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प्रश्न
Determine an initial basic feasible solution of the following transportation problem by north west corner method.
| Bangalore | Nasik | Bhopal | Delhi | Capacity | |
| Chennai | 6 | 8 | 8 | 5 | 30 |
| Madurai | 5 | 11 | 9 | 7 | 40 |
| Trickly | 8 | 9 | 7 | 13 | 50 |
| Demand (Units/day) |
35 | 28 | 32 | 25 |
उत्तर
Let B, N, Bh, D represent the destinations Bangalore, Nasik, Bhopal, and Delhi respectively.
Let C, M, T represent the starting places Chennai, Madurai, and Trichy respectively.
The given transportation table is
| Bangalore | Nasik | Bhopal | Delhi | Capacity (ai) |
|
| Chennai | 6 | 8 | 8 | 5 | 30 |
| Madurai | 5 | 11 | 9 | 7 | 40 |
| Trickly | 8 | 9 | 7 | 13 | 50 |
| Demand (bj) |
35 | 28 | 32 | 25 | 120 |
Total capacity = Total Demand = 120.
So the given problem is a balanced transportation problem.
Hence there exists a feasible solution to the given problem.
First allocation:
| Bangalore | Nasik | Bhopal | Delhi | Capacity (ai) |
|
| Chennai | (30)6 | 8 | 8 | 5 | 30/0 |
| Madurai | 5 | 11 | 9 | 7 | 40 |
| Trickly | 8 | 9 | 7 | 13 | 50 |
| Demand (bj) |
35/5 | 28 | 32 | 25 | 120 |
Second allocation:
| Bangalore | Nasik | Bhopal | Delhi | (ai) | |
| Chennai | (30)6 | 8 | 8 | 5 | 30/0 |
| Madurai | (5)5 | 11 | 9 | 7 | 40/35 |
| Trickly | 8 | 9 | 7 | 13 | 50 |
| (bj) | 35/5/0 | 28 | 32 | 25 | 120 |
Third allocation:
| Bangalore | Nasik | Bhopal | Delhi | (ai) | |
| Chennai | (30)6 | 8 | 8 | 5 | 30/0 |
| Madurai | (5)5 | (28)11 | 9 | 7 | 40/35/7 |
| Trickly | 8 | 9 | 7 | 13 | 50 |
| (bj) | 35/5/0 | 28/0 | 32 | 25 | 120 |
Fourth allocation:
| Bangalore | Nasik | Bhopal | Delhi | (ai) | |
| Chennai | (30)6 | 8 | 8 | 5 | 30/0 |
| Madurai | (5)5 | (28)11 | (7)9 | 7 | 40/35/7/0 |
| Trickly | 8 | 9 | 7 | 13 | 50 |
| (bj) | 35/5/0 | 28/0 | 32/25 | 25 | 120 |
Fifth allocation:
| Bangalore | Nasik | Bhopal | Delhi | (ai) | |
| Chennai | (30)6 | 8 | 8 | 5 | 30/0 |
| Madurai | (5)5 | (28)11 | (7)9 | 7 | 40/35/7/0 |
| Trickly | 8 | 9 | (25)7 | 13 | 50/25 |
| (bj) | 35/5/0 | 28/0 | 32/25/0 | 25 | 120 |
Final allocation:
| Bangalore | Nasik | Bhopal | Delhi | (ai) | |
| Chennai | (30)6 | 8 | 8 | 5 | 30/0 |
| Madurai | (5)5 | (28)11 | (7)9 | 7 | 40/35/7/0 |
| Trickly | 8 | 9 | (25)7 | (25)13 | 50/25/0 |
| (bj) | 35/5/0 | 28/0 | 32/25/0 | 25/0 | 120 |
Transportation schedule: Chennai to Bangalore, Madurai to Bangalore, Madurai to Nasik, Madurai to Bhopal, Trichy to Bhopal, Trichy to Delhi.
i.e x11 = 30
x21 = 5
x22 = 28
x23 = 7
x33 = 25
x34 = 25
The total transportation cost = (30 × 6) + (5 × 5) + (28 × 11) + (7 × 9) + (25 × 7) + (25 × 13)
= 180 + 25 + 308 + 63 + 175 + 325
= 1076
Thus the minimum cost is ₹ 1076 by the northwest comer method.
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