Mixed Integer Linear Programming

Mixed Integer Linear Programming

The Mixed integer linear programming (MILP) is a mathematical modelling approach used to get the best outcome of a system with some restrictions. This model is broadly used in many optimisation areas such as production planning, transportation, network design, etc.
MILP comprises a linear objective function along with some limitation constraints constructed by continuous and integer variables. The main objective of this model is to get an optimal solution of the objective function. This may be the maximum or minimum value but it should be achieved without violating any of the constraints imposed.
We can say that MILP is a special case of linear programming that uses binary variables. When compared with normal linear programming models, they are slightly tough to solve. Basically, the MILP models are solved by commercial and non-commercial solvers, for example, Fico Xpress or SCIP.Image result for Mixed Integer Linear Programming in Management
A mixed-integer linear program is a problem with Linear objective function, fTx, where f is a column vector of constants, and x is the column vector of unknowns Bounds and linear constraints, but no nonlinear constraints (for definitions, see Write Constraints)
Restrictions on some components of x to have integer values
In mathematical terms, given vectors f, lb, and up, matrices A and Aeq, corresponding vectors b and be, and a set of indices into, find a vector x to solve

minxfT x subject to 
x(icon) are integers
A⋅x≤b
Aeq⋅x=beq
lb≤x≤ub.