DigitalUM :: Browsing by browse.metadata.contributordepartment "Estadística e Investigación Operativa"

Browsing by browse.metadata.contributordepartment "Estadística e Investigación Operativa"

Now showing 1 - 20 of 32

Open Access
A decision theoretic framework for reliability-based optimal wind turbine selection
(Elsevier, 2022-05) Eryilmaz, S.; Navarro, J.; Estadística e Investigación Operativa
The problem of choosing the optimal wind turbine for a specific site is of special importance in the design process of wind farm. Manifestly, the selection of the optimal wind turbine should depend on a certain criteria. In this paper, optimal wind turbine selection is studied in terms of the capacity factor of wind turbine generator and the Expected Energy not Supplied which is one of the most commonly used reliability indices for power systems. The latter one considers the load profile of the system and is suitable to compare different wind farm compositions while the former one completely ignores the load profile of the system. This paper presents general theoretical results that are helpful to compare performance of wind turbines and wind farms without data collection and further numerical assessment. In particular, the conditions on wind turbine characteristics and availability values of wind turbines are determined to compare wind turbines and wind farms in terms of the capacity factor and Expected Energy not Supplied.
Open Access
A Discrete Competitive Facility Location Model with Minimal Market Share Constraints and Equity-Based Ties Breaking Rule
(IOS PRESS, 2020) Fernández Hernández, Pascual; Lancinskas, Algirdas; Pelegrín Pelegrín, Blas; Zilinskas, Julius; Estadística e Investigación Operativa
We consider a geographical region with spatially separated customers, whose demand is currently served by some pre-existing facilities owned by different firms. An entering firm wants to compete for this market locating some new facilities. Trying to guarantee a future satisfactory captured demand for each new facility, the firm imposes a constraint over its possible locations (a finite set of candidates): a new facility will be opened only if a minimal market share is captured in the short-term. To check that, it is necessary to know the exact captured demand by each new facility. It is supposed that customers follow the partially binary choice rule to satisfy its demand. If there are several new facilities with maximal attraction for a customer, we consider that the proportion of demand captured by the entering firm will be equally distributed among such facilities (equity-based rule). This ties breaking rule involves that we will deal with a nonlinear constrained discrete competitive facility location problem. Moreover, minimal attraction conditions for customers and distances approximated by intervals have been incorporated to deal with a more realistic model. To solve this nonlinear model, we first linearize the model, which allows to solve small size problems because of its complexity, and then, for bigger size problems, a heuristic algorithm is proposed, which could also be used to solve other constrained problems.
Open Access
A discrete competitive facility location model with proportional and binary rules sequentially applied
(SPRINGER, 2023) Fernández Hernández, Pascual; Lancinskas, Algirdas; Pelegrín Pelegrín, Blas; Zilinskas, Julius; Estadística e Investigación Operativa
The paper is focused on discrete competitive facility location problem for an entering firm considering different customer behavior models: for essential goods, customers generally spread their buying power among all facilities within an attraction area, but if there are no facilities nearby, then customers choose a single highly attractive facility outside the attraction area to satisfy their demand. The new facility location model has been proposed considering the proportional customer choice rule for customers with facilities within the attraction area and the binary rule—for customers which facilities are located outside the attraction area. The model has been formulated as a non-linear binary programming problem and a heuristic optimization algorithm has been applied to find the optimal solutions for different instances of the problem using real geographical coordinates and population data of thousands of municipalities in Spain.
Open Access
A new stochastic dominance criterion for dependent random variables with applications
(Elsevier, 2022-12-09) Martínez Riquelme, Carolina; Félix Belzunce; Belzunce Torregrosa, Félix; Martínez Riquelme, Carolina; Estadística e Investigación Operativa; Facultad de Matemáticas
In this paper we develop a new tool for the comparison of paired data based on a new criterion of stochastic dominance that takes into account the dependence structure of the random variables under comparison. This new procedure provides a more detailed comparison of dependent random variables and overcomes some di culties of standard techniques like Student’s t and Wilcoxon-Mann-Whitney tests for non normal data. This tool provides an alternative to the usual stochastic dominance criterion which only considers the marginal distributions in the comparison. We show how this new tool can be fruitfully used for the comparison of paired asset returns.
Open Access
A study on multi-level redundancy allocation in coherent systems formed by modules
(Elsevier, 2021-09) Torrado, N.; Arriaza, A.; Navarro, J.; Estadística e Investigación Operativa
The present work studies the effect of redundancies on the reliability of coherent systems formed by modules. Different redundancies at components’ level versus redundancies at modules’ level are investigated, including active and standby redundancies. For that, a new model is presented. This model takes into account the dependence among the components, as well as, the dependence among the modules of the system. In both cases, the dependence structure is modeled by copula functions. Several results are provided to compare systems consisting of heterogeneous components. The comparisons are distribution-free with respect to the components. In particular, we consider the cases when the components in the modules are independent and connected (or not) in series, and when the components are dependent within the modules. In both cases, it is assumed that the modules can be dependent. Furthermore, the case in which the components in each module are identically distributed (dependent or independent) is also considered. We illustrate the theoretical results with several examples.
Open Access
A variance-based importance index for systems with dependent components.
(Elsevier, 2023-09-15) Arriaza, A.; Navarro, J.; Sordo, M.A.; Suárez-Llorens, A.; Estadística e Investigación Operativa
This paper proposes a variance-based measure of importance for coherent systems with dependent and heterogeneous com-ponents. The particular cases of independent components and homogeneous components are also considered. We model the dependence structure among the components by the concept of copula. The proposed measure allows us to provide the best estima-tion of the system lifetime, in terms of the mean squared error, under the assumption that the lifetime of one of its components is known. We include theoretical results that are useful to calculate a closed-form of our measure and to compare two components of a system. We also provide some procedures to approximate the importance measure by Monte Carlo simulation methods. Finally, we illustrate the main results with several examples.
Open Access
Aggregation and signature based comparisons of multi-state systems via decompositions of fuzzy measures
(Elsevier, 2020-10-01) Navarro, J.; Spizzichino, F.; Estadística e Investigación Operativa
In the reliability literature, several results have been presented to compare binary (two states) systems. Often, such results are obtained from copula-based extensions of fuzzy measures, where a fuzzy measure describes the structure of a system and a copula describes the stochastic dependence among the lifetimes of its components. Other similar results have been obtained in terms of the concept of signature. Here, we extend all those results to multi-state systems made up from binary components by suitably constructing corresponding mixed binary systems. For such a construction, we show how any fuzzy measure can be decomposed as a convex combination of {0,1}-valued fuzzy measures and how such a decomposition extends to the corresponding aggregation function. For a mixed system we can furthermore consider its signature and so we can also define a signature for the multi-state system. For mixed systems associated to different multi-state systems, we can thus obtain different comparison results, which can be translated into the corresponding comparisons for the parent multi-state systems. Stochastic comparisons are obtained for the discrete random variables which represent the states of two systems at time t, as well. The arguments in the paper will be illustrated by means of examples and related remarks.
Open Access
An automated process for supporting decisions in clustering-based data analysis
(Elsevier, ) Bernabé Díaz, José Antonio; Franco Nicolás, Manuel; Vivo Molina, Juana María; Quesada Martínez, Manuel; Fernández Breis, Jesualdo Tomás; Informática y Sistemas; Estadística e Investigación Operativa
Open Access
An optimization-based approach to ranking aggregation with weak order outputs
(2026) Aledo, Juan A.; Landete, Mercedes; Domínguez Sánchez, Concepción; Jaime Alcántara, Juan de Dios; Estadística e Investigación Operativa; Facultades de la UMU::Facultad de Matemáticas
Rank aggregation problems combine individual orderings of a common set of items into a consensus ranking reflecting collective preferences. This paper introduces a general Integer Linear Programming (ILP) framework to model and solve aggregation problems whose solutions are weak orders (bucket orders). The framework provides a flexible and tractable architecture that incorporates structural and normative constraints required in practice. Within this setting, we develop several ILP formulations embedding additional structural requirements on the consensus bucket order, including a fixed number of buckets, predefined bucket sizes, top-$k$ constraints, and group-based fairness conditions. The formulations are modular and adaptable to different aggregation contexts. A particularly relevant case is the Optimal Bucket Order Problem (OBOP), for which we present the first exact mixed-integer linear programming formulation. We evaluate the models through computational experiments, comparing optimal solutions with the heuristics of Aledo et al.\ (2018) and assessing scalability on benchmark instances from the PrefLib library. Finally, we present a real-world case study on Spanish universities, where the proposed models aggregate competing rankings under structural and fairness constraints.
Open Access
Birnbaum importance measure for reliability systems with dependent components
(Institute of Electrical and Electronics Engineers, 2019-02-22) Miziula, P; Navarro, J.; Estadística e Investigación Operativa
Component importance measures are relevant to improve the system design and to develop optimal replacement policies. Birnbaum’s importance measure is one of the most relevant measures. If the components are (stochastically) independent, this measure can be defined using several equivalent expressions. However, in many practical situations, the independence assumption is unrealistic. It also turns out that in the case of dependent components, different Birnbaum’s measure definitions lead to different concepts. In this paper,we extend Birnbaum’s importance measure to the case of dependent components in a way allowing us to obtain relevant properties including connections and comparisons with other measures proposed and studied recently. The dependence is modeled through copulas and the new measure is based on the contribution of the component to the system reliability.
Open Access
Boolean valued representation of random Sets and markov kernels with application to large deviations
(MDPI, 2020-10-20) Avilés López, Antonio; Estadística e Investigación Operativa
We establish a connection between random set theory and Boolean valued analysis by showing that random Borel sets, random Borel functions, and Markov kernels are respectively represented by Borel sets, Borel functions, and Borel probability measures in a Boolean valued model. This enables a Boolean valued transfer principle to obtain random set analogues of available theorems. As an application, we establish a Boolean valued transfer principle for large deviations theory, which allows for the systematic interpretation of results in large deviations theory as versions for Markov kernels. By means of this method, we prove versions of Varadhan and Bryc theorems, and a conditional version of Cramér theorem.
Open Access
Comparisons of policies based on relevation and replacement by a new one unit in reliability
(Springer, 2020-04-20) Belzunce Torregrosa, Félix; Martínez Riquelme, Carolina; Mercader, José A.; Ruiz Gómez, José María; Estadística e Investigación Operativa; Facultades de la UMU::Facultad de Matemáticas
The purpose of this paper is to study the role of the relevation transform, where a failed unit is replaced by a used unit with the same age as the failed one, as an alternative to the policy based on the replacement by a new one. In particular, we compare the stochastic processes arising from a policy based on the replacement of a failed unit by a new one and from the one in which the unit is being continuously subjected to a relevation policy. The comparisons depend on the ageing properties of the units under repair.
Open Access
Computation of multi-facility location Nash equilibria on a network under quantity competition.
(SPRINGER, 2018) Pelegrín Pelegrín, Blas; Fernández Hernández, Pascual; García Pérez, María Dolores; Estadística e Investigación Operativa
We deal with the location-quantity problem for competing firms when they locate multiple facilities and offer the same type of product. Competition is performed under delivered quantities that are sent from the facilities to the customers. This problem is reduced to a location game when the competing firms deliver the Cournot equilibrium quantities. While existence conditions for a Nash equilibrium of the location game have been discussed in many contributions in the literature, computing an equilibrium on a network when multiple facilities are to be located by each firm is a problem not previously addressed. We propose an integer linear programming formulation to fill this gap. The formulation solves the profit maximization problem for a firm, assuming that the other firms have fixed their facility locations. This allows us to compute location Nash equilibria by the best response procedure. A study with data of Spanish municipalities under different scenarios is presented and conclusions are drawn from a sensitivity analysis.
Open Access
Conditions on marginals and copula of component lifetimes for signature representation of system lifetime.
(Elsevier, 2021-07-15) Navarro, J.; Rychlik, T.; Spizzichino, F.; Estadística e Investigación Operativa
The signature of a system is a probability vector that depends only on the system structure. Under the classic IID (independent and identically distributed) assumption on the component lifetimes, the system lifetime distribution is the convex combination of consecutive component failure times, and the signature coordinates constitute the mixture coefficients. In this case the signature representations are very useful in determining the system lifetime distributions and for stochastic comparisons of them. This first representation was obtained in 1985 by Samaniego. Then it was extended to the more general case of exchangeable component lifetimes. In 2011 Marichal, Mathonet and Waldhauser presented necessary and sufficient conditions assuring the Samaniego repre-sentation. There were expressed in terms of distributional properties of families of auxiliary indicator random vectors parametrized by positive numbers. In the paper we obtain other necessary and sufficient conditions represented in terms of the marginal distri-butions of component lifetimes and the dependence copula of them. Moreover, we study symmetry conditions for the equality of structural and probabilistic signatures.
Embargo
Duality and stable compactness in orlicz-type modules
(Springer, 2023-10-30) Zapata García, José Miguel; Orihuela Calatayud, José; Estadística e Investigación Operativa
Orlicz-type modules are module analogues of classical Orlicz spaces. We study duality and stable compactness in Orlicz-type modules. We characterize the conditional Köthe dual of an Orlicz-type module as the space of all sigma-order continuous module homomorphisms. We find an order continuity criterion for stable compactness in Orlicz-type modules. As an application, we obtain a robust representation result for conditional risk measures on Orlicz spaces.
Open Access
Exact and heuristic solutions of a discrete competitive location model with Pareto-Huff customer choice rule
(ELSERVIER, 2021) Fernández Hernández, Pascual; Pelegrín Pelegrín, Blas; Lancinskas, Algirdas; Zilinskas, Julius; Estadística e Investigación Operativa
An entering firm wants to compete for market share of an area by opening some new facilities selected among a finite set of potential locations (discrete space). Customers are spatially separated and there already are other firms operating in that area. In this paper, we use a variant of the well known Huff (proportional) customer choice rule, the so called Pareto-Huff, which have had little attention on the literature because of its nonlinear formulation. This untested rule considers that customers split their demand among the facilities that are Pareto optimal with respect to quality (to be maximized) and distance (to be minimized), proportionally to their attractions, i.e., a distant facility will capture demand of a customer only if it has higher quality than any other closer facility. A first formulation as a nonlinear programming problem is proposed, and then an equivalent formulation as a linear programming problem is presented, which allows us to obtain exact solutions for medium size problems. For large size problems, a heuristic procedure is also proposed to obtain the best approximate solutions. Its performance is checked for small size problems and its solutions are compared with the optimal solutions given by a standard optimizer, Xpress, using real geographical coordinates and population data of municipalities in Spain.
Restricted
Large deviations built on max-stability
(2021-05) Kupper, Michael; Estadística e Investigación Operativa
In this paper, we show that the basic results in large deviations theory hold for general monetary risk measures, which satisfy the crucial property of max-stability. A max-stable monetary risk measure fulfills a lattice homomorphism property, and satisfies under a suitable tightness condition the Laplace Principle (LP), that is, admits a dual representation with affine convex conjugate. By replacing asymptotic concentration of probability by concentration of risk, we formulate a Large Deviation Principle (LDP) for max-stable monetary risk measures, and show its equivalence to the LP. In particular, the special case of the asymptotic entropic risk measure corresponds to the classical Varadhan–Bryc equivalence between the LDP and LP. The main results are illustrated by the asymptotic shortfall risk measure.
Open Access
Minimal repair of failed components in coherent systems
(Elsevier, 2019-12) Navarro, J.; Arriaza ., A; Suárez-Llorens, A.; Estadística e Investigación Operativa
The minimal repair replacement is a reasonable assumption in many practical systems. Under this as- sumption a failed component is replaced by another one whose reliability is the same as that of the component just before the failure, i.e., a used component with the same age. In this paper we study the minimal repair in coherent systems. We consider both the cases of independent and dependent compo- nents. Three replacement policies are studied. In the first one, the first failed component in the system is minimally repaired while, in the second one, we repair the component which causes the system fail- ure. A new technique based on the relevation transform is used to compute the reliability of the systems obtained under these replacement policies. In the third case, we consider the replacement policy which assigns the minimal repair to a fixed component in the system. We compare these three options un- der different stochastic criteria and for different system structures. In particular, we provide the optimal strategies for all the coherent systems with 1–4 independent and identically distributed components.
Open Access
On the Existence and Computation of Nash Equilibrium in Network Competitive Location Under Delivered Pricing and Price Sensitive Demand
(SPRINGER, 2023) Pelegrín Pelegrín, Blas; Fernández Hernández, Pascual; García Pérez, María Dolores; Estadística e Investigación Operativa
We address the location-price decision problem for firms that offer the same type of product and compete on delivered pricing. If firms set equilibrium prices at demand points, the problem can be seen as a location game for which the Nash equilibrium (NE) is used as solution concept. For spatially separated markets, with inelastic demand, there exists a NE and it can be found by social cost minimization, as happens in network and planar location. However, with price sensitive demand, the existence of a NE has not been proven yet and socially optimal locations may not be a NE. In this paper we show that a NE can be found in discrete and network location when demand is price sensitive. A Mixed Integer Linear Programming formulation is implemented in the best response procedure which allow to find a NE for a variety of demand functions. An empirical study with data of Spanish municipalities is performed in which the procedure is applied to 200 large size test problems with linear, quadratic, exponential and hyperbolic demand functions.
Embargo
Parameter-Dependent Stochastic Optimal Control in Finite Discrete Time
(2020-07-17) Jamneshan, Asgar; Kupper, Michael; Zapata García, José Miguel; Estadística e Investigación Operativa
We prove a general existence result in stochastic optimal control in discrete time, where controls, taking values in conditional metric spaces, depend on the current information and past decisions. The general form of the problem lies beyond the scope of standard techniques in stochastic control theory, the main novelty is a formalization in conditional metric space and the use of conditional analysis. We illustrate the existence result by several examples such as wealth-dependent utility maximization under risk constraints and utility maximization with a conditional dimension. We also provide a discussion as to how our methods compare to techniques based on random sets.