62 Int. J. Mathematical Modelling and Numerical Optimisation, Vol. 8, No. 1, 2017 Copyright © 2017 Inderscience Enterprises Ltd. Cost parametric analysis of linear programming problems with fuzzy cost coefficients based on ranking functions Ali Ebrahimnejad Department of Mathematics, Qaemshahr Branch, Islamic Azad University, P.O. Box 163, 4765161964, Qaemshahr, Iran Fax: +98-1142155025 Email: aemarzoun@gmail.com Email: a.ebrahimnejad@qaemiau.ac.ir Abstract: Parametric analysis (PA) as a basic tool for studying perturbations in optimisation problems is applied to study the effect of the continuous variations of several parameters in the objective function coefficients on the optimum solution. To the best of our knowledge, till now there is no study in the literature to deal with the PA of the fuzzy linear programming problem in which the cost coefficients are represented by LR flat fuzzy numbers. In this paper, the parametric analysis for the same problem is investigated to determine the optimal solution and the fuzzy optimal objective values as a function of parameters when the fuzzy cost coefficients are perturbed along a new fuzzy cost vector. Then, its main advantages over the existing fuzzy sensitivity analysis problems are discussed. Finally, to show the application of fuzzy PA problem, an existing real-life fuzzy transportation problem is solved and the obtained results are explored. Keywords: cost parametric analysis; fuzzy linear programming; fuzzy numbers; ranking function. Reference to this paper should be made as follows: Ebrahimnejad, A. (2017) ‘Cost parametric analysis of linear programming problems with fuzzy cost coefficients based on ranking functions’, Int. J. Mathematical Modelling and Numerical Optimisation, Vol. 8, No. 1, pp.62–91. Biographical note: Ali Ebrahimnejad serves as an Associate Professor at the Mathematics Department, Qaemshahr Branch, Islamic Azad University. He obtained his PhD in Applied Mathematics in the Department of Mathematics at the Islamic Azad University (Sciences and Research Branch), Tehran, Iran. He received his BS from Mazandaran University, Iran and his MSc from Tehran University, Iran. He is on the Editorial Board of the International Journal of Fuzzy System Applications (IJFSA), Annals of Fuzzy Mathematics and Informatics (AFMI), International Journal of Information and Decision Sciences (IJIDS), Iranian Journal of Optimization (IJO), International Journal of Strategic Decision Sciences (IJSDS) and International Journal of Enterprise Information Systems (IJEIS). His research interests include operations research, network OWS, data envelopment analysis and fuzzy optimisation.