Application of Decision Theory methods for a Community of Madrid Soil classification case

A land classi���cation method was designed for the Community of Madrid (CM), which has lands suitable for either agriculture use or natural spaces. The process started from an extensive previous CM study that contains sets of land attributes with data for 122 types and a minimum-requirements method providing a land quality classi���cation (SQ) for each land. Borrowing some tools from Operations Research (OR) and from Decision Science, that SQ has been complemented by an additive valuation method that involves a more restricted set of 13 representative attributes analysed using Attribute Valuation Functions to obtain a quality index, QI, and by an original composite method that uses a fuzzy set procedure to obtain a combined quality index, CQI, that contains relevant information from both the SQ and the QI methods.

Some past decision theory models for euro construction model codes and for road drainage in Spain, and modest hints with multi-criteria methods for agro and environmental assurance

The authors are from UPM and are relatively grouped, and all have intervened in different academic or real cases on the subject, at different times as being of different age. With precedent from E. Torroja and A. P��ez in Madrid Spain Safety Probabilistic models for concrete about 1957, now in ICOSSAR conferences, author J.M. Ant��n involved since autumn 1967 for euro-steel construction in CECM produced a math model for independent load superposition reductions, and using it a load coefficient pattern for codes in Rome Feb. 1969, practically adopted for European constructions, giving in JCSS Lisbon Feb. 1974 suggestion of union for concrete-steel-al.. That model uses model for loads like Gumbel type I, for 50 years for one type of load, reduced to 1 year to be added to other independent loads, the sum set in Gumbel theories to 50 years return period, there are parallel models. A complete reliability system was produced, including non linear effects as from buckling, phenomena considered somehow in actual Construction Eurocodes produced from Model Codes. The system was considered by author in CEB in presence of Hydraulic effects from rivers, floods, sea, in reference with actual practice. When redacting a Road Drainage Norm in MOPU Spain an optimization model was realized by authors giving a way to determine the figure of Return Period, 10 to 50 years, for the cases of hydraulic flows to be considered in road drainage. Satisfactory examples were a stream in SE of Spain with Gumbel Type I model and a paper of Ven Te Chow with Mississippi in Keokuk using Gumbel type II, and the model can be modernized with more varied extreme laws. In fact in the MOPU drainage norm the redacting commission acted also as expert to set a table of return periods for elements of road drainage, in fact as a multi-criteria complex decision system. These precedent ideas were used e.g. in wide Codes, indicated in symposia or meetings, but not published in journals in English, and a condensate of contributions of authors is presented. The authors are somehow involved in optimization for hydraulic and agro planning, and give modest hints of intended applications in presence of agro and environment planning as a selection of the criteria and utility functions involved in bayesian, multi-criteria or mixed decision systems. Modest consideration is made of changing in climate, and on the production and commercial systems, and on others as social and financial.

The Learning of the Mathematical Models to Aid Decision Making in the High Level Engineering Schools?

At present, in the University curricula in most countries, the decision theory and the mathematical models to aid decision making is not included, as in the graduate program like in Doctored and Master��s programs. In the Technical School of High Level Agronomic Engineers of the Technical University of Madrid (ETSIA-UPM), the need to offer to the future engineers training in a subject that could help them to take decisions in their profession was felt. Along the life, they will have to take a lot of decisions. Ones, will be important and others no. In the personal level, they will have to take several very important decisions, like the election of a career, professional work, or a couple, but in the professional field, the decision making is the main role of the Managers, Politicians and Leaders. They should be decision makers and will be paid for it. Therefore, nobody can understand that such a professional that is called to practice management responsibilities in the companies, does not take training in such an important matter. For it, in the year 2000, it was requested to the University Board to introduce in the curricula an optional qualified subject of the second cycle with 4,5 credits titled " Mathematical Methods for Making Decisions ". A program was elaborated, the didactic material prepared and programs as Maple, Lingo, Math Cad, etc. installed in several IT classrooms, where the course will be taught. In the course 2000-2001 this subject was offered with a great acceptance that exceeded the forecasts of capacity and had to be prepared more classrooms. This course in graduate program took place in the Department of Applied Mathematics to the Agronomic Engineering, as an extension of the credits dedicated to Mathematics in the career of Engineering.

Phase transitions in number theory: from the birthday problem to Sidon sets

In this work, we show how number theoretical problems can be fruitfully approached with the tools of statistical physics. We focus on g-Sidon sets, which describe sequences of integers whose pairwise sums are different, and propose a random decision problem which addresses the probability of a random set of k integers to be g-Sidon. First, we provide numerical evidence showing that there is a crossover between satisfiable and unsatisfiable phases which converts to an abrupt phase transition in a properly defined thermodynamic limit. Initially assuming independence, we then develop a mean-field theory for the g-Sidon decision problem. We further improve the mean-field theory, which is only qualitatively correct, by incorporating deviations from independence, yielding results in good quantitative agreement with the numerics for both finite systems and in the thermodynamic limit. Connections between the generalized birthday problem in probability theory, the number theory of Sidon sets and the properties of q-Potts models in condensed matter physics are briefly discussed

Contributions to trajectory prediction theory and its application to arrival management for air traffic control

La gesti��n del tr��fico a��reo (Air Traffic Management, ATM) est�� experimentando un cambio de paradigma hacia las denominadas operaciones basadas trayectoria. Bajo dicho paradigma se modifica el papel de los controladores de tr��fico a��reo desde una operativa basada su intervenci��n t��ctica continuada hacia una labor de supervisi��n a m��s largo plazo. Esto se apoya en la creciente confianza en las soluciones aportadas por las herramientas automatizadas de soporte a la decisi��n m��s modernas. Para dar soporte a este concepto, se precisa una importante inversi��n para el desarrollo, junto con la adquisici��n de nuevos equipos en tierra y embarcados, que permitan la sincronizaci��n precisa de la visi��n de la trayectoria, basada en el intercambio de informaci��n entre ambos actores. Durante los ��ltimos 30 a 40 a��os las aerol��neas han generado uno de los menores retornos de la inversi��n de entre todas las industrias. Sin beneficios tangibles, la industria a��rea tiene dificultades para atraer el capital requerido para su modernizaci��n, lo que retrasa la implantaci��n de dichas mejoras. Esta tesis tiene como objetivo responder a la pregunta de si las capacidades actualmente instaladas en las aeronaves comerciales se pueden aplicar para lograr la sincronizaci��n de la trayectoria con el nivel de calidad requerido. Adem��s, se analiza en ella si, conjuntamente con mejoras en las herramientas de predicci��n trayectorias instaladas en tierra en para facilitar la gesti��n de las arribadas, dichas capacidades permiten obtener los beneficios esperados en el marco de las operaciones basadas en trayectoria. Esto podr��a proporcionar un incentivo para futuras actualizaciones de la avi��nica que podr��an llevar a mejoras adicionales. El concepto operacional propuesto en esta tesis tiene como objetivo permitir que los aviones sean pilotados de una manera consistente con las t��cnicas actuales de vuelo optimizado. Se permite a las aeronaves que desciendan en el denominado ���modo de ��ngulo de descenso gestionado��� (path-managed mode), que es el preferido por la mayor��a de las compa����as a��reas, debido a que conlleva un reducido consumo de combustible. El problema de este modo es que en ��l no se controla de forma activa el tiempo de llegada al punto de inter��s. En nuestro concepto operacional, la incertidumbre temporal se gestiona en mediante de la medici��n del tiempo en puntos estrat��gicamente escogidos a lo largo de la trayectoria de la aeronave, y permitiendo la modificaci��n por el control de tierra de la velocidad de la aeronave. Aunque la base del concepto es la gesti��n de las ordenes de velocidad que se proporcionan al piloto, para ser capaces de operar con los niveles de equipamiento t��picos actualmente, dicho concepto tambi��n constituye un marco en el que la avi��nica m��s avanzada (por ejemplo, que permita el control por el FMS del tiempo de llegada) puede integrarse de forma natural, una vez que esta tecnolog��a este instalada. Adem��s de gestionar la incertidumbre temporal a trav��s de la medici��n en m��ltiples puntos, se intenta reducir dicha incertidumbre al m��nimo mediante la mejora de las herramienta de predicci��n de la trayectoria en tierra. En esta tesis se presenta una novedosa descomposici��n del proceso de predicci��n de trayectorias en dos etapas. Dicha descomposici��n permite integrar adecuadamente los datos de la trayectoria de referencia calculada por el Flight Management System (FMS), disponibles usando Futuro Sistema de Navegaci��n A��rea (FANS), en el sistema de predicci��n de trayectorias en tierra. FANS es un equipo presente en los aviones comerciales de fuselaje ancho actualmente en la producci��n, e incluso algunos aviones de fuselaje estrecho pueden tener instalada avionica FANS. Adem��s de informar autom��ticamente de la posici��n de la aeronave, FANS permite proporcionar (parte de) la trayectoria de referencia en poder de los FMS, pero la explotaci��n de esta capacidad para la mejora de la predicci��n de trayectorias no se ha estudiado en profundidad en el pasado. La predicci��n en dos etapas proporciona una soluci��n adecuada al problema de sincronizaci��n de trayectorias aire-tierra dado que permite la sincronizaci��n de las dimensiones controladas por el sistema de guiado utilizando la informaci��n de la trayectoria de referencia proporcionada mediante FANS, y tambi��n facilita la mejora en la predicci��n de las dimensiones abiertas restantes usado un modelo del guiado que explota los modelos meteorol��gicos mejorados disponibles en tierra. Este proceso de predicci��n de la trayectoria de dos etapas se aplic�� a una muestra de 438 vuelos reales que realizaron un descenso continuo (sin intervenci��n del controlador) con destino Melbourne. Dichos vuelos son de aeronaves del modelo Boeing 737-800, si bien la metodolog��a descrita es extrapolable a otros tipos de aeronave. El m��todo propuesto de predicci��n de trayectorias permite una mejora en la desviaci��n est��ndar del error de la estimaci��n del tiempo de llegada al punto de inter��s, que es un 30% menor que la que obtiene el FMS. Dicha trayectoria prevista mejorada se puede utilizar para establecer la secuencia de arribadas y para la asignaci��n de las franjas horarias para cada aterrizaje (slots). Sobre la base del slot asignado, se determina un perfil de velocidades que permita cumplir con dicho slot con un impacto m��nimo en la eficiencia del vuelo. En la tesis se propone un nuevo algoritmo que determina las velocidades requeridas sin necesidad de un proceso iterativo de b��squeda sobre el sistema de predicci��n de trayectorias. El algoritmo se basa en una parametrizaci��n inteligente del proceso de predicci��n de la trayectoria, que permite relacionar el tiempo estimado de llegada con una funci��n polin��mica. Resolviendo dicho polinomio para el tiempo de llegada deseado, se obtiene de forma natural el perfil de velocidades optimo para cumplir con dicho tiempo de llegada sin comprometer la eficiencia. El dise��o de los sistemas de gesti��n de arribadas propuesto en esta tesis aprovecha la avi��nica y los sistemas de comunicaci��n instalados de un modo mucho m��s eficiente, proporcionando valor a��adido para la industria. Por tanto, la soluci��n es compatible con la transici��n hacia los sistemas de avi��nica avanzados que est��n desarroll��ndose actualmente. Los beneficios que se obtengan a lo largo de dicha transici��n son un incentivo para inversiones subsiguientes en la avi��nica y en los sistemas de control de tr��fico en tierra. ABSTRACT Air traffic management (ATM) is undergoing a paradigm shift towards trajectory based operations where the role of an air traffic controller evolves from that of continuous intervention towards supervision, as decision making is improved based on increased confidence in the solutions provided by advanced automation. To support this concept, significant investment for the development and acquisition of new equipment is required on the ground as well as in the air, to facilitate the high degree of trajectory synchronisation and information exchange required. Over the past 30-40 years the airline industry has generated one of the lowest returns on invested capital among all industries. Without tangible benefits realised, the airline industry may find it difficult to attract the required investment capital and delay acquiring equipment needed to realise the concept of trajectory based operations. In response to these challenges facing the modernisation of ATM, this thesis aims to answer the question whether existing aircraft capabilities can be applied to achieve sufficient trajectory synchronisation and improvements to ground-based trajectory prediction in support of the arrival management process, to realise some of the benefits envisioned under trajectory based operations, and to provide an incentive for further avionics upgrades. The proposed operational concept aims to permit aircraft to operate in a manner consistent with current optimal aircraft operating techniques. It allows aircraft to descend in the fuel efficient path managed mode as preferred by a majority of airlines, with arrival time not actively controlled by the airborne automation. The temporal uncertainty is managed through metering at strategically chosen points along the aircraft���s trajectory with primary use of speed advisories. While the focus is on speed advisories to support all aircraft and different levels of equipage, the concept also constitutes a framework in which advanced avionics as airborne time-of-arrival control can be integrated once this technology is widely available. In addition to managing temporal uncertainty through metering at multiple points, this temporal uncertainty is minimised by improving the supporting trajectory prediction capability. A novel two-stage trajectory prediction process is presented to adequately integrate aircraft trajectory data available through Future Air Navigation Systems (FANS) into the ground-based trajectory predictor. FANS is standard equipment on any wide-body aircraft in production today, and some single-aisle aircraft are easily capable of being fitted with FANS. In addition to automatic position reporting, FANS provides the ability to provide (part of) the reference trajectory held by the aircraft���s Flight Management System (FMS), but this capability has yet been widely overlooked. The two-stage process provides a ���best of both world���s��� solution to the air-ground synchronisation problem by synchronising with the FMS reference trajectory those dimensions controlled by the guidance mode, and improving on the prediction of the remaining open dimensions by exploiting the high resolution meteorological forecast available to a ground-based system. The two-stage trajectory prediction process was applied to a sample of 438 FANS-equipped Boeing 737-800 flights into Melbourne conducting a continuous descent free from ATC intervention, and can be extrapolated to other types of aircraft. Trajectories predicted through the two-stage approach provided estimated time of arrivals with a 30% reduction in standard deviation of the error compared to estimated time of arrival calculated by the FMS. This improved predicted trajectory can subsequently be used to set the sequence and allocate landing slots. Based on the allocated landing slot, the proposed system calculates a speed schedule for the aircraft to meet this landing slot at minimal flight efficiency impact. A novel algorithm is presented that determines this speed schedule without requiring an iterative process in which multiple calls to a trajectory predictor need to be made. The algorithm is based on parameterisation of the trajectory prediction process, allowing the estimate time of arrival to be represented by a polynomial function of the speed schedule, providing an analytical solution to the speed schedule required to meet a set arrival time. The arrival management solution proposed in this thesis leverages the use of existing avionics and communications systems resulting in new value for industry for current investment. The solution therefore supports a transition concept from mixed equipage towards advanced avionics currently under development. Benefits realised under this transition may provide an incentive for ongoing investment in avionics.

A group decision-making methodology with incomplete individual beliefs applied to e-Democracy

We consider the situation where there are several alternatives for investing a quantity of money to achieve a set of objectives. The choice of which alternative to apply depends on how citizens and political representatives perceive that such objectives should be achieved. All citizens with the right to vote can express their preferences in the decision-making process. These preferences may be incomplete. Political representatives represent the citizens who have not taken part in the decision-making process. The weight corresponding to political representatives depends on the number of citizens that have intervened in the decision-making process. The methodology we propose needs the participants to specify for each alternative how they rate the different attributes and the relative importance of attributes. On the basis of this information an expected utility interval is output for each alternative. To do this, an evidential reasoning approach is applied. This approach improves the insightfulness and rationality of the decision-making process using a belief decision matrix for problem modeling and the Dempster?Shafer theory of evidence for attribute aggregation. Finally, we propose using the distances of each expected utility interval from the maximum and the minimum utilities to rank the alternative set. The basic idea is that an alternative is ranked first if its distance to the maximum utility is the smallest, and its distance to the minimum utility is the greatest. If only one of these conditions is satisfied, a distance ratio is then used.

Dominance measuring methods within MAVT/MAUT with imprecise information concerning decision-makers'preferences

Dominance measuring methods are an approach for dealing with complex decision-making problems with imprecise information within multi-attribute value/utility theory. These methods are based on the computation of pairwise dominance values and exploit the information in the dominance matrix in different ways to derive measures of dominance intensity and rank the alternatives under consideration. In this paper we review dominance measuring methods proposed in the literature for dealing with imprecise information (intervals, ordinal information or fuzzy numbers) about decision-makers? preferences and their performance in comparison with other existing approaches, like SMAA and SMAA-II or Sarabando and Dias? method.

Veto values in Group Decision Making within MAUT: aggregating complete rankings derived from dominance intensity measures

We consider a groupdecision-making problem within multi-attribute utility theory, in which the relative importance of decisionmakers (DMs) is known and their preferences are represented by means of an additive function. We allow DMs to provide veto values for the attribute under consideration and build veto and adjust functions that are incorporated into the additive model. Veto functions check whether alternative performances are within the respective veto intervals, making the overall utility of the alternative equal to 0, where as adjust functions reduce the utilty of the alternative performance to match the preferences of other DMs. Dominance measuring methods are used to account for imprecise information in the decision-making scenario and to derive a ranking of alternatives for each DM. Specifically, ordinal information about the relative importance of criteria is provided by each DM. Finally, an extension of Kemeny's method is used to aggregate the alternative rankings from the DMs accounting for the irrelative importance.

Hybrid wind-diesel power plant valuation and optimization using real option theory and dynamic programming

El sistema de energ��a e��lica-diesel h��brido tiene un gran potencial en la prestaci��n de suministro de energ��a a comunidades remotas. En comparaci��n con los sistemas tradicionales de diesel, las plantas de energ��a h��bridas ofrecen grandes ventajas tales como el suministro de capacidad de energ��a extra para "microgrids", reducci��n de los contaminantes y emisiones de gases de efecto invernadero, y la cobertura del riesgo de aumento inesperado del precio del combustible. El principal objetivo de la presente tesis es proporcionar nuevos conocimientos para la evaluaci��n y optimizaci��n de los sistemas de energ��a h��brido e��lico-diesel considerando las incertidumbres. Dado que la energ��a e��lica es una variable estoc��stica, ��sta no puede ser controlada ni predecirse con exactitud. La naturaleza incierta del viento como fuente de energ��a produce serios problemas tanto para la operaci��n como para la evaluaci��n del valor del sistema de energ��a e��lica-diesel h��brido. Por un lado, la regulaci��n de la potencia inyectada desde las turbinas de viento es una dif��cil tarea cuando opera el sistema h��brido. Por otro lado, el bene.cio econ��mico de un sistema e��lico-diesel h��brido se logra directamente a trav��s de la energ��a entregada a la red de alimentaci��n de la energ��a e��lica. Consecuentemente, la incertidumbre de los recursos e��licos incrementa la dificultad de estimar los beneficios globales en la etapa de planificaci��n. La principal preocupaci��n del modelo tradicional determinista es no tener en cuenta la incertidumbre futura a la hora de tomar la decisi��n de operaci��n. Con lo cual, no se prev�� las acciones operativas flexibles en respuesta a los escenarios futuros. El an��lisis del rendimiento y simulaci��n por ordenador en el Proyecto E��lico San Crist��bal demuestra que la incertidumbre sobre la energ��a e��lica, las estrategias de control, almacenamiento de energ��a, y la curva de potencia de aerogeneradores tienen un impacto significativo sobre el rendimiento del sistema. En la presente tesis, se analiza la relaci��n entre la teor��a de valoraci��n de opciones y el proceso de toma de decisiones. La opci��n real se desarrolla con un modelo y se presenta a trav��s de ejemplos pr��cticos para evaluar el valor de los sistemas de energ��a e��lica-diesel h��bridos. Los resultados muestran que las opciones operacionales pueden aportar un valor adicional para el sistema de energ��a h��brida, cuando esta flexibilidad operativa se utiliza correctamente. Este marco se puede aplicar en la optimizaci��n de la operaci��n a corto plazo teniendo en cuenta la naturaleza dependiente de la trayectoria de la pol��tica ��ptima de despacho, dadas las plausibles futuras realizaciones de la producci��n de energ��a e��lica. En comparaci��n con los m��todos de valoraci��n y optimizaci��n existentes, el resultado del caso de estudio num��rico muestra que la pol��tica de operaci��n resultante del modelo de optimizaci��n propuesto presenta una notable actuaci��n en la reducci��n del con- sumo total de combustible del sistema e��lico-diesel. Con el .n de tomar decisiones ��ptimas, los operadores de plantas de energ��a y los gestores de ��stas no deben centrarse s��lo en el resultado directo de cada acci��n operativa, tampoco deber��an tomar decisiones deterministas. La forma correcta es gestionar din��micamente el sistema de energ��a teniendo en cuenta el valor futuro condicionado en cada opci��n frente a la incertidumbre. ABSTRACT Hybrid wind-diesel power systems have a great potential in providing energy supply to remote communities. Compared with the traditional diesel systems, hybrid power plants are providing many advantages such as providing extra energy capacity to the micro-grid, reducing pollution and greenhouse-gas emissions, and hedging the risk of unexpected fuel price increases. This dissertation aims at providing novel insights for assessing and optimizing hybrid wind-diesel power systems considering the related uncertainties. Since wind power can neither be controlled nor accurately predicted, the energy harvested from a wind turbine may be considered a stochastic variable. This uncertain nature of wind energy source results in serious problems for both the operation and value assessment of the hybrid wind-diesel power system. On the one hand, regulating the uncertain power injected from wind turbines is a difficult task when operating the hybrid system. On the other hand, the economic profit of a hybrid wind-diesel system is achieved directly through the energy delivered to the power grid from the wind energy. Therefore, the uncertainty of wind resources has increased the difficulty in estimating the total benefits in the planning stage. The main concern of the traditional deterministic model is that it does not consider the future uncertainty when making the dispatch decision. Thus, it does not provide flexible operational actions in response to the uncertain future scenarios. Performance analysis and computer simulation on the San Cristobal Wind Project demonstrate that the wind power uncertainty, control strategies, energy storage, and the wind turbine power curve have a significant impact on the performance of the system. In this dissertation, the relationship between option pricing theory and decision making process is discussed. A real option model is developed and presented through practical examples for assessing the value of hybrid wind-diesel power systems. Results show that operational options can provide additional value to the hybrid power system when this operational flexibility is correctly utilized. This framework can be applied in optimizing short term dispatch decisions considering the path-dependent nature of the optimal dispatch policy, given the plausible future realizations of the wind power production. Comparing with the existing valuation and optimization methods, result from numerical example shows that the dispatch policy resulting from the proposed optimization model exhibits a remarkable performance in minimizing the total fuel consumption of the wind-diesel system. In order to make optimal decisions, power plant operators and managers should not just focus on the direct outcome of each operational action; neither should they make deterministic decisions. The correct way is to dynamically manage the power system by taking into consideration the conditional future value in each option in response to the uncertainty.