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A Streamlined Artificial Variable Free Version of Simplex Method

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  • Syed Inayatullah
  • Nasir Touheed
  • Muhammad Imtiaz

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.

Suggested Citation

  • Syed Inayatullah & Nasir Touheed & Muhammad Imtiaz, 2015. "A Streamlined Artificial Variable Free Version of Simplex Method," PLOS ONE, Public Library of Science, vol. 10(3), pages 1-28, March.
    • Handle: RePEc:plo:pone00:0116156
    DOI: 10.1371/journal.pone.0116156
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    References listed on IDEAS

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    1. Harvey M. Wagner, 1956. "A Two-Phase Method for the Simplex Tableau," Operations Research, INFORMS, vol. 4(4), pages 443-447, August.
    2. Ron Shamir, 1987. "The Efficiency of the Simplex Method: A Survey," Management Science, INFORMS, vol. 33(3), pages 301-334, March.
    3. Oliver Serang, 2012. "Conic Sampling: An Efficient Method for Solving Linear and Quadratic Programming by Randomly Linking Constraints within the Interior," PLOS ONE, Public Library of Science, vol. 7(8), pages 1-12, August.
    4. Stojkovic, Nebojsa V. & Stanimirovic, Predrag S., 2001. "Two direct methods in linear programming," European Journal of Operational Research, Elsevier, vol. 131(2), pages 417-439, June.
    5. Illes, Tibor & Terlaky, Tamas, 2002. "Pivot versus interior point methods: Pros and cons," European Journal of Operational Research, Elsevier, vol. 140(2), pages 170-190, July.
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    Cited by:

    1. Rujira Visuthirattanamanee & Krung Sinapiromsaran & Aua-aree Boonperm, 2020. "Self-Regulating Artificial-Free Linear Programming Solver Using a Jump and Simplex Method," Mathematics, MDPI, vol. 8(3), pages 1-15, March.

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