A streamlined artificial variable free version of simplex method.

Inayatullah S, Touheed N, Imtiaz M - PLoS ONE (2015)

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pone.0116156.g001: A short simplex table structure showing optimality of current basis.
Mentions: A basis B is called primal feasible if xB ≥ 0 or one may conclude that the primal problem has a feasible solution x(B) while if yN ≥ 0 then B is called dual feasible or one may conclude that the dual problem has a feasible solution y(B). Also if B is both primal and dual feasible then B is optimal. Usually dB0 is referred as certificate column of primal feasibility; and d0N is referred as certificate row of dual feasibility, see Fig. 1.

Bottom Line: This paper proposes a streamlined form of simplex method which provides some great benefits over traditional simplex method.For instance, it does not need any kind of artificial variables or artificial constraints; it could start with any feasible or infeasible basis of an LP.Last but not the least, it provides a teaching aid for the teachers who want to teach feasibility achievement as a separate topic before teaching optimality achievement.

View Article: PubMed Central - PubMed

Affiliation: Department of Mathematical Sciences, University of Karachi, Karachi, Pakistan.

ABSTRACT
This paper proposes a streamlined form of simplex method which provides some great benefits over traditional simplex method. For instance, it does not need any kind of artificial variables or artificial constraints; it could start with any feasible or infeasible basis of an LP. This method follows the same pivoting sequence as of simplex phase 1 without showing any explicit description of artificial variables which also makes it space efficient. Later in this paper, a dual version of the new method has also been presented which provides a way to easily implement the phase 1 of traditional dual simplex method. For a problem having an initial basis which is both primal and dual infeasible, our methods provide full freedom to the user, that whether to start with primal artificial free version or dual artificial free version without making any reformulation to the LP structure. Last but not the least, it provides a teaching aid for the teachers who want to teach feasibility achievement as a separate topic before teaching optimality achievement.

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