The Linear Programming Solver
- Overview
- Getting Started
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Syntax
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DetailsPresolvePricing Strategies for the Primal and Dual Simplex AlgorithmsThe Network Simplex AlgorithmThe Interior Point AlgorithmIteration Log for the Primal and Dual Simplex AlgorithmsIteration Log for the Network Simplex AlgorithmIteration Log for the Interior Point AlgorithmIteration Log for the Crossover AlgorithmConcurrent LPParallel ProcessingProblem 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 AlgorithmMigration to OPTMODEL: Generalized NetworksMigration to OPTMODEL: Maximum FlowMigration to OPTMODEL: Production, Inventory, DistributionMigration to OPTMODEL: Shortest Path
- References
Several pricing strategies for the primal and dual simplex algorithms are available. Pricing strategies determine which variable enters the basis at each simplex pivot. These can be controlled by specifying the PRICETYPE= option.
The primal simplex algorithm has the following five pricing strategies:
- PARTIAL
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scans a queue of decision variables to find an entering variable. You can optionally specify the QUEUESIZE= option to control the length of this queue.
- FULL
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uses Dantzig’s most violated reduced cost rule (Dantzig, 1963). It compares the reduced cost of all decision variables, and selects the variable with the most violated reduced cost as the entering variable.
- DEVEX
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implements the Devex pricing strategy developed by Harris (1973).
- STEEPESTEDGE
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uses the steepest-edge pricing strategy developed by Forrest and Goldfarb (1992).
- HYBRID
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uses a hybrid of the Devex and steepest-edge pricing strategies.
The dual simplex algorithm has only three pricing strategies available: FULL, DEVEX, and STEEPESTEDGE.