The OPTMILP Procedure

ODS Tables

PROC OPTMILP creates two Output Delivery System (ODS) tables by default unless you specify a value other than 1 for the PRINTLEVEL= option. The first table, "ProblemSummary," is a summary of the input MILP problem. The second table, "SolutionSummary," is a brief summary of the attempt to solve the problem. You can refer to these tables when using ODS. An example output of PROC OPTMILP is shown in Output 16.5 (Problem Summary) and Output 16.6 (Solution Summary). 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 a third table, "ProblemStatistics," is produced. This table contains information about the problem data. See the section "Problem Statistics" for more information.

Table 16.11: ODS Tables Produced by PROC OPTMILP

ODS Table Name	Description	PRINTLEVEL=
ProblemSummary	Summary of the input MILP problem	1 (default)
SolutionSummary	Summary of the solution status	1 (default)
ProblemStatistics	Description of input problem data	2

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

Figure 16.5: Example PROC OPTMILP Output: Problem Summary

Solution Summary 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

Figure 16.6: Example PROC OPTMILP Output: Solution Summary

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 Output 16.7 and Output 16.8, where you can also find variable names for the tables used in the ODS template of the OPTMILP procedure.

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 16.7: ODS Output Data Set: Problem Summary

Solution Summary Obs Label1 cValue1 nValue1 1 Objective Function COST . 2 Solution Status Optimal . 3 Objective Value -7 -7.000000 4     . 5 Relative Gap 0 0 6 Absolute Gap 0 0 7 Primal Infeasibility 0 0 8 Bound Infeasibility 0 0 9 Integer Infeasibility 0 0 10     . 11 Best Bound . . 12 Nodes 0 0 13 Iterations 0 0 14 Presolve Time 0.00 0 15 Solution Time 0.00 0

Figure 16.8: ODS Output Data Set: Solution Summary

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 Output 16.9 demonstrates the contents of the ODS table "ProblemStatistics."

The OPTMILP 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

Figure 16.9: ODS Table ProblemStatistics

The variable names in the ODS table "ProblemStatistics" are Label1, cValue1, and nValue1.