Two-dimensional minkowski-sum optimization of ganged stamping blank layouts for use on precut sheet metal for convex and concave parts

Journal UnknownAs the number of parts that manufacturers need to place on a piece of material such as sheet metal increases, the need for more sophisticated algorithms for part orientation and spacing also increases. With greater part shape complexity, the ability of a skilled craftsman becomes challenged to minimize waste. Building upon the previous work of Nye, we present a Minkowski-sum method for maximizing the number of parts within gangs on a rectangular sheet of material. The example provided uses a simply shaped part to illustrate the presented method, yielding a packing efficiency of 62% that is identical to the efficiency that a skilled worker would produce without the algorithm. We also provide results for laying out a more complex part in ganged sections, demonstrating a result that would be difficult for a human to reproduce. Our work extends that of Nye by adding practical constraints such as the number of parts that can be blanked at once as well as the amount of horizontal and vertical spacing between ganged blanking sets. Additionally we add an algorithm for laying out polygons with concave geometries by separating the part into a set of convex polygons. Two examples for optimization, one of a chevron-shaped part and one of a complex shape previously used by Nye (2000) and Choi et al. (1998) are provided demonstrating the existence of a local maximum number of parts that may be stamped within a single ganged blank. Our algorithm is extendable to a program that may provide stamping manufacturers with a tool that can maximize the total number of parts stamped on stock sheet metal, or for other tiling problems

Modelado y solución del problema del corte irregular : aplicación en la industria del cuero Colombiana

El problema del Irregular Two Dimensional Cutting Stock Problem (ITDCSP) está presente en diversas aplicaciones industriales que incluyen la confección, fabricación del calzado y la marroquinería. Debido a su naturaleza matemática NP completa, ha sido particularmente difícil de formular y resolver. Este Trabajo de Grado propone una Formulación Lineal Mixta base que sirve como base para emplear diversos procedimientos meta heurísticos para la búsqueda de soluciones cercanas al óptimo. Al respecto, se expone el uso de dos herramientas meta heurísticas, GRASP y Algoritmos Genéticos, para su solución. En estos casos se han encontrado soluciones de calidad aceptables en tiempos de ejecución razonable.The problem of Two Dimensional Irregular Cutting Stock Problem (ITDCSP) is present in various industrial applications including clothing, shoemaking and leather. Because NP complete mathematical nature, has been particularly difficult to formulate and solve. This work proposes a linear formulation Grade Mixed base that serves as the basis for meta heuristics use various procedures for finding near-optimal solutions. In this regard, we discuss the use of two tools meta heuristics, GRASP and Genetic Algorithms for settlement. In these cases, solutions have been found acceptable quality in reasonable runtimes.Magíster en Ingeniería IndustrialMaestrí