Simplex tableau

A schematic, numerical representation which displays the transformed data set associated with a basic solution to a linear-programming problem. For the problem: Minimize cx,v subject to Axv = b, xv ≥ 0, if we let the m × m matrix Bv be a feasible basis and the m × 1 row vector c ₀ be the ordered cost coefficients for the variables in the basis, then the simplex tableau displays the following information in an (m + 1) × (n + 1) rectangular array

where π, the pricing vector, is equal to cv₀ Bv⁻¹. The last or (m+ 1)st, row of the tableau contains the reduced costs and the current value of the objective function, respectively. If the simplex method is in Phase I, then an additional row is added to the tableau which contains the reduced costs associated with the artificial basis. In some arrangements of the tableau, the rows associated with the reduced costs are given at the top of the tableau; also, a reduced tableau is obtained by leaving out the columns that correspond to the columns...