On the Optimal Cutting of Defective Sheets

Hahn, S.

doi:10.1287/opre.16.6.1100

Cited by 69 publications

(13 citation statements)

References 5 publications

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“…Según [11], [12], [13], los patrones de corte pueden ser generados a través de la programación dinámica, y según [14] a través de la generación constructiva de cortes con guillotina, o por los métodos mixtos propuestos por [11]. Obteniendo un límite para los problemas de dos dimensiones con un gran número de variables estructurales y la resolución del dual del CSP [15].…”

Section: Antecedentesunclassified

El Problema de patrones de corte, clasificación y enfoques/Cutting stock problem, classification and approaches

2017

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RESUMENEl Problema de patrones es de gran importancia para empresas manufactureras que involucran el proceso de cortar grandes rollos de algún material y pasarlos a rollos más pequeños de diferentes anchos, considerando el efecto que este tienen sobre los inventarios de producto en proceso y materias primas. Una apropiada gestión de este problema no solo genera benéficos económicos, sino que también genera impactos sostenibles, en la medida que busca un equilibrio entre el costo de inventario y los desperdicios del proceso. Conscientes de la importancia de este problema en este trabajo se presenta inicialmente una introducción de lo que significa en complejidad la solución de un problema de este tipo en una empresa. Luego se enuncian sus antecedentes mediante los trabajos más importantes encontrados en la literatura, destacando algunos trabajos colombianos. Posteriormente, se aborda la clasificación del problema y se aportan sugerencias de otros aspectos a tener en cuenta en el problema. Finalmente se enmarcan los cuatro enfoques de solución más comunes dando ideas para investigaciones futura esperando con esto contribuir al desarrollo del tema.Palabras clave: Planeación del inventario; Proceso de cortado; Modelación matemática; Planeación de operaciones; Minimización de desperdicios. El problema de patrones de corte o cutting stock problem. ABSTRACTThe Cutting stock problem is of great importance for manufacturing companies that involving the process of cutting large rolls of some material into small strips of different widths, considering the effect this has on product inventories in process and raw materials. Proper management of this problem not only generates beneficial economic but also generates sustainable impacts, to the extent that seeks a balance between the cost of inventory and process waste. This paper first presents an overview of what complexity means in solving a problem of this type in a company. His background is set out with the most important works in the literature, highlighting some Colombian jobs. Then, we present classification problem and suggestions from other aspects are provided to consider when addressed cutting stock problem. Finally are framed the four most common approaches to solution giving ideas for future research, hoping thereby contribute to the development of the topic.

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Section: Antecedentesunclassified

El Problema de patrones de corte, clasificación y enfoques/Cutting stock problem, classification and approaches

2017

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“…Here, the authors study the one and two dimensional versions of the static cutting stock problem wherethe value of the cut product depends on its position and propose a recursive algorithm to solve both. In [6], Hahn studies a cutting stock problem with defects and guillotine cuts where the products cannot be placed on areas with defects. The authorapplies the dynamic programming method suggested [7] to solve this problem.…”

Section: Related Literaturementioning

confidence: 99%

A genetic algorithm based solution for the online cutting problem with defects

Durak

Aksu

2015

2015 IEEE International Conference on Industrial Engineering and Engineering Management (IEEM)

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In flat glass production, glass products of various sizes and quality classes are cut from a continuously moving glass ribbon. If a product is placed on a part of the glass ribbon that has more defects than allowed by that product's quality class, it is discarded as scrap. Scrap glass is sent back to the furnace to be recycled. This process creates additional production costs and reduces the productivity of the line. Therefore, the main objective of the cutting process is the minimization of scrap glass. In this study, we propose an online solution approach that uses a look-ahead mechanism to make cutting decisions in real time. This approach solves a series of static cutting problems over a rolling horizon using a genetic algorithm. The proposed approach has been tested successfully on realistic problem instances that are based on parameters of contemporary glass production lines.

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“…Gomory (1965, 1966) [1,21] developed a fundamental solution strategy based on the revised simplex method with column generation technique. Hahn (1968) [22] was the first one to consider the problem of cutting rectangular pieces out of rectangular defective stocks, then Scheithauer and Terno (1988) [23] improved the solution process, but these studies are insufficient. Later, Twisselmann (1999) [24] put forward an effective algorithm to find all usable restricted rectangles and not the maximum empty rectangle only.…”

Section: Introductionmentioning

confidence: 99%

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

Jin

Ren

2015

Teh. vjesn.

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Original scientific papers 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. Keywords: combinatorial optimization; cutting and packing; defects; heuristics Novi heuristički algoritam za problem rezanja giljotinom dvodimenzijske oštećene robe s višestrukom veličinomIzvorni znanstveni članak 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.

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On the Optimal Cutting of Defective Sheets

Cited by 69 publications

References 5 publications

El Problema de patrones de corte, clasificación y enfoques/Cutting stock problem, classification and approaches

El Problema de patrones de corte, clasificación y enfoques/Cutting stock problem, classification and approaches

A genetic algorithm based solution for the online cutting problem with defects

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

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