Mixed-Integer Programming (MIP) – A Primer on the Basics
Note, you can also see a list of code and modeling examples, across a range of programming languages on our code examples and modeling examples pages.
The integrality constraints allow MIP models to capture the discrete nature of some decisions. For example, a variable whose values are restricted to 0 or 1, called a binary variable, can be used to decide whether or not some action is taken, such as building a warehouse or purchasing a new machine.
MIP models with a quadratic objective but without quadratic constraints are called Mixed Integer Quadratic Programming (MIQP) problems. MIP models with quadratic constraints are called Mixed Integer Quadratically Constrained Programming (MIQCP) problems. Models without any quadratic features are often referred to as Mixed Integer Linear Programming (MILP) problems.
What follows is a description of the algorithm used by Gurobi to solve MILP models. The extension to MIQP and MIQCP is mostly straightforward, but we won’t describe them here.
