An Effective Generalization of the Direct Support Method

The main objective of our paper is to solve a problem which wasencountered in an industrial firm. It concerns the conception of a weeklyproduction 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: thefirst ones are upper and lower bounded, and the second ones are nonnegative.During the resolution process of the multiobjective case, we were faced with thenecessity of developing an effective method to solve the mono-objective casewithout any increase in the linear program size, since the industrial case tosolve is already very large. So, we propose an extension of the direct supportmethod presented in this paper. Its particularity is that it avoids the preliminary transformation of the decision variables. It handles the bounds asthey are initially formulated. The method is really effective, simple to use, andpermits speeding up the resolution process