Construct the Initial Tableau
|Construct the Tableau
When the start button is clicked, the add-in prepares the tableau form of the transportation simplex algorithm and places it lower on the worksheet. Each cell in the original data is represented by four cells in the tableau. The key for the four cells is below.
The upper left cell, outlined and shown in white holds the transportation cost from the supplier to the demander identified by the cell. The upper right cell holds the reduced cost, computed from the dual variables and the original arc costs.
The lower left entry, in green, shows the flow assigned to the cells. Initially these values are zero. The lower right entry holds the letter N or B, indicating whether the cell is not basic (N) or basic (B).
Most of the images that follow are presented in separate windows. This allows the student to read the description while studying the image. Click on the title to see the image. When finished, just close the window.
The Northwest Corner Rule (Click on the title to see the image)
To begin the simplex method an initial basis must be selected. The easiest basis is the one constructed by the Northwest Corner rule. The image shows the dialog where the add-in is asking whether the student wants to begin with the basis defined by this rule. Responding with an OK is the easiest choice. The cancel option allows the student to provide his or her own basis. A basis is defined by placing a capital B in each of the basic cells.
The Northwest corner solution assigns flow to cells starting in the upper left corner. As each cell is considered, flow is assigned to use up all of the supply for a row or all the demand for a column. A complete description is in the textbook. The graphic shows the feasible flow that is determined by the Northwest Corner rule. The flows appear in the green cells. The dual variables have not been computed and have the value 0 in the image. With these dual variables, the reduced costs, shown in the yellow cells, are the same as the original cell costs.
On the next page we complete an iteration.
Research Models and Methods
by Paul A. Jensen and Jon Bard, University of Texas, Copyright by the Authors