The OPTLP Procedure
Data Input and Output
This subsection describes the PRIMALIN= and DUALIN= data tables required to warm start the primal and dual simplex algorithms, and the PRIMALOUT= and DUALOUT= output data tables.
Definitions of Variables in the PRIMALIN= Data Table
The PRIMALIN= data table must contain the following variables:
Note: The PRIMALIN= data table is created from the PRIMALOUT= data table that is obtained from a previous "normal" run of PROC OPTLP (one that uses only the DATA= data table as the input).
Definitions of Variables in the DUALIN= Data Table
The DUALIN= data table also must contain the following variables:
Note: The DUALIN= data table is created from the DUALOUT= data table that is obtained from a previous "normal" run of PROC OPTLP (one that uses only the DATA= data table as the input).
Definitions of Variables in the PRIMALOUT= Data Table
The PRIMALOUT= data table contains the primal solution to the LP model; each observation corresponds to a variable of the LP problem. The PRIMALOUT= data table can contain an intermediate solution, if one is available. See Example 5.1 for an example of the PRIMALOUT= data table. The variables in the data table have the following names and meanings:
- _OBJ_ID_
-
specifies the name of the objective function. This is particularly useful when there are multiple objective functions, in which case each objective function has a unique name.
Note: PROC OPTLP does not support simultaneous optimization of multiple objective functions in this release.
- _RHS_ID_
specifies the name of the variable that contains the right-hand-side value of each constraint.
- _VAR_
- _TYPE_
-
specifies the type of the decision variable. _TYPE_ can take one of the following values:
- N
nonnegative
- D
bounded (with both lower and upper bound)
- F
free
- X
fixed
- O
other (with either lower or upper bound)
- _OBJCOEF_
specifies the coefficient of the decision variable in the objective function.
- _LBOUND_
- _UBOUND_
- _VALUE_
- _STATUS_
-
specifies the status of the decision variable. _STATUS_ can take one of the following values:
- B
basic variable
- L
nonbasic variable at its lower bound
- U
nonbasic variable at its upper bound
- F
free variable
- A
superbasic variable (a nonbasic variable that has a value strictly between its bounds)
- I
LP model infeasible (all decision variables have _STATUS_ equal to I)
For the interior point algorithm when IIS=FALSE, _STATUS_ is blank.
The following values can appear only if IIS=TRUE. For more information, see the section Irreducible Infeasible Set.
- I_L
the lower bound of the variable is needed for the IIS
- I_U
the upper bound of the variable is needed for the IIS
- I_F
both bounds of the variable needed for the IIS (the variable is fixed or has conflicting bounds)
- _R_COST_
-
specifies the reduced cost of the decision variable, which is the amount by which the objective function is increased per unit increase in the decision variable. The reduced cost associated with the ith variable is the ith entry of the following vector:
where
denotes the basis (matrix composed of basic columns of the constraints matrix 
), 
is the vector of objective function coefficients, and 
is the vector of objective coefficients of the variables in the basis.
In addition, the following variables are returned if sensitivity analysis is used for the corresponding pieces of the input data:
Definitions of Variables in the DUALOUT= Data Table
The DUALOUT= data table contains the dual solution to the LP model; each observation corresponds to a constraint of the LP problem. The DUALOUT= data table can contain an intermediate solution, if one is available. Information about the objective rows of the LP problems is not included. See Example 5.1 for an example of the DUALOUT= data table. The variables in the data table have the following names and meanings:
- _OBJ_ID_
-
specifies the name of the objective function. This is particularly useful when there are multiple objective functions, in which case each objective function has a unique name.
Note: PROC OPTLP does not support simultaneous optimization of multiple objective functions in this release.
- _RHS_ID_
specifies the name of the variable that contains the right-hand-side value of each constraint.
- _ROW_
- _TYPE_
-
specifies the type of the constraint. _TYPE_ can take one of the following values:
- L
"less than or equals" constraint
- E
equality constraint
- G
"greater than or equals" constraint
- R
ranged constraint (both "less than or equals" and "greater than or equals")
- _RHS_
specifies the value of the right-hand side of the constraint. It takes a missing value for a ranged constraint.
- _L_RHS_
specifies the lower bound of a ranged constraint. It takes a missing value for a non-ranged constraint.
- _U_RHS_
specifies the upper bound of a ranged constraint. It takes a missing value for a non-ranged constraint.
- _VALUE_
specifies the value of the dual variable associated with the constraint.
- _STATUS_
-
specifies the status of the slack variable for the constraint. _STATUS_ can take one of the following values:
- B
basic variable
- L
nonbasic variable at its lower bound
- U
nonbasic variable at its upper bound
- F
free variable
- A
superbasic variable (a nonbasic variable that has a value strictly between its bounds)
- I
LP model infeasible (all decision variables have _STATUS_ equal to I)
The following values can appear only if IIS=TRUE. For more information, see the section Irreducible Infeasible Set.
- I_L
the "GE" (
) condition of the constraint is needed for the IIS - I_U
the "LE" (
) condition of the constraint is needed for the IIS - I_F
both conditions of the constraint are needed for the IIS (the constraint is an equality or a range constraint with conflicting bounds)
- _ACTIVITY_
specifies the left-hand-side value of a constraint. In other words, the value of _ACTIVITY_ for the ith constraint would be equal to
, where 
refers to the ith row of the constraints matrix and 
denotes the vector of current decision variable values.
In addition, the following variables are returned if sensitivity analysis is used for the corresponding pieces of the input data: