One‐dimensional cutting stock with a limited number of open stacks: bounds and solutions from a new integer linear programming model

Arbib, Claudio; Marinelli, Fabrizio; Ventura, Paolo

doi:10.1111/itor.12134

Cited by 35 publications

(19 citation statements)

References 13 publications

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“…In literature, various types of cutting stock problems have been investigated [7][8][9][10]. Effective algorithms for solving cutting stock problems are beneficial to reduce production cost and improve material utilization [11].…”

Section: Literature Reviewmentioning

confidence: 99%

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

et al. 2020

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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.

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Section: Literature Reviewmentioning

confidence: 99%

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

et al. 2020

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“…A more compact formulation, where the number of constraints increases polynomially with n, was then proposed by [9]. The formulation is based on the idea of feasible track, a 0-1 matrix B with n rows that has the Consecutive Ones Property (C1P) and exactly θ max 1's per column.…”

Section: The Stack-constrained Cspmentioning

confidence: 99%

Pricing-based primal and dual bounds for selected packing problems

Pizzuti¹

2020

4OR-Q J Oper Res

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“…Posteriormente, se genera un subproblema el cual permite identificar columnas o variables adicionales que no han sido incluidas en el programa maestro y que mejoran el valor de la función objetivo. En los problemas unidimensionales este es el equivalente a resolver el problema de la "mochila" unidimensional [32], trabajos similares son presentados en [34].…”

Section: Programación Lineal Enteraunclassified

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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One‐dimensional cutting stock with a limited number of open stacks: bounds and solutions from a new integer linear programming model

Cited by 35 publications

References 13 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

Pricing-based primal and dual bounds for selected packing problems

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

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