Characterization of Operational Constraints in Two-Dimensional Cutting Problems and Tool Trajectory in Sheet Metal

Over the last decades, the two-dimensional cutting problem has received considerable attention from the scientific community, leading to significant advances in both solution methods and the incorporation of real-world constraints. Despite these advances, there is still room for the identification, analysis, and incorporation of operational constraints arising from the production process. The generation of cutting patterns based exclusively on geometric criteria, disregarding manufacturing and execution parameters, may compromise operational feasibility and reduce the applicability of the resulting solutions to real industrial needs. In this work, two relevant operational constraints are characterized: common-edge cutting and tool-path planning. For this purpose, the  rthogonal two-dimensional cutting problem of rectangular pieces on CNC machines is considered. The identification and characterization of these constraints were conducted through discussions with experienced CNC machine operators and programmers, as well as through a review of the scientific literature. Common-edge cutting occurs when the tool simultaneously cuts adjacent edges of two pieces positioned side by side, with a separation compatible with the cutting width (kerf). This configuration can reduce material losses, non-productive movements, and total processing time. However, its practical implementation depends not only on the geometric placement of the pieces, but also on constraints associated with the manufacturing process. In thicker metal sheets, where the process requires an initial piercing operation (piercing), a tool path is considered feasible only when sufficient free space is available for the piercing operation, as well as for the proper execution of entry and exit movements (lead-in and lead-out). Additionally, common-edge cuts are subject to precedence constraints and therefore cannot be performed during the final stages of the cutting process. Similarly, internal regions isolated from the external cutting path, referred to as cutting islands, require additional piercing operations to be reached, imposing further constraints on the tool path. From this perspective, in which the tool must traverse a set of cutting edges while satisfying precedence constraints and minimizing non-productive movements, the tool-path planning problem presents similarities to the Chinese Postman Problem with precedence constraints. Given that few studies explicitly address common-edge cutting together with the corresponding tool-path planning problem, it is argued that the study of these characteristics brings academic research closer to the actual needs of industrial environments. Preliminary studies indicate that incorporating these constraints into integer programming models significantly increases the combinatorial complexity of the problem, requiring dedicated formulations and specialized solution strategies.