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294 CHAPTER 7 TRANSPORTATION, ASSIGNMENT AND TRANSSHIPMENT PROBLEMS

Table 7.10 Net Evaluation Indexes for the Initial Feasible Solution to the Foster
Electronics Problem Calculated Using the MODI Method

v j
u i 3 2 –2 –1
3 2 7 6
0 1 000 4 000 9 7

7 5 2 3
4 2 500 –1 2 000 1 500

2 5 4 5
–1 2 500 4 7 7

Table 7.11 Cycle of Adjustments in Occupied Cells Necessary to Maintain
Feasibility When Shipping One Unit from Brazil to Dubai
Boston Dubai Singapore London Supply
3 2 7 6
Czech 1 001 3 999 5 000
Republic 1000 4000

7 5 2 3
Brazil 2 499 1 2 000 1 500 6 000
2500
2 5 4 5

China 2 500 2 500

Demand 6 000 4 000 2 000 1500

increase the flow on the Czech Republic–Boston arc to 1001 so that the total Czech
Republic supply of 5000 units could be shipped. Finally, we would have to reduce
the flow on the Brazil–Boston arc by 1 to satisfy the Boston demand exactly. Table
7.11 summarizes this cycle of adjustments.
The cycle of adjustments needed in making an allocation to the Brazil–Dubai cell
required changes in four cells: the incoming cell (Brazil–Dubai) and three currently
occupied cells. We can view these four cells as forming a stepping-stone path in the
tableau, where the corners of the path are currently occupied cells. The idea behind
the stepping-stone name is to view the tableau as a pond with the occupied cells as
stones sticking up in it. To identify the stepping-stone path for an incoming cell, we
start at the incoming cell and move horizontally and vertically using occupied cells as

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