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298 CHAPTER 7 TRANSPORTATION, ASSIGNMENT AND TRANSSHIPMENT PROBLEMS

Table 7.16 Transportation Tableau with a Degenerate Initial Feasible Solution
v j

u i 3 6 Supply
3 6 7
0 35 25 60

8 5 7

–1 30 30

4 9 11

30 30

Demand 35 55 30

artificially occupied cell will enable us to calculate v 3 and u 3 , but placing it in row 2
and column 1 will not.
As we previously stated, whenever an artificially occupied cell is created, we
assign a flow of zero to the corresponding arc. Table 7.17 shows the results of
creating an artificially occupied cell in row 2 and column 3 of Table 7.16. Creation
of the artificially occupied cell results in five occupied cells, so we can now calculate
the remaining row and column indexes. Using the row 2 index (u 2 ¼ 1) and the
artificially occupied cell in row 2, we calculate the column index for column 3; thus,
v 3 ¼ c 23 u 2 ¼ 7 ( 1) ¼ 8. Then, using the column 3 index (v 3 ¼ 8) and the
occupied cell in row 3 and column 3 of the tableau, we calculate the row 3 index:

Table 7.17 Transportation Tableau With An Artificial Cell in Row 2 and Column 3
v j

u i 3 6 8 Supply
3 6 7

0 35 25 –1 60

8 5 7
–1 6 30 0 30

Artificially
4 9 11 occupied cell

3 –2 0 30 30

Demand 35 55 30

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