On April 27, 1802, I gave a shout of joy ... It was seven years ago I proposed to myself a problem which I have not been able to solve directly, but for which I had found by chance a solution, and I knew that it was correct, without being able to prove it. The matter often returned to my mind and I had sought twenty times unsuccessfully for this solution. For some days I had carried the idea about with me continually. At last, I do not know how, I found it, together with a large number of curious and new considerations concerning the theory of probability. Andre Marie Ampere. Facility location problems (or plant location problems) are general models that can be used when a set of clients has to be served by facilities. More precisely, we are given a set of potential facility locations and a set of clients. The optimization problem is to select a subset of the locations at which to place facilities and then to assign clients to theses facilities so as to minimize total cost. Most formulations considered in this thesis can be viewed as general models that can be applied to a wide range of context and practical situations. However, as this research has been partly initiated by the interest of the author in telecommunication network design we will introduce these models by considering problems in this particular area. In the context of telecommunication network design an application of discrete location theory is the optimization of access networks with concentrators. Typically, we have a number of terminal points that must be connected to a service point. An obvious solution is to use a dedicated link for each terminal (star network). However, it is clear that this solution can be very expensive when the number of terminals is large and when they are far from the service point. Access networks are often constructed by inserting concentrators between the terminals and the service point. Many terminals are connected to a facility which in turn is connected by a single link to the service point. The objective is to build a network that will provide the service at minimum cost. If no extra constraints are involved the mmimum cost network problem can be expressed as an uncapacitated facility location problem (UFL). If the number of terminals that can be connected to a concentrator is limited we obtain a so-called capacitated facility location problem (CFL). CFL can be extended to consider various types of concentrators with various capacities. This problem is the multi-capacitated facility location problem (MCFL). MCFL is a straightforward model for low speed packet switched data networks typical among which are networks connecting sellingpoint terminals to a database. For other networks, the problem may involve various traffic constraints. In chapter 1 we present those problems and compare solutions obtained by Lagrangian relaxation and simulated annealing algorithms. The architecture mentioned above can be extended with more than one hierarchical level of concentrator. Unfortunately, we pay for this cost saving through a decrease of reliability. Therefore, the number of levels is often limited to one or two. In chapter 2 we study an extension of UFL and CFL to two levels of concentrators. Obviously, the structure of a network changes according to the way requirements vary with time. In order to plan investments and to develop strategies, the evolution of a network has to be determined for several years ahead (typically four or five years). In this case the main questions to answer are: Where and when to establish concentrators and of what size? In chapter 3 we study this problem for the dynamic version of UFL. Now, with the network optimization problem, there naturally arises the problem of allocating the total minimum cost among customers fairly. Namely, we would like to allocate the cost in such a way that no subgroup of users would have incentive to withdraw and build their own network. The standard way to approach such a problem is by the means of cooperative game theory. In chapter 4 we study the core of location games derived from UFL and CFL, and in chapter 5 we propose methods to compute the nucleolus of these games.

Digital time is coming, digital applications are getting bigger to the bandwidth demand, the optical fiber communication industry getting more important. Taiwan businessman joined the supply chain by flexible production support and reduced the costs of spare parts and components. With the cost thrust force and the Asian market attraction, the production center of huge plants have moved toward the Asian and Pacific area, and it makes Taiwan manufacturers become low-cost and good-quality suppliers of spare parts and components. Under price's pressure and Chinese market's fast rising, this is a good opportunity for Taiwan manufacturers. This research is about foreign investment of location choice theories, clustering effects, and eclectic paradigms to find out its best model and location. The finding pointed out that Taiwan optical communication entrepreneur must expanded upstream or formed alliances downstream, ex. equipment manufacturers. The enterprise must get off low-cost opinion, and endeavor to research and developing work. The optical communication industry Clustering effect is not only on manufacturing, but also being emphasized on function communications between research and marketing. The globalization lies in whether to have the conformity resources and operation ability. This research shows the investment environment vicissitude and the global thinking, and is expected to help the decision-making suggestions offering.

Το αντικείμενο το οποίο πραγματεύεται η παρούσα εργασία αφορά στη λήψη αποφάσεων λειτουργίας καταστημάτων στα πλαίσια συγχώνευσης μεταξύ δύο τραπεζικών ιδρυμάτων. Σε πιο ειδικό πλαίσιο, γίνεται αναφορά στη λήψη αποφάσεων μέσω της πολυκριτηριακής ανάλυσης κάνοντας αναφορά στις βασικές μεθόδους ανάλυσης και των κριτηρίων τους, καθώς επίσης και των συντελεστών βαρύτητας. Στην συνέχεια, παρουσιάζεται το θεωρητικό υπόβαθρο της θεωρίας χωροθέτησης. Γίνεται αναφορά στην χρηστική αξία και στην αναγκαιότητα που έχει στη λήψη στρατηγικών αποφάσεων, ενώ γίνεται και εκτενής αναφορά στο θεωρητικό υπόβαθρο της ανάπτυξης του τραπεζικού δικτύου και της χωροθέτησης σε συγκεκριμένη αγορά. Ακολούθως, παρατίθεται η θεωρία παιγνίων, όσον αφορά στην αλληλεπίδραση μεταξύ δύο επιχειρήσεων στα πλαίσια του ανταγωνισμού. Συγκεκριμένα γίνεται κατανοητή η έννοια του παιγνίου και οι κανόνες που το πλαισιώνουν, ενώ περιγράφονται οι κατηγορίες στις οποίες σύμφωνα με την βιβλιογραφία διακρίνονται. Έπειτα, γίνεται περιγραφή εφαρμογής του μοντέλου που χρησιμοποιούμε κάνοντας παράλληλα περιγραφή της περιοχής ενδιαφέροντος μας και παρουσιάζοντας τα αποτελέσματα αυτού. Τελειώνοντας την εργασία παρουσιάζουμε τα συμπεράσματα μας σύμφωνα με τα αποτελέσματα που προέκυψαν από την εφαρμογή του μοντέλου που χρησιμοποιήσαμε. / -

The main aim of this thesis is to find regularities and patterns of banking branches distribution in particular regions. In the first part of the work there is a detailed overview of location behaviour of the selected banks in the Czech regions and districts. The second part represents simple process of finding ideal location for future bank branches establishing. This process is also applied to case studies, which are part of this thesis as well. The results show that geographical distribution of selected banks corresponds to the urban system of the Czech Republic. The capital city of Prague proved to be exceptional considering urban structure of the Czech republic. The analysis shows quite high differences in bank branches distribution in Czech districts. Very high concentration in relation to number of inhabitants was recorded in border districts of Plzeňský region and Jihočeský region. On the other hand, Most district and Ústí nad Labem district still offer high potential for bank branches expansion. We can expect continuing of bank branches expansion, because branches still have irreplaceable position regarding bank operations and creating new bank accounts.

Ο Τραπεζικός τομέας έχει προσελκύσει πληθώρα μελετών που καλύπτουν μια ευρύτατη θεματολογική γκάμα και, ειδικότερα για το τραπεζικό κατάστημα εστιάζουν, στο θέμα της χωροθέτησης και της αξιολόγησης της απόδοσης των καταστημάτων. Η παρούσα μελέτη σκοπεύει να συνεισφέρει στην πληρέστερη κατανόηση του τρόπου λειτουργίας του σύγχρονου ελληνικού τραπεζικού συστήματος, αναφορικά με την εξέλιξη και τη στρατηγική ανάπτυξης του φυσικού δικτύου διανομής, που είναι το τραπεζικό κατάστημα. Ο κύριος ερευνητικός στόχος της μελέτης είναι διττός : 1. να διαπιστωθεί το γεγονός ότι υπάρχουν οι μεταβλητές εκείνες, που εκφράζουν τους στρατηγικούς στόχους μιας Τράπεζας (π.χ. μεγέθους, κερδοφορίας, κ.α.) και οι οποίες επεξηγούν τις μεταβολές στον αριθμό των τραπεζικών Καταστημάτων, ώστε να καταλήξουμε στη δημιουργία ενός υποδείγματος. Ταυτόχρονα διερευνάται κατά πόσο το υπόδειγμα αυτό έχει προβλεπτική αξία ώστε να μπορεί να αξιοποιηθεί για να εκτιμηθεί ο «επιθυμητός» αριθμός τραπεζικών καταστημάτων προκειμένου να επιτευχθούν συγκεκριμένοι στρατηγικοί στόχοι μιας Τράπεζας. 2. να δοθεί ένα παράδειγμα ούτως ώστε να γίνει αντιληπτή η διαδικασία επιλογής της τοποθεσίας για την εγκατάσταση ενός νέου καταστήματος, αν κριθεί από την ανωτάτη Διοίκηση μια τράπεζας, βάσει της προηγούμενης διαδικασίας, ότι απαιτείται η επέκταση του φυσικού δικτύου. Τα βήματα της ερευνητικής μεθοδολογίας που ακολουθήθηκε είναι τα εξής: • Επιλέχθηκε η τράπεζα προς μελέτη και συλλέχθηκαν οικονομικά δεδομένα από δημοσιευμένες πηγές για την περίοδο 1990-2003 • Καταγράφηκε η βασική ερευνητική μας υπόθεση υπό τη μορφή μιας εξίσωσης, όπου ο αριθμός των Καταστημάτων μιας Τράπεζας (εξαρτημένη μεταβλητή) είναι συνάρτηση των στρατηγικών στόχων μιας Τράπεζας σε τομείς όπως μερίδια αγοράς, κερδοφορία, αποτελεσματικότητα, κ.α. (ανεξάρτητες μεταβλητές). • Μέσω της ανάλυσης παλινδρόμησης, καταλήξαμε σε μια σειρά πολλαπλών γραμμικών παλινδρομήσεων όπου εντοπίσθηκαν στατιστικά σημαντικές σχέσεις με ορισμένες από τις μεταβλητές μας. Διενεργήθηκαν όλοι οι απαραίτητοι στατιστικοί (διαγνωστικοί) έλεγχοι. • Μέσω της ασαφούς αναλυτικής ιεράρχησης δεδομένων ( fuzzy AHP ) και της μεθόδου TOPSIS επεξεργάστηκαν τα σημαντικότερα κριτήρια που λαμβάνονται υπόψη σε μια διαδικασία χωροθέτησης τραπεζικού καταστήματος και έγινε επιλογή της προτιμότερης τοποθεσίας, αφού ταξινομήθηκαν όλες οι εναλλακτικές επιλογές βάσει της ελκυστικότητάς τους. Η εν λόγω διπλωματική εργασία ακολουθεί την παρακάτω δομή-λογική: Στο πρώτο μέρος παρουσιάζεται η δομή και μια συνοπτική ιστορική εξέλιξη του ελληνικού τραπεζικού συστήματος ώστε να γίνεται κατανοητό το πλαίσιο στο οποίο αναπτύχθηκε το δίκτυο των τραπεζικών καταστημάτων, ως κυρίαρχο κανάλι διανομής. Επίσης αναπτύσσονται οι θεωρίες που αφορούν το τραπεζικό κατάστημα, το ρόλο του, τη δομή του, την εξέλιξή του στα πλαίσια της τραπεζικής αγοράς. Παράλληλα εξετάζεται η βιβλιογραφία που αφορά στις θεωρίες ανάπτυξης, αξιολόγησης και χωροθέτησης των τραπεζικών καταστημάτων. Επιπροσθέτως, παρατίθενται συνοπτικά τρεις μελέτες – άρθρα που αποδελτιώθηκαν από τον ηλεκτρονικό τύπο τα οποία εστιάζουν στη σημασία του δικτύου καταστημάτων μιας τράπεζας, και τελικά, δείχνουν να εξαίρουν τη σπουδαιότητά του ως προς την επίτευξη των επιχειρησιακών στόχων. Στο δεύτερο μέρος παρουσιάζεται μια μελέτη πραγματικής περίπτωσης ενός μοντέλου παλινδρόμησης με το οποίο επιχειρείται να εκτιμηθεί το κατά πόσον επηρεάζεται η μεταβολή του αριθμού των τραπεζικών καταστημάτων συγκεκριμένης τράπεζας από κάποιες μεταβλητές, οι οποίες εκφράζουν συγκεκριμένους στρατηγικούς στόχους της τράπεζας. Στο τρίτο μέρος διενεργείται μελέτη ανάλυσης χωροθέτησης για μια πραγματική περίπτωση, αφού πρώτα παρουσιαστούν οι τεχνικές που εφαρμόστηκαν (AHP, fuzzy AHP, TOPSIS). Στην ουσία πρόκειται για μια μελέτη χωροθέτησης που γίνεται στην τουρκική επικράτεια προκειμένου να επιλεγεί η κατάλληλη περιοχή εγκατάστασης ενός νέου τραπεζικού καταστήματος. Η ιεράρχηση των εξεταζόμενων κριτηρίων επιλογής γίνεται με τη μέθοδο TOPSIS, ενώ η επιλογή της τοποθεσίας πραγματοποιείται με τη βοήθεια της ασαφούς αναλυτικής ιεράρχησης δεδομένων (fuzzy AHP). Μπορούμε να πούμε ότι επιχειρείται να προσεγγιστεί το θέμα της χωροθέτησης με τρόπο παραγωγικό. Από το γενικό, την ανάγκη για νέα καταστήματα σε μια ευρύτερη περιοχή όπως το σύνολο της χώρας-αυτό παρουσιάζεται στο δεύτερο μέρος της συγκεκριμένης διατριβής-πάμε στο ειδικό, την απόφαση για την τοποθεσία του νέου καταστήματος του οποίου την ανάγκη ίδρυσης η προηγούμενη διαδικασία ανέδειξε-πρόκειται για το τρίτο μέρος της διατριβής. Και όλα αυτά, μετά την αναφορά στο τραπεζικό σύστημα, τις λειτουργίες του, τις δομές του και τη διαχρονική εξέλιξή του και ΚΥΡΙΩΣ αφού επισημάνθηκε η σημασία του φυσικού δικτύου μιας και παρουσιάστηκαν μελέτες από διαφορετικές πηγές που ωστόσο συγκλίνουν προς τη συνεχιζόμενη σπουδαιότητα του δικτύου καταστημάτων. / -

As cidades, como um laboratório cotidiano de relacionamentos e produção de renda são, sobretudo nos tempos atuais, elemento decisivo para a construção de soluções capazes de equacionar os grandes desafios do Planeta. Esses aglomerados de pessoas, produtos e atividades, configuram um enorme complexo de inputs desafiadores às questões da sustentabilidade. Os modelos espaciais, apoiados em zoneamento de atividades e acessibilidade física, predominantemente incentivadores da mobilidade com o uso intensivo de veículos automotores, produzem deseconomias sistêmicas, impactam o meio ambiente, retardam, segregam e deterioram a vida comunitária nas cidades. Neste processo de expansão contínua, principalmente as cidades das regiões de menor desenvolvimento econômico, como Ásia, África e América Latina/Caribe consolidam a conformação de Megacidades, requerendo uma nova interpretação para os modelos de mobilidade, capazes de restituir espaços públicos e possibilidades de promoção da vida comunitária. Nessa condição, o domínio das tecnologias de comunicação e informação e o uso cada vez mais frequente da internet pela população jovem incrementam a mobilidade virtual, proporcionam um ciclo de conectividade no espaço urbano e definem um novo modo de viver nas cidades – “o ir e vir, sem sair do lugar”. Este trabalho apresenta uma abordagem, baseada na teoria da localização, no princípio da acessibilidade como formação de valor da terra urbana e nos conceitos da microeconomia e teoria de consumidor, das potencialidades do uso da internet e da realização de deslocamentos virtuais, como elementos novos a serem considerados no planejamento da mobilidade das megacidades. É este novo desafio de como deslocar-se no meio urbano adensado que constituí a principal questão a ser solucionada no desenvolvimento das cidades do futuro. O que se busca observar é a percepção das variações refletidas no valor do tempo e na renda marginal dos usuários do sistema urbano, assim como, os reflexos comportamentais decorrentes desta percepção de utilidade produzida pelo uso e influência das tecnologias digitais na realização de deslocamentos. / Cities, as a daily relationship and income production laboratory, are nowadays a decisive element for building solutions capable of addressing the challenges of the planet. Clusters of people, products and activities constitute a large complex of challenging factors of sustainability issues. However, spatial models, supported by zoning activities and physical accessibility —predominantly mobility incentive-intensive vehicles—can produce systemic diseconomies, impact the environment, as well as delay, segregate and degrade the community life of cities. In this continuous expansion process, the cities in less developed regions, such as Asia, Africa, and Latin America / Caribbean, consolidate with the conformation of Megacities, requiring a new interpretation for models of mobility, that are able to restore public spaces and promote the possibilities of community life. Under these conditions, in the field of information and communication technologies, it can be observed an increasingly frequent use of the Internet by young populations. This increase impact virtual mobility and connectivity by providing a new cycle in the urban space. A new way of living is defined: “you go and come, without leaving your seat”. This paper presents an approach based on location theory and the principle of accessibility as a training value of urban landscapes and the concepts of microeconomics and consumer theory. It also considers the potential use of the Internet and the emergence of virtual displacement, as new elements to consider when planning the mobility of megacities. How to move in urban areas is a major issue that must be solved for the development of cities of the future. Basically, it is pursued the perception of the changes reflected in the value of time and marginal income users and behavioral consequences arising from this perception of usefulness and influence produced by the use of digital technologies in the realization of urban trips.

As cidades, como um laboratório cotidiano de relacionamentos e produção de renda são, sobretudo nos tempos atuais, elemento decisivo para a construção de soluções capazes de equacionar os grandes desafios do Planeta. Esses aglomerados de pessoas, produtos e atividades, configuram um enorme complexo de inputs desafiadores às questões da sustentabilidade. Os modelos espaciais, apoiados em zoneamento de atividades e acessibilidade física, predominantemente incentivadores da mobilidade com o uso intensivo de veículos automotores, produzem deseconomias sistêmicas, impactam o meio ambiente, retardam, segregam e deterioram a vida comunitária nas cidades. Neste processo de expansão contínua, principalmente as cidades das regiões de menor desenvolvimento econômico, como Ásia, África e América Latina/Caribe consolidam a conformação de Megacidades, requerendo uma nova interpretação para os modelos de mobilidade, capazes de restituir espaços públicos e possibilidades de promoção da vida comunitária. Nessa condição, o domínio das tecnologias de comunicação e informação e o uso cada vez mais frequente da internet pela população jovem incrementam a mobilidade virtual, proporcionam um ciclo de conectividade no espaço urbano e definem um novo modo de viver nas cidades – “o ir e vir, sem sair do lugar”. Este trabalho apresenta uma abordagem, baseada na teoria da localização, no princípio da acessibilidade como formação de valor da terra urbana e nos conceitos da microeconomia e teoria de consumidor, das potencialidades do uso da internet e da realização de deslocamentos virtuais, como elementos novos a serem considerados no planejamento da mobilidade das megacidades. É este novo desafio de como deslocar-se no meio urbano adensado que constituí a principal questão a ser solucionada no desenvolvimento das cidades do futuro. O que se busca observar é a percepção das variações refletidas no valor do tempo e na renda marginal dos usuários do sistema urbano, assim como, os reflexos comportamentais decorrentes desta percepção de utilidade produzida pelo uso e influência das tecnologias digitais na realização de deslocamentos. / Cities, as a daily relationship and income production laboratory, are nowadays a decisive element for building solutions capable of addressing the challenges of the planet. Clusters of people, products and activities constitute a large complex of challenging factors of sustainability issues. However, spatial models, supported by zoning activities and physical accessibility —predominantly mobility incentive-intensive vehicles—can produce systemic diseconomies, impact the environment, as well as delay, segregate and degrade the community life of cities. In this continuous expansion process, the cities in less developed regions, such as Asia, Africa, and Latin America / Caribbean, consolidate with the conformation of Megacities, requiring a new interpretation for models of mobility, that are able to restore public spaces and promote the possibilities of community life. Under these conditions, in the field of information and communication technologies, it can be observed an increasingly frequent use of the Internet by young populations. This increase impact virtual mobility and connectivity by providing a new cycle in the urban space. A new way of living is defined: “you go and come, without leaving your seat”. This paper presents an approach based on location theory and the principle of accessibility as a training value of urban landscapes and the concepts of microeconomics and consumer theory. It also considers the potential use of the Internet and the emergence of virtual displacement, as new elements to consider when planning the mobility of megacities. How to move in urban areas is a major issue that must be solved for the development of cities of the future. Basically, it is pursued the perception of the changes reflected in the value of time and marginal income users and behavioral consequences arising from this perception of usefulness and influence produced by the use of digital technologies in the realization of urban trips.

As cidades, como um laboratório cotidiano de relacionamentos e produção de renda são, sobretudo nos tempos atuais, elemento decisivo para a construção de soluções capazes de equacionar os grandes desafios do Planeta. Esses aglomerados de pessoas, produtos e atividades, configuram um enorme complexo de inputs desafiadores às questões da sustentabilidade. Os modelos espaciais, apoiados em zoneamento de atividades e acessibilidade física, predominantemente incentivadores da mobilidade com o uso intensivo de veículos automotores, produzem deseconomias sistêmicas, impactam o meio ambiente, retardam, segregam e deterioram a vida comunitária nas cidades. Neste processo de expansão contínua, principalmente as cidades das regiões de menor desenvolvimento econômico, como Ásia, África e América Latina/Caribe consolidam a conformação de Megacidades, requerendo uma nova interpretação para os modelos de mobilidade, capazes de restituir espaços públicos e possibilidades de promoção da vida comunitária. Nessa condição, o domínio das tecnologias de comunicação e informação e o uso cada vez mais frequente da internet pela população jovem incrementam a mobilidade virtual, proporcionam um ciclo de conectividade no espaço urbano e definem um novo modo de viver nas cidades – “o ir e vir, sem sair do lugar”. Este trabalho apresenta uma abordagem, baseada na teoria da localização, no princípio da acessibilidade como formação de valor da terra urbana e nos conceitos da microeconomia e teoria de consumidor, das potencialidades do uso da internet e da realização de deslocamentos virtuais, como elementos novos a serem considerados no planejamento da mobilidade das megacidades. É este novo desafio de como deslocar-se no meio urbano adensado que constituí a principal questão a ser solucionada no desenvolvimento das cidades do futuro. O que se busca observar é a percepção das variações refletidas no valor do tempo e na renda marginal dos usuários do sistema urbano, assim como, os reflexos comportamentais decorrentes desta percepção de utilidade produzida pelo uso e influência das tecnologias digitais na realização de deslocamentos. / Cities, as a daily relationship and income production laboratory, are nowadays a decisive element for building solutions capable of addressing the challenges of the planet. Clusters of people, products and activities constitute a large complex of challenging factors of sustainability issues. However, spatial models, supported by zoning activities and physical accessibility —predominantly mobility incentive-intensive vehicles—can produce systemic diseconomies, impact the environment, as well as delay, segregate and degrade the community life of cities. In this continuous expansion process, the cities in less developed regions, such as Asia, Africa, and Latin America / Caribbean, consolidate with the conformation of Megacities, requiring a new interpretation for models of mobility, that are able to restore public spaces and promote the possibilities of community life. Under these conditions, in the field of information and communication technologies, it can be observed an increasingly frequent use of the Internet by young populations. This increase impact virtual mobility and connectivity by providing a new cycle in the urban space. A new way of living is defined: “you go and come, without leaving your seat”. This paper presents an approach based on location theory and the principle of accessibility as a training value of urban landscapes and the concepts of microeconomics and consumer theory. It also considers the potential use of the Internet and the emergence of virtual displacement, as new elements to consider when planning the mobility of megacities. How to move in urban areas is a major issue that must be solved for the development of cities of the future. Basically, it is pursued the perception of the changes reflected in the value of time and marginal income users and behavioral consequences arising from this perception of usefulness and influence produced by the use of digital technologies in the realization of urban trips.

This dissertation studies in depth the structure of the Discrete Ordered Median Problem (DOMP), to define new formulations and resolution algorithms. Furthermore we analyze an interesting extension for DOMP, namely MDOMP (Monotone Discrete Ordered Median Problem). This thesis is structured in three main parts.First, a widely theoretical and computational study is reported. It presents several new formulations for the Discrete Ordered Median Problem (DOMP) based on its similarity with some scheduling problems. Some of the new formulations present a considerably smaller number of constraints to define the problem with respect to some previously known formulations. Furthermore, the lower bounds provided by their linear relaxations improve the ones obtained with previous formulations in the literature even when strengthening is not applied. We also present a polyhedral study of the assignment polytope of our tightest formulation showing its proximity to the convex hull of the integer solutions of the problem. Several resolution approaches, among which we mention a branch and cut algorithm, are compared. Extensive computational results on two families of instances, namely randomly generated and from Beasley's OR-library, show the power of our methods for solving DOMP. One of the achievements of the new formulation consists in its tighter LP-bound. Secondly, DOMP is addressed with a new set partitioning formulation using an exponential number of variables. This chapter develops a new formulation in which each variable corresponds to a set of demand points allocated to the same facility with the information of the sorting position of their corresponding distances. We use a column generation approach to solve the continuous relaxation of this model. Then, we apply a branch-cut-and-price algorithm to solve to optimality small to moderate size of DOMP in competitive computational time.To finish, the third contribution of this dissertation is to analyze and compare formulations for the monotone discrete ordered median problem. These formulations combine different ways to represent ordered weighted averages of elements by using linear programs together with the p-median polytope. This approach gives rise to two efficient formulations for DOMP under a hypothesis of monotonicity in the lambda vectors. These formulations are theoretically compared and also compared with some other formulations valid for the case of general lambda vector. In addition, it is also developed another new formulation, for the general case, that exploits the efficiency of the rationale of monotonicity. This representation allows to solve very efficiently some DOMP instances where the monotonicity is only slightly lost. Detailed computational tests on all these formulations is reported in the dissertation. They show that specialized formulations allow to solve to optimality instances with sizes that are far beyond the limits of those that can solve in the general case. / Cette dissertation étudie en profondeur la structure du "Discrete Ordered Median Problem" (DOMP), afin de proposer de nouvelles formulations et de nouveaux algorithmes de résolution. De plus, une extension intéressante du DOMP nommée MDOMP ("Monotone Discrete Ordered Median Problem") a été étudiée.Cette thèse a été structurée en trois grandes parties.La première partie présente une étude riche aux niveaux théorique et expérimentale. Elle développe plusieurs formulations pour le DOMP qui sont basées sur des problèmes d'ordonnancement largement étudiés dans la littérature. Plusieurs d'entres elles nécessitent un nombre réduit de contraintes pour définir le problème en ce qui concerne certaines formulations connues antérieurement. Les bornes inférieures, qui sont obtenues par la résolution de la relaxation linéaire, donnent de meilleurs résultats que les formulations précédentes et ceci même avec tout processus de renforcement désactivé. S'ensuit une étude du polyhèdre de notre formulation la plus forte qui montre sa proximité entre l'enveloppe convexe des solutions entières de notre problème. Un algorithme de branch and cut et d'autres méthodes de résolution sont ensuite comparés. Les expérimentations qui montrent la puissance de nos méthodes s'appuient sur deux grandes familles d'instances. Les premières sont générées aléatoirement et les secondes proviennent de Beasley's OR-library. Ces expérimentations mettent en valeur la qualité de la borne obtenue par notre formulation.La seconde partie propose une formulation "set partitioning" avec un nombre exponentiel de variables. Dans ce chapitre, la formulation comporte des variables associées à un ensemble de demandes affectées à la même facilité selon l'ordre établi sur leurs distances correspondantes. Nous avons alors développé un algorithme de génération de colonnes pour la résolution de la relaxation continue de notre modèle mathématique. Cet algorithme est ensuite déployé au sein d'un Branch-and-Cut-and-Price afin de résoudre des instances de petites et moyennes tailles avec des temps compétitifs.La troisième partie présente l'analyse et la comparaison des différentes formulations du problème DOMP Monotone. Ces formulations combinent plusieurs manières de formuler l'ordre des éléments selon les moyennes pondérées en utilisant plusieurs programmes linéaires du polytope du p-median. Cette approche donne lieu à deux formulations performantes du DOMP sous l'hypothèse de monotonie des vecteurs lambda. Ces formulations sont comparées de manière théorique puis comparées à d'autres formulations valides pour le cas général du vecteur lambda. Une autre formulation est également proposée, elle exploite l'efficacité du caractère rationnel de la monotonie. Cette dernière permet de résoudre efficacement quelques instances où la monotonie a légèrement disparue. Ces formulations ont fait l'objet de plusieurs expérimentations dècrites dans ce manuscrit de thèse. Elles montrent que les formulations spécifiques permettent de résoudre des instances plus importantes que pour le cas général. / Este trabajo estudia en profundidad la estructura del problema disctreto de la mediana ordenada (DOMP, por su acrónimo en inglés) con el objetivo de definir nuevas formulaciones y algoritmos de resolución. Además, analizamos una interesante extensión del DOMP conocida como el problema monótono discreto de la mediana ordenada (MDOMP, de su acrónimo en inglés).Esta tesis se compone de tres grandes bloques.En primer lugar, se desarrolla un detallado estudio teórico y computacional. Se presentan varias formulaciones nuevas para el problema discreto de la mediana ordenada (DOMP) basadas en su similaridad con algunos problemas de secuenciación. Algunas de estas formulaciones requieren de un cosiderable menor número de restricciones para definir el problema respecto a algunas de las formulaciones previamente conocidas. Además, las cotas inferiores proporcionadas por las relajaciones lineales mejoran a las obtenidas con formulaciones previas de la literatura incluso sin reforzar la nueva formulación. También presentamos un estudio poliédrico del politopo de asignación de nuestra formulación más compacta mostrando su proximidad con la envolvente convexa de las soluciones enteras del problema. Se comparan algunos procedimientos de resolución, entre los que destacamos un algoritmo de ramificación y corte. Amplios resultados computacionales sobre dos familias de instancias -aleatoriamente generadas y utilizando la Beasley's OR-library- muestran la potencia de nuestros métodos para resolver el DOMP.En el segundo bloque, el problema discreto de la mediana ordenada es abordado con una formulación de particiones de conjuntos empleando un número exponencial de variables. Este capítulo desarrolla una nueva formulación en la que cada variable corresponde a un conjunto de puntos de demanda asignados al mismo servidor con la información de la posición obtenida de ordenar las distancias correspondientes. Utilizamos generación de columnas para resolver la relajación continua del modelo. Después, empleamos un algoritmo de ramificación, acotación y "pricing" para resolver a optimalidad tamaños moderados del DOMP en un tiempo computacional competitivo.Por último, el tercer bloque de este trabajo se dedica a analizar y comparar formulaciones para el problema monótono discreto de la mediana ordenada. Estas formulaciones combinan diferentes maneras de representar medidas de pesos ordenados de elementos utilizando programación lineal junto con el politopo de la $p$-mediana. Este enfoque da lugar a dos formulaciones eficientes para el DOMP bajo la hipótesis de monotonía en su vector $lambda$. Se comparan teóricamente las formulaciones entre sí y frente a algunas de las formulaciones válidas para el caso general. Adicionalmente, se desarrolla otra formulación válida para el caso general que explota la eficiencia de las ideas de la monotonicidad. Esta representación permite resolver eficientemente algunos ejemplos donde la monotonía se pierde ligeramente. Finalmente, llevamos a cabo un detallado estudio computacional, en el que se aprecia que las formulaciones ad hoc permiten resolver a optimalidad ejemplos cuyo tamaño supera los límites marcados en al caso general. / Doctorat en Sciences / info:eu-repo/semantics/nonPublished

This work addresses the following question: How has the prominent scholarly literature on the Cayman Islands promoted a discourse that serves to undermine the acknowledgment of African contributions as well as African self-identification in the country? Utilizing an Afrocentric inquiry, the method of content analysis was employed to interrogate selected texts using location theory. It was found that the majority of literature on the Cayman Islands, as well as the dominant ideology within the Caribbean has indeed undermined the acknowledgement of African contributions as well as African self-identification in the country. More scholarship is needed that examines the experiences of African descended people living in the Caribbean from their own perspective, and critically engages dislocated texts. / African American Studies