The LP Procedure
- Overview
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Getting Started
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Syntax
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DetailsMissing ValuesDense Data Input FormatSparse Data Input FormatConverting Any PROC LP Format to an MPS-Format SAS Data SetConverting Standard MPS Format to Sparse FormatThe Reduced Costs, Dual Activities, and Current TableauMacro Variable _ORLP_PricingScalingPreprocessingInteger ProgrammingSensitivity AnalysisRange AnalysisParametric ProgrammingInteractive FacilitiesMemory ManagementOutput Data SetsInput Data SetsDisplayed OutputODS Table and Variable NamesMemory Limit
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ExamplesAn Oil Blending ProblemA Sparse View of the Oil Blending ProblemSensitivity Analysis: Changes in Objective CoefficientsAdditional Sensitivity AnalysisPrice Parametric Programming for the Oil Blending ProblemSpecial Ordered Sets and the Oil Blending ProblemGoal-Programming a Product Mix ProblemA Simple Integer ProgramAn Infeasible ProblemRestarting an Integer ProgramAlternative Search of the Branch-and-Bound TreeAn Assignment ProblemA Scheduling ProblemA Multicommodity Transshipment Problem with Fixed ChargesConverting to an MPS-Format SAS Data SetMigration to OPTMODEL: AssignmentMigration to OPTMODEL: Multicommodity Transshipment
- References
The Reduced Costs, Dual Activities, and Current Tableau
The evaluation of reduced costs and the dual activities is independent of problem structure. For a basic solution, let B be the matrix composed of the basic columns of A and let N be the matrix composed of the nonbasic columns of A. The reduced cost associated with the ith variable is
![\[ (c^ T - c^ T_ B B^{-1} A)_ i \]](images/ormplpug_lp0041.png)
and the dual activity of the jth row is
![\[ (c^ T_ B B^{-1})_ j \]](images/ormplpug_lp0042.png)
The Current Tableau is a section displayed when you specify either the TABLEAUPRINT option in the PROC LP statement or the TABLEAU option in the PRINT statement. The output contains a row for each basic variable and a column for each nonbasic variable. In addition, there is a row for the reduced costs and a column for the product
![\[ B^{-1} b \]](images/ormplpug_lp0043.png)
This column is labeled INV(B)*R. The body of the tableau contains the matrix
![\[ B^{-1} N \]](images/ormplpug_lp0044.png)