The Mixed-Integer Linear Programming Solver

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

$\text{[math]}$

where

$\text{[math]}$	$\text{[math]}$	$\text{[math]}$	is the vector of structural variables
$\text{[math]}$	$\text{[math]}$	$\text{[math]}$	is the matrix of technological coefficients
$\text{[math]}$	$\text{[math]}$	$\text{[math]}$	is the vector of objective function coefficients
$\text{[math]}$	$\text{[math]}$	$\text{[math]}$	is the vector of constraints right-hand sides (RHS)
$\text{[math]}$	$\text{[math]}$	$\text{[math]}$	is the vector of lower bounds on variables
$\text{[math]}$	$\text{[math]}$	$\text{[math]}$	is the vector of upper bounds on variables
$\text{[math]}$			is a nonempty subset of the set $\text{[math]}$ 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.

For further details, see the SAS/OR^® User's Guide: Mathematical Programming: The Mixed-Integer Linear Programming Solver.
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The Mixed-Integer Linear Programming Solver

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