Robust mixed-integer linear programming models for the irregular strip packing problem

Cherri, Luiz Henrique; Mundim, Leandro Resende; Andretta, Marina; Toledo, Franklina Maria Bragion de; Oliveira, José Fernando; Carravilla, Maria Antónia

doi:10.1016/j.ejor.2016.03.009

Cited by 75 publications

(92 citation statements)

References 15 publications

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“…Casos especiais onde itens são empacotados em forma de linhas são discutidos em detalhes. Dois modelos robustos de programação linear inteira mista são propostos em [13] para o problema de empacotamento de tirar irregulares, com o objetivo de contornar as limitações dos modelos existentes quantoà complexidade dos algoritmos de manipulação geométrica, necessários para as restrições de não sobreposição de peças. Novas instâncias baseadas no mundo real com geometrias mais complexas são propostas e utilizadas para verificar a robustez dos novos modelos.…”

Section: Introductionunclassified

Modelagem e solução de problemas de corte e empacotamento por meio da programação linear

Bressan¹,

Belinelli²

2016

C.Q.D.

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Modelagem e solução de problemas de corte e empacotamento por meio da programação linearModeling and solution of cutting and packing problems using linear programming Resumo Muitas indústrias que trabalham com processos de corte e empacotamento podem gerar sobras indesejáveis de materiais que muitas vezes não podem ser reaproveitadas. O estudo de problemas por meio da modelagem matemática e da Programação Linear permite estabelecer padrões de corte e de empacotamento que resultem na perda ou no custo mínimo. Neste contexto, este trabalho tem o objetivo de estudar a modelagem matemática dos problemas de corte e de empacotamento, por meio da Programação Linear, aplicados em duas fábricas distintas. O primeiro estudo minimiza a perda de alimento durante o processo de empacotamento de amendoins de uma fábrica do município de Nova Fátima-PR, por meio da aplicação do Problema de Empacotamento. O segundo estudo minimiza a perda de matéria-prima durante o processo de corte e acabamento de papéis, por meio da aplicação do Problema do Corte, numa gráfica do município de Ibaití-PR. Os resultados foram obtidos por meio da aplicação do Método Simplex com apoio computacional. Palavras-chave: Programação Linear. Método Simplex. Problema do Corte. Problema de Empacotamento. AbstractMany industries that work with cutting and packing processes can generate undesirable waste materials that often cannot be reused. The study of problems using mathematical modeling and Linear Programming allows us to establish cutting and packaging standards that result in minimum loss or minimum cost. In this context, the goal of this paper is to study the mathematical modeling of cutting and packaging problems, using Linear Programming and to apply its in two distinct companies. The first study minimizes loss of product during the process of packaging of peanuts from a factory in the Nova Fátima-PR city, by applying the packaging problem. The second study minimizes the loss of raw material during the paper cutting process, by applying the cutting problem from a printing company located in Ibaití-PR city. The results were obtained using the Simplex Method with computational support.

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Section: Introductionunclassified

Modelagem e solução de problemas de corte e empacotamento por meio da programação linear

Bressan¹,

Belinelli²

2016

C.Q.D.

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“…The main difficulty in tackling irregular shape item problems is the great number of binary variables determining the relative position between each pair of aircraft in the container. Generally, solving an instance including more than 10 irregular items becomes challenging and intractable with the current approaches [26]. In our problem, we assume that each aircraft has to select an individual safety margin within the admissible discrete range and .…”

Section: Introductionmentioning

confidence: 99%

“…The item cutting and packing problem in twodimensional space has been widely studied in the literature because of its practical use in various industries, and such packing problems can be classified as either regular items packing problems or irregular items packing problems [15,[17][18][19][20][21][22][23][24]. Many mathematical formulations solving irregular items packing problems have been proposed in the literature [25][26][27][28][29][30]. The No-Fit Polygon (NFP) has been widely used in detecting if two irregular items overlap with each other [31,32], while other approaches also exist [33].…”

Section: Introductionmentioning

confidence: 99%

A Family of Heuristic-Based Inequalities for Maximizing Overall Safety Margins in Aircraft Parking Stands Arrangement Problems

Qin

Wang

Chan

et al. 2018

Mathematical Problems in Engineering

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We consider the problem of arranging a set of aircraft in a maintenance hangar operated by an independent aircraft service provider. The overall safety margins of the parking layout need to be maximized within the limited available space, measured by the weighted sum of the individual discrete safety margins of each aircraft. A mixed-integer linear programming model is developed, and the positions of the aircraft are determined by the position-controlling binary variables associated with a set of revised No-Fit Polygons (NFPs). Due to the nonconvex irregular shape of aircraft, the model involves a great number of binary variables associated with the revised NFP. The default branch-and-bound algorithm is inefficient in solving such a model as the infeasibility information of the precedent visited solution cannot be directly utilized by the default method to update the bounds. A heuristic algorithm is developed to provide practical solutions, and the intermediate infeasible solutions identified during searching are utilized to develop valid and approximate inequalities, tightening the optimality gap. The computational results demonstrate that the addition of inequalities improves the computational efficiency in solving a wide range of instances and in tightening the optimality gap while the stopping criterion is met.

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“…Many different types of cutting and packing problems have been studied in the literature [3,7,11,15,25]. Among them, problems of packing rectangles and those of irregular shapes have been extensively studied, and many exact and heuristic algorithms have been proposed [5,8,14,16,18,19,24].…”

Section: Introductionmentioning

confidence: 99%

Efficient Overlap Detection and Construction Algorithms for the Bitmap Shape Packing Problem

Fukatsu

Hashimoto

et al. 2018

JORSJ

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The two-dimensional strip packing problem arises in wide variety of industrial applications. In this paper, we focus on the bitmap shape packing problem in which a set of arbitrarily shaped objects represented in bitmap format should be packed into a larger rectangular container without overlap. The complex geometry of bitmap shapes and the large amount of data to be processed make it difficult to check for overlaps. In this paper, we propose an efficient method for checking for overlaps and design efficient implementations of two construction algorithms, which are based on the bottom-left strategy. In this strategy, starting from an empty layout, items are packed into the container one by one. Each item is placed in the lowest position where there is no overlap relative to the current layout. We consider two algorithms, the bottom-left and the best-fit algorithm, which adopt this strategy. The computational results for a series of instances that are generated from well-known benchmark instances show that the proposed algorithms obtain good solutions in remarkably short time and are especially effective for large-scale instances.

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Robust mixed-integer linear programming models for the irregular strip packing problem

Cited by 75 publications

References 15 publications

Modelagem e solução de problemas de corte e empacotamento por meio da programação linear

Modelagem e solução de problemas de corte e empacotamento por meio da programação linear

A Family of Heuristic-Based Inequalities for Maximizing Overall Safety Margins in Aircraft Parking Stands Arrangement Problems

Efficient Overlap Detection and Construction Algorithms for the Bitmap Shape Packing Problem

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