0000000000139814
AUTHOR
Carlos Ivorra
The fuzzy p-median problem
In many location models, the strong crisp assumptions, like known demands and distances, are not realistic in most cases. The fuzzy p-median problem relaxes this hypothesis giving to the decision maker a necessary degree of freedom to solve real-world problems. It allows a decision maker to improve an optimal covering of a location problem by considering partially feasible solutions in which some demand is left uncovered. Here we revise the main facts and results about this problem emphasising different specific algorithms of resolution. Finally we show that this fuzzy version can be used to analyse the global structure of a given instance of the crisp problem.
Controlling risk through diversification in portfolio selection with non-historical information
We deal with the portfolio selection problem for investors having information on the expected returns of the assets based not only on historical data. In the absence of a way of measuring the risk of non-historical information, the investor may try to adjust it through the consideration of a suitable set of diversification constraints. With this aim, we relate the concept of value of information (recently introduced by Kao and Steuer) to a qualitative subjective measure of the investor’s level of confidence in his/her non-historical information. As an illustration, we analyze the behavior of the proposed indicator in the Spanish IBEX35 index for risk, upper bound, semicontinuous variable an…
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.
Finding socially responsible portfolios close to conventional ones
Abstract An increasing number of investors are interested in sustainable, responsible and impact investment (SRI). However, there is a concern about the possible financial sacrifice associated to this kind of investments. The design of Decision Support Systems assisting socially responsible investors in their investment decisions can contribute to stimulate SRI. In this paper the financial content of a portfolio selection model is discussed in order to justify that it can be integrated into a Decision Support System designed for investors interested in socially responsible investment but initially reluctant to pay a financial cost in exchange for increasing the social responsibility of thei…
Grading investment diversification options in presence of non-historical financial information
Modern portfolio theory deals with the problem of selecting a portfolio of financial assets such that the expected return is maximized for a given level of risk. The forecast of the expected individual assets’ returns and risk is usually based on their historical returns. In this work, we consider a situation in which the investor has non-historical additional information that is used for the forecast of the expected returns. This implies that there is no obvious statistical risk measure any more, and it poses the problem of selecting an adequate set of diversification constraints to mitigate the risk of the selected portfolio without losing the value of the non-statistical information owne…
Finding Satisfactory Near-Optimal Solutions in Location Problems
We develope and analyze a heuristic procedure to solve a fuzzy version of the p-median problem in which we allow part of the demand not to be covered in order to reduce the transport cost. This can be used to improve a given solution of the crisp p-median problem as well as to give to the decision-maker a range of alternative locations that can be adequate according to his or her own criteria.
On the Computation of the Efficient Frontier of the Portfolio Selection Problem
An easy-to-use procedure is presented for improving theε-constraint method for computing the efficient frontier of the portfolio selection problem endowed with additional cardinality and semicontinuous variable constraints. The proposed method provides not only a numerical plotting of the frontier but also an analytical description of it, including the explicit equations of the arcs of parabola it comprises and the change points between them. This information is useful for performing a sensitivity analysis as well as for providing additional criteria to the investor in order to select an efficient portfolio. Computational results are provided to test the efficiency of the algorithm and to i…
Fuzzy Techniques for Improving Satisfaction in Economic Decisions
The authors use fuzzy set theory to improve classical decision-making problems by incorporating the inherent vagueness in decision-makers’ preferences into the model. They specifically study two representative models: the p-median problem and the portfolio selection problem. The first one is a location problem, which on the one hand fits many real world management situations and on the other hand is suitable for a theoretical analysis of the techniques. The version of the portfolio selection problem presented here is a harder problem, which allows the authors to show the scope of their methods. Some numerical examples are provided to illustrate how fuzzy optimal solutions improve classical …
Fuzzy portfolio selection based on the analysis of efficient frontiers
We present an algorithm for analyzing the geometry of the efficient frontier of the portfolio selection problem with semicontinuous variable and cardinality constraints, and use it as a basis to solve a fuzzy version of the problem, designed to obtain efficient portfolios, in the Markowitz's sense, for which the trade-off between expected return and assumed risk fits better the investor's subjective criteria. We illustrate our proposal with an example solved with LINGO and Mathematica.
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 functio…
Marginal analysis for the fuzzy p-median problem
The solutions to the fuzzy p-median problem make it possible to leave part of the demand uncovered in order to obtain significant reductions in costs. Moreover, the fuzzy formulation provides the decision-maker with many flexible solutions that he or she may prefer to the classical crisp solution. We introduce some marginal analysis techniques to study how solutions depend on membership functions. Taking into account the internal structure of the problem, we propose a practical criterion to fix the tolerances for the uncovered demand, which happens to be the most sensitive aspect of the fuzzy p-median.
Fuzzy Portfolio Selection Models for Dealing with Investor’s Preferences
This chapter provides an overview of the authors’ previous work about dealing with investor’s preferences in the portfolio selection problem. We propose a fuzzy model for dealing with the vagueness of investor preferences on the expected return and the assumed risk, and then we consider several modifications to include additional constraints and goals.
Soft Computing Techniques for Portfolio Selection: Combining SRI with Mean-Variance Goals
A fuzzy portfolio selection model is presented incorporating a socially responsible goal without discarding a priori financially good portfolios or weakening a priori the financial goals. Hence, the optimal portfolios it provides could be either efficient from the strictly financial point of view or non-efficient if leaving the efficient frontier substantially improves the degree of social responsibility. The model can be used to direct heuristic procedures in order to select a reduced number of various alternatives from which the investor can directly make a final decision.
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 Hakimi's works and we compare the crisp and the fuzzy approach by means of an example.