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High electricity prices have become the title of several news articles recently in Sweden and the prices have experienced large sudden fluctuations during certain periods. In this thesis work, a smart control model for the electricity usage in three different households has been developed with the main purpose to minimize the electricity cost. This has been implemented by using mixed-integer linear programming (MILP) to optimize the cost 24 hours ahead, and by forecasting two of the main inputs; the load and the electricity spot prices for bidding zone three (SE3) in Sweden. The units included in the model are the photovoltaic system, the batteries, the electricity consumption in the house and the electric vehicles. However, the main task of the smart control was to determine when and in which amount the energy should flow from one unit to another, or to/from the grid. In other words, it decides the charging/discharging of the batteries, the selling/buying of electricity and the charging of the electric vehicle (EV). Different amounts of cost savings/profits have been obtained when applying the smart control on the three houses, which have different annual consumption, capacities of the components, heating systems and more. The results showed that it is most optimal to run the model between the time interval 13.00-00.00, when the spot prices for the next day are known, in order to avoid the remarkable impact accompanied with the use of forecasted electricity prices as input to the model. The forecasting of the load is, on the other hand, required to run the model, but this thesis showed that the effect of the uncertainties in this forecast is relatively small. Three types of machine learning methods were implemented to perform the forecasts, namely linear regression (LR), decision tree regression and random forest regression. After measuring especially the mean absolute error (MAE) to validate the results, the random forest regression showed the least error and the other methods showed close results when looking at the electric load prognosis.

For unmanned vehicles, autonomy means that the vehicle’s route can be planned and executed according to some pre-defined rules in the absence of human intervention. Autonomous vehicles (AVs) have become a common type of vehicle for various kinds of transport, for example autonomous forklifts within a warehouse environment. Volvo Autonomous Solution (VAS) works with autonomous vehicles in different areas. To better understand how different methods can be used for planning of autonomous vehicles, VAS initiated this project. To increase the efficiency of AVs, several problems can be examined. One such problem is the allocation problem, also called Multi-Robot Task Allocation, which aims to find out which vehicle should execute which task to achieve a global goal cooperatively. The AVs used by VAS handle Planning Missions (PMs). A PM is, for example, to move goods from a loading point to an unloading point. So, the problem examined in this study is how to assign PMs to vehicles in the most efficient way. The thesis also includes a collection of publications on the area. The problem is solved by using three methods: Mixed Integer Linear Programming (MILP), a Genetic Algorithm that was originally proposed for task assignment in a warehouse environment (GA – Warehouse), and a Genetic Algorithm that was initially proposed for train scheduling (GA – Train). With the MILP method, the problem has been formulated mathematically and the method guarantees an optimal solution. However, the major drawback of this approach is the large computational time required to retrieve a solution. The GA – Warehouse method has a quite simple allocation process but a more complicated path planning part and is, in its entirety, not as flexible as the other methods. The GA – Train method has a lower computational time and can consider many different aspects. All three methods generate similar solutions for the limited set of simple scenarios in this study, but an optimal solution can only be guaranteed by the MILP method. Regardless of which method is used, there is always a trade-off: a guarantee of the optimal solution at the expense of high computational time or a result where no optimal solution can be guaranteed but can be generated quickly. Which method to use depends on the context, what resources are available, and what requirements are placed on the solution. / <p>Examensarbetet är utfört vid Institutionen för teknik och naturvetenskap (ITN) vid Tekniska fakulteten, Linköpings universitet</p>

A crucial challenge introduced by the decentralized installations of photovoltaic (PV) systems in the residential sector, is the mismatch between PV electricity generation and the load curve for energy consumption. To overcome this incompatibility between production and consumption, energy storage and demand response are seen as effective solutions. Smart meters and the installation of intelligent smart appliances in homes have paved the way for efficient energy consumption monitoring and active household load control in the residential sector.  The aim of the thesis work is to develop a dynamic energy management algorithm tailored to optimize the energy consumption pattern of controllable household assets to maximize PV selfconsumption. A rolling horizon algorithm based dynamic model was designed using mixedinteger linear programming (MILP) and later compared with the baseline model to understand the real-time operational benefits of the rolling horizon approach.  Analyzing device scheduling patterns based on the feed-in-tariff showed considerable differences in the scheduling approach for both optimization models. A comparative analysis was conducted to understand the system benefits offered by both optimization models under different feed-in-tariff structures. Higher self-consumption rates were achieved through annual scheduling approach, but it does not reflect the real-time operation of the systems in the household. A rolling horizon optimization reflects the real-time operation of the energy system and has a lower self-consumption rate due to a limited optimization horizon. The method indicates the significant potential of self-consumption specially in lieu of decreasing feed-in tariffs. / En viktig utmaning som de decentraliserade installationerna av solcellssystem i bostadssektorn innebär är att elproduktionen från solcellerna inte stämmer överens med belastningskurvan för energiförbrukningen. För att komma till rätta med denna oförenlighet mellan produktion och konsumtion ses energilagring och efterfrågeflexibilitet som effektiva lösningar. Smarta mätare och installation av intelligenta smarta apparater i hemmen har banat väg för effektiv övervakning av energiförbrukningen och aktiv styrning av hushållens belastning i bostadssektorn.  Syftet med avhandlingen är att utveckla en dynamisk energihanteringsalgoritm som är skräddarsydd för att optimera energiförbrukningsmönstret för kontrollerbara hushållstillgångar för att maximera självförbrukningen av solceller. En dynamisk modell baserad på en algoritm med rullande horisont utformades med hjälp av blandad linjär programmering (MILP) och jämfördes senare med basmodellen för att förstå de operativa realtidsfördelarna med metoden med rullande horisont. Analysen av schemaläggningsmönster för enheter baserat på inmatningstariffen visade att det fanns betydande skillnader i schemaläggningsmetoden för båda optimeringsmodellerna. En jämförande analys genomfördes för att förstå de systemfördelar som erbjuds av de båda optimeringsmodellerna under olika strukturer för inmatningstariffer. Högre självförbrukningsnivåer uppnåddes genom den årliga schemaläggningsmetoden, men den återspeglar inte realtidsdriften av systemen i hushållet. En optimering med rullande horisont återspeglar energisystemets drift i realtid och har en lägre självförbrukningsgrad på grund av en begränsad optimeringshorisont. Metoden visar på den betydande potentialen för självförbrukning speciellt i stället för minskande inmatningstariffer.

Tesis por compendio / [ES] La innovación en los métodos de trabajo con nuevos sistemas de producción ajustados, sostenibles y resilientes, así como la gestión tecnológica eficaz son las tendencias actuales para mejorar el rendimiento en las organizaciones. Así, esta tesis doctoral investiga las contribuciones teóricas y formula un modelo conceptual con el uso de herramientas de fabricación ajustada o lean manufacturing (LM) y de la industria 4.0 (I4.0) para procesos de planificación de la producción en las cadenas de suministro. Además, se utiliza la optimización como tecnología facilitadora de la I4.0 para desarrollar la propuesta de solución. La metodología que se utiliza es bibliográfica, exploratoria y experimental; se aplican técnicas de investigación operativa, normalización de datos y casos de estudio en empresas industriales. Como punto de partida se revisa la literatura existente relacionada con la LM y las tecnologías de la I4.0 en el contexto de la cadena de suministro. Seguidamente, se diseña un modelo conceptual denominado LSCP 4.0 para facilitar la toma de decisiones en los niveles de decisión estratégico, táctico y operativo. Se trata de una relación estructurada entre los paradigmas lean, ágil, sostenible, resiliente y flexible para mejorar el rendimiento de las cadenas de suministro mediante la aplicación de las tecnologías facilitadoras de I4.0. Basado en esto, se propone un modelo matemático de optimización lineal entera-mixta, denominado LSCP 4.0, para maximizar los beneficios y planificar simultáneamente la producción, inventario de materiales y productos terminados satisfaciendo la demanda proveniente de previsiones y pedidos en firme en una cadena de suministro de cinco niveles. Novedosamente, se combinan enfoques de producción de just in time (JIT) y planificación de requerimientos de materiales (MRP). Ambos modelos para LSCP 4.0, i.e., conceptual y matemático, se validan en casos de estudio reales de la industria de calzado. Adicionalmente, se considera el uso de otra tecnología facilitadora de la I4.0 como la computación en nube para abordar el problema del intercambio de información entre los nodos de la cadena de suministro. Así, se propone un modelo de datos normalizado para la fabricación colaborativa en la nube aplicado a la industria del calzado. / [CA] La innovació en els mètodes de treball amb nous sistemes de producció ajustats, sostenibles i resilients, així com la gestió tecnològica eficaç són les tendències actuals per a millorar el rendiment en les organitzacions. Així, aquesta tesi doctoral investiga les contribucions teòriques i formula un model conceptual amb l'ús d'eines de fabricació ajustada o lean manufacturing (LM) i de la indústria 4.0 (I4.0) per a processos de planificació de la producció en les cadenes de subministrament. A més, s'utilitza l'optimització com a tecnologia facilitadora de la I4.0 per a desenvolupar la proposta de solució. La metodologia que s'utilitza és bibliogràfica, exploratòria i experimental; s'apliquen tècniques d'investigació operativa, normalització de dades i casos d'estudi en empreses industrials. Com a punt de partida es revisa la literatura existent relacionada amb laLM i les tecnologies de la I4.0 en el context de la cadena de subministrament. Seguidament, es dissenya un model conceptual denominat LSCP 4.0 per a facilitar la presa de decisions en els nivells de decisió estratègic, tàctic i operatiu. Es tracta d'una relació estructurada entre els paradigmes lean, àgil, sostenible, resilient i flexible per a millorar el rendiment de les cadenes de subministrament mitjançant l'aplicació de les tecnologies facilitadores d'I4.0. Basat en això, es proposa un model matemàtic d'optimització lineal entera-mixta, denominat LSCP 4.0, per a maximitzar els beneficis i planificar simultàniament la producció, inventari de materials i productes acabats satisfent la demanda provinent de previsions i comandes en ferma en una cadena de subministrament de cinc nivells. Novament, es combinen enfocaments de producció de just in time (JIT) i planificació de requeriments de materials (MRP). Tots dos models per a LSCP 4.0, i.e., conceptual i matemàtic, es validen en casos d'estudi reals de la indústria de calçat. Addicionalment, es considera l'ús d'una altra tecnologia facilitadora de la I4.0 com la computació en núvol per a abordar el problema de l'intercanvi d'informació entre els nodes de la cadena de subministrament. Així, es proposa un model de dades normalitzat per a la fabricació col·laborativa en el núvol aplicat a la indústria del calçat. / [EN] Innovation in working methods with new lean, sustainable and resilient production systems, as well as effective technology management, are current trends to improve performance in organisations. This PhD thesis investigates the theoretical contributions and formulates a conceptual model with the use of lean manufacturing (LM) and Industry 4.0 (I4.0) tools for production planning processes in supply chains (SCs). In addition, optimisation is employed as an enabling technology of I4.0 to develop the proposed solution. The applied methodology is bibliographic, exploratory and experimental; operational research techniques, data standardisation and case studies in industrial companies are applied. As a starting point, the existing literature related to LM and I4.0 technologies in the SC context is reviewed. Then a conceptual model, known as LSCP 4.0, is designed to facilitate decision making at the strategic, tactical and operational decision levels. It is a structured relation among lean, agile, sustainable, resilient and flexible paradigms to improve SCs' performance via the application of I4.0 enabling technologies. Based on this, an integer-mixed linear optimisation mathematical model, termed LSCP 4.0, is proposed to maximise profits and to simultaneously plan production, material inventory and finished goods by satisfying the demand from forecasts and firm orders in a five-tier SC. Novel just-in-time (JIT) production and material requirements planning (MRP) approaches are combined. Both models for LSCP 4.0, i.e., conceptual and mathematical, are validated in real case studies from the footwear industry. The use of another I4.0 enabling technology, such as cloud computing, is considered to address the problem of information exchange between SC nodes. Thus a standardised data model for collaborative manufacturing in the cloud applied to the footwear industry is proposed. / This thesis has been developed at the Research Centre on Production Management and Engineering (CIGIP) of the Universitat Politècnica de Valencia, within the framework of the projects: "Industrial Data Services for Quality Control in Smart Manufacturing (i4Q)" funded by the European Union H2020 Programme with grant agreement No. 958205; the MCIN/AEI/10.13039/501100011033 and by European Union Next GenerationEU/PRTR with grant agreement PDC2022-133957-100); "Industrial production and loginics optimization in industry 4.0 (i40PT)" funded by the Generalitat Valenciana within the framework of the research groups of excellence project PROMETEO/2021/065; "Optimisation of zero-defects production technologies enabling supply chains 4.0 (CADS4.0)" funded by the Spanish Ministry of Science, Innovation and Universities with grant agreement RTI2018-101344-B-100; "Operational Programme of the European Regional Development Fund (ERDF) of the Autonomous Valencian Community 2014-2020" (Ref. IDIFEDER/2018/025); "Resilient, Sustainable and People-Oriented Supply Chain 5.0 Optimisation Using Hybrid Intelligence" (RESPECT) (Ref. CIGE/2021/159); and a PhD grant from the Technical University of Ambato. / Reyes Vásquez, JP. (2024). Conceptual and optimisation modelling for lean supply chain planning in Industry 4.0 [Tesis doctoral]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/203818 / Compendio

本文提出一個新的混合整數線性規劃模型建立投資組合。這個模型所採用的風險函數為最大損失的絕對值，而不是一般常用的損失變異數。在給定的報酬水準下，模型尋找在觀測期間中最小的最大損失的投資組合，即為大中取小的原則。模型也同時考慮實務上常遇見之情況，如：交易成本、最小交易單位、固定交易費用比率、資產總類數等限制。因此，模型內需使用整數變數及二元變數，導致模型的計算求解過程變得比不含整數變數及二元變數的模型困難許多。我們以固定整數變數的啟發式演算法增進求解的效率，並以台灣股票市場的資料做為實證計算的對象。 / A new mixed integer linear program (MILP) for selecting portfolio based on historical return is proposed. This model uses the downside risk rather than the variance as a risk measure. The portfolio is chosen that minimizes the maximum downside risk over all past observation periods to reach a given return level. That is a mini-max principle. The model incorporates the practical characteristics such as transaction costs, minimum transaction units, fixed proportional transaction rates, and cardinality constraint. For this reason a set of integer variables and binary variables are introduced. The introduction, however, increases the computational complexity in model solution. Due to the difficulty of the MILP problem, a heuristic algorithm has been developed for the solution. The computational results are presented by applying the model to the Taiwan stock market.

在全球化的環境下推出新產品，企業除了面臨隨著產品生命週期改變的顧客需求以及成本上的不確定因素外，同時還必須考量全球營運帶來的種種挑戰。 許多供應鏈管理數量模式相關文獻針對全球運籌、新產品供應鏈等議題多有所探討，利用數量模式的計算以反應真實世界中的種種不確定性，讓管理者在供應鏈策略規劃時有所依據，但卻少有同時探討全球運籌以及新產品供應鏈的相關文獻。學者Butler, Ammons, and Sokol認為過去新產品供應鏈模式忽略了新產品將有可能無法存活下來的情形，因此發展一套新產品供應鏈模式，使新產品供應鏈能夠順利從上市成長到成熟階段，並利用此模式決定新設施、新機器購入的時機。 本研究延伸Butler等人之新產品供應鏈模式，考量更完整之全球運籌相關議題，透過混合整數線性規劃描述新產品發展時全球運籌配置問題，並利用情境為基礎的穩健最佳化以取得低風險的供應鏈配置，此外加入可靠度的影響，以彌補供應鏈規劃與實際操作的差距，並加入缺貨之懲罰成本，最後以範例資料進行計算與分析此數量模式，經由模式計算結果發現本研究規劃之結果，相較於原Butler等人之模式有較低的缺貨的發生可能性，且所求得之配置整體可靠度皆有所提升。 本研究所提出之規劃與分析方法可提供決策者在進行新產品全球佈局規劃時，能當作其新產品運籌配置之決策參考。 / When putting out new products under the environment of globalization, enterprise not only faces the uncertain factors in the demand of the customers and the costs that change with product life cycles, but considers all sorts of challenges which come with global operation. Many researches into supply chain quantitative model that probe into global logistics and the new product supply chain employ the quantitative model to reflect all sorts of uncertainty in the real world. They provide managers with the basis for the supply chain strategy and management. But few researches discuss about the global logistics and the new product supply chain simultaneously. Bulter, Ammons, and Sokol argue that the model of new product supply chain of the past neglects the condition which new products may not survive. Thus they developed a new product supply chain model to enable new products to launch the market and grow to maturity as well as decide when to purchase new supply chain facilities and equipments. This research which extends the new product supply chain model of Bulter et al. considers issues on global logistics from a more integrated view. First of all, it solves the global logistic settings problem in new product development by means of mixed-integer linear programming. Secondly, it uses the scenario-based robust optimization to lower the risk in the supply chain design. Then it adds the reliability calculation to make up for the gap between the plan and the real operation. At last it calculates and analyzes the quantitative model on the basis of the case data. This research establishes a methodology for decision makers to apply to plan and analyzing their new product supply chain when they make the global arrangement of new products.

Afin de répondre à la problématique de la régulation multi-objectif et multi-mode des carrefours à feux, nous proposons trois modèles de programmation linéaire mixte en nombres entiers constituant les moteurs d'un système de régulation pleinement adaptatif, ainsi que deux procédures interactives d'optimisation multi-objectif permettant d'adapter itérativement une “politique de régulation” à la situation de trafic. Les critères pris en compte, tous à minimiser, sont le temps d'attente et le nombre d'arrêts des véhicules particuliers, et un critère dédié aux transports en commun permettant de fixer un temps d'attente souhaité pour chaque bus. Des expérimentations ont montré qu'un des trois modèles, dit hybride, se démarque positivement des deux autres. Ce modèle a alors été mis en œuvre avec une des deux procédures interactives, permettant de contrôler un trafic simulé sur une période d'une heure dans différents scénarios types, et comparé à un système de régulation semi-adaptatif. / In order to answer the multi-objective and multi-mode adaptive traffic control problem, we propose three models of mixed integer linear programming, usable with two multi-objective optimization interactive methods, allowing to adapt a “traffic control policy” iteratively to the current traffic situation. The considered criteria, all of them to be minimized, are the total waiting time and the number of stops for private vehicles and a criterion dedicated to public transports allowing to set a target waiting time for every bus. Experiments showed that one of the three models, called hybrid model, distinguishes itself positively from the others. This model was implemented with one of the two interactive methods, allowing to control a traffic simulated over one hour in different scenarios, and was compared to a semi-adaptive traffic control system.

La production des circulations ferroviaires a la sncf repose actuellement sur un processus essentiellement sequentiel dans lequel la conception des grilles horaires de circulation (reservation de l'infrastructure pour la circulation des trains de l'offre de transport de la sncf) conditionne largement la conception des planifications des engins ferroviaires (les roulements engins), puis celle des agents de conduite (adc) (les grilles de service des adc). cette strategie de planification sequentielle des ressources ferroviaires a ete massivement adoptee pour des raisons pratiques et scientifiques (historique, savoir-faire, complexite du systeme ferroviaire, etc.). toutefois, cette strategie de planification sequentielle genere des solutions qui peuvent etre de cout eleve et moins robustes aux aleas, car les decisions prises a une etape donnee peuvent reduire considerablement l'ensemble des solutions realisables aux etapes suivantes. face a ce constat et a la forte interaction entre ces trois ressources heterogenes et tres couteuses, la sncf a souhaite investiguer la praticabilite et les apports d'une demarche d'optimisation du plan de transport par planification integree de ces ressources critiques. dans cette optique, les travaux de these ont porte sur l'etude de faisabilite, le prototypage et la validation d'une demarche de planification integree des ressources permettant d'ameliorer l'efficacite globale du plan de transport, d'accroitre la competitivite de la sncf et d'ameliorer la qualite de ses services. nous avons propose une formalisation du probleme de planification integree engins/adc et des algorithmes performants qui s'appuient sur une approche par relaxation lagrangienne pour resoudre de maniere efficace la problematique etudiee. cette approche repose sur l'exploitation de deux briques logicielles developpees a la sncf pour resoudre chacun des sous-problemes de planification des engins et des adc. les algorithmes ont ete testes experimentalement avec des donnees reelles de la region ter bretagne. differentes evolutions des modeles et des algorithmes ont ete etudiees pour rendre ces derniers plus efficaces. les tests de validation sur des jeux de donnees reelles a une echelle industrielle sont encourageants et montrent des gains potentiels allant jusqu'a 4% des adc exploites par rapport a une approche traditionnelle (sequentielle). / The planning of railway production at the french national railways (sncf) is currently based on a mainly sequential process in which the design of railway timetabling widely conditioning design planning of railway equipment (rolling stock), then one of the train drivers (driver rosters). this strategy of sequential planning of railway resources massively adopted for practical and scientific reasons (expertise, complexity of the railway system, etc.). however, this strategy generates solutions which can be more expensive and less robust to uncertainties, because decisions taken at any given stage can significantly reduce the overall feasible solutions of the following steps.given this situation and the strong interaction between these heterogeneous and very expensive resources, the thesis deals with the feasibility and inputs of a process where these critical resources could be planned and optimized in an integrated way. the thesis focuses on the feasibility study, prototyping and validation of an integrated approach for planning rolling stocks and drivers, so as to improve the efficiency of the overall transportation plan, increase sncf competitiveness and enhance the quality of its services. we propose a mixed integer linear programming formulation of the rolling stock/ train drivers integrated planning problem. in this mathematical model, each planning sub-problem is formalized and coupling constraints are further introduced to model the interdependencies of these two resources when they are simultaneously used for train production. in this heuristic, the solution of the lagrangian dual and the calculation of feasible solutions are performed by calling two proprietary software modules available at sncf for planning rolling stocks and train drivers. the heuristic is tested experimentally with real data from the ter bretagne region, and several evolutions are introduced in the models and algorithms so as to improve their performances.validation tests on of real data sets at an industrial scale are encouraging and, when compared to a traditional (sequential) approach, show gain of up to 4% for train drivers used.

Atualmente, os hospitais se veem obrigados a melhorar sua produtividade. Os centros cirúrgicos, além de ser um dos setores com maiores custos, também é o que mais gera receita dentro de um hospital, dessa forma torna-se extremamente importante o gerenciamento eficiente desse setor. Os métodos de otimização para programação de cirurgias podem ser usados como ferramentas para reduzir filas e ociosidade nos centros cirúrgicos, aumentando sua produtividade. O Problema de Programação de Cirurgias Eletivas com Múltiplos Recursos e Múltiplas Etapas consiste em alocar os recursos às etapas do processo cirúrgico dos pacientes, considerando as diferentes necessidades e rotas de cada paciente e, então, programar essas etapas no tempo respeitando a disponibilidade dos recursos e a sequência das etapas do processo cirúrgico dos pacientes. Esse problema é classificado na literatura como NP-hard e pode ser descrito como um Job Shop Flexível com blocking e função objetivo de minimização do número de pacientes não atendidos e do instante de término da última etapa, o makespan. O Objetivo desse trabalho é propor um modelo matemático e uma heurística construtiva para a resolução desse problema. O modelo matemático Multi-Mode Blocking Job Shop (MMBJS) apresentado em Pham e Klikert (2008) é explorado e algumas melhorias são apontadas neste trabalho. Um modelo matemático de Programação Linear Inteira Mista alternativo é proposto, a fim de reduzir o esforço computacional, ajustar o cálculo do makespan e sugerir uma estratégia de priorização de pacientes. Testes computacionais foram realizados, afim de comparar o modelo MMJBS e o modelo proposto. Para instâncias em que todos os pacientes são atendidos, as soluções encontradas pelo CPLEX para ambos modelos são iguais, porém o tempo computacional necessário para encontrar uma solução ótima é em média 45% menor no modelo proposto. Também foram realizados testes computacionais com objetivo de observar o comportamento do modelo com diferentes configurações de recursos. Para instâncias com 15 pacientes, os testes apontam que o tempo computacional para encontrar a solução ótima é superior a 2h de processamento. Dessa forma, uma heurística construtiva é proposta, com objetivo de gerar soluções factíveis com pouco esforço computacional. A heurística proposta aloca cada etapa do tratamento de cada paciente aos recursos necessários, respeitando as janelas de disponibilidade dos recursos e buscando reduzir a folga no sistema. Um exemplo de aplicação da heurística construtiva é apresentado. As propostas para trabalhos futuros são apresentadas no capítulo final desta dissertação. / For the past few years, hospitals have been forced to improve their productivity, with surgical centers being one of the sectors with higher costs within such organizations, but also the ones that generate the most revenue. Thus, optimization methods for surgical programming are tools that can be used to reduce queues and idleness in these sectors and consequently achieve the aforementioned goals. The \"Problem of Programming Multiple Surgical Resources with Multiple Steps\"consists in allocating the existing resources to each surgery stage that a patient will need to go through, considering the different needs, sequence and specificities of each of them, and then scheduling these steps in time. This type of problem is classified in the current literature as an NP-hard problem, being described as a Flexible Job Shop with blocking and an objective function that seeks to minimize the number of patients not served and the total makespan. The general purpose of this research is to propose a mathematical model and a constructive heuristic for this type problem. The proposed model explores the mathematical model Multi-Mode Blocking Job Shop (MMBJS) presented in Pham and Klikert (2008) suggesting improvements through the use of an alternative Mixed Integer Linear Programming that aims to: reduce the computational effort, adjust the makespan calculation and suggest a strategy of patients prioritization. In order to prove the benefits of the proposed enhancements, computational tests were performed to compare the MMJBS model and the proposed model, identifying that for instances where in which all patients are attended, the solutions found by CPLEX for both models are the same, but with a lower computational time the proposed model (45% average reduction). Also, other computational tests were performed to observe the behavior of the model with different configurations of resources. For instances with 15 patients, the tests indicate that the computational time to find the optimal solution is greater than 2 hours of processing. Thus a constructive heuristic is proposed, it aims to generate feasible solutions with little computational effort. The proposed heuristic allocates each surgery stage of a patient to the necessary resources, respecting the available windows and seeking to reduce the total slack in the system. An example of the application of the constructive heuristic is also presented. At last, future works proposals are presented in the final chapter of this dissertation.