Total supply = 25 + 35 + 40 = 100 = Σai
Total requirement = 30 + 25 + 45 = 100 = Σbj
Since Σai = Σbj the given transportation problem is balanced and we can find an initial basic feasible solution.
(i) North West Corner Rule
First allocation:
Second allocation:
Third allocation:
Fourth allocation:
We first allot 5 units to cell (S2 , D3 ). Then balance 40 units we allot to cell (S3 , D3 ).
The final allotment is given as follows
Transportation schedule:
S1 → D1 , S2 → D1 , S2 → D2 , S2 → D3 , S3 → D3
(i.e) x11 = 25, x 21= 5, x22 = 25, x23 = 5, x33 = 40
Total cost is = (25 × 9) + (5 × 6) + (25 × 8) + (5 × 4) + (40 × 9)
= 225 + 30 + 200 + 20 + 360
= 835
Hence the minimum cost is Rs. 835 by NWC method.
(ii) Least cost method (LCM)
First allocation:
Second allocation:
Third allocation:
Fourth allocation:
We first allot 15 units to cell (S3 , D1) since it has the least cost. Then we allot the balance 15 units to cell (S1 , D1 ).
The final allotment is given as follows
Transportation schedule:
S1 → D1 , S1 → D3 , S2 → D3 , S3 → D1 , S3 → D2
(i.e) x11 = 15, x13 = 10, x23 = 35, x31 = 15, x32 = 25
Total cost is = (15 × 9) + (10 × 5) + (35 × 4) + (15 × 7) + (25 × 6)
= 136 + 50 + 140 + 105 + 150
= 580
The optimal cost by LCM is Rs. 580.