Este texto trata de um dos temas fundamentais no planejamento de produção, o problema de dimensionamento de lotes de um único item. Uma descrição sucinta e informal do problema segue abaixo. Considere um intervalo de tempo dividido em períodos e que a cada período de tempo está associada a demanda de um item. Dados os custos e as eventuais restrições na produção e no armazenamento, determine os períodos em que se produzirá e em que quantidade para que as demandas sejam atendidas com o menor custo possível, respeitando as restrições impostas. Apresentamos aqui resultados sobre a estrutura ótima do problema, sobre complexidade e algoritmos para os casos básicos do problema / This text studies one of the core subjects in production planning, the single-item lot-sizing problem. A brief and informal description of this problem follows below. Considering a time interval split into time periods and that there is a demand of an item associated with each time period. Given production and holding costs and possibly production and holding restrictions, determine in which periods the production must occur and in which quantity, in order to attend the demands with a minimum cost, without violate any restriction. Here, it will be shown some results about the optimal structure of the problem, about the complexity and algorithms for the simpler cases

Production planning problems are of paramount importance within supply chain planning, supporting decisions on the transformation of raw materials into finished products. Lot sizing in production planning refers to the tactical/operational decisions related to the size and timing of production orders to satisfy a demand. The objectives of lot-sizing problems are generally economical-related, such as saving costs or increasing profits, though other aspects may be taken into account such as quality of the customer service and reduction of inventory levels. Lot-sizing problems are very common in production activities and an efficient planning of such activities gives the company a clear advantage over concurrent organizations. To that end it is required the consideration of realistic features of the industrial environment and product characteristics. By means of mathematical modelling, such considerations are crucial, though their inclusion results in more complex formulations. Although lot-sizing problems are well-known and largely studied, there is a lack of research in some real-world aspects. This thesis addresses two main characteristics at the lot-sizing context: (a) setup crossover; and (b) perishable products. The former allows the setup state of production line to be carried over between consecutive periods, even if the line is not yet ready for processing production orders. The latter characteristic considers that some products have fixed shelf-life and may spoil within the planning horizon, which clearly affects the production planning. Furthermore, two types of perishable products are considered, according to the duration of their lifetime: medium-term and short-term shelf-lives. The latter case is tighter than the former, implying more constrained production plans, even requiring an integration with other supply chain processes such as distribution planning. Research on stronger mathematical formulations and solution approaches for lot-sizing problems provides valuable tools for production planners. This thesis focuses on the development of mixed-integer linear programming (MILP) formulations for the lot-sizing problems considering the aforementioned features. Novel modelling techniques are introduced, such as the proposal of a disaggregated setup variable and the consideration of lot-sizing instead of batching decisions in the joint production and distribution planning problem. These formulations are subjected to computational experiments in state-of-the-art MILP-solvers. However, the inherent complexity of these problems may require problemdriven solution approaches. In this thesis, heuristic, metaheuristic and matheuristic (hybrid exact and heuristic) procedures are proposed. A lagrangean heuristic addresses the capacitated lot-sizing problem with setup carryover and perishable products. A novel dynamic programming procedure is used to achieve the optimal solution of the uncapacitated single-item lot-sizing problem with setup carryover and perishable item. A heuristic, a fix-and-optimize procedure and an adaptive large neighbourhood search approach are proposed for the operational integrated production and distribution planning. Computational results on generated set of instances based on the literature show that the proposed methods yields competitive performances against other literature approaches. / Problemas de planejamento da produção são de suma importância no planejamento da cadeia de suprimentos, dando suporte às decisões da transformação de matérias-primas em produtos acabados. O dimensionamento de lotes em planejamento de produção é definido pelas decisões tático-operacionais relacionadas com o tamanho das ordens de produção e quando fabricá-las para satisfazer a demanda. Os objetivos destes problemas são geralmente de cunho econômico, tais como a redução de custos ou o aumento de lucros, embora outros aspectos possam ser considerados, tais como a qualidade do serviço ao cliente e a redução dos níveis de estoque. Problemas de dimensionamento de lotes são muito comuns em atividades de produção e um planejamento eficaz de tais atividades, estabelece uma clara vantagem à empresa em relação à concorrência. Para este objetivo, é necessária a consideração de características realistas do ambiente industrial e do produto. Para a modelagem matemática do problema, estas considerações são cruciais, embora sua inclusão resulte em formulações mais complexas. Embora os problemas de dimensionamento de lotes sejam bem conhecidos e amplamente estudados, várias características reais importantes não foram estudadas. Esta tese aborda, no contexto de dimensionamento de lotes, duas características muito relevantes: (a) preservação da preparação total e parcial; e (b) produtos perecíveis. A primeira permite que o estado de preparação de uma linha de produção seja mantido entre dois períodos consecutivos, mesmo que a linha de produção ainda não esteja totalmente pronta para o processamento de ordens de produção. A ultima característica determina que alguns produtos tem prazo de validade fixo, menor ou igual do que o horizonte de planejamento, o que afeta o planejamento da produção. Além disso, de acordo com a duração de sua vida útil, foram considerados dois tipos de produtos perecíveis: produtos com tempo de vida de médio e curto prazo. O ultimo caso resulta em um problema mais apertado do que o anterior, o que implica em planos de produção mais restritos. Isto pode exigir uma integração com outros processos da cadeia de suprimentos, tais como o planejamento de distribuição dos produtos acabados. Pesquisas sobre formulações matemáticas mais fortes e abordagens de solução para problemas de dimensionamento de lotes fornecem ferramentas valiosas para os planejadores de produção. O foco da tese reside no desenvolvimento de formulações de programação linear inteiro-mistas (MILP) para os problemas de dimensionamento de lotes, considerando as características mencionadas anteriormente. Novas técnicas de modelagem foram introduzidas, como a proposta de variáveis de preparação desagregadas e a consideração de decisões de dimensionamento de lotes ao invés de decisões de agrupamento de ordens de produção no problema integrado de planejamento de produção e distribuição. Estas formulações foram submetidas a experimentos computacionais em MILP-solvers de ponta. No entanto, a complexidade inerente destes problemas pode exigir abordagens de solução orientadas ao problema. Nesta tese, abordagens heurísticas, metaheurísticas e matheurísticas (híbrido de métodos exatos e heurísticos) foram propostas para os problemas discutidos. Uma heurística lagrangeana aborda o problema de dimensionamento de lotes com restrições de capacidade, preservação da preparação total e produtos perecíveis. Um novo procedimento de programação dinâmica e utilizado para encontrar a solução ótima do problema de dimensionamento de lotes de um único produto perecível, sem restrições de capacidade e preservação da preparação total. Uma heurística, um procedimento x-and-optimize e uma abordagem por buscas adaptativas em grande vizinhanças são propostas para o problema integrado de planejamento de produção e distribuição. Resultados computacionais em conjuntos de instâncias geradas com base na literatura mostram que os métodos propostos obtiveram performances competitivas com relação a outras abordagens da literatura.

Este texto trata de um dos temas fundamentais no planejamento de produção, o problema de dimensionamento de lotes de um único item. Uma descrição sucinta e informal do problema segue abaixo. Considere um intervalo de tempo dividido em períodos e que a cada período de tempo está associada a demanda de um item. Dados os custos e as eventuais restrições na produção e no armazenamento, determine os períodos em que se produzirá e em que quantidade para que as demandas sejam atendidas com o menor custo possível, respeitando as restrições impostas. Apresentamos aqui resultados sobre a estrutura ótima do problema, sobre complexidade e algoritmos para os casos básicos do problema / This text studies one of the core subjects in production planning, the single-item lot-sizing problem. A brief and informal description of this problem follows below. Considering a time interval split into time periods and that there is a demand of an item associated with each time period. Given production and holding costs and possibly production and holding restrictions, determine in which periods the production must occur and in which quantity, in order to attend the demands with a minimum cost, without violate any restriction. Here, it will be shown some results about the optimal structure of the problem, about the complexity and algorithms for the simpler cases

Nesta dissertação abordamos o problema de dimensionamento e sequenciamento de lotes com aceitação de pedidos. As demandas dos clientes são agregadas em pedidos, os quais podem ou não ser aceitos e devem ser entregues dentro de uma janela de tempo. Os itens são perecíveis e podem permanecer no estoque somente por um tempo determinado (shelf-life). O objetivo do problema é maximizar a receita gerada pelo atendimento dos pedidos, descontando os custos de estoque e das preparações da máquina. Para tratar o problema são propostas formulações matemáticas e abordagens heurísticas contendo uma etapa construtiva seguida por uma heurística de melhoramento. Testes computacionais foram realizados e os resultados obtidos foram analisados. As heurísticas obtiveram desempenho superior ao branch-and-cut do solver de otimização na obtenção de soluções de boa qualidade, no limite de tempo estabelecido. / In this dissertation, we approach the lot sizing and scheduling problem with order acceptance. Customers demands are aggregated into orders, which may or may not be accepted and must be delivered within a time window. The items are perishable and can remain in inventory only for a limited time (shelf-life). The aim of the problem is profit maximizing generated by orders acceptance, discounting inventory and machine setups costs. To deal with this problem math formulations, constructive and improvement heuristics were proposed. Computational tests were performed and the results obtained were analyzed. The heuristics obtained superior performance then branch-and-cut of the optimization solver obtaining good quality solutions within the established time limit.

Orientador: Adriana Cristina Cherri Nicola / Banca: Silvio Alexandre de Araujo / Banca: Sonia Cristina Poltroniere Silva / Resumo: Este trabalho aborda o Problema de Redimensionamento de Lotes (PRL) capacitado, com múltiplos produtos e máquinas paralelas. O redimensionamento de lotes é uma variação do problema de dimensionamento de lotes que pode ser identificado em sistemas produtivos com elevada taxa de interrupções, como quebras, refugos, entre outros, fazendo com que o plano de produção seja prejudicado, necessitando de atualizações a medida que ocorrem as interrupções. São considerados três parâmetros de interrupção: manutenção corretiva, mão de obra insuficiente e indisponibilidade de matéria-prima. É permitido o atendimento da demanda nos períodos com atrasos e utilização de hora extra. O problema tem por objetivo minimizar os custos de preparação, estoque, atraso e hora extra. Baseado em um modelo matemático proposto na literatura para resolver problemas de dimensionamento de lotes, um modelo matemático para representar o PRL foi proposto. O PRL foi formulado como um problema de programação linear inteira mista (PLIM) e resolvido através do método exato branch and bound. Testes computacionais foram realizados com exemplares adaptados da literatura e abrangem os três parâmetros de interrupção / Abstract: This work approaches the capacitated Lot Resizing Problem (LRP) with multi-products and parallel machines. The lot resizing problem is a lot sizing problem variation which can be identified in productive systems with high rate of interruptions, as breaks, refuse, and others, impairing the planning production and making update needed as soon as interruptions happens. Three parameters for interruption were considered: corrective maintenance, insufficient man power and unavailability of raw material. Demand can be performed with back-orders and overtime requests. This work has the objective of minimize inventory holding costs, back-orders, setup and overtime costs. Based on a mathematical model proposed in the literature to solve the lot sizing problem, a mathematical model to represent the LRP was proposed. The LRP was formulated as a mixed integer problem and solved by branch and bound exact method. Computational experiments were performed with adapted literature instances embracing the three parameters of interruption / Mestre

Dans cette thèse, nous traitons des problèmes d'intégration des décisions prises aux niveaux planification (tactique) et ordonnancement (opérationnel). Que ce soit en théorie ou en pratique, ces deux niveaux sont habituellement traités indépendamment l'un de l'autre. Ainsi, les objectifs de production à réaliser sont souvent incohérents avec la capacité réelle de l'atelier. Cette thèse propose des méthodes de résolution pour des problèmes intégrés de planification et d'ordonnancement. Nous développons un nouveau modèle mathématique qui prend en compte de manière originale les contraintes de séquencement des opérations sur les machines, garantissant ainsi la faisabilité du plan de production. Ce modèle est résolu à l'aide d'une heuristique Lagrangienne pour une séquence des opérations axée. Notre approche est originale à double titre : dans la mise à jour des multiplicateurs Lagrangiens (puisque il existe un nombre exponentiel de contraintes de capacité dans notre modèle), et par la proposition d'une nouvelle procédure de lissage pour la construction d'une solution réalisable. Nous développons ensuite deux approches, basées sur le recuit simulé et la recherche taboue, qui permettent d'améliorer la séquence des opérations sur les ressources et ainsi de chercher un plan de production optimal associé à une séquence réalisable. De nombreux résultats expérimentaux ont été effectués et valident l'efficacité de nos approches.

L'évolution de l'environnement des entreprises a transformé la nature des relations entre elles, qui de simple relations d'achat entre clients et fournisseurs se sont transformées en des rapports plus contractualisés et plus durables. Ces derniers imposent à ces entreprises de revoir leurs méthodes de gestion et de production pour une meilleure synchronisation de leurs flux. Nous nous intéressons dans ce mémoire à une relation particulière entre clients et fournisseurs, celle fondée sur le principe de livraisons cycliques, selon lequel le fournisseur s 'engage à livrer des quantités de produits à des intervalles de temps fixes et de façon répétitive. L'intérêt de ce mode de livraison et qu'il permet, aux donneurs d'ordres, une gestion extrêmement simple des approvisionnements et facilite l'organisation des activités. Comme réponse à ce type de livraisons et afin de synchroniser leurs flux de production à ceux de livraisons, les entreprises adoptent la production cyclique. L'avantage de cette dernière est qu ;elle permet entre autres de réduire les coûts engendrés par la fabrication, et de simplifier l'organisation du travail. Notre travail consiste alors en l'évaluation et la mise en oeuvre d'un plan de production cyclique, pour un atelier de type Flow Shop pur fabricant plusieurs produits, lorsque les appels de livraisons sont cycliques. Nous proposons une nouvelle méthode déterminant un plan de production cyclique minimisant des coûts de lancements, coûts de stockage et des coûts de fabrication. Nous introduisons dans un premier temps le contexte -de notre travail en précisant les différentes hypothèses que 1 'on pose. Nous proposons par la suite une revue de la littérature sur les différents travaux réalisés, et proposons une classification des problèmes traitant de la production cyclique étudiés par la communauté scientifique. Nous exposons également la méthode que l'on propose pour la détermination d'un plan de production cyclique minimisant les différents coûts que l'on considère. Nous présentons une analyse des résultats issus de l'application de notre approche ainsi que ses variantes sur un ensemble de benchmarks générés aléatoirement et respectant les traits caractéristiques des problèmes réels. Nous réalisons une étude comparative d?s approches que l'on propose à 1 'une de celles proposées dans la littérature. Nous terminons ce mémoire par une conclusion et un ensemble de voies de recherches futures.

In this thesis, we study a series of closely related multi-stage stochastic programming models in production planning, from both a modeling and an algorithmic point of view. We first consider a very simple multi-stage stochastic lot-sizing problem, involving a single item with no fixed charge and capacity constraint. Although a multi-stage stochastic integer program, this problem can be shown to have a totally unimodular constraint matrix. We develop primal and dual algorithms by exploiting the problem structure. Both algorithms are strongly polynomial, and therefore much more efficient than the Simplex method. Next, motivated by applications in semiconductor tool planning, we develop a general capacity planning problem under uncertainty. Using a scenario tree to model the evolution of the uncertainties, we present a multi-stage stochastic integer programming formulation for the problem. In contrast to earlier two-stage approaches, the multi-stage model allows for revision of the capacity expansion plan as more information regarding the uncertainties is revealed. We provide analytical bounds for the value of multi-stage stochastic programming over the two-stage approach. By exploiting the special simple stochastic lot-sizing substructure inherent in the problem, we design an efficient approximation scheme and show that the proposed scheme is asymptotically optimal. We conduct a computational study with respect to a semiconductor-tool-planning problem. Numerical results indicate that even an approximate solution to the multi-stage model is far superior to any optimal solution to the two-stage model. These results show that the value of multi-stage stochastic programming for this class of problem is extremely high. Next, we extend the simple stochastic lot-sizing model to an infinite horizon problem to study the planning horizon of this problem. We show that an optimal solution of the infinite horizon problem can be approximated by optimal solutions of a series of finite horizon problems, which implies the existence of a planning horizon. We also provide a useful upper bound for the planning horizon.

The focuses of this dissertation are problems of batch production scheduling problems for perishable products with setup times, with the main applications in answering production planning problems faced by manufacturers of perishable products, such as beers, vaccines and yoghurts. The benefits of effective production plans can help companies reduce their total costs substantially to gain the competitive advantages without reduction of the service level in a globalize economy. We develop concepts and methodologies that are applied in two fundamental problems: (i) the batch production scheduling problem for perishable products with sequence-independent setup times (BPP-SI) and (ii) the batch production scheduling problem for perishable products with sequence-dependent setup times (BPP-SD). The problem is that given a set of forecast demand for perishables products to be produced by a set of parallel machines in the single stage of batch production, with each product having fixed shelf-life times and each machine requiring setup times before producing a batch of product, find the master production schedule which minimizes total cost over a specified time horizon. We present the new models for both problems by formulating them as a Mixed Integer Program (MIP) on the discrete time. Computational studies in BPP-SI and BPP-SD for industrial problems are presented. In order to efficiently solve the large BPP-SI problems in practice, we develop the five efficient heuristics. The extensive computational results show that the developed heuristics can obtain the good solution for the very large problem size and require very short amount of computational time.

Coordinated lot sizing problems, which assume a joint setup is shared by a product family, are commonly encountered in supply chain contexts. Total system costs include a joint set-up charge each time period any item in the product family is replenished, an item set-up cost for each item replenished in each time period, and inventory holding costs. Silver (1979) and subsequent researchers note the occurrence of coordinated replenishment problems within manufacturing, procurement, and transportation contexts. Due to their mathematical complexity and importance in industry, coordinated lot-size problems are frequently studied in the operations management literature. In this research, we address both uncapacitated and capacitated variants of the problem. For each variant we propose new problem formulations, one or more construction heuristics, and a simulated annealing metaheuristic (SAM). We first propose new tight mathematical formulations for the uncapacitated problem and document their improved computational efficiency over earlier models. We then develop two forward-pass heuristics, a two-phase heuristic, and SAM to solve the uncapacitated version of the problem. The two-phase and SAM find solutions with an average optimality gap of 0.56% and 0.2% respectively. The corresponding average computational requirements are less than 0.05 and 0.18 CPU seconds. Next, we propose tight mathematical formulations for the capacitated problem and evaluate their performance against existing approaches. We then extend the two-phase heuristic to solve this more general capacitated version. We further embed the six-phase heuristic in a SAM framework, which improves heuristic performance at minimal additional computational expense. The metaheuristic finds solutions with an average optimality gap of 0.43% and within an average time of 0.25 CPU seconds. This represents an improvement over those reported in the literature. Overall the heuristics provide a general approach to the dynamic demand lot-size problem that is capable of being applied as a stand-alone solver, an algorithm embedded with supply chain planning software, or as an upper-bounding procedure within an optimization based algorithm. Finally, this research investigates the performance of alternative coordinated lotsizing procedures when implemented in a rolling schedule environment. We find the perturbation metaheuristic to be the most suitable heuristic for implementation in rolling schedules.