Title: A fuzzy linear programming model with fuzzy parameters and decision variables

Authors: Saber Saati; Madjid Tavana; Adel Hatami-Marbini; Elham Hajiakhondi

Addresses: Department of Mathematics, Tehran-North Branch, Islamic Azad University, P.O. Box 19585-936,Tehran, Iran ' Business Systems and Analytics Department, Lindback Distinguished Chair of Information Systems and Decision Sciences, La Salle University, Philadelphia, PA 19141, USA; Business Information Systems Department, Faculty of Business Administration and Economics, University of Paderborn, D-33098 Paderborn, Germany ' Louvain School of Management, Center of Operations Research and Econometrics (CORE), Universite catholique de Louvain, 34 voie du roman pays, L1.03.01, B-1348 Louvain-la-Neuve, Belgium ' Department of Mathematics, Payame Noor University, P.O. Box: 19395-4697, Lashkarak Highway, Nakhl St., 19569 Tehran, Iran

Abstract: Linear programming (LP) is an optimisation technique most widely used for optimal allocation of limited resources amongst competing activities. Precise data are fundamentally indispensable in standard LP problems. However, the observed values of the data in real-world problems are often imprecise or vague. Fuzzy set theory has been extensively used to represent ambiguous, uncertain or imprecise data in LP by formalising the inaccuracies inherent in human decision-making. We propose a new method for solving fuzzy LP (FLP) problems in which the right-hand side parameters and the decision variables are represented by fuzzy numbers. A new fuzzy ranking model and a new supplementary variable are utilised in the proposed FLP method to obtain the fuzzy and crisp optimal solutions by solving one LP model. Moreover, we introduce an alternative model with deterministic variables and parameters derived from the proposed FLP model. Interestingly, the result of the alternative model is identical to the crisp solution of the proposed FLP model. We use a numerical example from the FLP literature for comparison purposes and to demonstrate the applicability of the proposed method and exhibit the efficacy of the procedure.

Keywords: fuzzy linear programming; FLP; trapezoidal fuzzy numbers; duality; complementary slackness theory; decision variables; fuzzy set theory.

DOI: 10.1504/IJIDS.2015.074129

International Journal of Information and Decision Sciences, 2015 Vol.7 No.4, pp.312 - 333

Available online: 12 Jan 2016 *

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