An effective solution approach for multi-objective fractional fixed charge problem with fuzzy parameters

Abstract

A multi-objective fixed charge problem in existence of several fractional objective functions with triangular fuzzy parameters is considered in this study. The problem previously has been tackled only by Upmanyu and Saxena [1] with a method containing wrong mathematical concepts (see the commentary of Kaur and Kumar [2]). To overcome the shortcomings of the literature, an effective solution approach based on a typical goal programming approach is proposed to solve the problem for obtaining a Paretooptimal solution. The proposed approach considers the shortcomings of the method of Upmanyu and Saxena [1] and applies no ranking function of fuzzy numbers. In addition, the goal programming stage considers no preference from decision maker. The computational experiments provided by an example of the literature, prove the effectiveness of the proposed approach. Conflicts of interest: noneRemainder of the paper is organized by five sections. Section 2, describes some basic definitions and concepts of fuzzy theory and optimization theory. Section 3, introduces the FMFFCP, analyzes its formulation and deals with its non-linearity. Section 4, organizes the goal programming based solution approach proposed for the FMFFCP. Section 6, contains an illustrative numerical example from the literature to analyze the performance of the proposed solution approach provided by Section 4. Finally, the paper is ended by remarking some conclusions in Section 6. Basic conceptsSome basic definitions from fuzzy theory which will be applied later in this paper are explained in this sub-section. fuzzy theory, exact and meta-heuristic solution approaches.

An Uncertain Allocation Models in Data Envelopment Analysis: A Case in the Iranian Stock Market

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