The Simplex Method in Matrix Form Augmented form for the linear programming

The simplex method in matrix form augmented form for

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The Simplex Method in Matrix Form Augmented form for the linear programming model Introduce the column vector of slack variables 6
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The Simplex Method in Matrix Form General approach of simplex method: Obtain a sequence of improving BF solutions until optimal solution reached Key feature of matrix form Way in which it solves for a new BF solution After identifying its basic and nonbasic variables Step-by-step instructions for using matrix form are given on Page 180 of the text 7
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The Simplex Method in Matrix Form Drawback of matrix form Must calculate the inverse of the updated basis matrix At the end of each iteration Efficient procedure exists (known as revised simplex method) 8
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5.3 A Fundamental Insight Coefficients of the slack variables Reveal how the entire rows of the current simplex tableau were obtained from the rows in the initial tableau 9
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A Fundamental Insight After any iteration: Application of the insight After optimal solution has been obtained Knowing model parameters in initial tableau and only coefficients of the slack variables in the final tableau Calculate all other numbers in the final tableau using the above equations 0
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A Fundamental Insight Adapting to other model forms Adjustments needed Identity matrix I in initial tableau becomes S* in the final tableau If artificial variables must be introduced to serve as initial basic variables: Then the set of columns (appropriately ordered) for all the initial basic variables forms I The same columns in the final tableau provide S* and y* for the equations T* = S*T and t* = t + y*T 1
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