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.
Northwest
Corner Solution
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.
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