Simplex Algorithm Solver
A C++ implementation of the Simplex method for solving Linear Programming problems. This program efficiently finds the optimal solution to a given set of linear constraints and an objective function using the tableau method.
✅ Implements the Simplex Algorithm for Linear Programming ✅ Iterative approach to ensure optimality ✅ Detects unbounded solutions ✅ User-friendly output with formatted tableau representation ✅ Structured and modular code for easy understanding and modification
1️⃣ Compile the Program
Ensure you have a C++ compiler installed (e.g., g++ for GCC).
g++ simplex_solver.cpp -o simplex_solver 2️⃣ Run the Program
./simplex_solver 📂 Project Structure
📁 Simplex Solver Project │── simplex_solver.cpp # Main program implementing the Simplex method │── README.md # Project documentation 📌 How It Works
1️⃣ Initial Tableau Creation: Represents the LP problem as a tableau. 2️⃣ Pivot Column Selection: Identifies the most negative coefficient in the objective function row. 3️⃣ Pivot Row Selection: Uses the minimum ratio test to determine the leaving variable. 4️⃣ Pivoting Operation: Converts the pivot element to 1 and other elements in the column to 0. 5️⃣ Iteration Until Optimality: The algorithm repeats until all coefficients in the last row are non-negative.
📊 Example Output
Initial Tableau: 2.00 3.00 1.00 0.00 0.00 100.00 4.00 1.00 0.00 1.00 0.00 80.00 3.00 2.00 0.00 0.00 1.00 60.00 -3.00 -5.00 0.00 0.00 0.00 0.00
Pivot Column: 1 Pivot Row: 1 Updated Tableau: ...
Optimal Solution: Z = 166.67