Simplex Method Solver

Description

A Python-based Simplex Method Solver for linear programming problems. This tool allows users to input an objective function and constraints, and it solves the linear programming problem using the Simplex method.

Features

• Input objective function and constraints
• Formulate and display the linear programming model
• Perform Simplex method iterations
• Display intermediate and final Simplex tables
• Handle fractions and floating-point numbers

Requirements

• Python 3.x (Download it here)
  • Downloading Python is required to run this program since it is written in Python
• git (Download it here)
  • git is required to be able to install this project seamlessly into your computer

Installation

1. Clone the Repository:

   git clone https://github.com/lirrnaiad/Simplex-Method-Solver.git
   cd Simplex-Method-Solver

2. Create a Virtual Environment:

   python -m venv venv

3. Activate the Virtual Environment:

   • On Windows:

     venv\Scripts\activate

   • On macOS/Linux:

     source venv/bin/activate

4. Install Dependencies:

   pip install -r requirements.txt

Usage

1. Run the Script:

   python simplex.py

2. Input the Objective Function:

   Enter objective function: z = 120x + 100y
   

3. Input the Number of Constraints:

   Enter the number of constraints (excluding non-negativity constraints): 2
   

4. Input Each Constraint:

   Enter constraint 1: 2x + 2y <= 8
   Enter constraint 2: 5x + 3y <= 15
   

5. View the Formulated LP Model:

   LP Model:
   Max 120x + 100y
   subject to the constraints
     2x + 2y <= 8
     5x + 3y <= 15
     x, y >= 0
   

6. View the Initial Simplex Table:

   Initial table:
   +-----+-----+-----+-----+-----+-----+
   | B.V |  x  |  y  | S1  | S2  | RHS |
   +-----+-----+-----+-----+-----+-----+
   |  S1 |  2  |  2  |  1  |  0  |  8  |
   |  S2 |  5  |  3  |  0  |  1  | 15  |
   |  z  | -120| -100|  0  |  0  |  0  |
   +-----+-----+-----+-----+-----+-----+
   

7. Follow the Simplex Method Iterations:

   • The program will display each step of the Simplex method, showing the intermediate tables and the pivot operations.

8. View the Final Simplex Table and Solution:

   • The program will display the final Simplex table and the optimal solution for the given linear programming problem.