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Advances in Decision Sciences
Volume 2014 (2014), Article ID 306456, 7 pages
http://dx.doi.org/10.1155/2014/306456
Research Article

An Improved Method for Solving Multiobjective Integer Linear Fractional Programming Problem

Department of Operational Research, Faculty of Mathematics, Houari Boumediene University of Sciences and Technology, P.O. Box 32, El-Alia Bab Ezzouar, 16111 Algiers, Algeria

Received 10 February 2014; Revised 28 May 2014; Accepted 6 June 2014; Published 1 July 2014

Academic Editor: Shelton Peiris

Copyright © 2014 Meriem Ait Mehdi et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We describe an improvement of Chergui and Moulaï’s method (2008) that generates the whole efficient set of a multiobjective integer linear fractional program based on the branch and cut concept. The general step of this method consists in optimizing (maximizing without loss of generality) one of the fractional objective functions over a subset of the original continuous feasible set; then if necessary, a branching process is carried out until obtaining an integer feasible solution. At this stage, an efficient cut is built from the criteria’s growth directions in order to discard a part of the feasible domain containing only nonefficient solutions. Our contribution concerns firstly the optimization process where a linear program that we define later will be solved at each step rather than a fractional linear program. Secondly, local ideal and nadir points will be used as bounds to prune some branches leading to nonefficient solutions. The computational experiments show that the new method outperforms the old one in all the treated instances.