Hands-On Mathematical Optimization with Python

The particular feature of linear optimization problems is that as long as the decision variables satisfy all the constraints, they can take any value. However, there are many situations in which it makes sense to restrict the solution space in a way that cannot be expressed using linear (in)equality constraints. For example, some numbers might need to be integers, such as the number of people to be assigned to a task. Another situation is when certain constraints need to hold only if another constraint holds. For example, the amount of power generated by a power plant must not be less than a certain minimum threshold only if that generator is turned on. Neither of these two examples can be expressed using only linear constraints, as we have seen up to this point. In these cases, it is often still possible to formulate the problem as an LO problem, although some additional restrictions may be needed on certain variables, requiring them to take integer values only. We will refer to this type of LO problem in which some variables are constrained to be integers as mixed-integer linear optimization (MILO) problems.