The Linear Programming Solver
- Overview
- Getting Started
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Syntax
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DetailsPresolvePricing Strategies for the Primal and Dual Simplex SolversThe Network Simplex AlgorithmThe Interior Point AlgorithmIteration Log for the Primal and Dual Simplex SolversIteration Log for the Network Simplex SolverIteration Log for the Interior Point SolverIteration Log for the Crossover AlgorithmConcurrent LPProblem StatisticsVariable and Constraint StatusIrreducible Infeasible SetMacro Variable _OROPTMODEL_
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ExamplesDiet ProblemReoptimizing the Diet Problem Using BASIS=WARMSTARTTwo-Person Zero-Sum GameFinding an Irreducible Infeasible SetUsing the Network Simplex SolverMigration to OPTMODEL: Generalized NetworksMigration to OPTMODEL: Maximum FlowMigration to OPTMODEL: Production, Inventory, DistributionMigration to OPTMODEL: Shortest Path
- References
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 OPTMODEL procedure
causes the ODS table “ProblemStatistics” to be generated when the LP solver is called. This table provides basic data magnitude information that enables you to improve
the formulation of your models.
The example output in Figure 6.3 demonstrates the contents of the ODS table “ProblemStatistics.”
Figure 6.3: ODS Table ProblemStatistics
| Problem Statistics | |
|---|---|
| Number of Constraint Matrix Nonzeros | 6 |
| Maximum Constraint Matrix Coefficient | 3 |
| Minimum Constraint Matrix Coefficient | 1 |
| Average Constraint Matrix Coefficient | 2.1666666667 |
| Number of Objective Nonzeros | 3 |
| Maximum Objective Coefficient | 1 |
| Minimum Objective Coefficient | 1 |
| Average Objective Coefficient | 1 |
| Number of RHS Nonzeros | 2 |
| Maximum RHS | 1 |
| Minimum RHS | 1 |
| Average RHS | 1 |
| Maximum Number of Nonzeros per Column | 2 |
| 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 | 3 |
| Average Number of Nonzeros per Row | 3 |