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.