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300 CHAPTER 7 TRANSPORTATION, ASSIGNMENT AND TRANSSHIPMENT PROBLEMS

Table 7.19 New Row and Column Indexes Obtained after Allocating 30 Units to
the Incoming Cell

v j
u i 3 6 8 Supply
3 6 7
0 5 55 –1 60

8 5 7
–1 6 0 30 30

4 9 11
1 30 2 2 30

Demand 35 55 30

The cell in row 2 and column 3 is the outgoing cell; the tableau after this iteration
is shown in Table 7.21. Note that we have found the optimal solution and that,
even though several earlier iterations were degenerate, the final solution is not
degenerate.

Summary of the Transportation Simplex Method
The transportation Simplex method is a special-purpose solution procedure appli-
cable to any network model having the structure of the transportation problem. It is
actually a clever implementation of the general Simplex method for linear

Table 7.20 Stepping-Stone Path Associated with the Incoming Cell in Row 1 and
Column 3

v j
3 6 8 Supply
u i
3 – 6 7
0 5 60
55

8 + 5 – 7
–1 30
0 30

4 9 11
1 30 30

Demand 35 55 30

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