The meaning of mixed integer linear programming model:

Linear Programming (LP): The definition of LP is relatively simple. It means that the objective function is linear and all constraints It is also linear. Finally, the decision variable can take on any real number. If some of the decision variables in the linear programming problem are required to be integers, then the planning problem at this time is transformed into a mixed integer linear programming problem.

In other words, the optimization problem not only has conditional constraints, but also integer constraints.

To understand what a mixed integer linear programming model is, the first step is to understand what a linear programming model (Linear Programming, LP) is. The definition of LP is relatively simple. It means that the objective function is linear, all constraints are also linear, and finally, the decision variables can take on any real number.

For example:

There are three kinds of food sold in the supermarket, corn, milk and bread. The price, vitamin A and calories contained in them are shown in the table above. The question now is how many portions of corn, milk, and bread to buy so that the total price is the lowest. The total intake of vitamin A is not less than 500 but not more than 50,000, and the total intake of calories is not less than 2,000 but not more than 2,250.

Now back to the previous question, if there are some decision variables in the linear programming problem, for example, the above X_corn requirement must be an integer, then the planning problem at this time will be transformed into a mixed integer linear programming problem.