Linear and Integer Programming Made Easy by T. C. Hu & Andrew B. Kahng

Author:T. C. Hu & Andrew B. Kahng
Language: eng
Format: epub
Publisher: Springer International Publishing, Cham

Assume that we have put this into diagonal form with respect to x 1, …, x m , and –z. This gives

The basic solution is , , . We shall assume that all are non-negative so that we have a starting feasible basis.

Let us rewrite the diagonal form as (omitting the bar over coefficients)

where , , , and .

We then put this into the following tableau.

The top row of the tableau expresses x 0 in terms of all variables. Every row in the tableau is an equation. To the left of the tableau are the current basic variables. We start with a tableau in which . This condition is called primal feasible.

Definition

A primal feasible condition is a condition that implies that we have a feasible solution for the program which we want to solve. For example, the condition that the basic variables =a i0 is primal feasible.

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