The OPTMODEL procedure provides a framework for specifying and solving mixed integer linear programs (MILPs). A standard mixed integer linear program has the formulation
where



is the vector of structural variables 



is the matrix of technological coefficients 



is the vector of objective function coefficients 



is the vector of constraints righthand 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, available in the OPTMODEL procedure, implements an linearprogrammingbased branchandbound algorithm. This divideandconquer 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; see the section Warm Start Option for details.