GENERALISED FUZZY LINEAR PROGRAMMING
Abstract
Linear programming is one of the widely used methods for optimising business systems, which includes organisational, financial, logistic and control subsystems of energy systems in general. It is possible to express numerous real-world problems in a form of linear program and then solve by simplex method [1]. In the development of linear programming, we are facing a number of upgrades and generalisations, as well as replenishment. Particularly interesting in recent years is an option that decision variables and coefficients are fuzzy numbers. In this case we are dealing with fuzzy linear programming. If we also include in a fuzzy linear program a generalisation with respect to Wolfe’s modified simplex method [1], we obtain a generalised fuzzy linear program (GFLP). Usenik and Žulj introduced methods for solving those programs and proved the existence of the optimal solution in [2]. In the article, the simplex algorithm which enables the determining of an optimal solution for GFLP is described. There is a numerical example at the end of the article that illustrates the algorithm.
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References
G.B. Dantzig: Linear Programming and Extensions, Princeton University Press, Princeton, New Jersey, 1998), eleventh printing
J. Usenik and M. Žulj: Generalizirano mehko linearno programiranje, Novo mesto: Fakulteta za organizacijske študije, 2021
V. Rupnik: Zvezno dinamično linearno programiranje, Ekonomska, poslovna in organizacijska knjižnica, 24, Založba Obzorja Maribor, Maribor, 1978
J. Usenik: Fuzzy dynamic linear programming in energy supply planning, Journal of energy technology, Oct. 2011, vol. 4, iss. 4, pp. 45–62
J. Usenik: Generalizirano zvezno variabilno dinamično linearno programiranje, Novo mesto: Fakulteta za industrijski inženiring, 2017
L. A. Zadeh: Fuzzy sets, Information and control, 8(3):338–353, 1965
H.-J. Zimmermann: Fuzzy Set Theory and its Applications, Kluwer Academic Publishers (2001), Fourth edition
S. Chen, C. Hwang, P. Hwang: Fuzzy Multiple Attribute Decision Making, Springer-Verlag, (Berlin, Heidelberg, New York, 1992)
M. Repnik and D. Bokal: A Basis for Taxonomy of Fuzzy Linear Programming Methods, In 13th International Symposium on Operational Research in Slovenia, Bled, Slovenia, September 23-25, 2015. ZADNIK STIRN, Lidija (ur.), et al. SOR ’15 proceedings, pages 188–192. Ljubljana: Slovenian Society Informatika, Section for Operational Research, 2015
