This thesis presents the mixed integer bilevel programming problems where some optimality conditions and solution algorithms are derived. Bilevel programming problems are optimization problems which are partly constrained by another optimization problem. The theoretical part of this dissertation is mainly based on the investigation of optimality conditions of mixed integer bilevel program. Taking into account both approaches (optimistic and pessimistic) which have been developed in the literature to deal with this type of problem, we derive some conditions for the existence of solutions. After that, we are able to discuss local optimality conditions using tools of variational analysis for each different approach. Moreover, bilevel optimization problems with semidefinite programming in the lower level are considered in order to formulate more optimality conditions for the mixed integer bilevel program. We end the thesis by developing some algorithms based on the theory presented

This thesis concerns solutions to problems that arise in optimizing fixed interval scheduling under situations of uncertainty such as when there are random delays in job process times. These problems can be solved by using a vertex coloring with random edges and problems can be formulated using integer linear, quadratic and stochastic programming. In this thesis is propo- sed a new integer linear formulation. Under certain conditions there is proved its equivalence with stochastic formulation, where is maximized the schedule reliability. Moreover, we modified the proposed formulation to obtain bet- ter corresponding to real life situations. In a numerical study we compared computational time of individual formulations. It turns out that the propo- sed formulation is able to solve scheduling problems considerably faster than other formulations. 1

De senaste åren har en större mängd decentraliserad och variabel energiproduktion tagit plats inom elsystemet, mer specifikt vindkraft och solkraft, och etablering av mer distribuerad produktion kommer att fortsätta i enlighet med mål från nationer och världsorganisationer att fasa ut fossila bränslen och minska på växthusgasutsläpp. I takt med nedläggning av storskaliga kraftverk baserade på fossila bränslen påverkar detta möjligheterna att möta upp elbehovet med den tillgängliga produktionen. Mycket variabel produktion har samtidigt en negativ påverkan på elnätstabiliteten och kan skapa höga effekttoppar. Detta har skapat ett ökat behov av mer flexibilitet på kundsidan för att skapa balans på elnätet. Elektrokemiska batterilager kan lösa många av problemen som uppstår med intermittent förnybar energiproduktion. Batterilager har både utvecklats teknologiskt och minskats i pris avsevärt de senaste tio åren och kostnaderna kommer fortsätta att gå ned. För att batterilager på allvar ska bli intressant behöver aktörer som investerar i denna teknologi veta om det någon gång inom en snar framtid kommer att vara en positiv affär. Syftet med detta arbete har därför varit att undersöka lönsamheten med batterilager i kommersiella fastigheter idag och inom de närmsta 10 åren på den svenska marknaden. Studien har, med hjälp av blandad heltalsprogrammering (MILP) i MATLAB, tagit fram en modell som optimalt schemalägger energiflöden för en fastighet som har ett batterisystem och egen produktion installerat baserat på olika prisbilder. Modellen har i sin tur använts för att beräkna de ekonomiska möjligheterna som erbjuds på Sveriges elmarknad med ett batterisystem i en mängd olika scenarier både vad gäller pris på el, olika effektabonnemang, integration med solpaneler, olika batteristorlekar och systemlivslängd. Resultatet visar att det inte finns någon lönsamhet i att investera i batterier för de undersökta fastigheterna så som Sveriges elmarknad ser ut idag och någon hög lönsamhet kommer inte att ske även om pristrenden på batterier fortsätter nedåt. Ett mindre batterisystem på 28 kWh kan ge, beräknat med internräntan, en positiv avkastning på 1 % år 2020 men ju större batteriet är desto mindre blir avkastningen. Högst avkastningen som kan fås med dagens el- och nätpriser är 4-5 % om en investering görs med 2025-2030 års batteripriser. Om elnätsägarna går mot att endast erbjuda tidsdifferentierade nättariffer året om och det implementeras högre effektavgifter finns det möjligheter att avkastningen kan bli så hög som 15-18 % med 2025-2030 års batteripriser. Arbetet visar också att kapandet av effekttoppar med större batterilager än 28 kWh inte är kostnadseffektivt för de undersökta fastigheterna. / The world has seen a rapid deployment of distributed and time-varying renewable energy systems (RES) within the electricity grids for the past 20 years, especially from wind and solar power. The deployment RES is expected to increase even more as world organizations and nations will continue the phase-out of fossil fuels as the main source of energy for electricity production. As large scale power plants reliant on fossil fuels will shut down it will be harder for the system to balance production and demand. At the same time, time-varying production might have a negative effect on the grid stability which has spurred an increased interest in flexibility on the demand side and a call for technologies and strategies that can create balance on the grid. Energy storage, especially electrochemical battery storage, is seen as a part of a bigger solution to the problems that comes with intermittent energy production. Battery storage has had a fast technological development and a sharp downtrend in pricing the latest ten years and the costs are expected to keep on decreasing. For battery storage to be a serious contender on the electricity market there is a need to understand if and when an investment in this technology might give a positive outcome. The aim of this study has therefore been to analyse the profitability of battery storage within commercial real estate today, and in the oncoming 10-15 years on the Swedish electricity market. The study has, using mixed integer linear programming (MILP) within MATLAB, created a model which optimally schedules power flows for buildings that has a battery system and its own electricity production. The model has in turn been used to evaluate the economical possibilities that exist with a battery system within commercial real estate under various different scenarios that looks into pricing structures on electricity and demand, integration with and without solar panels, different battery sizes and system lifetimes. The results show that there is currently no profitability to invest in a battery system for the specific buildings analysed in this study. While break-even is possible just a couple of years from now, a high profitability will not be reached even with the future downtrend in battery prices under the current electricity market circumstances. A smaller battery system with a capacity of 28 kWh could give an internal rate of return (IRR) of 1 % year 2020. Larger battery systems are generally not cost-effective when compared to smaller battery systems when its primary purpose is utilized for demand reduction. Highest return with today’s electricity and utility pricing is 4-5 % somewhere between 2025 and 2030. However, if the market goes towards exclusively time-of-use billing structures on electricity and higher demand charges, the IRR can reach towards 15-18 % between 2025 and 2030.

[pt] As doenças vasculares são enfermidades graves e seus tratamentos são complexos e necessitam de procedimentos cirúrgicos. Para a realização desses procedimentos, são necessários equipamentos, equipes qualificadas e unidade de terapia intensiva (UTI) equipada para o pós-operatório. Hospitais de ensino devem atender à legislação vigente que preconiza um número mínimo de cirurgias para aprovação do residente no programa de formação. Assim, propõe-se, via otimização, encontrar soluções eficientes para o planejamento e programação de cirurgias eletivas que atendam à legislação. Este problema é tratado em 2 níveis. O primeiro é relativo ao planejamento e é chamado de Master Surgical Schedule (MSS) que consiste em definir os recursos necessários para a realização de um conjunto de procedimentos. O segundo se refere à programação e é chamado de Surgical Case Assigment Problem (SCAP) e tem por objetivo alocar o médico a cada cirurgia. Assim, foram propostos dois modelos de programação matemática, um para o MSS e outro para o SCAP. Estes modelos foram aplicados no caso real da alocação de residentes para cirurgias vasculares no Hospital Universitário Pedro Ernesto. Como resultado do modelo MSS, identificou-se a necessidade de mais anestesistas e maior disponibilidade de equipamentos para atender à legislação de formação de residentes. Por fim, como resultado do SCAP, o quantitativo de cirurgias foi distribuído entre os cirurgiões de forma balanceada. / [en] Vascular diseases are serious diseases and their treatments are complex and require surgical procedures. In order to perform these procedures, is required equipment, qualified teams and an intensive care unit (ICU) equipped for the postoperative period. Teaching hospitals must comply with current legislation that recommend a minimum number of surgeries for the resident s approval in the training program. Thus, it is proposed, through optimization, to find efficient solutions for the planning and programming of elective surgeries that comply with the legislation. This problem is dealt with on two levels. The first is relative to planning and is called the Master Surgical Schedule (MSS), which consists of defining the necessary resources to perform a set of procedures. The second one refers to programming and is called Surgical Case Assigment Problem (SCAP) and aims to allocate the doctor to each surgery. Thus, two models of mathematical programming were proposed, one for MSS and another for SCAP. These models were applied in the real case of residents allocation for vascular surgeries at Pedro Ernesto University Hospital. As a result of MSS model were identified the need for more anesthesiologists and greater availability of equipment ensure the cover of resident training legislation. Finally, as a result of SCAP, the quantity of surgeries was distributed equitably distributed among surgeons.

This dissertation presents a comprehensive and comparative progress in sequencing approaches of mixed-model just-in-time (JIT) sequencing problem together with discrete apportioment problem (DAP). The goal of JIT sequencing problem (JITSP) is to keep the rate of usage of parts as constant as possible along the assembly lines, and the goal of DAP is to divide a given integer number of delegates proportionally among the states or the parties according to their population or votes. Furthermore, the supply chain logistics problem is also reported in here with some real life applications.The single-level JITSP, known as the product rate variation problem (PRVP), is pseudo-polynomially solvable. The total PRVP minimizes sum deviation and the bottleneck PRVP minimizes the maximum deviation between the actual production and the ideal production. The assignment approach solves total PRVP whereas the perfect matching works for bottleneck PRVP solving the problem in pseudo-polynomial time. The multi-level JITSP, known as the output rate variation problem (ORVP), is NP-hard in most of the cases. However, some sequencing heuristics and dynamic programming are devised for near optimal solutions. And the pegging assumption reduces the ORVP into weighted case of PRVP. In this dissertation, the total PRVP with square and absolute deviations are considered and mean-based divisor methods are devised for the equitably efficient solution. The simultaneous dealing to the PRVP and DAP establishes the interlink between the production sequencing problem and integer seat allocating problem. The new upper bottlenecks are investigated and the problems are solved comparatively. The bottleneck PRVP instances for small deviations and cyclic sequences for total PRVP are shown to be optimal. The bicriterion sequencing is discussed with Pareto optimal solutions.The production sequencing problem is simultaneously dealt with supply chain logistics to balance overall supply chain system. The cross-docking supply chain logistics problem is formulated with a proposition to be solved. The real-world applications of JITSP and supply chain are listed and some open problems are pointed out as the closing of the dissertation.

In this dissertation we focus on two main topics. Under the first topic, we develop a new framework for stochastic network interdiction problem to address ambiguity in the defender risk preferences. The second topic is dedicated to computational studies of two-stage stochastic integer programs. More specifically, we consider two cases. First, we develop some solution methods for two-stage stochastic integer programs with continuous recourse; second, we study some computational strategies for two-stage stochastic integer programs with integer recourse. We study a class of stochastic network interdiction problems where the defender has incomplete (ambiguous) preferences. Specifically, we focus on the shortest path network interdiction modeled as a Stackelberg game, where the defender (leader) makes an interdiction decision first, then the attacker (follower) selects a shortest path after the observation of random arc costs and interdiction effects in the network. We take a decision-analytic perspective in addressing probabilistic risk over network parameters, assuming that the defender's risk preferences over exogenously given probabilities can be summarized by the expected utility theory. Although the exact form of the utility function is ambiguous to the defender, we assume that a set of historical data on some pairwise comparisons made by the defender is available, which can be used to restrict the shape of the utility function. We use two different approaches to tackle this problem. The first approach conducts utility estimation and optimization separately, by first finding the best fit for a piecewise linear concave utility function according to the available data, and then optimizing the expected utility. The second approach integrates utility estimation and optimization, by modeling the utility ambiguity under a robust optimization framework following \cite{armbruster2015decision} and \cite{Hu}. We conduct extensive computational experiments to evaluate the performances of these approaches on the stochastic shortest path network interdiction problem. In third chapter, we propose partition-based decomposition algorithms for solving two-stage stochastic integer program with continuous recourse. The partition-based decomposition method enhance the classical decomposition methods (such as Benders decomposition) by utilizing the inexact cuts (coarse cuts) induced by a scenario partition. Coarse cut generation can be much less expensive than the standard Benders cuts, when the partition size is relatively small compared to the total number of scenarios. We conduct an extensive computational study to illustrate the advantage of the proposed partition-based decomposition algorithms compared with the state-of-the-art approaches. In chapter four, we concentrate on computational methods for two-stage stochastic integer program with integer recourse. We consider the partition-based relaxation framework integrated with a scenario decomposition algorithm in order to develop strategies which provide a better lower bound on the optimal objective value, within a tight time limit.

The objective of this project is to develop an operational scheduling model for Sasol Mining’s coal handling facility, Sasol Coal Supply (referred to as SCS), to optimise daily operations. In this document, the specific scheduling problem at SCS is presented and solved using Mixed Integer Non-Linear Programming (MINLP) continuous time representation techniques. The most recent MINLP scheduling techniques are presented and applied to an example problem. The assumption is made that the results from the example problem will display trends which will apply to the SCS scheduling problem as well. Based on this assumption, the unit-specific event based continuous time formulation is chosen to apply to the SCS scheduling problem. The detail mathematical formulation of the SCS scheduling problem, based on the chosen technique, is discussed and the necessary changes presented to customise the formulation for the SCS situation. The results presented show that the first phase model does not solve within 72 hours. A solution time of more than three days is not acceptable for an operational scheduling model in a dynamic system like SCS. Various improvement approaches are applied during the second phase of the model development. Special Ordered Sets of Type 1 (SOS1) variables are successfully applied in the model to reduce the amount of binary variables. The time and duration constraints are restructured to simplify the structure of the model. A specific linearization and solution technique is applied to the non-linear equations to ensure reduced model solution times and reliable results. The improved model for one period solves to optimality within two minutes. This dramatic improvement ensures that the model will be used operationally at SCS to optimise daily operations. The scheduling model is currently being implemented at SCS. Examples of the input variables and output results are presented. It is concluded that the unit-specific event based MINLP continuous time formulation method, as presented in the literature, is not robust enough to be applied to an operational industrial-sized scheduling problem such as the SCS problem. Customised modifications to the formulation are necessary to ensure that the model solves in a time acceptable for operational use. However, it is proved that Mixed Integer Non-linear Programming (MINLP) can successfully be applied to optimise the scheduling of an industrial-sized plant such as SCS. Although more research is required to derive robust formulation techniques, the principle of using mathematical methods to optimise operational scheduling in industry can dramatically impact the way plants are operated. The optimisation of daily schedules at SCS by applying the MINLP continuous time scheduling technique, has made a significant contribution to the coal handling industry. Finally, it can be concluded that the SCS scheduling problem was successfully modelled and the operational scheduling model will add significant value to the Sasol Group. / Dissertation (MEng (Industrial Engineering))--University of Pretoria, 2006. / Industrial and Systems Engineering / unrestricted

L’optimisation de la planification de la maintenance des équipements de production d’électricité est une question importante pour éviter des temps d’arrêt inutiles et des coûts opérationnels excessifs. Dans cette thèse, nous présentons une classification multidimensionnelle des études de Recherche Opérationnelle portant sur ce sujet. Le secteur des énergies renouvelables étant en pleine expansion, nous présentons et discutons ensuite d’un problème de maintenance de parcs éoliens terrestres. Le problème est traité sur un horizon à court terme et l’objectif est de construire un planning de maintenance qui maximise le revenu lié à production d’électricité des éoliennes tout en prenant en compte des prévisions de vent et en gérant l’affectation de techniciens. Nous présentons plusieurs modélisations du problème basées sur la programmation linéaire. Nous décrivons aussi une recherche à grands voisinages basée sur la programmation par contraintes.Cette méthode heuristique donne des résultats probants.Nous résolvons ensuite le problème avec une approche exacte basée sur une décomposition du problème. Dans cette méthode, nous construisons successivement des plannings de maintenance optimisés et rejetons, à l’aide de coupes spécifiques, ceux pour lesquels la disponibilité des techniciens est insuffisante. Les résultats suggèrent que cette méthode est la mieux adaptée pour ce problème. Enfin, pour prendre en compte l’incertitude inhérente à la prévision de vitesses de vent, nous proposons une approche robuste dans laquelle nous prenons des décisions garantissant la réalisabilité du planning de maintenance et le meilleur revenu pour les pires scénarios de vent. / Efficiently scheduling maintenance operations of generating units is key to prevent unnecessary downtime and excessive operational costs. In this work, we first present a multidimensional classification of the body of work dealing with the optimization of the maintenance scheduling in the operations research literature. Motivated by the recent emergence of the renewable energy sector as an Environmental priority to produce low-carbon power electricity, we introduce and discuss a challenging Maintenance scheduling problem rising in the onshore wind industry. Addressing the problem on a short-term horizon, the objective is to find a maintenance plan that maximizes the revenue generated by the electricity production of the turbines while taking into account wind predictions, multiple task execution modes, and technician-to-task assignment constraints. We start by presenting several integer linear Programming formulations of the problem. We then describe a constraint programming-based large neighborhood search which proves to be an efficient heuristic solution method. We then design an exact branch-and-check approach based on a decomposition of the problem. In this method, we successively build maintenance plans while discarding – using problem-specific cuts – those that cannot be performed by the technicians. The results suggest that this method is the best suited to the problem. To tackle the Inherent uncertainty on the wind speed, we also propose a robust approach in which we aim to take risk-averse decisions regarding the revenue associated with the maintenance plan and its feasibility.

Dans ce travail, nous présentons trois nouveaux algorithmes pour le problème de la clique de poids maximum. Les trois algorithmes dépendent d'un ordre initial des sommets. Deux ordres sont considérés, l'un en fonction de la pondération des sommets et l'autre en fonction de la taille voisinage des sommets. Le premier algorithme, que nous avons appelé BITCLIQUE, est une algorithme de séparation et évaluation. Il réunit efficacement plusieurs idées déjà utilisées avec succès pour résoudre le problème, comme l'utilisation d'une heuristique de coloration pondérée en nombres entiers pour l'évaluation ; et l'utilisation de vecteurs de bits pour simplifier les opérations sur le graphe. L'algorithme proposé surpasse les algorithmes par séparation et évaluation de l'état de l'art sur la plupart des instances considérées en terme de nombre de sous-problèmes énumérés ainsi que en terme de temps d'exécution. La seconde version est un algorithme des poupées russes, BITRDS, qui intègre une stratégie d'évaluation et de ramification de noeuds basée sur la coloration pondérée. Les simulations montrent que BITRDS réduit à la fois le nombre de sous-problèmes traités et le temps d'exécution par rapport à l'algorithme de l'état de l'art basée sur les poupées russes sur les graphes aléatoires avec une densité supérieure à 50%. Cette différence augmente à la mesure que la densité du graphe augmente. D'ailleurs, BITRDS est compétitif avec BITCLIQUE avec une meilleure performance sur les instances de graphes aléatoires avec une densité comprise entre 50% et 80%. Enfin, nous présentons une coopération entre la méthode poupées russes et la méthode de ``Resolution Search''. L'algorithme proposé, appelé BITBR, utilise au même temps la coloration pondérée et les limites supérieures donnés par les poupées pour trouver un ``nogood''. L'algorithme hybride réduit le nombre d'appels aux heuristiques de coloration pondérée, atteignant jusqu'à 1 ordre de grandeur par rapport à BITRDS. Plusieurs simulations sont réalisées avec la algorithmes proposés et les algorithmes de l'état de l'art. Les résultats des simulations sont rapportés pour chaque algorithme en utilisant les principaux instances disponibles dans la littérature. Enfin, les orientations futures de la recherche sont discutées. / In this work, we present three new exact algorithms for the maximum weight clique problem. The three algorithms depend on an initial ordering of the vertices. Two ordering are considered, as a function of the weights of the vertices or the weights of the neighborhoods of the vertices. This leads to two versions of each algorithm. The first one, called BITCLIQUE, is a combinatorial Branch & Bound algorithm. It effectively combines adaptations of several ideas already successfully employed to solve the problem, such as the use of a weighted integer coloring heuristic for pruning and branching, and the use of bitmap for simplifying the operations on the graph. The proposed algorithm outperforms state-of-the-art Branch & Bound algorithms in most instances of the considered in terms of the number of enumerated subproblems as well in terms of computational time The second one is a Russian Dolls, called BITRDS, which incorporates the pruning and branching strategies based on weighted coloring. Computational tests show that BITRDS reduces both the number of enumerated subproblems and execution time when compared to the previous state-of-art Russian Dolls algorithm for the problem in random graph instances with density above 50%. As graph density increases, this difference increases. Besides, BITRDS is competitive with BITCLIQUE with better performance in random graph instances with density between 50% and 80%. Finally, we present a cooperation between the Russian Dolls method and the Resolution Search method. The proposed algorithm, called BITBR, uses both the weighted coloring and upper bounds given by the dolls to find a nogood. The hybrid algorithm reduces the number of coloring heuristic calls, reaching up to 1 order of magnitude when compared with BITRDS. However, this reduction decreases the execution time only in a few instances. Several computational experiments are carried out with the proposed and state-of-the-art algorithms. Computational results are reported for each algorithm using the main instances available in the literature. Finally, future directions of research are discussed.

Le moteur de traction ferroviaire est destiné à fonctionner dans de larges gammes de couple/vitesse. L'objectif principal de cette thèse est de développer des méthodes de conception par optimisation de machines électriques pour la traction ferroviaire avec la prise en compte des cycles (missions). Puis, d'incorporer ces méthodes dans un outil informatique. Après une prise en main des modèles électromagnétiques existants et leur transfert dans le langage Matlab, des modèles thermiques transitoires ont été établis et validés par rapport aux mesures expérimentales. À partir de là, la problématique des temps de simulations prohibitifs sur cycles a été mise en évidence et des solutions de réduction de cycles ont été proposées et validées sur les différents types de cycle. Enfin, une approche de conception par optimisation en deux niveaux a été développée. Le premier niveau concerne les variables continues et le second gère les variables discrètes. / The rail traction motor is designed to operate in wide range of torque/speed performance. The main aims of this thesis is to develop methods of designing by optimization electric machines over railway driving cycle. Then, to implement these methods in a usable software. Firstly, existing electromagnetic models were transferred to Matlab and two thermal models were developed and validated by experimental measurements. The use of accurate models for the optimization over à driving cycle is highly time consuming so, after identification of this constraint, some solutions to reduce this time without losing the accuracy were proposed and validated. Finally, multi-level optimization approach has been developed for electric machine design to solve mixed integer problem. This approach takes into account the driving cycle by using the methods of cycle reduction developed during this thesis.