2DCP). These problems are about to produce smaller rectangles (items or pieces), from larger rectangles (objects), by using cutting operations that split materials in two rectangles and respect the amount of times that the pieces may appear in the cutting patterns, without restriction on the number of stages. Although the C2DCP is present in some industrial environments, there are no records in the literature of mathematical formulations for this problem. This project proposes the development of mathematical programming models and solution methods for C2DCP. The C2DCP will be analyzed in the context of the following problems: Placement Problem, Cutting Stock Problem and Bin Packing Problem. Three solution strategies are proposed. The first strategy involves the development of a compact formulation for these problems to deal with small item and object sets. The second and third strategies involve larger sets of items and objects from the development of extensive formulations for these problems, in a Column Generation context. The second strategy deals with the development of a mathematical programming model to generate cutting patterns for C2DCP and the third strategy proposes the use of dynamic programming methods to generate these patterns. The development of mathematical models contributes to the research of solution methods to the problem, from the analysis of particular structures that allow the reformulation of the problem through decomposition or relaxation techniques. The robustness of the methods will be evaluated by computational experiments using instances of the literature, which also will be compared to other approaches.
News published in Agência FAPESP Newsletter about the scholarship: