Function GMP::Benders::CreateMasterProblem(GMP, Variables, Variables, name, feasibilityOnly, addConstraints)

GMP::Benders::CreateMasterProblem

The function GMP::Benders::CreateMasterProblem creates a Benders’ master problem for a generated mathematical program. This master problem is typically used in a Benders’ decomposition algorithm.

GMP::Benders::CreateMasterProblem(
     GMP,                ! (input) a generated mathematical program
     Variables,          ! (input) a set of variables
     name,               ! (input) a string expression
     [feasibilityOnly],  ! (optional, default 0) a scalar value
     [addConstraints]    ! (optional, default 0) a scalar value
)

Arguments

GMP

An element in the set AllGeneratedMathematicalPrograms.

Variables

A subset of AllVariables.

name

A string that holds the name for the Benders’ master problem.

feasibilityOnly

A scalar binary value to indicate whether this function should (temporary) reformulate the original problem such that the Benders’ subproblem becomes a pure feasibility problem.

addConstraints

A scalar binary value to indicate whether this function should try to automatically add tightening constraints to the Benders’ master problem.

Return Value

A new element in the set AllGeneratedMathematicalPrograms with the name as specified by the name argument.

Note

• A call to GMP::Benders::CreateMasterProblem is typically followed by a call to the function GMP::Benders::CreateSubProblem.

• The GMP must have type LP, MIP or RMIP.

• This function cannot be used if the GMP is created by the function GMP::Instance::GenerateStochasticProgram.

• The Variables argument specifies the variables that become part of the Benders’ master problem. All other variables will become part of the Benders’ subproblem. The objective variable should be part of the set of master problem variables; if the objective variable is not included in the set Variables then this procedure will automatically add it.

• If the GMP contains integer variables then they all must be included in the set Variables.

• The feasibilityOnly argument is discussed in more detail in Subproblem as Pure Feasibility Problem of the Language Reference.

• The addConstraints argument is discussed in more detail in Subproblem as Pure Feasibility Problem of the Language Reference.

Example

If the math program has type MIP then often the set of master problem variables equals the set AllIntegerVariables.

myGMP := GMP::Instance::Generated( MP );

gmpM := GMP::Benders::CreateMasterProblem( myGMP, AllIntegerVariables,
                                           'BendersMasterProblem', 0, 0 );

See also

The routines GMP::Benders::CreateSubProblem, GMP::Benders::AddFeasibilityCut and GMP::Benders::AddOptimalityCut.