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.