Simplex Solver

This program Solves linear programs using the simplex algorithm (general formulas)

How to use

1. Download a Python file (Simplex.py)

2. Create a CSV file for the linear problem in the standard form (standard form is defined below)

3. Determine a file path for the CSV file in the " importData " function.

4. Determine a file path for reporting the minimum of the cost function and optimal point in the " reportAnswer " function.

Note: Currently, only linear programs in standard form are supported.

Standard form

Z=CX

AX=b

X>0

Where:

Z = Cost Function

C = vector of coefficients

A = the constraint matrix

b = the right-hand side vector

Note: all components of the vector 'b' must be Non-negative.

Example (Igor Griva, Stephen G. Nash, Ariela Sofer, Linear and Nonlinear Optimization, p. 126.)

1. basic form

Minimize Z = -X1 - 2X2

subject to

      -2X1 + X2 <= 2
       -X1 + 2X2<= 7
             X1 <= 3
         X1,X2>=0

2. standard form

Minimize Z = -X1 - 2X2

subject to

           -2X1 + X2 + X3 = 2
       -X1 + 2X2 + X4 = 7
              X1 + X5 = 3
         X1,X2,X3,X4,X5>=0              

So;

A = [[-2,1,1,0,0],[-1,2,0,1,0],[1,0,0,0,1]]

C = [-1,-2,0,0,0]

b=[2,7,3]

3. the CSV file for importing the problem is Example.csv

4. the results could be seen in Results.csv

Acknowledgments

The entire program is written by Ashkan Fouladi (fooladiashkang@gmail.com)