Abstract
This paper illustrates a procedure to generate pareto optimal solutions of multi-objective linear fractional programming problem (MOLFPP) with closed interval coefficients of decision variables both in objective and constraint functions. E-constraint method is applied to produce pareto optimal solutions comprising most preferred solution to satisfy all objectives. A numerical example is solved using our proposed method and the result so obtained is compared with that of fuzzy programming which justifies the efficiency and authenticity of the proposed method.
Highlights
Mathematical optimization is described as the science of determining the best solution to the mathematically modelled real world problems
In multi-objective optimization problems, usually there does not exist single solution which satisfies all the objectives, a set of pareto optimal(noninferior, non-dominated) solutions can be generated from which the decision maker (DM) has a choice to decide the most preferred pareto optimal solution
Several types of membership functions are available in fuzzy programming to solve a multi-objective optimization problem but a suitable one is to be chosen in order to determine the optimal solution
Summary
Mathematical optimization is described as the science of determining the best solution to the mathematically modelled real world problems. Multi-objective LFPP comprises many fractional objective functions to be optimized subject to a certain set of linear constraints. Milan [11] discussed linear fractional programming problem under interval uncertainty to obtain a range for optimal values of the objective functions. In this paper, closed intervals of certain values are assumed as the coefficients of the decision variables both in objective and constraint functions of a multi-objective LFPP. Relative minimum and maximum values of each objective function with respect to others are determined -constraint method due to Haimes et al [10] is used to derive a set of non-inferior solutions from which the decision maker(DM) decides the most preferred optimal solution to satisfy all the objectives with best compromising objective values on preference basis.
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