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Transportation Problem |
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North West Corner Rule
Luminous lamps has three factories - F1, F2, and
F3 with production capacity 30, 50, and 20 units per week respectively.
These units are to be shipped to four warehouses W1, W2,
W3, and W4 with requirement of 20, 40, 30, and 10
units per week respectively. The transportation costs (in Rs.) per unit
between factories and warehouses are given below. |
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Example 2| Factory | Warehouse | Supply | |||
|---|---|---|---|---|---|
| W1 | W2 | W3 | W4 | ||
| F1 | 1 | 2 | 1 | 4 | 30 |
| F2 | 3 | 3 | 2 | 1 | 50 |
| F3 | 4 | 2 | 5 | 9 | 20 |
| Demand | 20 | 40 | 30 | 10 | |
Find an initial basic feasible solution of the given transportation problem
Solution.
Starting from the North west corner, we allocate 20 units to F1W1. The demand for the first column is completely satisfied.
Table 1
| Factory | Warehouse | Supply | |||
|---|---|---|---|---|---|
| W1 | W2 | W3 | W4 | ||
| F1 |  |
2 | 1 | 4 | |
| F2 | 3 | 3 | 2 | 1 | 50 |
| F3 | 4 | 2 | 5 | 9 | 20 |
| Demand | |
40 | 30 | 10 | |
Proceeding in this way, we observe that F1W2 = 10, F2W2 = 30, F2W3 = 20, F3W3 = 10, F3W4 = 10. An initial basic feasible solution is exhibited below.
Final Table
| Factory | Warehouse | Supply | |||
|---|---|---|---|---|---|
| W1 | W2 | W3 | W4 | ||
| F1 | |
 |
1 | 4 | |
| F2 | 3 |  |
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1 | |
| F3 | 4 | 2 |  |
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| Demand | |
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Number of basic variables = m + n – 1 = 3 + 4 – 1 = 6.
Initial basic feasible solution
20 X 1 + 10 X 2 + 30 X 3 + 20 X 2 + 10 X 5 + 10 X 9 = 310.
