Question

For a transportation problem with cost matrix as given below:

Find a solution by north west corner rule and find transportation cost.

Answer 1

Here the availability; ai = requirement; bj = 112, thus the T.P. is balanced. 

Therefore there exists a feasible solution. 

Consider the north west corner cell at (1, 1) allocate as; minimum (a,, b,) 

= min (100, 30) x₁₁ = 30.

Here a₁ > b₁ and replace b₁ = 100 – 30 = 70.

Next, Allocate at (1,2) as: Min (70, 50) = 50; X₁₂ = 50. 

Here again a₁ > b₁ and replace, b₁ = 70 – 50 = 20

Next allocations meat (1,3) as; min (20, 32) 

= 20 and replace (32 – 20) – 12 A; So, X₁₃ = 20.

Next allocation is mode at (2, 3) as: 

Here b₃ > a₁ 

So, Min (12, 12) = 12 ; X₂₃ = 12. 

All allocations are made. 

Thus, initial feasible solutions is:- 

X₁₁ = 30, X₁₂ = 50, X₁₃ = 20, X₂₃ = 12 

The transportation cost is: Z = ΣΣCij.Xij 

= 3 × 30 + 7 × 50 + 4 × 20 + 2 × 12 

= 90 + 350 + 80 + 24 = Rs. 544. 

Note: In the problem m(rows) = 2, n(Columns) = 3 

∴ m + n – 1 = 2 + 3 – 1 =4 

The number of allocations = 4 is same as (m + n – 1). 

The initial feasible solutions a basic feasible solution.