RujalAcharya/Simplex

A simple python implementation of simplex method for linear programming

Simplex

This is a simple implementation of the simplex method, which is a simple method for solving linear programming problems (LPPs).

Installing the requirements

The only requirement for this progrram is numpy which can be installed as

pip install -r requirements.txt

Using the code

The LPP is divided into three numpy arrays (say A, B, C).

Consider the LPP as
Maximize F = c₁x₁+c₂x₂
Subject to constraints
a₁₁x₁+a₁₂x₂≤b₁
a₂₁x₁+a₂₂x₂≤b₂
x₁,x₂≥0

Then we define 3 numpy arrays A, B, C as:

A = np.array([[a11, a12]
            [a21, a22]])
B = np.array([b1, b2])
C = np.array([c1, c2])

Now we can use the LinearModel class to create the simplex tableau and then find the optimal solution.

lm = LinearModel(A, B, C)

OR

lm = LinearModel()
lm.setA(A)
lm.setB(B)
lm.setC(C)

Now we can optimize the solution using

lm.optimize()

Now, we can look at the optimized value of {x₁,x₂, ...} as a numpy array is returned by lm.optimalSoln() method.
Similarly, we can look at the optimized value of F using lm.optimialVal() method.

You can also look at the example program or example notebook to see how it is applied.

Note: Currently only maximization problems can be solved and minimization problems will soon be implemented as well. Further preetifying and visualization of simplex tableau is also planned to be implemented.
_{Feel free to review my code and roast me. I am just a dumbass.}