abstract: In this thesis, a single-level, multi-item capacitated lot sizing problem with setup carryover, setup splitting and backlogging is investigated. This problem is typically used in the tactical and operational planning stage, determining the optimal production quantities and sequencing for all the products in the planning horizon. Although the capacitated lot sizing problems have been investigated with many different features from researchers, the simultaneous consideration of setup carryover and setup splitting is relatively new. This consideration is beneficial to reduce costs and produce feasible production schedule. Setup carryover allows the production setup to be continued between two adjacent periods without incurring extra setup costs and setup times. Setup splitting permits the setup to be partially finished in one period and continued in the next period, utilizing the capacity more efficiently and remove infeasibility of production schedule. The main approaches are that first the simple plant location formulation is adopted to reformulate the original model. Furthermore, an extended formulation by redefining the idle period constraints is developed to make the formulation tighter. Then for the purpose of evaluating the solution quality from heuristic, three types of valid inequalities are added to the model. A fix-and-optimize heuristic with two-stage product decomposition and period decomposition strategies is proposed to solve the formulation. This generic heuristic solves a small portion of binary variables and all the continuous variables rapidly in each subproblem. In addition, the case with demand backlogging is also incorporated to demonstrate that making additional assumptions to the basic formulation does not require to completely altering the heuristic. The contribution of this thesis includes several aspects: the computational results show the capability, flexibility and effectiveness of the approaches. The average optimality gap is 6% for data without backlogging and 8% for data with backlogging, respectively. In addition, when backlogging is not allowed, the performance of fix-and-optimize heuristic is stable regardless of period length. This gives advantage of using such approach to plan longer production schedule. Furthermore, the performance of the proposed solution approaches is analyzed so that later research on similar topics could compare the result with different solution strategies. / Dissertation/Thesis / Masters Thesis Industrial Engineering 2015

[ES] Con la globalización de los mercados y el aumento de la competitividad, la coordinación se ha convertido en un punto estratégico en la gestión de la cadena de suministro. De hecho, cada actor de la cadena de suministro ya no debe tomar decisiones sin considerar todos los eslabones, sean proveedores, proveedores de proveedores o clientes y estos internos o externos a la organización. Las cadenas de suministro son cada vez más complejas y distribuidas, compuestas por múltiples organizaciones con diferentes objetivos y políticas. La coordinación se puede lograr utilizando uno de estos dos enfoques para la toma de decisiones coordinadas: centralizada o descentralizada con un mecanismo de coordinación. Pero, las empresas son reacias a compartir información, ya sea por la confidencialidad de los datos o porque los modelos centralizados resultantes son de gran complejidad que dificultan su manejo y actualización. Además, aquellas empresas que buscan tomar decisiones en tiempo real requieren de modelos ligeros y ágiles, que, con toda la información local y coordinada con el resto, permitan tomar decisiones rápidas. Las empresas interesadas en la coordinación descentralizada con un mecanismo de coordinación esperan obtener mejores resultados con respecto a la no coordinación, aunque deberían asumir tener peores resultados que con la coordinación centralizada. Para ello en esta tesis, se han estudiado los distintos mecanismos de coordinación para la toma de decisiones descentralizada, dentro de un entorno del procedimiento de horizontes rodantes y con herramienta de planificación y programación de las operaciones basada en el concepto de stroke, que extiende el concepto de lista de materiales más allá de las estructuras tradicionales. Estos permiten desarrollar la formulación de la programación matemática y los mecanismos de coordinación necesarios para resolver los problemas de planificación de operaciones. Esta tesis se presenta como una secuencia de capítulos, con el objeto de analizar y presentar la propuesta de mecanismo de coordinación distribuido con unos recursos compartidos. Los distintos capítulos han servido de base para la preparación de artículos científicos. Estos artículos han sido presentados en congresos de la materia y remitidos a revistas científicas. / [CAT] Amb la globalització dels mercats i l'augment de la competitivitat, la coordinació s'ha convertit en un punt estratègic en la gestió de la cadena de subministrament. De fet, cada actor de la cadena de subministrament ja no ha de prendre decisions sense considerar totes les baules, siguen proveïdors, sub-proveïdors o clients i aquests interns o externs a l'organització. Les cadenes de subministrament són cada vegada més complexes i distribuïdes, compostes per múltiples organitzacions amb diferents objectius i polítiques. La coordinació es pot aconseguir utilitzant un d'aquests dos enfocaments per a la presa de decisions coordinades: centralitzat o descentralitzat amb un mecanisme de coordinació. Però, les empreses són poc inclinades a compartir informació, ja siga per la confidencialitat de les dades o perquè els models centralitzats resultants són de gran complexitat que dificulten el seu maneig i actualització. A més, aquelles empresa que busquen prendre decisions en temps real requereixen de models lleugers i àgils, que, amb tota la informació local i coordinada amb la resta, permeten prendre decisions ràpides. Les empreses interessades en la coordinació descentralitzada amb un mecanisme de coordinació esperen obtindre millors resultats respecte de la no coordinació encara que haurien d'assumir tindre pitjors resultats que amb la coordinació centralitzada. Per a això en aquesta tesi, s'han estudiat els diferents mecanismes de coordinació per a la presa de decisions descentralitzada, dins d'un entorn d'horitzons rodant i amb eines de planificació i programació de les operacions basada en el concepte de stroke, que estén el concepte de llista de materials més enllà de les estructures tradicionals. Aquests permeten desenvolupar la formulació de la programació matemàtica i els mecanismes de coordinació necessaris per a resoldre els problemes de planificació d'operacions. Aquesta tesi es presenta com una seqüència de capítols, a fi d'analitzar i presentar la proposta de mecanisme de coordinació distribuït amb uns recursos compartits. Els diferents capítols han servit de base per a la preparació d'articles científics. Aquests articles han sigut presentats en congressos de la matèria i remesos a revistes científiques. / [EN] With the globalization of markets and the increase of competitiveness, coordination has become a strategic point in the management of the supply chain. In fact, each actor in the supply chain must no longer make decisions without considering all the links, whether suppliers, sub-suppliers or customers and those internal or external to the organization. Supply chains are increasingly complex and distributed, composed of multiple organizations with different objectives and policies. Coordination can be achieved using one of these two approaches to coordinate decision making: centralized or decentralized with a coordination mechanism. However, companies are reluctant to share information, either because of the confidentiality of the data or because the resulting centralized models are of great complexity that make their management and update them. In addition, those companies that seek to make decisions in real time require lightweight and agile models, which, with all the local information and coordinated with the rest, allow quick decisions. Companies interested in decentralized coordination with a coordination mechanism expect to obtain better results regarding non-coordination although they should assume to have worse results than with centralized coordination. To this end, in this thesis, the different coordination mechanisms for decentralized decision making have been studied, within an environment of rolling horizons and with tools for planning and scheduling operations based on the concept of stroke, which extends the concept of list of materials beyond traditional structures. These allow to develop the formulation of the mathematical programming and the coordination mechanisms necessary to solve the operations planning problems. This thesis is presented as a sequence of chapters, in order to analyse and present the proposal of distributed coordination mechanism with shared resources. The different chapters have served as the basis for the preparation of scientific articles. These articles have been presented at congresses of the subject and submitted to scientific journals. / Rius Sorolla, GV. (2019). Modelos y Algoritmos de Coordinación para la Planificación de Operaciones basadas en el concepto Stroke en Redes de Suministro distribuidas y con alternativas [Tesis doctoral no publicada]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/134017 / TESIS

IKEA Industry has factories in several locations where one location is in Hultsfred, Småland. IKEA Industry Hultsfred produces IKEA:s wardrobe collection PAX. In 2018, 2.8 million wardrobes were manufactured in Hultsfred. This thesis covers the subject of constructing and developing an optimization model which has the same characteristics as the plinth production at IKEA Industry Hultsfred. This means that the optimization model must consider production sequence; the setup time is different depending on which products that have been produced in the machine earlier. The thesis also covers to investigate how much time that is necessary to produce the plinths to Hultsfred, Portugal, and Germany under different circumstances. This thesis also balances inventory levels and setup time. I.e., how the inventory levels are changed if more emphasis is put into minimizing setup time, and the other way around. The results show that lower inventory levels and setup times are achievable over seven days if the production planning technique is changed.

O problema de dimensionamento de lotes com restrições de capacidade (CLSP) consiste em determinar um plano de produção que satisfaça a demanda requerida, respeitando as limitações de capacidade, com o menor custo possível, ou seja, minimizando os custos de produção, estocagem e preparação de máquina. Encontrar uma solução factível para o CLSP, considerando tempo de preparação de máquina, é NP-completo. Nesta dissertação, para a resolução do CLSP, utiliza-se a decomposição de Dantzig-Wolfe e o procedimento de geração de colunas, encontrando bons limitantes inferiores. Duas diferentes estratégias de decomposição são exploradas, decomposição por itens e períodos. Para a obtenção de uma solução inteira para o problema (limitante superior) foram exploradas heurísticas lagrangianas, onde a solução inicial para as heurísticas provém da geração de colunas. Os limitantes obtidos podem ser utilizados em métodos exatos, como por exemplo, em algoritmos do tipo branch-and-price. Experimentos computacionais, baseados em exemplares gerados aleatoriamente, foram realizados e os resultados analisados, as variações dos parâmetros das instâncias foram sugeridas na literatura / The Capacitated Lot Sizing Problem (CLSP) consists in determining a production plan such that all demands are met and the total costs of production, inventory and setup are minimized. Since the problem to find a feasible solution to the CLSP with setup times is NP-complete, large problem instances have been solved by heuristic methods. In this dissertation, we are particularly concerned in using the methodology of Dantzig-Wolfe decomposition and column generation to generate good bounds to the CLSP with setup times and costs. Here, we analyse two types of decomposition which are based on items and time periods (lower bound) and some lagrangian-based heuristics (upper bound). Numerical results based on randomly generated intances suggest that highquality lower bounds are obtained by column generation algorithms, such as well as upper bounds by heuristics. These bounds are useful in exact solution methods, such as branch-and-price algorithms

O problema de dimensionamento de lotes com restrições de capacidade (CLSP) consiste em determinar um plano de produção que satisfaça a demanda requerida, respeitando as limitações de capacidade, com o menor custo possível, ou seja, minimizando os custos de produção, estocagem e preparação de máquina. Encontrar uma solução factível para o CLSP, considerando tempo de preparação de máquina, é NP-completo. Nesta dissertação, para a resolução do CLSP, utiliza-se a decomposição de Dantzig-Wolfe e o procedimento de geração de colunas, encontrando bons limitantes inferiores. Duas diferentes estratégias de decomposição são exploradas, decomposição por itens e períodos. Para a obtenção de uma solução inteira para o problema (limitante superior) foram exploradas heurísticas lagrangianas, onde a solução inicial para as heurísticas provém da geração de colunas. Os limitantes obtidos podem ser utilizados em métodos exatos, como por exemplo, em algoritmos do tipo branch-and-price. Experimentos computacionais, baseados em exemplares gerados aleatoriamente, foram realizados e os resultados analisados, as variações dos parâmetros das instâncias foram sugeridas na literatura / The Capacitated Lot Sizing Problem (CLSP) consists in determining a production plan such that all demands are met and the total costs of production, inventory and setup are minimized. Since the problem to find a feasible solution to the CLSP with setup times is NP-complete, large problem instances have been solved by heuristic methods. In this dissertation, we are particularly concerned in using the methodology of Dantzig-Wolfe decomposition and column generation to generate good bounds to the CLSP with setup times and costs. Here, we analyse two types of decomposition which are based on items and time periods (lower bound) and some lagrangian-based heuristics (upper bound). Numerical results based on randomly generated intances suggest that highquality lower bounds are obtained by column generation algorithms, such as well as upper bounds by heuristics. These bounds are useful in exact solution methods, such as branch-and-price algorithms