Mixed Integer Programming
Mixed Integer Programming (MIP) is a mathematical optimization technique that involves solving problems where some variables are required to be integers, while others can be continuous. It extends linear programming by adding integer constraints, enabling modeling of discrete decisions like yes/no choices or whole-number quantities. MIP is widely used in operations research, logistics, scheduling, and resource allocation to find optimal or near-optimal solutions under complex constraints.
Developers should learn MIP when tackling optimization problems with discrete elements, such as production planning, vehicle routing, or network design, where binary or integer decisions are essential. It is particularly valuable in industries like manufacturing, finance, and telecommunications for maximizing efficiency or minimizing costs under specific constraints. Using MIP allows for precise modeling of real-world scenarios that pure linear programming cannot handle due to its continuous nature.