Mathematical Problems in Engineering
Volume 2011 (2011), Article ID 374390, 18 pages
doi:10.1155/2011/374390
Research Article

An Effective Generalization of the Direct Support Method

1Department of Mathematics, Faculty of Sciences, USTOMB, Oran 31000, Algeria
2Department of Operations Research, LAMOS Laboratory, University of Béjaia, Béjaia 06000, Algeria

Received 4 November 2010; Accepted 17 February 2011

Academic Editor: Ezzat G. Bakhoum

Copyright © 2011 Sonia Radjef and Mohand Ouamer Bibi. 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

The main objective of our paper is to solve a problem which was encountered in an industrial firm. It concerns the conception of a weekly production planning with the aim to optimize the quantities to be launched. Indeed, one of the problems raised in that company could be modeled as a linear multiobjective program where the decision variables are of two kinds: the first ones are upper and lower bounded, and the second ones are nonnegative. During the resolution process of the multiobjective case, we were faced with the necessity of developing an effective method to solve the mono-objective case without any increase in the linear program size, since the industrial case to solve is already very large. So, we propose an extension of the direct support method presented in this paper. Its particularity is that it avoids the preliminary transformation of the decision variables. It handles the bounds as they are initially formulated. The method is really effective, simple to use, and permits speeding up the resolution process.