Matrix Minimum Method Examples: Transportation Problem

In the previous section, we used matrix minimum method (Least cost method) to solve a transportation problem. In this section, we provide another example. Let's concentrate on the following example:

Example-1, Example-2

exampleMatrix Minimum Method: Example 2

Consider the transportation problem presented in the following table:

Factory Warehouse Supply
W1 W2 W3
F1 16 20 12 200
F2 14 8 18 160
F3 26 24 16 90
Demand 180 120 150 450

Solution.

We observe that F2W2 = 8, which is the minimum transportation cost and allocate 120 units to it. The demand for the second column is satisfied.

Table 1

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Factory Warehouse Supply
W1 W2 W3
F1 16 20 12 200
F2 14 18 160 40
F3 26 24 16 90
Demand 180 120 150 450

The resulting feasible solution is shown in the following table.

Final Table

Factory Warehouse Supply
W1 W2 W3
F1 20 200
F2 18 160
F3 24 16 90
Demand 180 120 150 450

Number of basic variables = m + n –1 = 3 + 3 – 1 = 5.

Initial basic feasible solution

The total transportation cost associated with this solution is calculated as given below:
50 X 16 + 150 X 12 + 40 X 14 + 120 X 8 + 90 X 26 = 6460.

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