L11_Explanation of Simplex Tableau Entries

L11_Explanation of Simplex Tableau Entries - Explanation of...

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Unformatted text preview: Explanation of the entries in any simplex tableau in terms of the entries of the starting tableau In this lecture we explain how the starting Simplex tableau (in matrix form) gets transformed after some iterations. We also give the meaning of the entries in the new tableau in terms of the entries of the starting tableau. We illustrate how we can write the simplex tableau from the starting tableau by choosing a different set of basic variables. The Simplex tableau in Matrix form Consider the LPP in matrix form as: z = cX Subject to = AX b X 0, b 0 Maximize (or Minimize) The problem can be written equivalently as 1 z- = c A X b Suppose B is a m x m non-singular sub-matrix of the coefficient matrix A. Let X B be the corresponding set of basic variables with c B as its associated objective vector. The corresponding solution (and the objective function value ) may be computed as follows: 1 1 0 0 1 z-- -- - = = = -1 1 B B B 1 1 B c c B c B b X 0 B b b 0 B B b 1 0 z = -B B c X 0 B b Size m 1 Hence The general simplex tableau in matrix form can be derived from the original equations as follows: 1 0 1 1 z- -- -- = 1 1 B B 1 1 c c B c B 0 A X b 0 B 0 B Multiplying out the matrices, we get 1 z---- = -1 1 B B 1 1 c B A C c B b X B A B b Thus in the new simplex tableau the z column will be 1 . . The column of x j (in the constraint equations) will be is the jth column of A ....
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This note was uploaded on 02/23/2011 for the course MATH 112 taught by Professor Ritadubey during the Spring '11 term at Amity University.

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L11_Explanation of Simplex Tableau Entries - Explanation of...

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