Finding a solution for Multi-Objective Linear Fractional Programming problem based on goal programming and Data Envelopment Analysis

¹ Faculty of Mathematics and Computer Sciences, Kharazmi University, Tehran, Iran.
jahanshahloomath@gmail.com; stdtalebianb@khu.ac.ir; stdj.sadeghi@khu.ac.ir
² Department of Mathematics, Science and Research Branch, Islamic Azad University, Tehran, Iran.
farhad@hosseinzadeh.ir

Received: 30 January 2015
Accepted: 12 February 2016

Abstract

The multi-objective linear fractional programming is an interesting topic with many applications in different fields. Until now, various algorithms have been proposed in order to solve the multi-objective linear fractional programming (MOLFP) problem. An important point in most of them is the use of non-linear programming with a high computational complexity or the use of linear programming with preferences of the objective functions which are assigned by the decision maker. The current paper, through combining goal programming and data envelopment analysis (DEA), proposes an iterative method to solve MOLFP problems using only linear programming. Moreover, the proposed method provides an efficient solution which fairly optimizes each objective function when the decision maker has no information about the preferences of the objective functions. In fact, along with normalization of the objective functions, their relative preferences are fairly determined using the DEA. The implementation of the proposed method is demonstrated using numerical examples.