The Mixed-Integer Linear Programming (MILP) Solver

Procedures in Online Documentation

The mixed-integer linear programming (MILP) solver in the OPTMODEL procedure enables you to solve mixed integer linear programming problems. A standard mixed-integer linear program has the formulation



is the vector of structural variables

is the matrix of technological coefficients

is the vector of objective function coefficients

is the vector of constraints right-hand sides (RHS)

is the vector of lower bounds on variables

is the vector of upper bounds on variables


is a nonempty subset of the set of indices

The MILP solver implements an LP-based branch-and-bound algorithm. This divide-and-conquer approach attempts to solve the original problem by solving linear programming relaxations of a sequence of smaller subproblems. The MILP solver also implements advanced techniques such as presolving, generating cutting planes, and applying primal heuristics to improve the efficiency of the overall algorithm.

The MILP solver provides various control options and solution strategies. In particular, you can enable, disable, or set levels for the advanced techniques previously mentioned. It is also possible to input an incumbent solution.


MILP solver examples