Linear Programming MATLAB Code: Simplex Method Implementations

This documentation presents three MATLAB implementations for solving linear programming problems. The first method, SimpleMthd, implements the standard simplex algorithm commonly used in practice. This implementation typically includes basic pivot operations, feasibility checks, and iterative optimization steps through tableau transformations. The second method, CmpSimpleMthd, implements the complete simplex method which incorporates advanced features such as improved pivot selection criteria, enhanced boundary handling, and comprehensive sensitivity analysis. This approach can provide more robust solutions for complex constraint environments and degenerate cases. The third method, ModifSimpleMthd, implements the revised simplex method, an optimized variant that reduces computational overhead by maintaining inverse basis matrices and performing efficient pricing operations. This implementation is particularly valuable for large-scale problems where memory efficiency and computational speed are critical. All three methods represent effective approaches for solving linear programming problems, each with distinct advantages and specific application scenarios. These MATLAB implementations include proper initialization routines, convergence checks, and solution validation mechanisms to ensure reliable performance. The documentation aims to enhance understanding of these algorithmic variations and their practical implementation details for solving diverse optimization problems.