A heuristic for packing boxes into a container

(2008). A heuristic for the container loading problem: A tertiary-tree-based dynamic space decomposition approach. European Journal of Operational Research, 191 (1) AbstractIncreasing fuel costs, post-911 security concerns, and economic globalization provide a strong incentive for container carriers to use available container space more efficiently, thereby minimizing the number of container trips and reducing socio-economic vulnerability. A heuristic algorithm based on a tertiary tree model is proposed to handle the container loading problem (CLP) with weakly heterogeneous boxes. A dynamic space decomposition method based on the tertiary tree structure is developed to partition the remaining container space after a block of homogeneous rectangular boxes is loaded into a container. This decomposition approach, together with an optimal-fitting sequencing and an inner-right-corner-occupying placement rule, permits a holistic loading strategy to pack a container. Comparative studies with existing algorithms and an illustrative example demonstrate the efficiency of this algorithm.

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“…Accordingly, heuristics are often the only viable option [George and Robinson, 1980;Mack et al, 2004;Ngoi et al 1994]. …”

Section: Introductionmentioning

confidence: 99%

A heuristic for the container loading problem: A tertiary-tree-based dynamic space decomposition approach

Wang

Levy

2008

European Journal of Operational Research

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“…Table 2 shows the results for instances generated according to the scheme suggested by Cecílio & Morabito (2004), who also proposed five heuristics that correspond to refinements of the approach by George & Robinson (1980). The best result obtained by the application of such heuristics to each instance is reported.…”

Section: Computational Experimentsmentioning

confidence: 99%

“…This computer was used by Mack et al (2004) who report a mean computational time of 205 seconds to solve the 700 instances BR1-BR7. We have also tested the performance of the proposed heuristic on a real life example reported by George & Robinson (1980), which consists of 784 boxes distributed in eight types to be loaded in a container with available dimensions in millimeters 579322362261 ××. For the stopping criterion of 240 evaluated solutions, AAR1 and AAR2 produce solutions in which all boxes are packed.…”

Section: Computational Experimentsmentioning

confidence: 99%

“…Such an approach was introduced by George & Robinson (1980) who suggested a sophisticated constructive heuristic based on vertical layers such that spaces not occupied in a layer can be used in subsequent layers. The ideas proposed by George & Robinson (1980) The stack building approach allows the decomposition of the original problem into two subproblems: the three-dimensional problem of packing the boxes into suitable stacks and the two-dimensional problem of locating the stacks at the floor of the container. A stack is built from the selection of a base box that is positioned at the floor of the container.…”

Section: Introductionmentioning

confidence: 99%

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A multi-start random constructive heuristic for the container loading problem

Araújo

Armentano

2007

Pesqui. Oper.

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This paper deals with the container loading problem which involves the selection of a subset of boxes, each box with a given volume, such that they fit in a single container and maximize its volume utilization subject to orientation and stability constraints. We propose a multi-start random constructive heuristic with a load arrangement that is based on maximal cuboids that fit in given empty spaces. Each instance is adaptively evaluated by a set of criteria, and at each step of the construction process one maximal cuboid is chosen probabilistically from a restricted list of candidates. In order to enhance the flexibility in the construction of a solution, a probabilistic reduction on such cuboids is allowed. Computational tests on several instances from the literature show that the proposed method performs better than other approaches.Keywords: container loading; cuboid arrangement; multi-start random constructive heuristic. ResumoNeste trabalho abordamos o problema de carregamento de contêiner que trata da seleção de um subconjunto de caixas, cada caixa com um dado volume, de forma a maximizar o volume ocupado de um único contêiner sujeito a restrições de orientação e estabilidade. Propomos uma heurística construtiva aleatória com múltiplos inícios que utiliza um arranjo de carga baseado em cubóides que maximizam a ocupação de espaços vazios. Cada instância é avaliada de forma adaptativa por um conjunto de critérios, e em cada passo do processo construtivo um cubóide é selecionado probabilisticamente de uma lista restrita de candidatos. Para aumentar a flexibilidade na construção de uma solução, permite-se uma redução probabilística no tamanho dos cubóides. Resultados computacionais em instâncias da literatura mostram que o método proposto apresenta um desempenho superior a outros enfoques sugeridos na literatura.

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“…A heurística H 1 aloca itens dentro de um bin de acordo com uma variação do preenchimento por camadas (prateleiras) sugerido em George & Robinson (1980); sendo que os pontos de inserção são pontos de cantos bi-dimensionais. O problema resultante torna-se, então, o BPP o qual é resolvido pela política de First-Fit.…”

Section: Experimentos Computacionaisunclassified

Um algoritmo polinomial para o problema de empacotamento de contêineres com estabillidade estática da carga

Silva

Soma

2003

Pesqui. Oper.

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ResumoO objetivo deste artigo é apresentar um algoritmo polinomial na quantidade de recursos computacionais utilizados, que encontre boas soluções para o problema de empacotamento de bins tridimensionais; tendo como maior contribuição, considerações sobre a estabilidade estática da carga. Os critérios para o empacotamento estável dos itens dentro dos bins são apresentados com detalhes. O procedimento para o preenchimento dos itens dentro dos bins utiliza o bem conhecido princípio da alocação em pontos de cantos. O problema é NP-difícil no sentido forte e extremamente difícil de ser resolvido na prática. Apresenta-se grande quantidade de experimentos computacionais para problemas com até 90 itens (com e sem estabilidade estática) e os resultados são comparados com aqueles obtidos da literatura. Palavras-chave: bin packing tridimensional; empacotamento com estabilidade estática. AbstractA polynomial computational bounded resources heuristic for the Three-Dimensional Bin Packing Problem (3D-BPP) is suggested. The major contribution is the introduction of static stability of the packing and the criteria used for such a packing are described in details. The filling process follows the well known 3-D corner approach. The problem is NP-Hard in the strong sense and extremely difficult to be solved in the practice. Extensive computational experiments are also presented, with instances up to 90 items, with and without static stability. The results are compared with those obtained from the literature.

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A heuristic for packing boxes into a container

Cited by 250 publications

References 4 publications

A heuristic for the container loading problem: A tertiary-tree-based dynamic space decomposition approach

A heuristic for the container loading problem: A tertiary-tree-based dynamic space decomposition approach

A multi-start random constructive heuristic for the container loading problem

Um algoritmo polinomial para o problema de empacotamento de contêineres com estabillidade estática da carga

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