Question

Determine an initial basic feasible solution to the following transportation problem by using north west corner rule

		Destination			Supply
		D1	D2	D3
	S1	9	8	5	25
Source	S2	6	8	4	35
	S3	7	6	9	40
	Requirement	30	25	45

Answer 1

Total supply = 25 + 35 + 40 = 100 = `sum"a"_"i"`

Total requirement = 30 + 25 + 45 = 100 = `sum"b"_"j"`

Since `sum"a"_"i" = sum"b"_"j"` 

The given transportation problem is balanced and we can find an initial basic feasible solution.

North West Corner Rule

First allocation:

	D1	D2	D3	(ai)
S1	(25)9	8	5	25/0
S2	6	8	4	35
S3	7	6	9	40
(bj)	30/5	25	45

Second allocation:

	D1	D2	D3	(ai)
S2	(5)6	8	4	35/30
S3	7	6	9	40
(bj)	5/0	25	45

Third allocation:

	D2	D3	(ai)
S2	(25)8	4	30/5
S3	6	9	40
(bj)	25/0	45

Fourth allocation:

	D3	(ai)
S2	(5)4	5/0
S3	(40)9	40/0
(bj)	45/40/0

We first allow 5 units to cell (S₂, D₃).

Then balance 40 units we allot to cell (S₃, D₃).

The final allotment is given as follows

	D1	D2	D3	Supply
S1	(25)9	8	5	25
S2	(5)6	(25)8	(5)4	35
S3	7	6	(40)9	40
Requirement	30	25	45

Transportation schedule:

S₁ → D₁

S₂ → D₁

S₂ → D₂

S₂ → D₃

S₃ → D₃

i.e x₁₁ = 25

x₂₁ = 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 ₹ 835 by NWC method.