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in Operations Research by (48.0k points)
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The following table summarizes the supply, demand and cost information for four factors S1 , S2 , S3 , S4 shipping goods to three warehouses D1 , D2 , D3 .

Find an initial solution by using the north-west corner rule. What is the total cost of this solution?

1 Answer

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by (48.4k points)
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Best answer

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.

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