The OPTMILP Procedure
ODS Tables
PROC OPTMILP creates three Output Delivery System (ODS) tables by default. The first table, ProblemSummary, is a summary of the input MILP problem. The second table, SolutionSummary, is a brief summary of the solution status. The third table, PerformanceInfo, is a summary of performance options. You can use ODS table names to select tables and create output data sets. For more information about ODS, see SAS Output Delivery System: User's Guide.
If you specify a value of 2 for the PRINTLEVEL= option, then the ProblemStatistics table is produced. This table contains information about the problem data. See the section Problem Statistics for more information.
If you specify the DETAILS option in the PERFORMANCE statement, then the Timing table is produced.
Table 11.13 lists all the ODS tables that can be produced by the OPTMILP procedure, along with the statement and option specifications required to produce each table.
Table 11.13: ODS Tables Produced by PROC OPTMILP
|
ODS Table Name |
Description |
Statement |
Option |
|---|---|---|---|
|
ProblemSummary |
Summary of the input MILP problem |
PROC OPTMILP |
PRINTLEVEL=1 (default) |
|
SolutionSummary |
Summary of the solution status |
PROC OPTMILP |
PRINTLEVEL=1 (default) |
|
ProblemStatistics |
Description of input problem data |
PROC OPTMILP |
PRINTLEVEL=2 |
|
PerformanceInfo |
List of performance options and their values |
PROC OPTMILP |
PRINTLEVEL=1 (default) |
|
Timing |
Detailed solution timing |
PERFORMANCE |
DETAILS |
A typical ProblemSummary table is shown in Figure 11.5.
Figure 11.5: Example PROC OPTMILP Output: Problem Summary
| Problem Summary | |
|---|---|
| Problem Name | EX_MIP |
| Objective Sense | Minimization |
| Objective Function | COST |
| RHS | RHS |
| Number of Variables | 3 |
| Bounded Above | 0 |
| Bounded Below | 0 |
| Bounded Above and Below | 3 |
| Free | 0 |
| Fixed | 0 |
| Binary | 3 |
| Integer | 0 |
| Number of Constraints | 3 |
| LE (<=) | 2 |
| EQ (=) | 0 |
| GE (>=) | 1 |
| Range | 0 |
| Constraint Coefficients | 8 |
A typical SolutionSummary table is shown in Figure 11.6.
Figure 11.6: Example PROC OPTMILP Output: Solution Summary
| Solution Summary | |
|---|---|
| Solver | MILP |
| Algorithm | Branch and Cut |
| Objective Function | COST |
| Solution Status | Optimal |
| Objective Value | -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 |
You can create output data sets from these tables by using the ODS OUTPUT statement. The output data sets from the preceding example are displayed in Figure 11.7 and Figure 11.8, where you can also find variable names for the tables used in the ODS template of the OPTMILP procedure.
Figure 11.7: ODS Output Data Set: Problem Summary
| Problem Summary |
| Obs | Label1 | cValue1 | nValue1 |
|---|---|---|---|
| 1 | Problem Name | EX_MIP | . |
| 2 | Objective Sense | Minimization | . |
| 3 | Objective Function | COST | . |
| 4 | RHS | RHS | . |
| 5 | . | ||
| 6 | Number of Variables | 3 | 3.000000 |
| 7 | Bounded Above | 0 | 0 |
| 8 | Bounded Below | 0 | 0 |
| 9 | Bounded Above and Below | 3 | 3.000000 |
| 10 | Free | 0 | 0 |
| 11 | Fixed | 0 | 0 |
| 12 | Binary | 3 | 3.000000 |
| 13 | Integer | 0 | 0 |
| 14 | . | ||
| 15 | Number of Constraints | 3 | 3.000000 |
| 16 | LE (<=) | 2 | 2.000000 |
| 17 | EQ (=) | 0 | 0 |
| 18 | GE (>=) | 1 | 1.000000 |
| 19 | Range | 0 | 0 |
| 20 | . | ||
| 21 | Constraint Coefficients | 8 | 8.000000 |
Figure 11.8: ODS Output Data Set: Solution Summary
| Solution Summary |
| Obs | Label1 | cValue1 | nValue1 |
|---|---|---|---|
| 1 | Solver | MILP | . |
| 2 | Algorithm | Branch and Cut | . |
| 3 | Objective Function | COST | . |
| 4 | Solution Status | Optimal | . |
| 5 | Objective Value | -7 | -7.000000 |
| 6 | . | ||
| 7 | Relative Gap | 0 | 0 |
| 8 | Absolute Gap | 0 | 0 |
| 9 | Primal Infeasibility | 0 | 0 |
| 10 | Bound Infeasibility | 0 | 0 |
| 11 | Integer Infeasibility | 0 | 0 |
| 12 | . | ||
| 13 | Best Bound | . | . |
| 14 | Nodes | 0 | 0 |
| 15 | Iterations | 0 | 0 |
| 16 | Presolve Time | 0.00 | 0 |
| 17 | Solution Time | 0.00 | 0 |
Problem Statistics
Optimizers can encounter difficulty when solving poorly formulated models. Information about data magnitude provides a simple
gauge to determine how well a model is formulated. For example, a model whose constraint matrix contains one very large entry
(on the order of 
) can cause difficulty when the remaining entries are single-digit numbers. The PRINTLEVEL=2 option in the OPTMILP procedure causes the ODS table ProblemStatistics to be generated. This table provides basic data magnitude
information that enables you to improve the formulation of your models.
The example output in Figure 11.9 demonstrates the contents of the ODS table ProblemStatistics.
Figure 11.9: ODS Table ProblemStatistics
| ProblemStatistics |
| Obs | Label1 | cValue1 | nValue1 |
|---|---|---|---|
| 1 | Number of Constraint Matrix Nonzeros | 8 | 8.000000 |
| 2 | Maximum Constraint Matrix Coefficient | 3 | 3.000000 |
| 3 | Minimum Constraint Matrix Coefficient | 1 | 1.000000 |
| 4 | Average Constraint Matrix Coefficient | 1.875 | 1.875000 |
| 5 | . | ||
| 6 | Number of Objective Nonzeros | 3 | 3.000000 |
| 7 | Maximum Objective Coefficient | 4 | 4.000000 |
| 8 | Minimum Objective Coefficient | 2 | 2.000000 |
| 9 | Average Objective Coefficient | 3 | 3.000000 |
| 10 | . | ||
| 11 | Number of RHS Nonzeros | 3 | 3.000000 |
| 12 | Maximum RHS | 7 | 7.000000 |
| 13 | Minimum RHS | 4 | 4.000000 |
| 14 | Average RHS | 5.3333333333 | 5.333333 |
| 15 | . | ||
| 16 | Maximum Number of Nonzeros per Column | 3 | 3.000000 |
| 17 | Minimum Number of Nonzeros per Column | 2 | 2.000000 |
| 18 | Average Number of Nonzeros per Column | 2 | 2.000000 |
| 19 | . | ||
| 20 | Maximum Number of Nonzeros per Row | 3 | 3.000000 |
| 21 | Minimum Number of Nonzeros per Row | 2 | 2.000000 |
| 22 | Average Number of Nonzeros per Row | 2 | 2.000000 |
The variable names in the ODS table ProblemStatistics are Label1, cValue1, and nValue1.