Restrições práticas do corte bidimensional retangular de chapas metálicas

Abstract

This research approaches the two-dimensional rectangular strip packing problem (2DSPP), where the main goal is to pack a determined number of rectangles, without overlap, to minimize the strip height. In the rectangular 2D-SPP, constraints are used to restrict the packing process, satisfying physical and real-life practical conditions which can impact the material cutting. From the 2D-SPP literature, there is a gap related to studies approaching constraints found in real-life scenarios, ensuing in a lack of practical application from the results obtained. The main goal is to determine the impact of the practical constraints found in the plasma cutting of metal sheets, in a raw material waste context. A systematic literature review was conducted, and 223 articles were selected and analyzed. Constraints concerning the rectangular 2D-SPP were classified into seven different groups, and a bibliometric analysis of the rectangular 2DSPP academic literature was developed. Also, a mathematical model from the literature was adapted considering the practical constraints found in the plasma cutting of metal sheets, and the constraints impact in well-known 2D-SPP instances was determined. The best solutions quality was found in scenarios with a low heterogeneity and low aspectratio and the worst solutions quality was found in scenarios with very high aspectratio and low heterogeneity. However, the combination of size and number of rectangles, as well as the strip width, was the main factor impacting the solution quality, hampering the allocation of rectangles in the packing layout and generating empty spaces. In summary, considering the raw material waste context, instances with smaller width should be avoided in practical operations for elevated minimum distance constraint values, returning the worst solutions quality. For low minimum distance constraint values, smaller width instances can be used in practical operations, as the solutions quality found was acceptable. Also, instances with low aspectratio and low heterogeneity should be prioritized, as improved raw material usage was found.