The DNA contained in every living cell not only stores the genetic information; it functions in a complex molecular network that can condense, transcribe, replicate and repair genes. The essential role played by the sequence dependent structure and deformability of DNA in these basic processes of life, has received increasing attention over the past years. The present work aims at better understanding sequence dependent elasticity of double stranded DNA elasticity, across biologically relevant length scales. A theoretical description is developed that makes is possible to relate structural, biochemical and biophysical experiments and simulation. It is based on the rigid base–pair chain (rbc) model which captures all basic deformation modes on the scale of individual base–pair (bp) steps. Existing microscopic parametrizations of the rbc model rely on indirect methods. A way to relate them to biochemical experiments is provided by the indirect readout mechanism, where DNA elasticity determines protein–DNA complexation affinities. By correlating theoretical affinity predictions with in vitro measurements in a well–studied test case, different parameter sets were evaluated. As a result a new, hybrid parameter set is proposed which greatly reduces prediction errors. Indirect readout occurs mostly at particular binding subsites in a complex. A statistical marker is developed which localizes indirect readout subsites, by detecting elastically optimized sub-sequences. By a systematic coarse–graining of the rbc to the well–characterized worm–like chain (wlc) model, a quantitative connection between microscopic and kbp scale elasticity is established. The general helical rbc geometry is mapped to an effective, linear ‘on-axis’ version, yielding the full set of wlc elastic parameters for any given sequence repeat. In the random sequence case, structural variability adds conformational fluctuations which are correlated by sequence continuity. The sequence disorder correction to entropic elasticity in the rbc model is shown to coincide with the conformational correction. The results show remarkable overall agree- ment of the coarse–grained with the mesoscale wlc parameters, lending support to the model and to the microscopic parameter sets. A continuum version of the rbc is formulated as Brownian motion on the rigid motion group. Analytic expressions for angular correlation functions and moments of the end–to–end distance distribution are given. In an equivalent Lagrangian approach, conserved quantities along, and the linear response around, a general equilibrium shape are explored. / Die in jeder lebenden Zelle enthaltene DNS speichert nicht nur die genetische Information; Sie funktioniert innerhalb eines komplexen molekularen Netzwerks, das in der Lage ist, Gene zu kondensieren, transkribieren, replizieren und reparieren. Die zentrale Rolle, welche der sequenzabhängigen Struktur und Deformierbarkeit von DNS in diesen grundlegenden Lebensprozessen zukommt, erregte in den letzten Jahren zunehmendes Interesse. Die vorliegende Arbeit hat ein besseres Verständnis der sequenzabhängigen elastischen Eigenschaften von DNS auf biologisch relevanten Längenskalen zum Ziel. Es wird eine theoretische Beschreibung entwickelt, die es ermöglicht, strukturbiologische, biochemische und biophysikalische Experimente und Simulationen in Beziehung zu setzen. Diese baut auf dem Modell einer Kette aus starren Basenpaaren (rbc) auf, das alle wichtigen Deformationsmoden von DNS auf der Ebene von einzelnen Basenpaar (bp)–Schritten abbildet. Bestehende Parametersätze des rbc-Modells beruhen auf indirekten Methoden. Eine direkte Beziehung zu biochemischen Experimenten kann mithilfe des indirekten Auslese-Mechanismus hergestellt werden. Hierbei bestimmt die DNS– Elastizität Komplexierungsaffinitäten von Protein–DNS–Komplexen. Durch eine Korrelation von theoretischen Vorhersagen mit in vitro Messungen in einem gut untersuchten Beispielfall werden verschiedene Parametersätze bewertet. Als Resultat wird ein neuer Hybrid–Parametersatz vorgeschlagen, der die Vorhersagefehler stark reduziert. Indirektes Auslesen tritt meistens an speziellen Teilbindungsstellen innerhalb eines Komplexes auf. Es wird eine statistische Kenngröße entwickelt, die indirektes Auslesen durch Detektion elastisch optimierter Subsequenzen erkennt. Durch ein systematisches Coarse–Graining des rbc-Modells auf das gut charakterisierte Modell der wurmartigen Kette (wlc) wird eine quantitative Beziehung zwischen der mikroskopischen und der Elastizität auf einer kbp-Skala hergestellt. Die allgemeine helikale Geometrie wird auf eine effektive, lineare Version der Kette ‘auf der Achse’ abgebildet. Dies führt zur Berechnung des vollen Satzes von wlc-elastischen Parameters für eine beliebig vorgegebene periodische Sequenz. Im Fall zufälliger Sequenz führt die Strukturvariabilität zu zusätzlichen Konformationsfluktuationen, die durch die Kontinuität der Sequenz kurzreichweitig korreliert sind. Es wird gezeigt, daß die Sequenzunordnungs-Korrektur zur entropischen Elastizität im rbc-Modell identisch ist zur Korrektur der Konformationsstatistik. Die Ergebnisse zeigen eine bemerkenswerte Übereinstimmung der hochskalierten mikroskopischen mit den mesoskopischen wlc-Parameter und bestätigen so die Wahl des Modells und seiner mikroskopischen Parametrisierung. Eine Kontinuumsversion des rbc-Modells wird formuliert als Brownsche Bewegung auf der Gruppe der Starrkörpertransformationen. Analytische Ausdrücke für Winkelkorrelationsfunktionen und Momente der Verteilung des End-zu-End–Vektors werden angegeben. In einem äquivalenten Lagrange-Formalismus werden Erhaltungsgrößen entlang von Gleichgewichtskonformationen und die lineare Antwort in ihrer Umgebung untersucht.

This dissertation is devoted to the modeling, analysis and development of solution approaches for some optimization-related problems encountered in industrial and manufacturing settings. We begin by introducing a special type of traveling salesman problem called "High Multiplicity Asymmetric Traveling Salesman Problem" (HMATSP). We propose a new formulation for this problem, which embraces a flow-based subtour elimination structure, and establish its validity for this problem. The model is, then, incorporated as a substructure in our formulation for a lot-sizing problem involving parallel machines and sequence-dependent setup costs, also known as the "Chesapeake Problem". Computational results are presented to demonstrate the efficacy of our modeling approach for both the generic HMATSP and its application within the context of the Chesapeake Problem. Next, we investigate an integrated lot-sizing and scheduling problem that is encountered in the primary manufacturing facility of pharmaceutical manufacturing. This problem entails determination of production lot sizes of multiple products and sequence in which to process the products on machines, which can process lots (batches) of a fixed size (due to limited capacity of containers) in the presence of sequence-dependent setup times/costs. We approach this problem via a two-stage optimization procedure. The lot-sizing decision is considered at stage 1 followed by the sequencing of production lots at stage 2. Our aim for the stage 1 problem is to allocate batches of products to time-periods in order to minimize the sum of the inventory and backordering costs subject to the available capacity in each period. The consideration of batches of final products, in addition to those for intermediate products, which comprise a final product, further complicates the lot-sizing problem. The objective for the stage 2 problem is to minimize sequence-dependent setup costs. We present a novel unifying model and a column generation-based optimization approach for this class of lot-sizing and sequencing problems. Computational experience is first provided by using randomly generated data sets to test the performances of several variants of our proposed approach. The efficacy of the best of these variants is further demonstrated by applying it to the real-life data collected with the collaboration of a pharmaceutical manufacturing company. Then, we address a single-lot, lot streaming problem for a two-stage assembly system. This assembly system is different from the traditional flow shop configuration. It consists of m parallel subassembly machines at stage 1, each of which is devoted to the production of a component. A single assembly machine at stage 2, then, assembles products after components (one each from the subassembly machines at the first stage) have been completed. Lot-detached setups are encountered on the machines at the first and second stages. Given a fixed number of transfer batches (or sublots) from each of the subassembly machines at stage 1 to the assembly machine at stage 2, our problem is to find sublot sizes so as to minimize the makespan. We develop optimality conditions to determine sublot sizes for the general problem, and present polynomial-time algorithms to determine optimal sublot sizes for the assembly system with two and three subassembly machines at stage 1. Finally, we extend the above single-lot, lot streaming problem for the two-stage assembly system to multiple lots, but still, for the objective of minimizing the makespan. Due to the presence of multiple lots, we need to address the issue of the sequencing of the lots along with lot-splitting, a fact which adds complexity to the problem. Some results derived for the single-lot version of this problem have successfully been generalized for this case. We develop a branch-and-bound-based methodology for this problem. It relies on effective lower bounds and dominance properties, which are also derived. Finally, we present results of computational experimentation to demonstrate the effectiveness of our branch-and-bound-based methodology. Because of the tightness of our upper and lower bounds, a vast majority of the problems can be solved to optimality at root node itself, while for others, the average gap between the upper and lower bounds computed at node zero is within 0.0001%. For a majority of these problems, our dominance properties, then, effectively truncate the branch-and-bound tree, and obtain optimal solution within 500 seconds. / Ph. D.

O sequenciamento e a programação da produção trazem grandes benefícios financeiros às empresas se realizados de forma adequada. Atualmente, soluções generalizadas apresentam resultados aceitáveis, porém têm como consequência benefícios inferiores quando comparados a estudos específicos. O ramo da otimização de resultados possui dois tipos de soluções: as exatas para problemas de menores dimensões e não exatas, ou heurísticas, para problemas de médias e grandes dimensões. Este trabalho apresenta algoritmos exatos do tipo Branch & Bound e Modelos de Programação Linear Inteira Mista para solucionar quatro variações de problemas de scheduling: Fm|block|∑Cjm, Fm|block|∑Tj, Fm|block, Sijk|∑Cjm e Fm|block, Sijk|∑Tj. As abordagens utilizadas são inéditas na literatura e apresentaram resultados animadores para a maioria dos cenários. O limitante para o tempo total de fluxo obteve resposta ótima em 100% dos casos para problemas de até 20 tarefas e 4 máquinas em menos de uma hora. Para o tempo total de atraso, o limitante se mostrou mais eficiente quando os valores das due dates apresentam alta taxa de dispersão. Para os casos com setup, foram elaboradas três variações de limitantes para cada problema. O limitante com setup que apresentou o melhor desempenho foi o que obteve a melhor relação entre o seu valor numérico e seu custo computacional. Os modelos MILP solucionaram 100% dos problemas sem setup para até 20 tarefas e 4 máquinas e para os casos com setup, foram solucionados problemas de até 14 tarefas e 4 máquinas no tempo limite de uma hora. Os testes computacionais mostram a eficiência na redução do número de nós e, consequentemente, no tempo de execução. Portanto, o estudo realizado indica que, para problemas de pequeno porte e médio, os métodos em questão possuem grande potencial para aplicações práticas. / Job Sequence and Programming give benefits both financial and organizational to any company when performed properly. Nowadays, there is still a gap between theory and practice due to solutions that are short in specification. The analyzed problems differ in type and dimension thus modifying its complexity. The results optimization field is divided into two types of solution: the exact solution for minor problems and the non-exact solution for greater dimension problems. The present paper presents exact algorithms to solve the problems Fm|block|∑Cjm, Fm|block|∑Tj, Fm|block, Sijk|∑Cjm by the Branch & Bounds and Mixed Integer Linear Program models. The approaches are new and presented good results for most cases. Bounds for the no-setup total flow time scenario solved 100% of the 20 jobs and 4 machines cases. High dispersion range due dates contributed for the effectiveness of the no-setup total tardiness bound\'s effectiveness. Three different approaches were developed for the setup cases. The best approach aimed to optimize the value/effort factor for the B&B. The Mixed Integer Linear Program models solved 100% of the no-setup cases for 20 jobs and 4 machines. The MILPs setup cases solved optimally 14 jobs and 4 machines cases. Computational tests were executed and analyzed and they highlighted the node count reduction and, consequently, the execution time. The present study points out that the exact methods can be applied to small and medium scheduling problems in practice.

O sequenciamento e a programação da produção trazem grandes benefícios financeiros às empresas se realizados de forma adequada. Atualmente, soluções generalizadas apresentam resultados aceitáveis, porém têm como consequência benefícios inferiores quando comparados a estudos específicos. O ramo da otimização de resultados possui dois tipos de soluções: as exatas para problemas de menores dimensões e não exatas, ou heurísticas, para problemas de médias e grandes dimensões. Este trabalho apresenta algoritmos exatos do tipo Branch & Bound e Modelos de Programação Linear Inteira Mista para solucionar quatro variações de problemas de scheduling: Fm|block|∑Cjm, Fm|block|∑Tj, Fm|block, Sijk|∑Cjm e Fm|block, Sijk|∑Tj. As abordagens utilizadas são inéditas na literatura e apresentaram resultados animadores para a maioria dos cenários. O limitante para o tempo total de fluxo obteve resposta ótima em 100% dos casos para problemas de até 20 tarefas e 4 máquinas em menos de uma hora. Para o tempo total de atraso, o limitante se mostrou mais eficiente quando os valores das due dates apresentam alta taxa de dispersão. Para os casos com setup, foram elaboradas três variações de limitantes para cada problema. O limitante com setup que apresentou o melhor desempenho foi o que obteve a melhor relação entre o seu valor numérico e seu custo computacional. Os modelos MILP solucionaram 100% dos problemas sem setup para até 20 tarefas e 4 máquinas e para os casos com setup, foram solucionados problemas de até 14 tarefas e 4 máquinas no tempo limite de uma hora. Os testes computacionais mostram a eficiência na redução do número de nós e, consequentemente, no tempo de execução. Portanto, o estudo realizado indica que, para problemas de pequeno porte e médio, os métodos em questão possuem grande potencial para aplicações práticas. / Job Sequence and Programming give benefits both financial and organizational to any company when performed properly. Nowadays, there is still a gap between theory and practice due to solutions that are short in specification. The analyzed problems differ in type and dimension thus modifying its complexity. The results optimization field is divided into two types of solution: the exact solution for minor problems and the non-exact solution for greater dimension problems. The present paper presents exact algorithms to solve the problems Fm|block|∑Cjm, Fm|block|∑Tj, Fm|block, Sijk|∑Cjm by the Branch & Bounds and Mixed Integer Linear Program models. The approaches are new and presented good results for most cases. Bounds for the no-setup total flow time scenario solved 100% of the 20 jobs and 4 machines cases. High dispersion range due dates contributed for the effectiveness of the no-setup total tardiness bound\'s effectiveness. Three different approaches were developed for the setup cases. The best approach aimed to optimize the value/effort factor for the B&B. The Mixed Integer Linear Program models solved 100% of the no-setup cases for 20 jobs and 4 machines. The MILPs setup cases solved optimally 14 jobs and 4 machines cases. Computational tests were executed and analyzed and they highlighted the node count reduction and, consequently, the execution time. The present study points out that the exact methods can be applied to small and medium scheduling problems in practice.

[EN] Nowadays, manufacturing systems meet different new global challenges and the existence of a collaborative manufacturing environment is essential to face with. Distributed manufacturing and assembly systems are two manufacturing systems which allow industries to deal with some of these challenges. This thesis studies a production problem in which both distributed manufacturing and assembly systems are considered. Although distributed manufacturing systems and assembly systems are well-known problems and have been extensively studied in the literature, to the best of our knowledge, considering these two systems together as in this thesis is the first effort in the literature. Due to the importance of scheduling optimization on production performance, some different ways to optimize the scheduling of the considered problem are discussed in this thesis. The studied scheduling setting consists of two stages: A production and an assembly stage. Various production centers make the first stage. Each of these centers consists of several machines which are dedicated to manufacture jobs. A single assembly machine is considered for the second stage. The produced jobs are assembled on the assembly machine to form final products through a defined assembly program. In this thesis, two different problems regarding two different production configurations for the production centers of the first stage are considered. The first configuration is a flowshop that results in what we refer to as the Distributed Assembly Permutation Flowshop Scheduling Problem (DAPFSP). The second problem is referred to as the Distributed Parallel Machine and Assembly Scheduling Problem (DPMASP), where unrelated parallel machines configure the production centers. Makespan minimization of the product on the assembly machine located in the assembly stage is considered as the objective function for all considered problems. In this thesis some extensions are considered for the studied problems so as to bring them as close as possible to the reality of production shops. In the DAPFSP, sequence dependent setup times are added for machines in both production and assembly stages. Similarly, in the DPMASP, due to technological constraints, some defined jobs can be processed only in certain factories. Mathematical models are presented as an exact solution for some of the presented problems and two state-of-art solvers, CPLEX and GUROBI are used to solve them. Since these solvers are not able to solve large sized problems, we design and develop heuristic methods to solve the problems. In addition to heuristics, some metaheuristics are also designed and proposed to improve the solutions obtained by heuristics. Finally, for each proposed problem, the performance of the proposed solution methods is compared through extensive computational and comprehensive ANOVA statistical analysis. / [ES] Los sistemas de producción se enfrentan a retos globales en los que el concepto de fabricación colaborativa es crucial para poder tener éxito en el entorno cambiante y complejo en el que nos encontramos. Una característica de los sistemas productivos que puede ayudar a lograr este objetivo consiste en disponer de una red de fabricación distribuida en la que los productos se fabriquen en localizaciones diferentes y se vayan ensamblando para obtener el producto final. En estos casos, disponer de modelos y herramientas para mejorar el rendimiento de sistemas de producción distribuidos con ensamblajes es una manera de asegurar la eficiencia de los mismos. En esta tesis doctoral se estudian los sistemas de fabricación distribuidos con operaciones de ensamblaje. Los sistemas distribuidos y los sistemas con operaciones de ensamblaje han sido estudiados por separado en la literatura. De hecho, no se han encontrado estudios de sistemas con ambas características consideradas de forma conjunta. Dada la complejidad de considerar conjuntamente ambos tipos de sistemas a la hora de realizar la programación de la producción en los mismos, se ha abordado su estudio considerando un modelo bietápico en la que en la primera etapa se consideran las operaciones de producción y en la segunda se plantean las operaciones de ensamblaje. Dependiendo de la configuración de la primera etapa se han estudiado dos variantes. En la primera variante se asume que la etapa de producción está compuesta por sendos sistemas tipo flowshop en los que se fabrican los componentes que se ensamblan en la segunda etapa (Distributed Assembly Permutation Flowshop Scheduling Problem o DAPFSP). En la segunda variante se considera un sistema de máquinas en paralelo no relacionadas (Distributed Parallel Machine and Assembly Scheduling Problem o DPMASP). En ambas variantes se optimiza la fecha de finalización del último trabajo secuenciado (Cmax) y se contempla la posibilidad que existan tiempos de cambio (setup) dependientes de la secuencia de trabajos fabricada. También, en el caso DPMASP se estudia la posibilidad de prohibir o no el uso de determinadas máquinas de la etapa de producción. Se han desarrollado modelos matemáticos para resolver algunas de las variantes anteriores. Estos modelos se han resuelto mediante los programas CPLEX y GUROBI en aquellos casos que ha sido posible. Para las instancias en los que el modelo matemático no ofrecía una solución al problema se han desarrollado heurísticas y metaheurísticas para ello. Todos los procedimientos anteriores han sido estudiados para determinar el rendimiento de los diferentes algoritmos planteados. Para ello se ha realizado un exhaustivo estudio computacional en el que se han aplicado técnicas ANOVA. Los resultados obtenidos en la tesis permiten avanzar en la comprensión del comportamiento de los sistemas productivos distribuidos con ensamblajes, definiendo algoritmos que permiten obtener buenas soluciones a este tipo de problemas tan complejos que aparecen tantas veces en la realidad industrial. / [CAT] Els sistemes de producció s'enfronten a reptes globals en què el concepte de fabricació col.laborativa és crucial per a poder tindre èxit en l'entorn canviant i complex en què ens trobem. Una característica dels sistemes productius que pot ajudar a aconseguir este objectiu consistix a disposar d'una xarxa de fabricació distribuïda en la que els productes es fabriquen en localitzacions diferents i es vagen acoblant per a obtindre el producte final. En estos casos, disposar de models i ferramentes per a millorar el rendiment de sistemes de producció distribuïts amb acoblaments és una manera d'assegurar l'eficiència dels mateixos. En esta tesi doctoral s'estudien els sistemes de fabricació distribuïts amb operacions d'acoblament. Els sistemes distribuïts i els sistemes amb operacions d'acoblament han sigut estudiats per separat en la literatura però, en allò que es coneix, no s'han trobat estudis de sistemes amb ambdós característiques conjuntament. Donada la complexitat de considerar conjuntament ambdós tipus de sistemes a l'hora de realitzar la programació de la producció en els mateixos, s'ha abordat el seu estudi considerant un model bietàpic en la que en la primera etapa es consideren les operacions de producció i en la segona es plantegen les operacions d'acoblament. Depenent de la configuració de la primera etapa s'han estudiat dos variants. En la primera variant s'assumix que l'etapa de producció està composta per sengles sistemes tipus flowshop en els que es fabriquen els components que s'acoblen en la segona etapa (Distributed Assembly Permutation Flowshop Scheduling Problem o DAPFSP). En la segona variant es considera un sistema de màquines en paral.lel no relacionades (Distributed Parallel Machine and Assembly Scheduling Problem o DPMASP). En ambdós variants s'optimitza la data de finalització de l'últim treball seqüenciat (Cmax) i es contempla la possibilitat que existisquen temps de canvi (setup) dependents de la seqüència de treballs fabricada. També, en el cas DPMASP s'estudia la possibilitat de prohibir o no l'ús de determinades màquines de l'etapa de producció. S'han desenvolupat models matemàtics per a resoldre algunes de les variants anteriors. Estos models s'han resolt per mitjà dels programes CPLEX i GUROBI en aquells casos que ha sigut possible. Per a les instàncies en què el model matemàtic no oferia una solució al problema s'han desenrotllat heurístiques i metaheurísticas per a això. Tots els procediments anteriors han sigut estudiats per a determinar el rendiment dels diferents algoritmes plantejats. Per a això s'ha realitzat un exhaustiu estudi computacional en què s'han aplicat tècniques ANOVA. Els resultats obtinguts en la tesi permeten avançar en la comprensió del comportament dels sistemes productius distribuïts amb acoblaments, definint algoritmes que permeten obtindre bones solucions a este tipus de problemes tan complexos que apareixen tantes vegades en la realitat industrial. / Hatami, S. (2016). The Distributed and Assembly Scheduling Problem [Tesis doctoral no publicada]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/64072 / TESIS

本研究將探討非等效平行機台問題中具備順序相依整備時間及不同開始工作時間（Unequal ready-time）之情況，並以最小化總延遲工件權重數為目標值，其目的在改善非等效平行機台問題應用於實際產業中製造環境裡所面對的各項挑戰，如印刷電路板的鑽孔和半導體的測試製程。因本研究欲求解之問題是屬於NP - Hard problems 性質之尋優問題，故利用啟發式方法(heuristics)求解為合適的選擇。此外，本研究計畫開發混合式巨集啟發式方法來求解非等效平行機台問題，主要以禁忌搜尋法為主，在鄰域的搜尋上，也藉由變動鄰域尋優法能夠透過鄰域轉換的機制，進而找出更多好的解。由於啟發式方法對於尋優問題常需花費許多時間來計算才能獲得更好的解，為確保增進求解效率與品質，將針對問題特性開發數種初始解產生法，並也嘗試定義幾個能夠減少尋找鄰近解之鄰域。在後續求解改善的過程中，主要整合變動鄰域(VND)及禁忌(TS)巨集啟發式演算法搜尋最佳解。此外，為了評估本文推導之演算法效能，本研究利用設定之條件隨機產生適量模擬現場狀況的測試情境，進而比較本研究所提出之混合式巨集啟發式方法及標準禁忌搜尋法在不同情境下之表現。 / The problem considered in this paper is a set of independent jobs on unrelated parallel machines with sequence-dependent setup times and with unequal ready times so as to minimize total weighted tardy jobs. These problems can be found in real-life manufacturing environments, such as PCB fabrication drilling operations and semiconductor wafer manufacturing dicing. Since the problems are NP-hard in the strong sense, heuristics are an acceptable practice to finding good solutions. A hybrid meta-heuristics are proposed to solve this scheduling problem. The proposed heuristics belong to a type of solution improvement heuristic; therefore, the heuristics start with an effective initial feasible solution then a meta-heuristic is applied to improve the solution. To enhance both the efficiency and efficacy of the heuristics, several different initial solution generators, based on the characteristics of problems, are developed. The meta-heuristic is a hybrid heuristic integrating the principles of Variable Neighborhood Descent approach (VND) and Tabu Search (TS). In order to evaluate the performance of the proposed heuristics, two sets of large number test scenarios will be designed to simulate practical shop floor problems. Computational experiments will be performed to compare the performance of the proposed heuristics, and a basic tabu search algorithm. The results show the proposed heuristic perform better than the basic tabu search algorithm.