O trabalho constitui-se numa investigação teórica da estrutura ordenada e intuitiva dos espaços coerentes, introduzidos por Girard [GIR 86], na definição do modelo de máquina geométrica para construção e interpretação de estados e processos computacionais rotulados por posições de um espaço geométrico. Esta interpretação poderá ser aplicada às construções determinísticas, incluindo dois tipos especiais de paralelismo - o espacial, com memória e processos infinitos definidos por estruturas matriciais, que operam sobre dimensões independentes, de forma sincronizada; e o temporal, na versão genérica do modelo, com memória global transfinita e processos distribuídos num conjunto enumerável de máquinas geométricas, sincronizadas no tempo. O modelo contempla interpretação para computações não-determinísticas e prevê a aplicação de operadores exponenciais na interpretação do espaço funcional. A noção mais intuitiva deste trabalho está na definição da relação de coerência, que define o grafo sobre o qual se constrói este domínio semántico. Sobre o conjunto de pontos compatíveis de tais grafos, a coerência estrita interpreta a condição implícita para modelar o paralelismo - a concorrência entre posições de memória. Na construção dual, justificada pela presença da negação involutiva no grafo complementar, a incoerência interpreta a condição para o não-determinismo - o conflito de acesso à memória. Para os demais construtores, o produto sequencial e a soma determinística, consideram-se os endofunctores produto e soma direta da categoria CospLin dos espaços coerentes e funções lineares. A estrutura ordenada deste modelo é formalizada pelo espaço coerente D∞ de todos os processos, construído em níveis a partir do espaço coerente D∞ dos processos elementares, seguindo a metodologia proposta por Scott [SCO 76]. Neste sentido, cada nível da construção está identificado por um subespaço Dn que reconstrói todos os objetos do nível anterior, preservando suas propriedades e relações, além de construir os novos objetos. Compatível com a abordagem algébrica, o relacionamento entre os níveis é expresso por funções lineares denominadas imersões e projeções, interpretanto os construtores de processos e seus destrutores, respectivamente. Pelo procedimento de completação, assegura-se a existência do menor ponto fixo para equações recursivas definidas pela composição infinita destes morfismos. Além disso, as interpretações para processos infinitos, construídos por prefixação, apresentadas em D→∞ comprovam que este modelo é compatível com a diversidade dos construtores. O espa¸co coerente D∞2 dos processos transfinitos generaliza a construção e define a estrutura ordenada do modelo de máquina geométrica distribuída. Seus objetos são subconjuntos coerentes de tokens rotulados por posições do espaço geométrico e indexados por subconjuntos isomorfos aos ordinais transfinitos. O espaço coerente S S dos traços lineares de funções definidas sobre o espaço coerente S dos estados computacionais constitui-se no modelo semântico para análise do comportamento associado a cada processo interpretado em D∞. A definição da função de representação introduz um domínio de expressões que formaliza uma linguagem capaz de expressar, de forma mais operacional, as interpretações obtidas neste modelo de m´aquina. Cada uma das expressões válidas na linguagem é compatível com uma expressão gráfica. / This work presents a theoretical investigation of the constructive, intuitive and ordered structure of the coherence spaces, introduced by Girard, in order to define the geometric machine model for interpretation of computational states and processes labelled by positions of a geometric space. This interpretation can be applied to deterministic process constructions, including two special types of parallelism - the temporal parallelism, with infinite memory and infinite processes defined over array structures, that operate over independent dimensions in a synchronized way; and the spatial parallelism, in a generic version of the model, with a transfinite global memory shared by transfinite processes distributed in a enumerable set of geometric machines, synchronized in the time. The work also provides interpretation to the non-deterministic computations and applies the exponential operators in the interpretation of the functional space. The most basic notion of this work is the definition of the coherence relation as the admissibility of parallelism between basic operations (elementary processes). That relation defines the web over which the coherence space of the whole set of deterministic and non-deterministic processes is step-wise and systematically build. Over the set of the compatible points of such graph, the strict coherence interprets the implicity condition to model parallelism - the true concurrence. In the dual construction, justified by the presence of involutive negation in the complementary graph, the incoherence interprets the condition that models non-determinism - the conflict of memory accesses. The other constructors, the sequential product and the deterministic sum, are defined by the endofunctors in the CospLin category of the coherence spaces and linear functions. The ordered structure of this model is formalized by the coherence space D∞ of all processes, constructed by levels from the coherence space D0 of the elementary processes, following the Scott’s methodology [SCO 76]. In this sense, each level is identified by a subspace Dn, which reconstructs all the objects from the level before, preserving their properties and relations, and drives the construction of the new objects. Compatible with the algebraic-theoretic approach to computational processes, the relationship between the levels is expressed by linear functions called embedding and projection-functions, which interpret constructors and destructors of processes, respectively. The completion procedure guarantees the existence of the least fixed point to the recursive equations, defined by infinite composition of these morphisms. In addition, the interpretation for infinite processes constructed by prefix is presented in D→∞ , confirms that the ordered structure of these model is compatible with the diversity of constructors. The coherence space D∞2 of transfinite processes generalizes the construction and defines the ordered structure of the distributed geometric machine model. Its objects are coherent subsets of tokens labelled by the positions of a geometric space and indexed by isomorphic subsets related to the transfinite ordinal numbers. In order to analyze the behavior related to the interpretations in D∞, the coherence space S S of the linear traces of functions, defined over the coherence space S of the computational states, is introduced. The definition of the representation-function induces the construction of the domain Ω of valid expressions and formalizes a (graphic) language which is able to express, in an more operational way, the interpretations obtained in the geometric machine model.

O trabalho constitui-se numa investigação teórica da estrutura ordenada e intuitiva dos espaços coerentes, introduzidos por Girard [GIR 86], na definição do modelo de máquina geométrica para construção e interpretação de estados e processos computacionais rotulados por posições de um espaço geométrico. Esta interpretação poderá ser aplicada às construções determinísticas, incluindo dois tipos especiais de paralelismo - o espacial, com memória e processos infinitos definidos por estruturas matriciais, que operam sobre dimensões independentes, de forma sincronizada; e o temporal, na versão genérica do modelo, com memória global transfinita e processos distribuídos num conjunto enumerável de máquinas geométricas, sincronizadas no tempo. O modelo contempla interpretação para computações não-determinísticas e prevê a aplicação de operadores exponenciais na interpretação do espaço funcional. A noção mais intuitiva deste trabalho está na definição da relação de coerência, que define o grafo sobre o qual se constrói este domínio semántico. Sobre o conjunto de pontos compatíveis de tais grafos, a coerência estrita interpreta a condição implícita para modelar o paralelismo - a concorrência entre posições de memória. Na construção dual, justificada pela presença da negação involutiva no grafo complementar, a incoerência interpreta a condição para o não-determinismo - o conflito de acesso à memória. Para os demais construtores, o produto sequencial e a soma determinística, consideram-se os endofunctores produto e soma direta da categoria CospLin dos espaços coerentes e funções lineares. A estrutura ordenada deste modelo é formalizada pelo espaço coerente D∞ de todos os processos, construído em níveis a partir do espaço coerente D∞ dos processos elementares, seguindo a metodologia proposta por Scott [SCO 76]. Neste sentido, cada nível da construção está identificado por um subespaço Dn que reconstrói todos os objetos do nível anterior, preservando suas propriedades e relações, além de construir os novos objetos. Compatível com a abordagem algébrica, o relacionamento entre os níveis é expresso por funções lineares denominadas imersões e projeções, interpretanto os construtores de processos e seus destrutores, respectivamente. Pelo procedimento de completação, assegura-se a existência do menor ponto fixo para equações recursivas definidas pela composição infinita destes morfismos. Além disso, as interpretações para processos infinitos, construídos por prefixação, apresentadas em D→∞ comprovam que este modelo é compatível com a diversidade dos construtores. O espa¸co coerente D∞2 dos processos transfinitos generaliza a construção e define a estrutura ordenada do modelo de máquina geométrica distribuída. Seus objetos são subconjuntos coerentes de tokens rotulados por posições do espaço geométrico e indexados por subconjuntos isomorfos aos ordinais transfinitos. O espaço coerente S S dos traços lineares de funções definidas sobre o espaço coerente S dos estados computacionais constitui-se no modelo semântico para análise do comportamento associado a cada processo interpretado em D∞. A definição da função de representação introduz um domínio de expressões que formaliza uma linguagem capaz de expressar, de forma mais operacional, as interpretações obtidas neste modelo de m´aquina. Cada uma das expressões válidas na linguagem é compatível com uma expressão gráfica. / This work presents a theoretical investigation of the constructive, intuitive and ordered structure of the coherence spaces, introduced by Girard, in order to define the geometric machine model for interpretation of computational states and processes labelled by positions of a geometric space. This interpretation can be applied to deterministic process constructions, including two special types of parallelism - the temporal parallelism, with infinite memory and infinite processes defined over array structures, that operate over independent dimensions in a synchronized way; and the spatial parallelism, in a generic version of the model, with a transfinite global memory shared by transfinite processes distributed in a enumerable set of geometric machines, synchronized in the time. The work also provides interpretation to the non-deterministic computations and applies the exponential operators in the interpretation of the functional space. The most basic notion of this work is the definition of the coherence relation as the admissibility of parallelism between basic operations (elementary processes). That relation defines the web over which the coherence space of the whole set of deterministic and non-deterministic processes is step-wise and systematically build. Over the set of the compatible points of such graph, the strict coherence interprets the implicity condition to model parallelism - the true concurrence. In the dual construction, justified by the presence of involutive negation in the complementary graph, the incoherence interprets the condition that models non-determinism - the conflict of memory accesses. The other constructors, the sequential product and the deterministic sum, are defined by the endofunctors in the CospLin category of the coherence spaces and linear functions. The ordered structure of this model is formalized by the coherence space D∞ of all processes, constructed by levels from the coherence space D0 of the elementary processes, following the Scott’s methodology [SCO 76]. In this sense, each level is identified by a subspace Dn, which reconstructs all the objects from the level before, preserving their properties and relations, and drives the construction of the new objects. Compatible with the algebraic-theoretic approach to computational processes, the relationship between the levels is expressed by linear functions called embedding and projection-functions, which interpret constructors and destructors of processes, respectively. The completion procedure guarantees the existence of the least fixed point to the recursive equations, defined by infinite composition of these morphisms. In addition, the interpretation for infinite processes constructed by prefix is presented in D→∞ , confirms that the ordered structure of these model is compatible with the diversity of constructors. The coherence space D∞2 of transfinite processes generalizes the construction and defines the ordered structure of the distributed geometric machine model. Its objects are coherent subsets of tokens labelled by the positions of a geometric space and indexed by isomorphic subsets related to the transfinite ordinal numbers. In order to analyze the behavior related to the interpretations in D∞, the coherence space S S of the linear traces of functions, defined over the coherence space S of the computational states, is introduced. The definition of the representation-function induces the construction of the domain Ω of valid expressions and formalizes a (graphic) language which is able to express, in an more operational way, the interpretations obtained in the geometric machine model.

O trabalho constitui-se numa investigação teórica da estrutura ordenada e intuitiva dos espaços coerentes, introduzidos por Girard [GIR 86], na definição do modelo de máquina geométrica para construção e interpretação de estados e processos computacionais rotulados por posições de um espaço geométrico. Esta interpretação poderá ser aplicada às construções determinísticas, incluindo dois tipos especiais de paralelismo - o espacial, com memória e processos infinitos definidos por estruturas matriciais, que operam sobre dimensões independentes, de forma sincronizada; e o temporal, na versão genérica do modelo, com memória global transfinita e processos distribuídos num conjunto enumerável de máquinas geométricas, sincronizadas no tempo. O modelo contempla interpretação para computações não-determinísticas e prevê a aplicação de operadores exponenciais na interpretação do espaço funcional. A noção mais intuitiva deste trabalho está na definição da relação de coerência, que define o grafo sobre o qual se constrói este domínio semántico. Sobre o conjunto de pontos compatíveis de tais grafos, a coerência estrita interpreta a condição implícita para modelar o paralelismo - a concorrência entre posições de memória. Na construção dual, justificada pela presença da negação involutiva no grafo complementar, a incoerência interpreta a condição para o não-determinismo - o conflito de acesso à memória. Para os demais construtores, o produto sequencial e a soma determinística, consideram-se os endofunctores produto e soma direta da categoria CospLin dos espaços coerentes e funções lineares. A estrutura ordenada deste modelo é formalizada pelo espaço coerente D∞ de todos os processos, construído em níveis a partir do espaço coerente D∞ dos processos elementares, seguindo a metodologia proposta por Scott [SCO 76]. Neste sentido, cada nível da construção está identificado por um subespaço Dn que reconstrói todos os objetos do nível anterior, preservando suas propriedades e relações, além de construir os novos objetos. Compatível com a abordagem algébrica, o relacionamento entre os níveis é expresso por funções lineares denominadas imersões e projeções, interpretanto os construtores de processos e seus destrutores, respectivamente. Pelo procedimento de completação, assegura-se a existência do menor ponto fixo para equações recursivas definidas pela composição infinita destes morfismos. Além disso, as interpretações para processos infinitos, construídos por prefixação, apresentadas em D→∞ comprovam que este modelo é compatível com a diversidade dos construtores. O espa¸co coerente D∞2 dos processos transfinitos generaliza a construção e define a estrutura ordenada do modelo de máquina geométrica distribuída. Seus objetos são subconjuntos coerentes de tokens rotulados por posições do espaço geométrico e indexados por subconjuntos isomorfos aos ordinais transfinitos. O espaço coerente S S dos traços lineares de funções definidas sobre o espaço coerente S dos estados computacionais constitui-se no modelo semântico para análise do comportamento associado a cada processo interpretado em D∞. A definição da função de representação introduz um domínio de expressões que formaliza uma linguagem capaz de expressar, de forma mais operacional, as interpretações obtidas neste modelo de m´aquina. Cada uma das expressões válidas na linguagem é compatível com uma expressão gráfica. / This work presents a theoretical investigation of the constructive, intuitive and ordered structure of the coherence spaces, introduced by Girard, in order to define the geometric machine model for interpretation of computational states and processes labelled by positions of a geometric space. This interpretation can be applied to deterministic process constructions, including two special types of parallelism - the temporal parallelism, with infinite memory and infinite processes defined over array structures, that operate over independent dimensions in a synchronized way; and the spatial parallelism, in a generic version of the model, with a transfinite global memory shared by transfinite processes distributed in a enumerable set of geometric machines, synchronized in the time. The work also provides interpretation to the non-deterministic computations and applies the exponential operators in the interpretation of the functional space. The most basic notion of this work is the definition of the coherence relation as the admissibility of parallelism between basic operations (elementary processes). That relation defines the web over which the coherence space of the whole set of deterministic and non-deterministic processes is step-wise and systematically build. Over the set of the compatible points of such graph, the strict coherence interprets the implicity condition to model parallelism - the true concurrence. In the dual construction, justified by the presence of involutive negation in the complementary graph, the incoherence interprets the condition that models non-determinism - the conflict of memory accesses. The other constructors, the sequential product and the deterministic sum, are defined by the endofunctors in the CospLin category of the coherence spaces and linear functions. The ordered structure of this model is formalized by the coherence space D∞ of all processes, constructed by levels from the coherence space D0 of the elementary processes, following the Scott’s methodology [SCO 76]. In this sense, each level is identified by a subspace Dn, which reconstructs all the objects from the level before, preserving their properties and relations, and drives the construction of the new objects. Compatible with the algebraic-theoretic approach to computational processes, the relationship between the levels is expressed by linear functions called embedding and projection-functions, which interpret constructors and destructors of processes, respectively. The completion procedure guarantees the existence of the least fixed point to the recursive equations, defined by infinite composition of these morphisms. In addition, the interpretation for infinite processes constructed by prefix is presented in D→∞ , confirms that the ordered structure of these model is compatible with the diversity of constructors. The coherence space D∞2 of transfinite processes generalizes the construction and defines the ordered structure of the distributed geometric machine model. Its objects are coherent subsets of tokens labelled by the positions of a geometric space and indexed by isomorphic subsets related to the transfinite ordinal numbers. In order to analyze the behavior related to the interpretations in D∞, the coherence space S S of the linear traces of functions, defined over the coherence space S of the computational states, is introduced. The definition of the representation-function induces the construction of the domain Ω of valid expressions and formalizes a (graphic) language which is able to express, in an more operational way, the interpretations obtained in the geometric machine model.

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / This work presents three evolutionary strategies to solve the problem of scheduling a given set of n jobs to m identical parallel machines with the objective of minimizing makespan. There is a sequence dependent setup times. We also compares our method with two other well succeeded heuristics, one is a tabu search based heuristic and the second is a memetic approach, which combines a population-based method with local search procedures. As benchmarks for smallsized instances, optimal values are used provide by a dichotomous search. For larger instances, the comparisons try to show the robust behavior in solution quality as well as in computational effort of our evolutionary strategy. / Este trabalho propõe três estratégias evolutivas para resolver o problema de seqüenciamento de n tarefas em m máquinas paralelas idênticas, buscando minimizar o tempo máximo de finalização (makespan). São considerados tempos de preparação dependentes da seqüência. Os métodos propostos são comparados com outras duas heurísticas de qualidade comprovada, uma baseada em Busca Tabu e outra baseada em Algoritmos Meméticos. Para algumas instâncias de pequeno porte, comparações são feitas com o valor ótimo obtido através de uma busca dicotômica. Para instâncias maiores, as comparações demonstram a robustez e a boa qualidade das soluções encontradas pelas estratégias evolutivas através da comparação com as outras heurísticas.

O problema de dimensionamento de lotes, objeto desse estudo, considera um ambiente composto por múltiplas plantas independentes, múltiplos itens e múltiplos períodos. O ambiente de produção tem capacidade limitada e as plantas podem produzir os mesmos itens. Cada planta tem uma demanda própria e é permitida a transferência de lotes entre as plantas, o que envolve um certo custo. Este problema tem como caso particular o de dimensionamento de lotes com máquinas paralelas. O objetivo desta dissertação é propor uma heurística baseada na meta-heurística GRASP (Greedy Randomized Adaptive Search Procedures). Além disso, uma estratégia path relinking foi incorporada ao GRASP como uma fase de melhoria do algoritmo. Para verificar a eficiência da heurística proposta, os seus resultados são comparados aos da literatura tanto no caso de máquinas paralelas quanto no de múltiplas plantas. Como resultado, o problema de múltiplas plantas obteve melhores resultados quando comparado aos da heurística da literatura. Com relação ao problema de máquinas paralelas, a heurística proposta se mostrou competitiva / The lot sizing problem, which is the aim of this study, considers an environment consisting of multiple independent plants, multiple items and multiple periods. The production environment has limited capacity and the plants can produce the same items. Each plant has its own demand and the lot transfers between the plants are permitted, which involves a certain cost. This problem has as a particular case the parallel machines lot sizing problem. The objective of this dissertation is to propose a heuristic based on the GRASP (Greedy Randomized Adaptive Search Procedures). Furthermore, a path relinking phase is embedded in the GRASP to obtain better performance. To verify the efficiency of the proposed heuristic, its results were compared with the literature as for the multi-plant as for parallel machines problem. Computational tests showed that the proposed heuristic performed better than other literature heuristic concerning the multiplant problem. Concerning the parallel machines, the heuristic is competitive

Submitted by Marlene Santos (marlene.bc.ufg@gmail.com) on 2016-10-20T17:39:38Z No. of bitstreams: 2 Dissertação - Fernanda Neiva Mesquita - 2015.pdf: 2481424 bytes, checksum: 2263ae4d21d732d49ebd0e6d2e2763c6 (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) / Approved for entry into archive by Jaqueline Silva (jtas29@gmail.com) on 2016-10-21T19:23:42Z (GMT) No. of bitstreams: 2 Dissertação - Fernanda Neiva Mesquita - 2015.pdf: 2481424 bytes, checksum: 2263ae4d21d732d49ebd0e6d2e2763c6 (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) / Made available in DSpace on 2016-10-21T19:23:42Z (GMT). No. of bitstreams: 2 Dissertação - Fernanda Neiva Mesquita - 2015.pdf: 2481424 bytes, checksum: 2263ae4d21d732d49ebd0e6d2e2763c6 (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) Previous issue date: 2015-12-15 / This study deals with problems of parallel machines with independent setup times, different dates of release and minimizing the makespan. The production environment is common in the auto industry that there may be jobs through the production line, they are added new machines or equal equipment to expand productive capacity. Any production process requires effective management by the Production Planning and Control (PCP). This activity includes the planning of production, so the allocation of resources for task execution on a time basis. The programming activity is one of the most complex tasks in the management of production because the need to deal with several different types of resources and concurrent activities. Furthermore, the number of solutions grows exponentially in several dimensions, according to the number of tasks, operations or machines, thereby generating a combinatorial nature of the problem. The environment treated in this work each task has the same processing time on any machine. Considering only the restriction independently of the task setup time waiting for processing and the presence of release dates different from zero very practical characteristics in industries. As were found in the literature work that deals of this work environment, even less that used the meta-heuristic Simulated Anneling, so we developed the method to the problem, along with the initial solution their disturbance schemes and the setting of lower bounds for the makespan. / Este estudo trata de problemas de máquinas paralelas com tempos de setup independentes, diferentes datas de liberação e minimização do makespan. Este ambiente de produção é comum na indústria automobilística que pode haver postos de trabalho em meio à linha de produção, em que são adicionadas novas máquinas ou equipamentos iguais para ampliar a capacidade produtiva. Qualquer processo produtivo requer um gerenciamento eficaz por meio do Planejamento e Controle da Produção (PCP). Esta atividade inclui a programação da produção, ou seja, a alocação de recursos para execução de tarefas em uma base de tempo. A atividade de programação é uma das tarefas mais complexas no gerenciamento da produção, pois a necessidade de lidar com diversos tipos diferentes de recursos e atividades simultâneas. Além disso, o número de soluções cresce exponencialmente em várias dimensões, de acordo com a quantidade de tarefas, operações ou máquinas, gerando assim uma natureza combinatória ao problema. O ambiente tratado neste trabalho cada tarefa tem o mesmo tempo de processamento em qualquer máquina. Considerando a restrição de tempos de setup independente apenas da tarefa que espera por processamento e a presença de datas de liberação diferentes de zero características muito práticas nas indústrias. Como não foram encontrados na literatura trabalho que tratasse desse ambiente de trabalho, ainda menos que utilizasse a meta-heurística Simulated Anneling, então foi desenvolvido o método para o problema, juntamente com a solução inicial os respectivos esquemas de perturbação e a definição de limitantes inferiores para o makespan.

O problema de dimensionamento de lotes, objeto desse estudo, considera um ambiente composto por múltiplas plantas independentes, múltiplos itens e múltiplos períodos. O ambiente de produção tem capacidade limitada e as plantas podem produzir os mesmos itens. Cada planta tem uma demanda própria e é permitida a transferência de lotes entre as plantas, o que envolve um certo custo. Este problema tem como caso particular o de dimensionamento de lotes com máquinas paralelas. O objetivo desta dissertação é propor uma heurística baseada na meta-heurística GRASP (Greedy Randomized Adaptive Search Procedures). Além disso, uma estratégia path relinking foi incorporada ao GRASP como uma fase de melhoria do algoritmo. Para verificar a eficiência da heurística proposta, os seus resultados são comparados aos da literatura tanto no caso de máquinas paralelas quanto no de múltiplas plantas. Como resultado, o problema de múltiplas plantas obteve melhores resultados quando comparado aos da heurística da literatura. Com relação ao problema de máquinas paralelas, a heurística proposta se mostrou competitiva / The lot sizing problem, which is the aim of this study, considers an environment consisting of multiple independent plants, multiple items and multiple periods. The production environment has limited capacity and the plants can produce the same items. Each plant has its own demand and the lot transfers between the plants are permitted, which involves a certain cost. This problem has as a particular case the parallel machines lot sizing problem. The objective of this dissertation is to propose a heuristic based on the GRASP (Greedy Randomized Adaptive Search Procedures). Furthermore, a path relinking phase is embedded in the GRASP to obtain better performance. To verify the efficiency of the proposed heuristic, its results were compared with the literature as for the multi-plant as for parallel machines problem. Computational tests showed that the proposed heuristic performed better than other literature heuristic concerning the multiplant problem. Concerning the parallel machines, the heuristic is competitive

[ES] En esta tesis doctoral se estudia el problema de secuenciación de máquinas paralelas no relacionadas con necesidad de ajustes y recursos adicionales asignados en los ajustes. En este problema, se tiene un grupo de tareas (también llamadas trabajos), donde cada una debe ser procesada en una de las máquinas paralelas disponibles. Para procesar una tarea después de otra en la misma máquina, se debe hacer un ajuste en la máquina. Se asume que estos ajustes deben ser realizados por un recurso adicional limitado (por ejemplo, operarios). En esta tesis doctoral se estudian dos variantes del problema planteado: 1) considerando el problema con el único objetivo de minimizar el tiempo máximo de finalización de todos los trabajos (makespan), y 2) considerando el problema multi-objetivo minimizando simultáneamente el makespan y el consumo máximo de recursos adicionales. Inicialmente, se realiza una completa revisión bibliográfica sobre estudios relacionados con el problema planteado. En esta revisión se detecta que, a pesar de existir numerosos estudios de secuenciación de máquinas paralelas, no muchos de estos estudios tienen en cuenta recursos adicionales. Posteriormente, para introducir el problema a estudiar antes de plantear métodos de resolución, se realiza una breve explicación de los principales problemas de secuenciación de máquinas paralelas. El problema de un solo objetivo está clasificado como NP-Hard. Por ello, para abordar su resolución se han diseñado e implementado heurísticas y metaheurísticas siguiendo dos enfoques diferentes. Para el primer enfoque, que ignora la información sobre el consumo de recursos adicionales en la fase constructiva, se adaptan dos de los mejores algoritmos existentes en la literatura para el problema de máquinas paralelas con ajustes sin necesidad de recursos adicionales. En el segundo enfoque, que sí tiene en cuenta la información sobre el consumo de recursos adicionales en la fase constructiva, se proponen nuevos algoritmos heurísticos y metaheurísticos para resolver el problema. Tras analizar los resultados de los experimentos computacionales realizados, concluimos que hay diferencias entre los dos enfoques, siendo significativamente mejor el enfoque que tiene en cuenta la información sobre los recursos adicionales. Al igual que en el caso de un solo objetivo, la complejidad del problema multi-objetivo obliga a presentar algoritmos heurísticos o metaheurísticos para resolverlo. En esta tesis se presenta un nuevo algoritmo metaheurístico multi-objetivo eficiente para encontrar buenas aproximaciones a la frontera de Pareto del problema. Además, se adaptaron otros tres algoritmos que han mostrado buenos resultados en diferentes estudios de problemas de secuenciación de máquinas multi-objetivo. Después de realizar experimentos computacionales exhaustivos, concluimos que el nuevo algoritmo propuesto en esta tesis es significativamente mejor que los otros tres algoritmos existentes, y que se han adaptado para resolver este problema. / [CAT] En aquesta tesi doctoral s'estudia el problema de seqüenciació de màquines paral·leles no relacionades amb necessitat d'ajustos i recursos addicionals assignats en els ajustos. En aquest problema, es tenen un grup de tasques (també anomenades treballs), on cadascuna ha de ser processada en una de les màquines paral·leles disponibles. Per processar una tasca després d'una altra en la mateixa màquina, s'ha de fer un ajustament en la màquina. S'assumeix que aquests ajustos en les màquines per a processar una tasca després del processament d'una altra, han de ser realitzats per un recurs addicional limitat (per exemple, operaris). En aquesta tesi doctoral s'estudien dos variants al problema plantejat: 1) considerant el problema com l'únic objectiu de minimitzar el temps màxim de finalització de tots els treballs (makespan), i 2) considerant el problema multi-objectiu minimitzant simultàniament el makespan i el consum màxim de recursos addicionals. Inicialment, es realitza una completa revisió bibliogràfica sobre estudis relacionats amb el problema plantejat. En esta revisió es detecta que, tot i existir nombrosos estudis de seqüenciació de màquines paral·leles, hi ha molts pocs que tenen en compte recursos addicionals. Posteriorment, per introduir el problema a estudiar abans de plantejar mètodes de resolució, es realitza una breu explicació dels principals problemes de seqüenciació de màquines paral·leles. El problema d'un sol objectiu està classificat com NP-Hard. Per això, per abordar la seua resolució s'han dissenyat i implementat heurístiques y metaheurístiques seguint dos enfocs diferents. El primer enfoc ignora la informació sobre el consum de recursos en la fase constructiva, adaptant dos dels millors algoritmes existents en la literatura per al problema de seqüenciació de màquines paral·leles amb ajustaments sense necessitat de recursos. Per al segon enfoc si es té en compte la informació sobre el consum de recursos en la fase constructiva. Després d'analitzar els resultats dels experiments computacionals realitzats, concloem que hi ha diferencies entre els dos enfocs, sent significativament millor l'enfoc que té en compte la informació sobre el recursos. De la mateixa manera que en el cas d'un sol objectiu, la complexitat del problema multi-objectiu obliga a presentar algoritmes heurístics o metaheurístics per a resoldre-ho. En aquesta tesi es presenta un nou algoritme metaheurístic multi-objectiu eficient per trobar bones aproximacions a la frontera de Pareto del problema. A més, es van adaptar altres tres algoritmes que han mostrat bons resultats en diferents estudis de problemes de seqüenciació de màquines multi-objectiu. Després de realitzar experiments computacionals exhaustius, concloem que el nou algoritme proposat en aquesta tesi és significativament millor que els altres tres algoritmes existents i que s'han adaptat per resoldre aquest problema. / [EN] In this thesis we study the unrelated parallel machine scheduling problem with setup times and additional limited resources in the setups. In this problem, we have a group of tasks (also called jobs), where each one must be processed on one of the available parallel machines. To process one job after another on the same machine, a setup must be made on the machine. It is assumed that these setups on machines must be made by a limited additional resource (eg, operators). In this thesis two variants of the problem are studied: 1) considering the problem with the objective of minimizing the maximum completion time of all jobs (makespan), and 2) considering the multi-objective problem, minimizing the makespan and the maximum consumption of additional resources. Initially, a complete literature review is carried out on studies related to the problem addressed in this thesis. This review finds that despite numerous parallel machine scheduling studies, there are very few that take into account additional resources. Subsequently, to introduce the problem addressed before proposing resolution methods, a brief explanation of the main parallel machines scheduling problems is made. The problem with a single objective is classified as NP-Hard. Therefore, to solve it, heuristics and metaheuristics have been designed and implemented following two different approaches. For the first approach, which ignores the information on the consumption of resources in the construction phase, two of the best algorithms existing in the literature for the problem of parallel machines with setups without additional resources are adapted. For the second approach, which does take into account information on the consumption of resources in the construction phase, new heuristic and metaheuristic algorithms are proposed to solve the problem. Following the results of the computational experiments, we conclude that there are differences between the two approaches, the approach that takes into account the information on resources being significantly better. As in the case of a single objective, the complexity of the multi-objective problem requires the formulation of heuristic or metaheuristic algorithms to solve it. In this thesis, a new efficient multi-objective metaheuristic algorithm is presented to find good approximations to the Pareto front of the problem. In addition, three other algorithms that have shown good results in different studies of multi-objective machine scheduling problems were adapted. After carrying out exhaustive computational experiments, we concluded that the new algorithm proposed in this thesis is significantly better than the other three adapted algorithms. / Yepes Borrero, JC. (2020). Secuenciación de máquinas con necesidad de ajustes y recursos adicionales [Tesis doctoral]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/158742 / TESIS

O presente trabalho trata do problema integrado de dimensionamento e sequenciamento de lotes de produção. O processo de dimensionar e sequenciar lotes de produção consiste em determinar quanto produzir de cada produto e a sequência de produção desses lotes em cada máquina a cada período a fim de atender a uma demanda prevista sob as condições e capacidades operacionais existentes. O caso estudado nesse trabalho aborda o cenário de uma empresa de grande porte da indústria de bens de consumo de higiene pessoal, um mercado bastante concorrido no qual o bom nível de serviço de atendimento e a gestão de custos mostram-se essenciais na competição pelos clientes. Nessa empresa, existe um ambiente operacional complexo, composto por máquinas distintas em paralelo com capacidade limitada de produção cujos tempos de preparação (setup) são dependentes da sequência de produção, além de uma restrição de capacidade de armazenagem dos produtos fabricados, característica não encontrada na literatura existente. Os clientes permitem que ocorram atrasos de atendimento da demanda, porém isso é extremamente indesejável. Esse tipo de problema é NP-difícil, sendo geralmente tratado na literatura por heurísticas. Nesse trabalho, elaboramos nove diferentes estratégias de resolução baseadas na heurística relax-and-fix. O objetivo é, não somente resolver um problema real complexo, como também avaliar se o modo de articionamento e a sequência de resolução dos subproblemas influencia no desempenho da heurística. Os testes computacionais foram conduzidos em instâncias geradas aleatoriamente e em casos reais. Os resultados mostraram um bom desempenho e robustez da abordagem proposta. Técnicas alternativas foram aplicadas na estratégia com os melhores resultados para potencializar seu desempenho. / This work adresses the integrated lot sizing and scheduling problem. The process of lot sizing and scheduling consists of determining how much to produce of each product and the scheduling of these lots in each machine in order to meet the demand under existing restrictions and operational capabilities. The case studied in this work describes the scenario of a big company in the industry of consumer goods for personal hygiene, a very competitive market in which the good service level for customers and the cost management show up in the competition for the clients. In this company, there is a complex operational environment, composed of distinct parallel machines with limited production capacity and sequence dependente setup times. There is also a limited finished goods storage capacity, a characteristic not found in the existing literature. Backordering is allowed but it is extremely undesirable. This problem is NP-hard and it has been treated by heuristics in the literature. In this work, we developed nine different solving strategies based on the relax-and-fix heuristics. The aim of this approach is not only to solve a complex real problem but also assess whether the form of partitioning and the sequence of solving the subproblems influences the performance of the relax-and-fix heuristics. The computational experiments were conducted on ramdomly generated instances and real problems. The results showed the good performance and the robustness of the proposed approach. Alternative techniques were applied in the strategy with the best results in the previous tests to enhance its performance.

The economy of a developing nation like India depends on various sectors such as: Agriculture, Commerce and Industries, Finance, Communication and Information Technology, etc. The manufacturing industries play a key role in contributing to the economy of a nation. They mainly consist of industries like steel casting, automobiles and other heavy manufacturing. This research study is related to automobile industry and particularly the gear manufacturers. The automobile industry is an important industry from the manufacturing point of view. This is due to the fact that it has deep forward and backward linkages with several key segments of the economy and it has a strong multiplier effect. Hence, it is capable of being the driver of economic growth. The recent trend among the automobile manufacturing organizations is to outsource individual components to sub-contractors and conduct the sub-assemblies and assemblies in-house. Some components like gears are important in terms of quality. So in case of these components the automobile manufacturing organizations normally partially outsource the components. They carry out the important finishing operations in-house. Due to this practice, many micro to medium scale gear manufacturers have emerged as sub-contractors to different automobile manufacturing organizations. There is a high amount of competition among different gear manufacturers. To survive the competition any gear manufacturer must focus on the three major aspects: cost, quality and delivery. The focus in this study is on the delivery aspect. Precisely, this thesis attempts to address the scheduling problems in automobile gear manufacturing by proposing efficient solution methodologies in order to aid the gear manufacturers in the delivery of orders in the form of semi-finished gears, to the customers (i.e. automobile manufacturing organizations). The automobile gear manufacturing process can be broadly divided into three distinct stages, starting from the machining of the gear blanks. These three stages in automobile gear manufacturing are: pre heat treatment (pre-HT), heat treatment (HT) and post heat treatment (post-HT). Out of these three stages, the gear manufacturers carry out the first two stages namely pre-HT and HT, and deliver the semi-finished gears to the automobile manufacturing organizations. As most of the operations are carried out by the gear manufacturers, the real research problem lies in identifying bottleneck operations in both pre-HT and HT stages. By addressing the bottleneck operations, one can expect to have a competitive advantage among the gear manufacturers and in turn among the automobile manufacturing organizations. Since every gear manufacturer is involved in both: the pre-HT stage and the HT stage of gear manufacturing, they will always try to achieve both: throughput (from their own company’s perspective) and due date compliance (from the customer’s i.e. automobile manufacturing organizations’ perspective). In order to meet these two objectives for the gear manufacturer, there are two research problems identified in this thesis based on the bottleneck operations: one at the pre-HT stage and the other at the HT stage. The Research Problem 1, identified in the pre HT stage consists of a variety of machining operations. In all the pre-HT operations, one single gear is processed on a machine at a time. The machines used in these operations are essentially the discrete processors as known in the scheduling literature. Among the different operations carried out in the pre-HT stage, the gear shaving operation is the final operation which takes a relatively longer processing time compared to other operations in this stage. Hence this operation becomes the bottleneck operation and the Research Problem 1 is related to this operation. Normally, there are more than one machines available for carrying out the gear shaving operations. The processing time of a job is independent of the type of machine used (identical parallel machines). However, since automobile gears vary widely in terms of size, all the available machines may not be able to process a given job (machine eligibility restrictions). The jobs are made available for processing as and when the job orders are received from the automobile manufacturing organizations. Thus all the jobs may not be available for processing at the same time (unequal release times or dynamic job arrivals). After a job is completed on a machine, a setup is incurred before processing the next job. The setup operations involve cleaning of the machine, changing of cutting tools and toolings, setting of the machining parameters and fine tuning of the machining parameters. The amount of time required for the setup depends on both, the job that has been completed and the job that is to be processed (sequence dependent setup time). Different jobs will have different priorities depending on the nature of the job order, monetary value of the job and urgency for the next stage (job weights). Since the pre-HT stage is an upstream stage in gear manufacturing, particularly to the heat treatment (HT) stage, the aim of this stage will be to feed the downstream stage as quickly as possible. Hence, a completion time based scheduling objective is considered. Since the release times of jobs are unequal, the flowtime of a job is of interest in determining the throughput. Also, since the jobs have different weights, the weighted flowtime is of significance. Therefore, the scheduling objective for Research Problem 1 is taken as minimizing the total weighted flowtime of the jobs in a scheduling window. A vast amount of literature is available on scheduling of parallel machines. However, to the best of our knowledge, no study has simultaneously addressed the job characteristics: unequal release times, sequence dependent setup times and machine eligibility restrictions for identical parallel machines to minimize the total weighted flowtime. The Research Problem 2 was identified at the HT stage of gear manufacturing. The aim of the HT stage in the metallurgical terms is to achieve case hardening of gears. The types of machines used in the HT stage are essentially the batch processing machines (BPM) or simply batch processors (BP). A BP unlike the discrete processor, can process several different jobs at a time. The constituent jobs that are processed together form a batch in the BP. The different operations of this stage are: hardening and soaking, quenching, tempering and shot blasting. The hardening and soaking operation typically takes a longer processing time (6-18 hours) as compared to the other operations (15 minutes to 90 minutes). Also, being the first operation of the HT stage, once the hardening and soaking operation is completed, the other operations can be streamlined. Hence the scheduling of this bottleneck operation is of managerial importance. The jobs arrive at the hardening and soaking operation as and when they are completed at the pre-HT stage (unequal release times). Different jobs may have different processing requirements corresponding to time and temperature setting. Therefore, although a BP can process multiple jobs at a time, jobs with different processing requirements cannot be processed together. Jobs that can be processed together are grouped in job families. Since jobs of different families cannot be processed together we get the situation of incompatible job families. The BP has a fixed and finite capacity (expressed in terms of mass). Jobs will have different masses – which represents the size of jobs (non-identical job sizes). While constructing a batch, a job can be split in case there is a capacity violation for the BP (job splitting). The same priorities of the jobs (job weights) as in the pre-HT stage, will continue in this stage as well. As the Research Problem 2 deals with downstream stage of the gear manufacturing the objective of scheduling will be efficient delivery of the job to the automobile manufacturing organizations. The non-conformance to the due date will result in tardiness of the job. Also, since the jobs have different weights, the weighted tardiness of a job is of significance. Therefore, the scheduling objective for Research Problem 2 is taken as minimizing the total weighted tardiness (TWT) of the jobs in a scheduling window. Compared to the discrete processors, the scheduling of batch processors is a relatively new field (about two decades old). However, a review of literature reveals that no study has simultaneously addressed in any problem domain, the characteristics: unequal release times, incompatible job families, non-identical job sizes and job splitting for scheduling batch processors to minimize the total weighted tardiness. For Research Problem 1, an integer linear programming (ILP) model is developed. A suitable numerical example is developed and the workability of the proposed ILP model is validated for a small sized problem. The computational intractability of the proposed ILP model is verified empirically. Due to the computational intractability, real life large-size problems cannot be solved using the proposed ILP model. This has motivated us to propose simple heuristic algorithms. Accordingly, ten heuristic algorithms are proposed. Out of these ten proposed heuristic algorithms, five heuristic algorithms allow the use of unforced idleness and the remaining five heuristic algorithms do not allow the use of unforced idleness. In scheduling, unforced idleness is a situation when a machine is kept idle even if there are jobs available for processing. In order to understand the performance of the proposed heuristic algorithms, various factors that can affect the performance of the heuristic algorithms are identified based on the literature as well as based on the knowledge gained from the industry. An experimental design is developed based on the identified factors with different levels. A series of computational experiments has been conducted for absolute evaluation of the heuristic algorithms: (a) in comparison with optimal solution for small size problem instances (there are 96 problem instances) and (b) in comparison with the estimated optimal solution for large size problem instances (there are 2880 problem instances). The evaluation is based on computational time and the quality of the solution. With respect to the computational time, it is observed that the time required for obtaining results from the heuristic algorithms is meager. For evaluating the quality of the solution, the two standard performance measures – Average Relative Percentage Deviation (ARPD) which indicates the average performance of the proposed heuristic algorithms and Maximum Relative Percentage Deviation (MRPD) which indicates the worst case performance of the proposed heuristic algorithms have been used. From the results of the experimental evaluation it is observed that the heuristic algorithms incorporating the information on machine eligibility restrictions along with other job characteristics worked relatively better compared to other proposed heuristic algorithms. It is also observed that system congestion plays an important role in determining the performance of the heuristic algorithms. Hence, a further study based on the effect of system congestion on different heuristic algorithms is carried out. The system congestion effect was controlled using the two problem factors: number of jobs and release time of jobs. The computational experiments were based on a total of 48 problem instances. Based on the results it was inferred that for congested systems, the proposed heuristic algorithms allowing unforced idleness perform better than the corresponding heuristic algorithms not allowing unforced idleness. For Research Problem 2, two situations are examined. The first situation pertains to the micro and small scale gear manufacturers. In this case, the gear manufacturers can have a single batch processor (BP) for the operation: hardening and soaking. The other situation pertains to small and medium scale gear manufacturers, and in this case, there are more than one batch processors with possibly different capacities (multiple non-identical batch processors). For the Research Problem 2 with single BP, an ILP model is developed. A suitable numerical example is developed and the workability of the proposed ILP model is validated for a small sized problem. The computational intractability of the proposed ILP model is verified empirically. Due to the computational intractability it is proposed to develop simple heuristic algorithms. Based on the pilot experimental analysis and based on the fact that allowing unforced idleness gave superior results in case of Research Problem 1, it is decided to incorporate unforced idleness while developing heuristic algorithms for the Research Problem 2 with single BP. Accordingly, three groups of heuristic algorithms are proposed for Research Problem 2 with single BP by allowing unforced idleness – (i) Seven variants of the heuristic algorithms are based on the computation of the weighted tardiness, (ii) Three variants of the heuristic algorithms based on computation of the composite job scores and (iii) Three variants of the heuristic algorithms based on the computation of composite family scores followed by the composite job scores. For evaluating the performance of the thirteen proposed heuristic algorithms various factors that can affect the workability of the heuristic algorithms are identified based on the literature as well as based on the knowledge gained from the industry. An experimental design is developed based on these factors with levels. A series of computational experiments has been conducted for absolute evaluation of the heuristic algorithms: (a) in comparison with optimal solution for small size problem instances (192 problem instances) and (b) in comparison with the estimated optimal solution for large size problem instances (7680 problem instances). The evaluation is based on computational time and the quality of the solution. With respect to the computational time, it is observed that the time required for obtaining results from the heuristic algorithms is meager. For evaluating the quality of the solution, the two standard performance measures – ARPD and MRPD, used in Research Problem 1, could not be used here due to the nature of the scheduling objective: minimizing the TWT (as the TWT tends to zero). Therefore, a suitable performance measure was identified in the literature and suitably modified for the Research Problem 2 with single BP under study. This performance measure gives stable results even when the TWT value approaches zero. From the results of the experimental evaluation it is observed that variants of heuristic algorithms based on accommodation of non-consecutive jobs while batch construction, perform better than the other variants of the heuristic algorithms. Following the research study on single BP sitaution, the multiple non-identical BPs situation of Research Problem 2 is studied. The ILP model proposed for the Research Problem 2 with single BP problem is suitably extended to account for multiple non-identical BPs and the workability of the model is demonstrated. Additionally, the proposed heuristic algorithms for the Research Problem 2 with single BP problem have been suitably modified for the multiple non-identical BP situation. After developing a suitable experimental design for Research Problem 2 with multiple non-identical BPs, a series of computational experiments has been conducted for absolute evaluation of the heuristic algorithms in comparison with the estimated optimal solution for large size problem instances, based on the 7680 problem instances. Similar performance measure as that used in the Research Problem 2 with single BP problem is used. The observations made from the experimental evaluation for the Research Problem 2 with multiple non-identical BPs are similar to and therefore consistent with those made for the Research Problem 2 with single BP problem. Finally, a sensitivity analysis to determine the effect of capacity of batch processor sets (BP sets) in terms of: number of batch processors and capacities of each batch processor, for Research Problem 2, is carried out. That is, considering different combinations of the two factors: number of batch processors and capacities of each batch processor, seven different BP sets are considered for the proposed sensitivity analysis. The effect on the scheduling objective: Total Weighted Tardiness for different problem configurations is studied by conducting computational experiments. It is observed that higher net capacities of the BP sets give a proportionately better advantage as compared to lower net capacities of the BP sets. Proportionately better advantage means that the percentage of improvement observed in the scheduling objective is higher than the percentage increase in the net capacity of the BP set. Another observation made is that for a given net capacity, it is better to have multiple BPs with smaller capacities than a single BP with high capacity. Although the problems pertaining to the gear manufacturing process simultaneously considering many real life situations have been addressed in this study, there are some limitations to it such as addressing of identical parallel machines instead of a general case of unrelated parallel machines (for Research Problem 1) and consideration of only deterministic situations for both the research problems. There are many immediate future research directions for the problem studied in this thesis such as overcoming the limitations mentioned in this study, proposing good lower bounds and additional heuristic algorithms, and coming up with integrating both, Research Problem 1 and Research Problem 2 and proposing solution methodologies for the integrated problem.