Introduction to Linear Programming and Optimization

Background

We all have to make choices at some point in our lives. These choices might allow us to maximize one thing while requiring us to sacrifice another. Whenever we are making such choices, we are performing optimization. A couple of examples are ones where we’re making decisions based on several factors:

1. We want to buy a new house and are considering parameters such as price, location, nearby schools, distance to shopping malls, nearby hospitals, neighborhood, or security.

2. We are planning to choose a graduate school for a bachelor’s degree in computer science studies. We have the parameters of the school’s ranking, tuition, loan availability, accommodations, distance to home, choices of majors offered, and so on.

Some of us might value one parameter over the other. However, the ultimate goal is to choose the best possible option from the available choices. If we can express the two examples above and any other problem in mathematical terms, we can solve it using linear programming.

What is linear programming?

In simple terms, linear programming, sometimes referred to as linear optimization, is one of the ways to perform optimization. It’s a simple technique that we can use to mathematically formulate complex relationships through linear functions and find the optimum points. This gives us the ability to solve problems of any scope by making a few simple assumptions.