Fixed interval scheduling problems have wide range of practical use in production planning, transportation, in hospitals or in schools when planning timetables. When solving these problems we often encounter requirement of integrality of solutions. Ignoring this condition is often not possible. In this thesis we propose some formulations of scheduling problems and their stochastic extensions. We also propone a new formulation of stochastic FIS problem, for which integrality of solution is byproduct of its definition. We present Gâteaux derivative and its relationship to stability of optimal value function of stochastic optimization problems under the influence of contamination. We propose a new theorem on the stability of such functions for fixed interval scheduling problems.

Mixed-Integer Programming has been a vital tool for the chemical engineer in the recent decades and is employed extensively in process design and control. This dissertation presents some new Mixed-Integer Programming formulations developed for two well-studied problems, one with a central role in the area of Optimisation, the other of great interest to the chemical industry. These are the Travelling Salesman Problem and the problem of scheduling cleaning actions for heat exchanger networks subject to fouling. The Travelling Salesman Problem finds a plethora of applications in many scientific disciplines, Chemical Engineering included. None of the mathematical programming formulations proposed for solving the problem considers fewer than O(n^2) binary degrees of freedom. The first part of this dissertation introduces a novel mathematical description of the Travelling Salesman Problem that succeeds in reducing the binary degrees of freedom to O(nlog2(n)). Three Mixed-Integer Linear Programming formulations are developed and the computational performance of these is tested through computational studies. Sophisticated methods are now available for scheduling the cleaning actions for networks of heat exchangers subject to fouling. In the majority of these, only one form of cleaning is used, which restores the performance of the exchanger back to its clean level. A recent study revised the scheduling problem for the case where there are several cleaning methods available. The second part of this dissertation extends their approach, developed for individual units, to heat exchanger networks and explores the concept of selection of cleaning techniques further. Mixed-Integer Programming formulations are proposed for the scheduling task, for two fouling scenarios: (i) chemical reaction fouling and (ii) biological fouling. A series of results are presented for the implementation of the scheduling formulations to networks of different sizes.

Fixed interval scheduling problems have wide range of practical use in production planning, transportation, in hospitals or in schools when planning timetables. When solving these problems we often encounter requirement of integrality of solutions. Ignoring this condition is often not possible. In this thesis we propose some formulations of scheduling problems and their stochastic extensions. We also propone a new formulation of stochastic FIS problem, for which integrality of solution is byproduct of its definition. We present Gâteaux derivative and its relationship to stability of optimal value function of stochastic optimization problems under the influence of contamination. We propose a new theorem on the stability of such functions for fixed interval scheduling problems.

Les télécommunications par satellite ont connu ces dernières années un regain d'intérêt important, du fait de leur capacité à permettre la réduction de la fracture numérique. En effet, un satellite en orbite géostationnaire peut s'appuyer sur une très grande couverture et une capacité importante pour atteindre des zones où le déploiement des réseaux terrestres n'est pas envisageable, comme les transports (bateau, avion), ou bien les zones blanches, où il serait difficilement rentable. Traditionnellement concentrés sur la diffusion de télévision numérique, les dernières générations de standards reflètent cet engouement en faisant une place de choix à la transmission de données bidirectionnelle, notamment en permettant une prise en charge simple des protocoles de l'Internet. Le problème de l'ordonnancement dans ces systèmes devient alors particulièrement important, puisqu'il doit prendre en compte deux processus évoluant de manière totalement décorrélée. D'un côté, l'évolution de la demande des utilisateurs, dépendante des applications (vidéo, voix, données). De l'autre, l'évolution de la capacité du système, celle-ci étant tributaire des conditions de transmission : les fréquences utilisées dans ces systèmes sont particulièrement sensibles à l'atténuation due à l'eau dans l'atmosphère. Cette thèse s'intéresse au problème de l'ordonnancement et de l'allocation de ressources, dans le but de fournir un service comparable aux réseaux terrestres en termes de services, en présentant les meilleures performances possibles. Si un certain nombre de propositions ont été faites sur le sujet, aucune ne prend en compte l'ensemble des contraintes d'un tel système. Outre le caractère variable de la capacité, la variabilité de la demande, conjuguée avec les contraintes de qualité de service constitue une difficulté supplémentaire. Enfin, il nous faut considérer la faisabilité de notre solution dans un contexte temps réel, nécessaire dans l'optique d'une implantation dans un système réel. Nous avons ainsi développé une architecture d'ordonnanceur pour la voie Aller, reposant sur des fonctions d'utilité, permettant ainsi une formulation simple du compromis entre demande et capacité. Nous montrons comment cet algorithme pourrait être utilisable dans un système complet, à travers une implantation détaillée, de faible complexité, ainsi que des simulations de cas réels. Nous portons ensuite notre attention sur la voie Retour, où nous proposons une méthode d'allocation de ressources prenant en compte de manière conjointe la qualité de service et la qualité du support pour délivrer une allocation à la fois conforme et performante. Les simulations montrent que notre algorithme obtient une efficacité et une meilleure gestion du trafic que des solutions de référence présentées dans la littérature. / Satellite telecommunications have seen a tremendous increase in interest, due to its ability to reduce the digital divide. In fact, a geostationary satellite can take advantage of its very wide coverage and high capacity to reach areas where deployment of a terrestrial network would not be possible, such as transports, or too expensive to be profitable, as in remote areas. Traditionally focused on digital television broadcasting, the latest generation of standards have evolved to reflect those new needs, dealing extensively with the transmission of interactive data, particularly by natively supporting Internet protocols. Scheduling has arisen as a major issue of those modern systems, since it has to deal with to highly uncorrelated processes: demand and capacity. Demand, on one side, evolves with user's needs, and therefore with the applications they are using: video, voice or data. Capacity, on the other side, depends on meteorological conditions over the satellite's cover, as the frequencies used in such systems are very sensitive to wet atmosphere attenuation. This thesis aims to study the problem of scheduling and resource allocation, hoping to achieve a service that can match with terrestrial networks in terms of services, while showing the best possible performances. If numerous solutions were proposed on this topic, none is taking into account all of the current system's constraints. In addition to the variable nature of system's capacity, the conjunction of variable demand and quality of service constraints constitutes an additional issue. Furthermore, we have to consider the practicability of our solution in a real-time context, necessary if we aim for industrial use. We have first developed a scheduler architecture for the Forward link, based on utility functions, thus allowing a simple formulation of the capacity versus demand compromise. We show, through a detailed low-complexity implementation and accurate simulations, how our algorithm could be used efficiently in an industrial context. We then focus on the Return link, where we propose a resource allocation method, taking into account quality of service and quality of transmission jointly to deliver an efficient yet consistent resource allocation. Simulations show that our algorithm achieves a better efficiency and traffic handling than reference solutions presented in the literature.