README.md

Two-Phase Simplex Method

This project implements the Two-Phase Simplex Method for solving linear programming problems. This program simulates the manual calculation of the simplex tableau, aiming to help users verify the correctness of their simplex tableau calculations.

Files

• two_phase_simplex.py: Contains the implementation of the Two-Phase Simplex Method.

Usage

To use this implementation, you need to transform your linear programming problem into standard form manually. The standard form requires all variables to be non-negative and all constraints to be equalities.

Example

Consider the following linear programming problem:

minimize: 0x1 + x2 - 4x3 + 0x4 + x5 + 0x6
subject to:
    x1 + x2 + x3 + x4 = 1
    -x2 - x3 - x4 + x5 = 1
    x1 + 2x3 - x5 - x6 = 0
    x1, x2, x3, x4, x5, x6 >= 0

You can solve this problem using the Two-Phase Simplex Method as follows:

1. Define the objective function coefficients c:

   c = np.array([0, 1, -4, 0, 1, 0])

2. Define the constraints matrix A:

   A = np.array([
       [1, 1, 1, 1, 0, 0],
       [0, -1, -1, -1, 1, 0],
       [1, 0, 2, 0, -1, -1]
   ])

3. Define the right-hand side of the constraints b:

   b = np.array([1, 1, 0])

4. Create an instance of the TwoPhaseSimplex class and solve the problem:

   simplex = TwoPhaseSimplex(c, A, b)
   simplex.solve()

Running the Example

To run the example provided in the two_phase_simplex.py file, execute the script: (require numpy)

python two_phase_simplex.py

Output

The script will print the intermediate steps and the final optimal solution, including the optimal value and the values of the decision variables.

License

This project is licensed under the MIT License.