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## Tuesday, February 21, 2023

### Mixed Integer Linear Programming (MILP)

Spent most of my early optimization career doing this kind of problem.    Here a technical introduction. Still has lots of value.   I post it here both for nostalgic and real life problem solving uses. Lots of software out there to help too.  Have you used it?

Mixed Integer Linear Programming: Formal definition and solution space  in TowardsDataScience.   By István Módos

Theoretical foundations on how MILP is defined and how its solution space looks like visually

This post is a continuation of the series (previous post) on the theory and applications of Mixed Integer Linear Programming (MILP). Today, we look at  the formal, general definition of MILP,

how its space of feasible solutions looks like.

The first part describes how MILP models look in general, what are and are not valid MILP expressions. The second part shows a little bit of theory behind MILP, which will be useful in the future posts when we will be talking about the actual algorithm for solving MILP  ....

This is quite a long post, so grab a coffee and dive in!  ... '

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ChatGPT Says:

MILP stands for Mixed-Integer Linear Programming, which is a type of mathematical optimization problem. In MILP, the objective function and the constraints are linear, and some of the variables are integer (i.e., they can only take on integer values). The remaining variables are allowed to take on real values.

MILP is a powerful tool for solving a wide range of problems that involve both discrete and continuous decision variables. Examples of applications of MILP include resource allocation, scheduling, production planning, and portfolio optimization.

Solving a MILP problem involves finding the values of the decision variables that optimize the objective function while satisfying the linear constraints. MILP solvers use a variety of algorithms and techniques, such as branch-and-bound, cutting planes, and heuristics, to efficiently search the solution space and find the optimal solution or a good approximation to it.       END