The revised primal simplex method uses matrix operations to compute the quantities used by the simplex method. We have implemented this technique with an Excel add-in called Teach LP. This unit is the introduction to that portion of the add-in that performs the revised simplex method. To run an exercise the student selects Revised Simplex from the menu.

The examples for this section are in the Teach LP demo (teachlpdem.xls). To solve or change the model you must have the Teach LP add-in loaded. Use the Relink buttons command to establish links to the worksheet buttons.

The dialog defining the model is the same as that used for the Tableau simplex method.

Initial Basis

Pressing the Phase 1 button, initiates the process that builds the vectors and matrices that implement the simplex procedure. The figure below shows the initial basis and basis inverse matrices. These are placed to the right of the LP model. The matrices change during the algorithm as the basic variables change.

Revised Simplex Matrices

The other information necessary for accomplishing the revised simplex procedure is placed in the rows below the LP model as shown below. All the cells in the yellowed area contain Excel formulas that compute the quantities necessary for the iteration. As for the tableau method, the Iterate button initiates the iteration, first asking for the variable to enter the basis, then the variable to leave the basis.

Selecting the Entering and Leaving Variables

For the first iteration of the method, we have selected variable 3 to enter and variable 9 to leave. The cells colored blue indicate the cells that will change with the pivot operation. Pressing the Pivot key replaces index 9 in the vector of basic variables with that of row 3. Since all the cell contents are controlled by equations, they all change to represent the new basis.

Phase 2

The first iteration completes phase 1 and places the Phase 2 button on the worksheet.

The Optimum Solution

One more step leads to the optimum solution.