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 $ 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 $ i$th variable is

\[  (c^ T - c^ T_ B B^{-1} A)_ i  \]

and the dual activity of the $ j$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

\[  B^{-1} N  \]