A New Mathematical Model for the Cutting Stock/Leftover Problem

Arenales, Marcos Nereu; Cherri, Adriana Cristina; Nascimento, Douglas Nogueira do; Vianna, Andréa Carla Gonçalves

doi:10.1590/0101-7438.2015.035.03.0509

Cited by 25 publications

(20 citation statements)

References 16 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…A. C. Cherri et al [31] considered the one-dimensional cutting stock problem with useable leftovers. M. N. Arenales et al [3] presented a new mathematical model for cutting stock problem using leftover which consisted of partially cutting the stocked items and keeping the remnants to be cut in the next periods. All other dimensions were considered straightforward and computational experiments were performed for a one-dimensional case.…”

Section: Literature Reviewmentioning

confidence: 99%

See 1 more Smart Citation

A Mathematical Model for Reduction of Trim Loss in Cutting Reels at a Make-to-Order Paper Mill

et al. 2020

View full text Add to dashboard Cite

One of the main issues in a paper mill is the minimization of trim loss when cutting master reels and stocked reels into reels of smaller required widths. The losses produced in trimming at a paper mill are reprocessed by using different chemicals which contributes to significant discharge of effluent to surface water and causes environmental damage. This paper presents a real-world industrial problem of production planning and cutting optimization of reels at a paper mill and differs from other cutting stock problems by considering production and cutting of master reels of flexible widths and cutting already stocked over-produced and useable leftover reels of smaller widths. The cutting process of reels is performed with a limited number of cutting knives at the winder. The problem is formulated as a linear programming model where the generation of all feasible cutting patterns determines the columns of the constraint matrix. The model is solved optimally using simplex algorithm with the objective of trim loss minimization while satisfying a set of constraints. The solution obtained is rounded in a post-optimization procedure in order to satisfy integer constraints. When tested on data from the paper mill, the results of the proposed model showed a significant reduction in trim loss and outperformed traditional exact approaches. The cutting optimization resulted in minimum losses in paper trimming and a lesser amount of paper is reprocessed to make new reels which reduced the discharge of effluent to the environment.

show abstract

Section: Literature Reviewmentioning

confidence: 99%

“…A one-dimensional approach has been devised and trim loss at the end of the reels is disregarded in the considered problem formulation. The same approach can also be applied in other industries as well, such as steel [1,2] wood, leather, and plastic industry [3].…”

Section: Introductionmentioning

confidence: 99%

A Mathematical Model for Reduction of Trim Loss in Cutting Reels at a Make-to-Order Paper Mill

et al. 2020

View full text Add to dashboard Cite

show abstract

“…Only the first 20 instances in each class were solved by the TPBNT to reduce the total computation time. As mentioned previously in the literature review, existing models (Cui and Yang, 2010;Arenales et al, 2015) can be used to solve the 1DCSPUL_BNT by specifying g UL-types as inputs, whereas the TPBNT optimizes the UL-types by explicitly considering the BT constraint. The TPBNT also specifies the UL-types if G g λ = = is used.…”

Section: Considering Bt Constraintmentioning

confidence: 99%

New model and heuristic solution approach for one-dimensional cutting stock problem with usable leftovers

Cui

Song

Chen

et al. 2017

Journal of the Operational Research Society

View full text Add to dashboard Cite

In the one-dimensional cutting stock problem with usable leftovers (1DCSPUL), items of the current order are cut from stock bars to minimize material cost. Here, stock bars include both standard ones bought commercially and old leftovers generated in processing previous orders, and cutting patterns often include new leftovers that are usable in processing subsequent orders. Leftovers of the same length are considered to be of the same type. The number of types of leftovers should be limited to simplify the cutting process and reduce the storage area. This paper presents an integer programming model for the 1DCSPUL with limited leftover types and describes a heuristic algorithm based on a column-generation procedure to solve it. Computational results show that the proposed approach is more effective than several published algorithms in reducing trim loss, especially when the number of types of leftovers is limited.

show abstract

“…Algunos investigaciones que modifican la técnica antes mencionada, se puede ver en [35], [36], [37] , en estos se restringe el número de veces que cualquier tamaño puede aparecer en un patrón de corte, y se basan en una programación lineal de dos fases: en la primera fase, una solución óptima es obtenida para un conjunto limitado de patrones, y en la segunda fase, la solución óptima es encontrada para todos los patrones.…”

Section: Programación Lineal Enteraunclassified

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

2017

View full text Add to dashboard Cite

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.

show abstract

A New Mathematical Model for the Cutting Stock/Leftover Problem

Cited by 25 publications

References 16 publications

A Mathematical Model for Reduction of Trim Loss in Cutting Reels at a Make-to-Order Paper Mill

A Mathematical Model for Reduction of Trim Loss in Cutting Reels at a Make-to-Order Paper Mill

New model and heuristic solution approach for one-dimensional cutting stock problem with usable leftovers

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

Contact Info

Product

Resources

About