Linear programming with fuzzy parameters: An interactive method resolution q Mariano Jime ´nez a, * , Mar Arenas b , Amelia Bilbao b , M. Victoria Rodrı ´guez b a Department of Applied Economy I, University of The Basque Country, Plaza On ˜ati 1. 20018-San Sebastia ´ n, Spain b Department of Quantitative Economy, University of Oviedo, Avda. del Cristo s/n. 33006-Oviedo, Spain Available online 16 November 2005 Abstract This paper proposes a method for solving linear programming problems where all the coefficients are, in general, fuzzy numbers. We use a fuzzy ranking method to rank the fuzzy objective values and to deal with the inequality rela- tion on constraints. It allows us to work with the concept of feasibility degree. The bigger the feasibility degree is, the worst the objective value will be. We offer the decision-maker (DM) the optimal solution for several different degrees of feasibility. With this information the DM is able to establish a fuzzy goal. We build a fuzzy subset in the decision space whose membership function represents the balance between feasibility degree of constraints and satisfaction degree of the goal. A reasonable solution is the one that has the biggest membership degree to this fuzzy subset. Finally, to illus- trate our method, we solve a numerical example. Ó 2005 Elsevier B.V. All rights reserved. Keywords: Fuzzy sets; Fuzzy linear programming; Ranking fuzzy numbers; Decision making 1. Introduction Linear programming (LP) is the optimisation technique most frequently applied in real-world problems and therefore it is very important to introduce new tools in the approach that allow the model to fit into the real world as much as possible. 0377-2217/$ - see front matter Ó 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.ejor.2005.10.002 q This work was supported by the Spanish Ministry of Education and Science (project MEC-04-MTM-07478) and by the University of the Basque Country. This support is gratefully acknowledged. * Corresponding author. Present address: Departamento de Economı ´a Aplicada I, Universidad del Paı ´s Vasco. Plaza On ˜ ati 1, 20018 San Sebastia ´n, Spain. Tel.: +34 43015818; fax: +34 43018360. E-mail addresses: mariano.jimenez@ehu.es (M. Jime ´nez), mariamar@uniovi.es (M. Arenas), ameliab@uniovi.es (A. Bilbao), vrodri@uniovi.es (M.V. Rodrı ´guez). European Journal of Operational Research 177 (2007) 1599–1609 www.elsevier.com/locate/ejor