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Preséntase unha introdución á programación e lineal e dúas ferramentas informáticas gratuítas que permiten a resolución dos problemas de programación lineal. Efectúase unha ilustración das ferramentas por medio de exemplos.

[Abstract]: One of the practical applications of cooperative transferable utility games involves determining the fee structure for users of a given facility, whose construction or maintenance costs need to be recouped. In this context, certain efficiency and equity criteria guide the considered solutions. This paper analyzes how to allocate the fixed costs of a highway among its users through tolls, considering that different classes of vehicles or travelers utilize the service. For this purpose, we make use of generalized highway games with a priori unions that represent distinct user groups, such as frequent travelers or truckers, who, due to enhanced bargaining power, often secure reductions in their fares in real-world scenarios. In particular, the Owen value, the coalitional Tijs value, and a new value termed the Shapley–Tijs value are axiomatically characterized. Additionally, straightforward formulations for calculating these values are provided. Finally, the proposed methodology is applied to actual traffic data from the AP-9 highway in Spain.

This paper presents a new formulation for the routing problem in which the available fleet consists of trucks and trailers divided into compartments. Solving the model for large instances is computationally expensive. Therefore, we introduce and implemented a two-phase heuristic algorithm. In the first phase, an initial solution is generated through a constructive heuristic algorithm based on concepts from the classic Clarke-Wright algorithm. In the second phase, the initial solution is improved by an iterated tabu search metaheuristic. Our algorithm was tested on 21 instances that were converted from the classic truck and trailer routing problem. The results of our computational study prove the effectiveness of our proposal; the algorithm always finds a feasible solution, which in small-sized problems it is proven to be of good quality. In addition, the algorithm outperforms previous approaches for some truck and trailer routing problem instances. Furthermore, an application of the proposed model and heuristic is demonstrated in the field of agricultural logistics by comparing the obtained results.

Based on Holler (1982), Colomer and Martínez (1995), and Armijos-Toro et al. (2021), we propose two power indices to measure the influence of the players in these classes of weighted majority games in partition function form. We compare the new power indices with their original versions on the class of games in characteristic function form. Finally, we use both new power indices and the two power indices for games in partition function form studied in Alonso-Meijide et al. (2017) to study the distribution of power in the National Assembly of Ecuador that emerged after the elections of February 7, 2021.

The identification of the most potentially hazardous agents in a terrorist organisation helps to prevent further attacks by effectively allocating surveillance resources and destabilising the covert network to which they belong. In this paper, several mechanisms for the overall ranking of covert networks members in a general framework are addressed based on their contribution to the overall relative effectiveness in the event of a merger. In addition, the possible organisation of agents outside of each possible merger naturally influences their relative effectiveness score, which motivates the innovative use of games in partition function form and specific ranking indices for individuals. Finally, we apply these methods to analyse the effectiveness of the hijackers of the covert network supporting the 9/11 attacks

Operations Research (OR) is a discipline in which advanced analytical methods are developed and used to solve problems and aid in decision-making. There are a wide variety of fields where OR can be applied, one of which is logistics. Optimizing and scheduling a certain network is a fundamental task, accomplished by proposing models and solving algorithms for each particular situation. Logistic problems are also often treated by the practitioners of OR from a cooperative standpoint, which can be approached through game theory. This thesis addresses several OR and game theoretical problems that have applications in the logistics domain. The performance of the proposed methodologies is analyzed and illustrated with real data applications.

In this paper, we first use the information we have on the patients of an oncology day hospital to distribute the treatment schedules they have in each of the visits to this centre. To do this, we propose a deterministic mathematical programming model in such a way that we minimise the duration of the waiting room stays of the total set of patients and taking into account the restrictions of the circuit. Secondly, we will look for a solution to the same problem under a stochastic approach. This model will explicitly consider the existing uncertainty in terms of the different times involved in the circuit, and this model also allows the reorganisation of the schedules of medical appointments with oncologists. The models are complemented by a tool that solves the problem of assigning nurses to patients. The work is motivated by the particular characteristics of a real hospital and the models are used and compared with data from this case.

Muchas situaciones de conflicto social o económico pueden modelizarse especificando los resultados sobre los que las partes implicadas pueden ponerse de acuerdo, y un resultado especial que resume lo que ocurre en caso de que no se llegue a un acuerdo. Este modelo se denomina juego de negociación, y una aplicación que asigna un resultado a cada juego de negociación se llama solución de negociación. En el enfoque cooperativo de la teoría de juegos, las soluciones de negociación se caracterizan matemáticamente por propiedades deseables, que suelen denominarse axiomas. En el enfoque no cooperativo, las soluciones se derivan como equilibrios de modelos estratégicos que describen un procedimiento de negociación subyacente. En este trabajo se propone un estudio de los modelos cooperativos y axiomáticos de la negociación, comenzando por el documento seminal de Nash, The Bargaining Problem. Se pretende una visión general de algunos de los principales resultados en esta área, así como una introducción a los modelos no cooperativos de negociación, en particular sobre aquellos modelos que conducen a soluciones de negociación que también resultan del enfoque axiomático. El foco principal estará en algunas de las principales axiomatizaciones existentes de soluciones para juegos de negociación, y se incluirá la herramienta necesaria de la teoría de la utilidad, así como alguna aplicación tomada de la vida real., Many situations of social or economic conflict can be modelled by specifying the outcomes on which the parties involved can agree, and a special result that summarizes what happens in the event of a no-deal. This model is called a negotiation game, and an application that assigns a result to each negotiation game is called a negotiation solution. In the cooperative approach of game theory, negotiation solutions are mathematically characterized by desirable properties, which are often referred to as axioms. In the non-cooperative approach, solutions are derived as balances of strategic models that describe an underlying trading procedure. This paper proposes a study of cooperative and axiomatic models of negotiation, starting with Nash’s seminal document, The Bargaining Problem. An overview of some of the main outcomes in this area is intended, as well as an introduction to non cooperative models of negotiation, in particular on those models that lead to negotiation solutions that also result from the axiomatic approach. The main focus will be on some of the main existing axiomatizations of solutions for trading games, and the necessary tool of utility theory will be included, as well as some application taken from real life.

A aprendizaxe profunda é unha disciplina que está en auxe dada a súa adecuación para resolver problemas complexos. Este traballo recolle a historia da aprendizaxe profunda dende os seus inicios, así como os conceptos básicos necesarios para a súa comprensión. Introdúcense as definicións formais dalgunhas funcións de activación, distintos tipos de redes neuronais como as redes recorrentes ou convolucionais e algoritmos e conceptos relativos ao seu adestramento. Finalmente, amósanse algunhas das aplicacións que ten no mundo real., Deep learning is a discipline that is on the rise given its suitability for solving complex problems. This project encompases the history of deep learning from its beginnings, as well as the basic concepts needed for its understanding. It introduces the formal definitions of some activation functions, several types of neural networks such as recurrent or convolutional networks and algorithms and concepts related to their training. Finally, it showcases some of the applications it has on the real world.

Esta tesis tiene como objetivo proponer nuevas representaciones distribucionales y métodos estadísticos en espacios métricos para modelar de forma eficaz los datos procedentes de la monitorización continua de los pacientes durante las actividades propias de su vida diaria. Proponemos nuevas pruebas de hipótesis para datos emparejados, modelos de regresión, algoritmos de cuantificación de la incertidumbre, pruebas de independencia estadística y algoritmos de análisis de conglomerados para las nuevas representaciones distribucionales y otros objetos estadísticos complejos. Los diferentes resultados recogidos a lo largo de la tesis muestran las ventajas en términos de predicción, interpretabilidad y capacidad de modelización de las nuevas propuestas frente a los metodos existentes.

This paper deals with an important subject in classification problems addressed by machine learning techniques: the evaluation of the influence of each of the features on the classification of individuals. Specifically, a measure of that influence is introduced using the Shapley value of cooperative games. In addition, an axiomatic characterisation of the proposed measure is provided based on properties of efficiency and balanced contributions. Furthermore, some experiments have been designed in order to validate the appropriate performance of such measure. Finally, the methodology introduced is applied to a sample of COVID-19 patients to study the influence of certain demographic or risk factors on various events of interest related to the evolution of the disease