Vicente Liern

A fuzzy mathematical programming approach to the assessment of efficiency with DEA models

In many real applications, the data of production processes cannot be precisely measured. This is particularly worrying when assessing efficiency with frontier-type models, such as data envelopment analysis (DEA) models, since they are very sensitive to possible data errors. For this reason, the possibility of having available a methodology that allows the analyst to deal with imprecise data becomes an issue of great interest in these contexts. To that end, we develop some fuzzy versions of the classical DEA models (in particular, the BCC model) by using some ranking methods based on the comparison of α-cuts. The resulting auxiliary crisp problems can be solved by the usual DEA software. We show, in a numerical example, how our models become specially useful for detecting sensitive decision-making units. Our approaches can be seen as an extension of the DEA methodology that provides users and practitioners with models which represent some real life processes more appropriately.

Viability of infeasible portfolio selection problems: A fuzzy approach☆

Abstract This paper deals with fuzzy optimization schemes for managing a portfolio in the framework of risk–return trade-off. Different models coexist to select the best portfolio according to their respective objective functions and many of them are linearly constrained. We are concerned with the infeasible instances of such models. This infeasibility, usually provoked by the conflict between the desired return and the diversification requirements proposed by the investor, can be satisfactorily avoided by using fuzzy linear programming techniques. We propose an algorithm to repair infeasibility and we illustrate its performance on a numerical example.

An exact algorithm for the fuzzy p-median problem

In this paper we propose a fuzzy version of the classical p-median problem. We consider a fuzzy set of constraints so that the decision-maker will be able to take into account solutions which provide significantly lower costs by leaving a part of the demand uncovered. We propose an algorithm for solving the problem which is based on Hakimis works and we compare the crisp and the fuzzy approach by means of an example.

The fuzzy p-median problem: A global analysis of the solutions

Abstract We apply fuzzy techniques to incorporate external data into p-median problems. So we can detect certain solutions that would be discarded by usual crisp and fuzzy algorithms but that contrasted with this additional information can be advantageous. This usually reveals a pathology of the model and hence our methods provide some fuzzy validation criteria for p-median models.

The Spanish Football Crisis

Abstract This article analyses the economic results of Spanish professional football teams using data collected over the past few years. These data differ substantially from the information presented in the annual reports of the “Liga de Fútbol Profesional” (Spanish professional football league), which are obtained from the initial budgets elaborated each season. Special attention is paid to the two most important teams in the Spanish league: Real Madrid and FC Barcelona. The results of this research show that Spanish football has the same problems as those evidenced by the Italian and English football leagues and, therefore, requires similar solutions in order to be able to survive in forthcoming years.

A fuzzy method to repair infeasibility in linearly constrained problems

Abstract In this paper we introduce a fuzzy method to deal with infeasibility in linearly constrained programs. Given an infeasible instance, we determine how much we should perturb the right-hand side coefficients in order to attain feasibility and propose a ‘feasible reformulation’ of the problem. Although we prove that our algorithm always finds such a reformulation the convenience of using it can be decided by the analyst. By this, we mean that the method also provides a simple way to compute lower bounds on the changes on every right-hand side coefficient, and if the decision maker considers that some of the magnitudes are unacceptable, he or she simply stops at this step. We think that it will be specially useful for those situations in which the cause of the infeasibility is in the requirement of specifying exact values for the parameters in the mathematical programs formulation.

RANKING DECISION MAKING UNITS BY MEANS OF SOFT COMPUTING DEA MODELS

This paper presents a method for ranking a set of decision making units according to their level of efficiency and which takes into account uncertainty in the data. Efficiency is analysed using fuzzy DEA techniques and the ranking is based on the statistical analysis of cases that include representative situations. The method enables the removal of the sometimes unrealistic hypothesis of a perfect trade-off between increased inputs and outputs. This model is compared with other DEA models that work with imprecise or fuzzy data. As an illustration, we apply our ranking method to the evaluation of a group of Spanish seaports, as well as teams playing in the Spanish football league. We compare the results with other methods and we show that our method enables a total ranking of the seaports, and that the ranking of football teams is found to be more consistent with final league positions.

Soft-computing based heuristics for location on networks: The p-median problem

We propose a genetic algorithm for the fuzzy p-median problem in which the optimal transport cost of the associated crisp problem is unknown. Our algorithm works with two populations: in one, the solutions with a better crisp transport cost are favored by the selection criterion, whereas in the second one, solutions with a better fuzzy satisfaction level are preferred. These populations are not independent. On the contrary, the first one periodically invades the second one, thus providing new starting points for finding fuzzy improvements. Our computational results also reveal the importance of choosing adequate functions for selecting the parents. Our best results are obtained with functions which are more sensitive to both objectives (crisp and fuzzy) and by increasing the invasion and mutation rates. We compare these results with other heuristic procedures.

Exact and heuristic procedures for solving the fuzzy portfolio selection problem

We propose a fuzzy model for the portfolio selection problem which takes into account the vagueness of the investor’s preferences regarding the assumed risk. We also describe an exact method for solving it as well as a hybrid meta-heuristic procedure which is more adequate for medium and large-sized problems or in cases in which a quick solution is needed. As an application, we solve several problems based on data from the IBEX35 index and the Spanish Stock Exchange Interconnection System.

Relativistic Simultaneity and Causality

We analyzed two types of relativistic simultaneity associated to an observer: the spacelike simultaneity, given by Landau submanifolds, and the lightlike simultaneity given by past-pointing horismos submanifolds. We study some geometrical conditions to ensure that Landau submanifolds are spacelike and we prove that horismos submanifolds are always lightlike. Finally, we establish some conditions to guarantee the existence of foliations in the space-time whose leaves are these submanifolds of simultaneity generated by an observer. These foliation structure allows us to incorporate the simultaneity submanifolds for studying some dynamical systems, for instance free elementary massless particles.