El modelo EOQ es un modelo de gestión de inventario de un único producto con demanda constante por unidad de tiempo al que se enfrenta una empresa. Su objetivo es encontrar el tamaño óptimo de pedido de modo que se minimice una determinada función de coste. Si varias empresas demandan el mismo producto pueden cooperar realizando pedidos conjuntos para minimizar el coste total. En esta situación ha estudiarse si resulta beneficioso esta acción y, en caso afirmativo, establecer cuál será el reparto del coste final soportado por cada empresa. En esta charla revisaremos algunos modelos cooperativos de inventario EOQ con diferentes funciones de coste y expondremos algunos repartos del coste final mostrando sus propiedades.

The design, management and use of any type of complex network requires a methodology to handle its parameters, detect deficiencies and coordinate their resources to solve the problems that arise. Developing methods to carry out such actions demands, among other things, the preliminary screening of large masses of data, quantitative analysis to design better information structures, often organized as networks, and the solution of optimization problems related to clustering, location, routes, allocation of flows and traffic of any kind, distribution of intelligent sensors, early detection of extreme observations, profiling user behavior and operations planning, often under an environment of risk or uncertainty, etc. All those operations involve large masses of data that must be integrated in all phases of the operational analysis. The standard approach of handling separately/sequentially data and design is defective and lacks the important gain of integration. Data integration, data reduction, feature selection, outliers detection, intelligent segmentation or separability are the driving challenges that relies on tools such as machine learning, statistical analysis, optimization, and mathematical programming.
One step forward to bring the gap of integration in data science is the application of techniques from optimization and statistics. In this talk, we focus on one important challenge: “integration of design, optimization and data”. This approach sets a very ambitious objective: to improve the data science paradigm integrating techniques of location and networks analysis and vice versa. The two features of datafication and universalization of the available information establish a subtle difference with the standard methodologies of location science and network analysis: the representation of complex environments with large masses of data imposes the need to apply more advanced tools of mathematics and machine learning to allow the design, the effective treatment and use of data at all levels and the optimization of the problems that arise from them.
In general terms, the challenge that is currently posed in this field is, not only, to incorporate the methodology of data science into the analysis of large scale networks, in order to deal with problems that involve large masses of data ("Big Data"); but also, reciprocally, how to make use of the tools and models of optimization and network design in data science. This talk will surf over recent results of our team (see references) in this respect, showing how modern location analysis techniques improve several machine learning methodologies including regression, unsupervised and supervised classification and community detection.

Las matemáticas pueden ayudarnos a entender nuestro comportamiento colectivo, también en redes sociales. La estructura de las redes y los algoritmos que regulan la información que recibimos y enviamos hacen que a veces se den fenómenos inesperados, no siempre positivos. Conocerlos puede ayudarnos a tener una mejor experiencia de acceso a las redes sociales. Y en este empeño, las matemáticas son un aliado insustituible.

In this presentation, we will embark on a journey through the realm of disease mapping, exploring both univariate and multivariate spatio-temporal statistical models. Some ideas related to the analysis of high-dimensional data in this context will also be presented. Moreover, we will spotlight the latest applications of these models, addressing both violence against women in India and cancer mortality.