MATLAB Implementation of Optimization Algorithms: Simplex Method, Two-Phase Method, Big M Method, and Dual-Phase Simplex Approach

This project presents a MATLAB-based graphical user interface (GUI) for solving arbitrary Linear Programming problems using fundamental optimization algorithms. The implementation includes core methods such as the Simplex Method (handling standard form problems with basic feasible solutions), Two-Phase Method (for problems without initial basic feasible solutions through artificial variable introduction), Big M Method (using penalty coefficients for artificial variables), and the Dual-Phase Simplex Method (combining phase I feasibility search and phase II optimization). The GUI incorporates matrix input validation, tableau initialization, pivot operations with Bland's anti-cycling rule, and sensitivity analysis visualization. Key MATLAB functions include constraint normalization, basis identification, reduced cost calculation, and solution space plotting. Users can interactively set objective functions, constraints, and algorithm parameters while observing real-time iterations through dynamic tableau updates and graphical solution progression.