An Efficient Method for Pivoting Free Variables in Linear Programming: A Computational Approach

  • Syed Inayatullah Department of Mathematics, University of Karachi, Karachi, Pakistan
  • Asma Rani Department of Mathematics, University of Karachi, Karachi, Pakistan
  • Tanveer Ahmed Siddiqi Department of Mathematics, University of Karachi, Karachi, Pakistan
  • Hina Zaheer Department of Mathematics, University of Karachi, Karachi, Pakistan
  • Muhammad Imtiaz Department of Mathematics, University of Karachi, Karachi, Pakistan
  • Hafsa Athar Jafree Department of Mathematics, University of Karachi, Karachi, Pakistan

Abstract

Commonly used simplex method to solve linear programming problem do not allow variables to be negative during solution process and suggest to break each free variable (variable allowed to be negative) into difference of two non-negative variables. This transformation significantly increases the number of variables as well as after this the problem leaves its original variable space. , thus making the geometry of problem (during solution process) difficult to handle and understand. In this paper, we developed a natural generalization of simplex pivots for free variables. Described approach is capable of handling any general linear programming in its original variable space. In our computational study, the primary results showed that the new method outperforms simplex method on general LPs.

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Published
2019-03-31
How to Cite
Inayatullah, S., Rani, A., Siddiqi, T. A., Zaheer, H., Imtiaz, M., & Jafree, H. A. (2019). An Efficient Method for Pivoting Free Variables in Linear Programming: A Computational Approach. European Scientific Journal, ESJ, 15(9), 1. https://doi.org/10.19044/esj.2019.v15n9p1