The OPTLP Procedure

ODS Tables

Subsections:

Problem Statistics

PROC OPTLP creates three Output Delivery System (ODS) tables by default. The first table, ProblemSummary, is a summary of the input LP 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: Procedures 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. For more information, see the section Problem Statistics. If you specify PRINTLEVEL=2 and ALGORITHM=CON, the ConcurrentSummary table is produced. This table contains solution status information for all algorithms that are run concurrently. For more information, see the section Concurrent LP.

If you specify the DETAILS option in the PERFORMANCE statement, then the Timing table is produced.

Table 11.5 lists all the ODS tables that can be produced by the OPTLP procedure, along with the statement and option specifications required to produce each table.

Table 11.5: ODS Tables Produced by PROC OPTLP

ODS Table Name	Description	Statement	Option
ProblemSummary	Summary of the input LP problem	PROC OPTLP	PRINTLEVEL=1 (default)
SolutionSummary	Summary of the solution status	PROC OPTLP	PRINTLEVEL=1 (default)
ProblemStatistics	Description of input problem data	PROC OPTLP	PRINTLEVEL=2
ConcurrentSummary	Summary of the solution status for all algorithms run concurrently	PROC OPTLP	PRINTLEVEL=2, ALGORITHM=CON
PerformanceInfo	List of performance options and their values	PROC OPTLP	PRINTLEVEL=1 (default)
Timing	Detailed solution timing	PERFORMANCE	DETAILS

A typical output of PROC OPTLP is shown in Figure 11.2.

Figure 11.2: Typical OPTLP Output

The OPTLP Procedure

Problem Summary
Problem Name	ADLITTLE
Objective Sense	Minimization
Objective Function	.Z....
RHS	ZZZZ0001

Number of Variables	97
Bounded Above	0
Bounded Below	97
Bounded Above and Below	0
Free	0
Fixed	0

Number of Constraints	56
LE (<=)	40
EQ (=)	15
GE (>=)	1
Range	0

Constraint Coefficients	383

Performance Information
Execution Mode	Single-Machine
Number of Threads	4

Solution Summary
Solver	LP
Algorithm	Dual Simplex
Objective Function	.Z....
Solution Status	Optimal
Objective Value	225494.96316

Primal Infeasibility	1.023182E-12
Dual Infeasibility	2.507661E-12
Bound Infeasibility	0

Iterations	81
Presolve Time	0.00
Solution Time	0.00

You can create output data sets from these tables by using the ODS OUTPUT statement. This can be useful, for example, when you want to create a report to summarize multiple PROC OPTLP runs. The output data sets corresponding to the preceding output are shown in Figure 11.3, where you can also find (at the row following the heading of each data set in display) the variable names that are used in the table definition (template) of each table.

Figure 11.3: ODS Output Data Sets

Problem Summary

Obs	Label1	cValue1	nValue1
1	Problem Name	ADLITTLE	.
2	Objective Sense	Minimization	.
3	Objective Function	.Z....	.
4	RHS	ZZZZ0001	.
5			.
6	Number of Variables	97	97.000000
7	Bounded Above	0	0
8	Bounded Below	97	97.000000
9	Bounded Above and Below	0	0
10	Free	0	0
11	Fixed	0	0
12			.
13	Number of Constraints	56	56.000000
14	LE (<=)	40	40.000000
15	EQ (=)	15	15.000000
16	GE (>=)	1	1.000000
17	Range	0	0
18			.
19	Constraint Coefficients	383	383.000000

Solution Summary

Obs	Label1	cValue1	nValue1
1	Solver	LP	.
2	Algorithm	Dual Simplex	.
3	Objective Function	.Z....	.
4	Solution Status	Optimal	.
5	Objective Value	225494.96316	225495
6			.
7	Primal Infeasibility	1.023182E-12	1.023182E-12
8	Dual Infeasibility	2.507661E-12	2.507661E-12
9	Bound Infeasibility	0	0
10			.
11	Iterations	81	81.000000
12	Presolve Time	0.00	0
13	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 OPTLP 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 11.4 demonstrates the contents of the ODS table ProblemStatistics.

Figure 11.4: ODS Table ProblemStatistics

The OPTLP Procedure

Problem Statistics
Number of Constraint Matrix Nonzeros	8
Maximum Constraint Matrix Coefficient	3
Minimum Constraint Matrix Coefficient	1
Average Constraint Matrix Coefficient	1.875

Number of Objective Nonzeros	3
Maximum Objective Coefficient	4
Minimum Objective Coefficient	2
Average Objective Coefficient	3

Number of RHS Nonzeros	3
Maximum RHS	7
Minimum RHS	4
Average RHS	5.3333333333

Maximum Number of Nonzeros per Column	3
Minimum Number of Nonzeros per Column	2
Average Number of Nonzeros per Column	2

Maximum Number of Nonzeros per Row	3
Minimum Number of Nonzeros per Row	2
Average Number of Nonzeros per Row	2