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No to sound naive but they look like they include the same steps to me, one's just the algorithmical representation of the other. Thanks in advance.

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The short answer is that they are both the simplex method; the revised version just uses a more efficient implementation.

The longer answer: The standard version of the simplex method updates the entire simplex tableau at each iteration. However, not all of the numbers in the tableau are actually needed in each iteration. What is needed is enough of the tableau to choose a variable to enter the current basis and a variable to leave the basis. Choosing the entering basic variable requires (in terms of the tableau) only the numbers in the row of objective function coefficients. Choosing the leaving basic variable then requires (again, in terms of the tableau) the numbers in the column corresponding to that entering basic variable and the numbers in the right-hand side of the tableau. That's only one row and two columns out of the entire $m \times n$ tableau. The revised simplex method uses the right matrix implementation and rules for avoiding inverting the basis matrix $B$ at every iteration to calculate only the numbers in this row and two columns. By doing so it can speed up the performance of the simplex method considerably.

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