Carlos Ivorra

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.

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.

On the Computation of the Efficient Frontier of the Portfolio Selection Problem

An easy-to-use procedure is presented for improving the -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 illustrate its applications. The procedure has been implemented in Mathematica.

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.

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.

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.

Fuzzy Portfolio Selection Including Cardinality Constraints and Integer Conditions

This paper is concerned with a fuzzy version of the portfolio selection problem, which includes diversification conditions and incorporates investor’s subjective preferences. The inclusion of diversification conditions leads to mixed-integer models, which are computationally demanding. On the other hand, the consideration of integer conditions makes the solution very sensitive to investor’s subjective preferences with regard to the trade-off between risk and expected return. These preferences are imprecise by their very nature. In this paper, we overcome these issues by proposing a solution method for a fuzzy quadratic portfolio selection model with integer conditions. The suitability of the proposed method is illustrated by means of two numerical examples.

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 and cardinality constraints.