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A streamlined artificial variable free version of simplex method
Syed Inayatullah1, Nasir Touheed2, Muhammad Imtiaz1
1Department of Mathematical Sciences, University of Karachi, Karachi, Pakistan.
Plos One
|March 14, 2015
Summary
This study introduces a streamlined simplex method, eliminating artificial variables and constraints for linear programming (LP). This artificial-free approach simplifies feasibility achievement and offers a dual version for enhanced LP problem-solving.
Area of Science:
- Operations Research
- Mathematical Optimization
Background:
- Traditional simplex methods often require artificial variables and constraints, complicating the initial phase.
- Achieving feasibility can be a distinct challenge in linear programming (LP) before optimizing.
Purpose of the Study:
- To propose a streamlined simplex method that bypasses the need for artificial variables and constraints.
- To present a dual version of the new method for simplifying dual simplex phase 1.
- To offer flexibility in handling primal and dual infeasible initial bases.
Main Methods:
- Development of an artificial-free simplex algorithm.
- Introduction of a dual variant for enhanced feasibility.
- Pivoting strategies mirroring simplex phase 1 without explicit artificial components.
Main Results:
- The proposed method eliminates the need for artificial variables and constraints.
- It allows starting with any feasible or infeasible basis in linear programming.
- A dual version facilitates the implementation of traditional dual simplex phase 1.
Conclusions:
- The artificial-free simplex method offers a more efficient and space-saving approach to LP.
- The dual version simplifies dual simplex phase 1 implementation.
- The method serves as a valuable teaching tool for demonstrating feasibility achievement.
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