The OPTMILP Procedure

ODS Tables

Subsections:

Problem Statistics

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 13.17 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 13.17: 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 13.5.

Figure 13.5: Example PROC OPTMILP Output: Problem Summary

The OPTMILP Procedure

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 13.6.

Figure 13.6: Example PROC OPTMILP Output: Solution Summary

The OPTMILP Procedure

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	-7
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 13.7 and Figure 13.8, where you can also find variable names for the tables used in the ODS template of the OPTMILP procedure.

Figure 13.7: 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 13.8: 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	-7	-7.000000
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 $10^9$ ) 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 13.9 demonstrates the contents of the ODS table ProblemStatistics.

Figure 13.9: 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.