Let ‘a ‘ denote the supply and ‘b ‘ denote the demand.
Then total supply = 5 + 8 + 7 + 14 = 34 and
Total demand = 7 + 9 + 18 = 34
Σai = Σbj . So the problem is a balanced transportation problem and we can find a basic feasible solution, by North-west comer rule.
First allocation:
Second allocation:
Third allocation:
Fourth allocation:
Fifth allocation:
We first allot 4 units to cell (S3, D3) and then the balance 14 units to cell (S4 , D3 ).
Thus we get the following allocations:
The transportation schedule:
S1 → D1 , S2 → D1 , S2 → D2 , S3 → D2 , S3 → D3 , S4 → D3
(i.e) x11 = 5, x21 = 2, x22 = 6, x32 = 3, x33 = 4, x43 = 14
Total cost = (5 × 2) + (2 × 3) + (6 × 3) + (3 × 4) + (4 × 7) + (14 × 2)
= 10 + 6+ 18 + 12 + 28 + 28
= 102
Thus the initial basic solution is got by NWC method and minimum cost is Rs. 102.