Solving Method for Linear Fractional Optimization Problem with Fuzzy Coefficients in the Objective Function
Keywords:
fuzzy programming, fractional programming, multi-objective programmingAbstract
The importance of linear fractional programming comes from the fact that many real life problems are based on the ratio of physical or economic values (for example cost/-time, cost/volume, profit/cost or any other quantities that measure the efficiency of a system) expressed by linear functions. Usually, the coefficients used in mathematical models are subject to errors of measurement or vary with market conditions. Dealing with inaccuracy or uncertainty of the input data is made possible by means of the fuzzy set theory.
Our purpose is to introduce a method of solving a linear fractional programming problem with uncertain coefficients in the objective function. We have applied recent concepts of fuzzy solution based on α-cuts and Pareto optimal solutions of a biobjective optimization problem.
As far as solving methods are concerned, the linear fractional programming, as an extension of linear programming, is easy enough to be handled by means of linear programming but complicated enough to elude a simple analogy. We follow the construction of the fuzzy solution for the linear case introduced by Dempe and Ruziyeva (2012), avoid the inconvenience of the classic weighted sum method for determining Pareto optimal solutions and generate the set of solutions for a linear fractional program with fuzzy coefficients in the objective function.
References
Chanas S., Kuchta D., Linear programming problem with fuzzy coefficients in the objective function, in: Delgado M., Kacprzyk J., Verdegay J.L., Vila M.A. (Eds.), Fuzzy Optimization, Physica-Verlag, Heidelberg, 148-157, 1994.
Dempe S., Ruziyeva A., On the calculation of a membership function for the solution of a fuzzy linear optimization problem, FUZZY SETS AND SYSTEMS, ISSN 0165-0114, 188(1): 58-67, 2012.
Duta L., Filip F.G., Henrioud J.-M., Popescu C., Disassembly line scheduling with genetic algorithms, INT J COMPUT COMMUN, ISSN 1841-9836, 3(3): 270-280, 2008.
Ehrgott M., Multicriteria Optimization, Springer Verlag, Berlin, 2005.
Harbaoui D.I., Kammarti R., Ksouri M., Multi-Objective Optimization for the m-PDPTW: Aggregation Method With Use of Genetic Algorithm and Lower Bounds, INT J COMPUT COMMUN, ISSN 1841-9836, 6(2): 246-257, 2011.
Cadenas J., Verdegay J., Towards a new strategy for solving fuzzy optimization problems, FUZZZY OPTIMIZATION AND DECISION MAKING, ISSN 1568-4539, 8: 231-244, 2009.
Lotfi, F.H., Noora, A.A., Jahanshahloo, G.R., Khodabakhshi, M., Payan, A., A linear programming approach to test efficiency in multi-objective linear fractional programming problems, APPLIED MATHEMATICAL MODELING, ISSN 0307-904X, 34: 4179-4183, 2010.
Stancu-Minasian I.M., Fractional Programing, Theory, Methods and Applications, Kluwer Academic Publishers, Dordrecht/Boston/London, 1997. http://dx.doi.org/10.1007/978-94-009-0035-6
A. Sengupta, T. Pal, On comparing interval numbers, EUROPEAN JOURNAL OPERATIONAL RESEARCH, ISSN 0377-2217, 127: 28-43, 2000.
Uhrig R.E., Tsoukalas L.H., Fuzzy and Neural Approaches in Engineering, John Wiley and Sons Inc., New York, 1997.
Zimmermann H.-J., Fuzzy Set Theory and its Applications, Kluwer Academic Publishers, 1996. http://dx.doi.org/10.1007/978-94-015-8702-0
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