The two-dimensional cutting stock problem within the roller blind production process

In this paper we consider a two-dimensional cutting stock problem encountered at a large manufacturer of window covering products. The problem occurs in the production process of made-to-measure roller blinds. We develop a solution method that takes into account the characteristics of the specific problem. In particular, we deal with the fact that fabrics may contain small defects that should end up with the waste. Comparison to previous practice shows significant waste reductions.cutting;trim loss;two-dimensional cutting stock problem

The Two-Dimensional, Rectangular, Guillotineable-Layout Cutting Problem with a Single Defect

In this paper, a two-dimensional cutting problem is considered in which a single plate (large object) has to be cut down into a set of small items of maximal value. As opposed to standard cutting problems, the large object contains a defect, which must not be covered by a small item. The problem is represented by means of an AND/OR-graph, and a Branch & Bound procedure (including heuristic modifications for speeding up the search process) is introduced for its exact solution. The proposed method is evaluated in a series of numerical experiments that are run on problem instances taken from the literature, as well as on randomly generated instances.Two-dimensional cutting, defect, AND/OR-graph, Branch & Bound

The two-dimensional cutting stock problem within the roller blind production process

In this paper we consider a two-dimensional cutting stock problem encountered at a large manufacturer of window covering products. The problem occurs in the production process of made-to-measure roller blinds. We develop a solution method that takes into account the characteristics of the specific problem. In particular, we deal with the fact that fabrics may contain small defects that should end up with the waste. Comparison to previous practice shows significant waste reductions

Cutting to Order in the Rough Mill: A Sampling Approach

A cutting order is a list of dimension parts along with demanded quantities. The cutting-order problem is to minimize the total cost of filling a cutting order from a given lumber supply. Similar cutting-order problems arise in many industrial situations outside of forest products. This paper adapts an earlier, linear programming approach that was developed for uniform, defect-free stock materials. The adaptation presented here allows the method to handle nonuniform stock material (e.g., lumber) that contains defects that are not known in advance of cutting. The main differences are the use of a random sample to construct the linear program and the use of prices rather than cutting patterns to specify a solution. The primary result of this research is that the expected cost of filling an order under the proposed method is approximately equal to the minimum possible expected cost for sufficiently large order and sample sizes. A secondary result is a lower bound on the minimum possible expected cost. Computer simulations suggest that the proposed method is capable of attaining nearly minimal expected costs in moderately large orders

Bun splitting: a practical cutting stock problem

We describe a new hierarchical 2D-guillotine Cutting Stock Problem. In contrast to the classic cutting stock problem, waste is not an issue. The problem relates to the removal of a defective part and assembly of the remaining parts into homogeneous size blocks. The context is the packing stages of cake manufacturing. The company's primary objective is to minimise total processing time at the subsequent, packing stage. This objective reduces to one of minimising the number of parts produced when cutting the tray load of buns. We offer a closed form optimization approach to this class of problems for certain cases, without recourse to mathematical programming or heuristics. The methodology is demonstrated through a case study in which the number of parts is reduced by almost a fifth, and the manufacturer's subsidiary requirement to reduce isolated single bun parts and hence customer complaints is also satisfied

The Two-Dimensional, Rectangular, Guillotineable-Layout Cutting Problem with a Single Defect

In this paper, a two-dimensional cutting problem is considered in which a single plate (large object) has to be cut down into a set of small items of maximal value. As opposed to standard cutting problems, the large object contains a defect, which must not be covered by a small item. The problem is represented by means of an AND/OR-graph, and a Branch & Bound procedure (including heuristic modifications for speeding up the search process) is introduced for its exact solution. The proposed method is evaluated in a series of numerical experiments that are run on problem instances taken from the literature, as well as on randomly generated instances

A new heuristic algorithm for two-dimensional defective stock guillotine cutting stock problem with multiple stock sizes

U radu se uglavnom raspravlja o problemu rezanja giljotinom dvodimenzijske oštećene robe raspoložive u različitim veličinama. Za raspravu o problemu predlaže se novi heuristički algoritam u obliku stabla. Takav se algoritam sastoji od dva dijela: prvi dio je početno rješenje problema rezanja robe kad ne postoje oštećenja robe; drugi dio je konačno rješenje optimizacije utemeljeno na prvom dijelu uz razmatranje oštećenja. U radu se također ocjenjuju rezultati predloženog algoritma. Eksperimentalnim se rezultatima demonstrira učinkovitost algoritma za problem rezanja dvodimenzijske oštećene robe i pokazuje da se algoritmom može poboljšati ne samo stopa iskoristivosti robe već i stopa ponovne uporabe ostataka smanjenjem fragmentacije ostataka.This paper mainly addresses a two-dimensional defective stocks guillotine cutting stock problem where stock of different sizes is available. Herein a new heuristic algorithm which is based on tree is proposed to discuss this problem. In particular, such an algorithm consists of two parts: the first part is an initial solution of the cutting stock problem where there are no defects on the stocks; the second part is the final optimization solution which is set up on the basis of the first part and takes the defects into consideration. This paper also evaluates the performance of the proposed algorithm. The experimental results demonstrate the effectiveness of the algorithm for the two-dimensional defective stocks cutting stock problem and show that the algorithm can improve not only the utilization rate of stocks, but also the reuse rate of remainders by reducing the fragmentation of remainders

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