Linear Programming Optimization: The Simplex Method | by Jarom Hulet | Sep, 2024

Part 3: The algorithm under the hood

Up until now, this series has covered the basics of linear programming. In this article, we are going to move from basic concepts into the details under the hood! This article will cover the simplex method, which is the algorithm that is often used to solve linear programming problems. While we will solve a simple linear programming example by hand with the simplex method, our focus will be on the intuition of the algorithm rather than memorizing the algorithmic steps (we have computers for that kind of stuff!).

Here is what we will cover:

1. Why the simplex method is needed
2. Moving from graphical solutions to algebraic
3. Demonstrating how the simplex method works with a simple example

In the first article of this series, we went over how the attributes of linear programming allow it to only consider the corner points of constraints as potential optimal solutions. This is a very powerful feature that narrows an infinite solution space to a finite solution space. In the examples we reviewed, we only had a few constraints and a few variables — we even solved some of them by hand! After looking at…