The OPTMILP Procedure
The following example illustrates the use of the OPTMILP procedure to solve mixed integer linear programs. For more examples, see the section Examples: OPTMILP Procedure. Suppose you want to solve the following problem:
![\[ \begin{array}{rlllllcrc} \mbox{min} & 2x_1 & - & 3x_2 & - & 4x_3 & & & \\ \mbox{s.t.} & & - & 2x_2 & - & 3x_3 & \geq & -5 & (\mbox{R1})\\ & x_1 & + & x_2 & + & 2x_3 & \leq & 4 & (\mbox{R2})\\ & x_1 & + & 2x_2 & + & 3x_3 & \leq & 7 & (\mbox{R3})\\ & & & x_1, & x_2, & x_3 & \geq & 0 & \\ & & & x_1, & x_2, & x_3 & \in \mathbb {Z} & & \\ \end{array} \]](images/ormpug_optmilp0015.png)
The corresponding MPS-format SAS data set follows:
data ex_mip; input field1 $ field2 $ field3 $ field4 field5 $ field6; datalines; NAME . EX_MIP . . . ROWS . . . . . N COST . . . . G R1 . . . . L R2 . . . . L R3 . . . . COLUMNS . . . . . . MARK00 'MARKER' . 'INTORG' . . X1 COST 2 R2 1 . X1 R3 1 . . . X2 COST -3 R1 -2 . X2 R2 1 R3 2 . X3 COST -4 R1 -3 . X3 R2 2 R3 3 . MARK01 'MARKER' . 'INTEND' . RHS . . . . . . RHS R1 -5 R2 4 . RHS R3 7 . . ENDATA . . . . . ;
You can also create this SAS data set from an MPS-format flat file (ex_mip.mps) by using the following SAS macro:
%mps2sasd(mpsfile = "ex_mip.mps", outdata = ex_mip);
This problem can be solved by using the following statement to call the OPTMILP procedure:
proc optmilp data = ex_mip objsense = min primalout = primal_out dualout = dual_out presolver = automatic heuristics = automatic; run;
The DATA= option names the MPS-format SAS data set that contains the problem data. The OBJSENSE= option specifies whether to maximize or minimize the objective function. The PRIMALOUT= option names the SAS data set to contain the optimal solution or the best feasible solution found by the solver. The DUALOUT= option names the SAS data set to contain the constraint activities. The PRESOLVER= and HEURISTICS= options specify the levels for presolving and applying heuristics, respectively. In this example, each option is set to its default value AUTOMATIC, meaning that the solver automatically determines the appropriate levels for presolve and heuristics.
The optimal integer solution and its corresponding constraint activities, stored in the data sets primal_out and dual_out, respectively, are displayed in Figure 11.1 and Figure 11.2.
Figure 11.1: Optimal Solution
| The OPTMILP Procedure |
| Primal Integer Solution |
| Obs | Objective Function ID |
RHS ID | Variable Name |
Variable Type |
Objective Coefficient |
Lower Bound |
Upper Bound |
Variable Value |
|---|---|---|---|---|---|---|---|---|
| 1 | COST | RHS | X1 | B | 2 | 0 | 1 | 0 |
| 2 | COST | RHS | X2 | B | -3 | 0 | 1 | 1 |
| 3 | COST | RHS | X3 | B | -4 | 0 | 1 | 1 |
Figure 11.2: Constraint Activities
| The OPTMILP Procedure |
| Constraint Information |
| Obs | Objective Function ID |
RHS ID | Constraint Name |
Constraint Type |
Constraint RHS |
Constraint Lower Bound |
Constraint Upper Bound |
Constraint Activity |
|---|---|---|---|---|---|---|---|---|
| 1 | COST | RHS | R1 | G | -5 | . | . | -5 |
| 2 | COST | RHS | R2 | L | 4 | . | . | 3 |
| 3 | COST | RHS | R3 | L | 7 | . | . | 5 |
The solution summary stored in the macro variable _OROPTMILP_ can be viewed by issuing the following statement:
%put &_OROPTMILP_;
This produces the output shown in Figure 11.3.
Figure 11.3: Macro Output
| STATUS=OK ALGORITHM=BAC SOLUTION_STATUS=OPTIMAL OBJECTIVE=-7 |
| RELATIVE_GAP=0 ABSOLUTE_GAP=0 PRIMAL_INFEASIBILITY=0 |
| BOUND_INFEASIBILITY=0 INTEGER_INFEASIBILITY=0 BEST_BOUND=. NODES=0 |
| ITERATIONS=0 PRESOLVE_TIME=0.00 SOLUTION_TIME=0.00 |
See the section Data Input and Output for details about the type and status codes displayed for variables and constraints.