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:

Matrix Minimum Method: Example 2

Consider the transportation problem presented in the following table:

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.