Cracking the Knapsack Problem: Python MIP for Beginners

An introduction to the Python MIP library for solving the knapsack problem.

Francesco Pastore
7 min readMar 4, 2024

Mathematical programming is a subclass of mathematical problems regarding the selection of the best decision among several options considering one or more criteria.

As a result, mathematical programming, and in particular the knapsack problem, finds many applications across diverse domains, ranging from investment selection to project scheduling.

In this article, we’re going to explore a way to solve this type of problem using the Python MIP library, without having to delve into the complicated mathematical theories behind it.

Image by Vinicius Imbroisi from Pixabay

Mathematical optimization in a nutshell

Mathematical programming is also called mathematical optimization because it usually consists of finding the best value (max/min) for a given function by manipulating its parameters.

To simplify the scenario a little, we will consider integer programming problems in which all variables must take only integer values (whole numbers).

The basic structure of any mathematical programming problem includes:

  • Sets and parameters: fixed values that define the problem and…



Francesco Pastore

An engineering student in Milan and a web developer for an IT company. Write about programming and cybersecurity topics.