One-Dimensional Cutting Stock Optimisation by Suborders

This paper introduces a method for solving a one-dimensional cutting stock problem by suborders. The method is used for large orders that for technological and logistical reasons cannot be filled in a single order, but only in several successive suborders. The method has two stages. In the first stage, the suborders are generated and in the second the trim-loss is minimised. All leftovers longer than D are returned to stock and reused. Shorter leftovers are treated as trim-loss and discarded. A detailed description of the method is provided by using a practical case. The method is tested by solving 108 randomly generated problem instances

Pattern Generation for Three Dimensional Cutting Stock Problem

We consider the problem of three-dimensional cutting of a large block that is to be cut into some small block pieces, each with a specific size and request. Pattern generation is an algorithm that has been used to determine cutting patterns in one-dimensional and two-dimensional problems. The purpose of this study is to modify the pattern generation algorithm so that it can be used in three-dimensional problems, and can determine the cutting pattern with the minimum possible cutting residue. The large block will be cut based on the length, width, and height. The rest of the cuts will be cut back if possible to minimize the rest. For three-dimensional problems, we consider the variant in which orthogonal rotation is allowed. By allowing the remainder of the initial cut to be rotated, the dimensions will have six permutations. The result of the calculation using the pattern generation algorithm for three-dimensional problems is that all possible cutting patterns are obtained but there are repetitive patterns because they suggest the same number of cuts.

Aplicación de Algoritmos Genéticos para la optimización del corte de material

[ES] Diseño, desarrollo, implementación y evaluación de algoritmos genéticos para la optimización del corte de material, a fin de minimizar la merma producida y/o optimizar la cantidad de las piezas obtenidas. Se trata de un problema realista, de optimización combinatoria y cuya solución optimizada requiere a menudo la aplicación de técncias metaheurísiticas. La aplicación del algoritmo desarrollado se realizará sobre casos de prueba realistas.[EN] Design, development, implementation and evaluation of genetic algorithms to optimize the cutting material to minimize waste produced and / or optimize the amount of the parts obtained. This is a realistic problem, combinatorial optimization and optimized solution which often requires the application of techniques behind metaheurísiticas. The application of the developed algorithm is performed on realistic test cases.Sánchez Rodríguez, I. (2016). Aplicación de Algoritmos Genéticos para la optimización del corte de material. http://hdl.handle.net/10251/68440.TFG

Heuristiken im Service Operations Management

This doctoral thesis deals with the application of operation research methods in practice. With two cooperation companies from the service sector (retailing and healthcare), three practice-relevant decision problems are jointly elicited and defined. Subsequently, the planning problems are transferred into mathematical problems and solved with the help of optimal and/or heuristic methods. The status quo of the companies could be significantly improved for all the problems dealt with.Diese Doktorarbeit beschäftigt sich mit der Anwendung von Operation Research Methoden in der Praxis. Mit zwei Kooperationsunternehmen aus dem Dienstleistungssektor (Einzelhandel und Gesundheitswesen) werden drei praxisrelevante Planungsprobleme gemeinsam eruiert und definiert. In weiterer Folge werden die Entscheidungsmodelle in mathematische Probleme transferiert und mit Hilfe von optimalen und/oder heuristischen Verfahren gelöst. Bei allen behandelten Problemstellungen konnte der bei den Unternehmen angetroffene Status Quo signifikant verbessert werden

Algorithms and data structures for three-dimensional packing

Cutting and packing problems are increasingly prevalent in industry. A well utilised freight vehicle will save a business money when delivering goods, as well as reducing the environmental impact, when compared to sending out two lesser-utilised freight vehicles. A cutting machine that generates less wasted material will have a similar effect. Industry reliance on automating these processes and improving productivity is increasing year-on-year. This thesis presents a number of methods for generating high quality solutions for these cutting and packing challenges. It does so in a number of ways. A fast, efficient framework for heuristically generating solutions to large problems is presented, and a method of incrementally improving these solutions over time is implemented and shown to produce even higher packing utilisations. The results from these findings provide the best known results for 28 out of 35 problems from the literature. This framework is analysed and its effectiveness shown over a number of datasets, along with a discussion of its theoretical suitability for higher-dimensional packing problems. A way of automatically generating new heuristics for this framework that can be problem specific, and therefore highly tuned to a given dataset, is then demonstrated and shown to perform well when compared to the expert-designed packing heuristics. Finally some mathematical models which can guarantee the optimality of packings for small datasets are given, and the (in)effectiveness of these techniques discussed. The models are then strengthened and a novel model presented which can handle much larger problems under certain conditions. The thesis finishes with a discussion about the applicability of the different approaches taken to the real-world problems that motivate them

Um modelo matemático para o problema de carregamento de múltiplos contêineres

Orientador : Prof. Dr. Cassius Tadeu ScarpinDissertação (mestrado) - Universidade Federal do Paraná, Setor de Tecnologia, Programa de Pós-Graduação em Métodos Numéricos em Engenharia. Defesa: Curitiba, 27/02/2015Inclui referências : f.73-81Resumo: Este trabalho apresenta um modelo de Programação Linear Inteira que visa carregar, de modo ortogonal e sem sobreposição, um subconjunto de caixas retangulares no interior de contêineres, de modo a minimizar o espaço não utilizado dos contêineres selecionados. Com base em propostas realizadas anteriormente na literatura, a formulação matemática descrita neste trabalho considera as restrições de limitação de peso do contêiner, orientação das caixas e estabilidade vertical da carga, além de utilizar uma técnica heurística para realizar o pré-processamento dos dados. Tanto conjuntos de teste gerados aleatoriamente quanto da literatura foram utilizados para avaliar o desempenho computacional da formulação matemática proposta, e um software de otimização foi empregado para a resolução dos modelos gerados. A análise dos resultados obtidos permite concluir que a proposta gera resultados satisfatórios, com padrões de carregamento que atendem as restrições abordadas neste trabalho, dentro de um limite de tempo estabelecido para a execução dos testes. Palavras-chave: Matemática Discreta e Combinatória. Programação Linear Inteira. Modelagem Matemática. Problemas de Corte e Empacotamento. Carregamento de Contêineres.Abstract: This work presents an Integer Linear Programming model that aims loading, orthogonally and without overlap, a subset of rectangular boxes inside containers, in order to minimize the idle space of the selected containers. Based on proposals previously made in the literature, the mathematical formulation described in this work regards the restrictions of weight limit of the container, box orientation and vertical stability of the load, and also uses a heuristic technique to preprocess the data. Both randomly generated sets of trials and ones from literature were used to evaluate the computational performance of the proposed mathematical formulation, and an optimization software was employed for the resolution of the generated models. The analysis of the obtained results allow the conclusion that the proposition generates satisfactory results, with loading patterns that meet the restrictions addressed in this work within a time limit set for the tests. Keywords: Discrete and Combinatorial Mathematics. Integer Linear Programming. Mathematical Modeling. Cutting and Packing Problems. Container Loading

Técnicas de solução exata para problemas de carregamento de contêineres

Orientador: Prof. Dr. Cassius Tadeu ScarpinCoorientador: Prof. Dr. José Eduardo Pécora JuniorTese (doutorado) - Universidade Federal do Paraná, Setor de Tecnologia, Programa de Pós-Graduação em Métodos Numéricos em Engenharia. Defesa: Curitiba, 18/02/2020Inclui referências: p. 72-79Resumo: Esta tese apresenta técnicas exatas de resolução de problemas de carregamento de contêineres. Tais problemas consistem em determinar um arranjo de caixas no interior de uma unidade de transporte de carga, de modo que os itens sejam alocados de modo ortogonal e sem sobreposição, otimizando uma função objetivo, que em geral busca maximizar o valor associado à carga ou definir a menor quantidade de contêineres necessários para efetuar o transporte dos itens. Formulações matemáticas para resolução destes problemas são apresentadas nesta tese. Quatro técnicas para determinar a posição que as caixas podem ocupar no interior do contêiner foram avaliadas. Estratégias para obtenção de bounds também foram apresentadas e testadas. As restrições de estabilidade de carga, orientação de caixas e separação de itens, comuns em situações reais de carregamento, foram incorporadas aos modelos apresentados neste trabalho. Testes computacionais em instâncias clássicas foram efetuados, e a comparação com outras abordagens da literatura de carregamento de contêineres mostrou que as técnicas apresentadas nesta tese foram capazes de obter soluções ótimas e aprimorar a melhor solução conhecida em diversas instâncias dos problemas abordados. Palavras-chaves: Problema de carregamento de contêineres. Considerações práticas. Formulações matemáticas. Discretizações.Abstract: This thesis presents exact techniques for solving container loading problems. Such problems consist in determining an arrangement of boxes within a cargo transport unit, so that items are placed orthogonally and without overlapping, optimizing an objective function, which generally seeks to maximize the value associated with the cargo or define the smallest number of containers needed to transport the items. Mathematical formulations for solving these problems are presented in this thesis. Four techniques for determining the position of boxes inside the container were evaluated. The constraints of loading stability, box orientation and separation of items, common in actual loading situations, were incorporated into the models presented in this work. Computational tests in classical instances were performed, and comparison with other approaches in the container loading literature showed that the techniques presented in this thesis were able to obtain optimal solutions and to improve the best known solution in several instances of the problems addressed. Key-words: Container loading problem. Practical considerations. Mathematical formulations. Discretization

Algorithm-aided Information Design: Hybrid Design approach on the edge of associative methodologies in AEC

Dissertação de mestrado em European Master in Building Information ModellingLast three decades have brought colossal progress to design methodologies within the common pursuit toward a seamless fusion between digital and physical worlds and augmenting it with the of computation power and network coverage. For this historically short period, two generations of methodologies and tools have emerged: Additive generation and parametric Associative generation of CAD. Currently, designers worldwide engaged in new forms of design exploration. From this race, two prominent methodologies have developed from Associative Design approach – Object-Oriented Design (OOD) and Algorithm-Aided Design (AAD). The primary research objective is to investigate, examine, and push boundaries between OOD and AAD for new design space determination, where advantages of both design methods are fused to produce a new generation methodology which is called in the present study AID (Algorithm-aided Information Design). The study methodology is structured into two flows. In the first flow, existing CAD methodologies are investigated, and the conceptual framework is extracted based on the state of art analysis, then analysed data is synthesized into the subject proposal. In the second flow, tools and workflows are elaborated and examined on practice to confirm the subject proposal. In compliance, the content of the research consists of two theoretical and practical parts. In the first theoretical part, a literature review is conducted, and assumptions are made to speculate about AID methodology, its tools, possible advantages and drawbacks. Next, case studies are performed according to sequential stages of digital design through the lens of practical AID methodology implementation. Case studies are covering such design aspects as model & documentation generation, design automation, interoperability, manufacturing control, performance analysis and optimization. Ultimately, a set of test projects is developed with the AID methodology applied. After the practical part, research returns to the theory where analytical information is gathered based on the literature review, conceptual framework, and experimental practice reports. In summary, the study synthesizes AID methodology as part of Hybrid Design, which enables creative use of tools and elaborating of agile design systems integrating additive and associative methodologies of Digital Design. In general, the study is based on agile methods and cyclic research development mixed between practice and theory to achieve a comprehensive vision of the subject.Last three decades have brought colossal progress to design methodologies within the common pursuit toward a seamless fusion between digital and physical worlds and augmenting it with the of computation power and network coverage. For this historically short period, two generations of methodologies and tools have emerged: Additive generation and parametric Associative generation of CAD. Currently, designers worldwide engaged in new forms of design exploration. From this race, two prominent methodologies have developed from Associative Design approach – Object-Oriented Design (OOD) and Algorithm-Aided Design (AAD). The primary research objective is to investigate, examine, and push boundaries between OOD and AAD for new design space determination, where advantages of both design methods are fused to produce a new generation methodology which is called in the present study AID (Algorithm-aided Information Design). The study methodology is structured into two flows. In the first flow, existing CAD methodologies are investigated, and the conceptual framework is extracted based on the state of art analysis, then analysed data is synthesized into the subject proposal. In the second flow, tools and workflows are elaborated and examined on practice to confirm the subject proposal. In compliance, the content of the research consists of two theoretical and practical parts. In the first theoretical part, a literature review is conducted, and assumptions are made to speculate about AID methodology, its tools, possible advantages and drawbacks. Next, case studies are performed according to sequential stages of digital design through the lens of practical AID methodology implementation. Case studies are covering such design aspects as model & documentation generation, design automation, interoperability, manufacturing control, performance analysis and optimization. Ultimately, a set of test projects is developed with the AID methodology applied. After the practical part, research returns to the theory where analytical information is gathered based on the literature review, conceptual framework, and experimental practice reports. In summary, the study synthesizes AID methodology as part of Hybrid Design, which enables creative use of tools and elaborating of agile design systems integrating additive and associative methodologies of Digital Design. In general, the study is based on agile methods and cyclic research development mixed between practice and theory to achieve a comprehensive vision of the subject