### Mixed-integer Linear Programming

Integer programming is a mathematical method for optimizing large and complex systems, and is often used in production and route planning as well as decision-making. The mathematical variables are a mixture of integers and fractions, and all the mathematical formulas included in the program are described by linear functions.

This form of mathematical modelling was originally developed and used by the Allies to plan military operations during World War II. After the war, integer programming became common in aviation for planning the aircrew roster and determining the routes of each aircraft in order to fully utilize capacity.

In production planning, this type of programming can be used to calculate how to produce a given quantity of a product at the right time when production capacity, shutdown periods, changeover time, and many other variables need to be accounted for to avoid overproduction or bottlenecks.

Source: Business Optimization Using Mathematical Programming (J. Kallrath, 2021).