arXiv subjects

Manuel Arana-Jiménez

Publications and source records attributed to Manuel Arana-Jiménez.

4 recordsLinked to original sources

arXiv2023

A novel slacks-based interval DEA model and application

This paper proposes a novel slacks-based interval DEA approach that computes interval targets, slacks, and crisp inefficiency scores. It uses interval arithmetic and requires solving a mixed-integer linear program. The corresponding super-efficiency formulation to discriminate among the efficient units is also presented. We also provide a case study of its application to sustainable tourism in the Mediterranean region, assessing the sustainable tourism efficiency of twelve Mediterranean regions to validate the proposed approach. The inputs and outputs cover the three sustainability dimensions and include GHG emissions as an undesirable output. Three regions were found inefficient, and the corresponding inputs and output improvements were computed. A total rank of the regions was also obtained using the super-efficiency model.

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arXiv2023

Developing solution algorithm for LR-type fully interval-valued intuitionistic fuzzy linear programming problems using lexicographic-ranking method

In this article, a new concept of LR-type interval-valued intuitionistic fuzzy numbers (LR-type IVIFN) has been introduced. The theory has also been enriched by demonstrating diagrammatic representations of LR-type IVIFNs and establishing arithmetic operations among these fuzzy numbers. The total order properties of lexicographic criteria have been used for ranking LR-type IVIFNs. Further, a linear programming problem having both equality as well as inequality type constraints with all the parameters as LR-type IVIFNs and unrestricted decision variables has been formulated. An algorithm to find a unique optimal solution to the problem using the lexicographic ranking method has been developed. In the proposed methodology, the given linear programming problem is converted to an equivalent mixed 0-1 lexicographic non-linear programming problem. Various theorems have been proved to show the equivalence of the proposed problem and its different constructions. The model formulation, algorithm and discussed results have not only developed a new idea but also generalized various well-known related works existing in the literature. A numerical problem has also been exemplified to show the steps involved in the approach. Finally, a practical application in production planning is framed, solved and analyzed to establish the applicability of the study.

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arXiv2019

On the fuzzy maximal covering location problem

In this paper studies the maximal covering location problem, assuming imprecise knowledge of all data involved. The considered problem is modeled from a fuzzy perspective producing suitable fuzzy Pareto solutions. Some properties of the fuzzy model are studied, which validate the equivalent mixed-binary linear multiobjective formulation proposed. A solution algorithm is developed, based on the augmented weighted Tchebycheff method, which produces solutions of guaranteed Pareto optimality. The effectiveness of the algorithm has been tested with a series of computational experiments, whose numerical results are presented and analyzed

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arXiv2018

On a fully fuzzy framework for minimax mixed integer linear programming

In this work, we present a modeling framework for minimax mixed 0-1 fuzzy linear problems. It is based on extending the usual rewriting of crisp minimax problems via auxiliary variables to model the maximum of a finite set of fuzzy linear functions. We establish that the considered problem can be equivalently formulated as a multiple objective mixed integer programming problem. The framework is applied to a fully fuzzy version of the capacitated center facility location problem.

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