PROC LP: The Reduced Costs, Dual Activities, and Current Tableau :: SAS/OR(R) 9.2 User's Guide: Mathematical Programming

The LP Procedure

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 be the matrix composed of the basic columns of and let be the matrix composed of the nonbasic columns of . The reduced cost associated with the th variable is

$(c^t - c^t_b b^{-1} a)_i$

and the dual activity of the

th row is

$(c^t_b b^{-1})_j$

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

$b^{-1} b$

This column is labeled INV(B)*R. The body of the tableau contains the matrix

$b^{-1} n$

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