Question

Determine basic feasible solution to the following transportation problem using North west Corner rule.

		Sinks
		A	B	C	D	E	Supply
	P	2	11	10	3	7	4
Origins	Q	1	4	7	2	1	8
	R	3	9	4	8	12	9
Demand		3	3	4	5	6

Answer 1

For the given problem, total supply is 4 + 8 + 9 = 21 and total demand is 3 + 3 + 4 + 5 + 6 = 21.

Since the total supply equals total demand, it is a balanced problem and we can find a feasible solution by the North West Comer rule.

First allocation:

	A	B	C	D	E	(ai)
P	(3)2	11	10	3	7	4/1
Q	1	4	7	2	1	8
R	3	9	4	8	12	9
(bj)	3/0	3	4	5	6

Second allocation:

	B	C	D	E	(ai)
P	(1)11	10	3	7	1/0
Q	4	7	2	1	8
R	9	4	8	12	9
(bj)	3/2	4	5	6

Third allocation:

	B	C	D	E	(ai)
Q	(2)4	7	2	1	8/6
R	9	4	8	12	9
(bj)	2/0	4	5	6

Fourth allocation:

	C	D	E	(ai)
Q	(4)7	2	1	6/2
R	4	8	12	9
(bj)	4/0	5	6

Fifth allocation:

	D	E	(ai)
Q	(2)2	1	2/0
R	8	12	9
(bj)	5/3	6

Final allocation:

	D	E	(ai)
R	(3)8	(6)12	9/6/0
(bj)	3/0	6/0

First, we allow 3 units to (R, D) cell.

Then balance 6 to (R, E) cell.

Thus we have the following allocations:

	A	B	C	D	E	Supply
P	(3)2	(1)11	10	3	7	4/1
Q	1	(2)4	(4)7	(2)2	1	8
R	3	9	4	(3)8	(6)12	9
Demand	3	3	4	5	6

Transportation schedule:

P → A

P → B

Q → B

Q → C

Q → D

R → D

R → E

i.e x₁₁ = 3

x₁₂ = 1

x₂₂ = 2

x₂₃ = 4

x₂₄ = 2

x₃₄ = 3

x₃₅ = 6

Total cost = (3 × 2) + (1 × 11) + (2 × 4) + (4 × 7) + (2 × 2) + (3 × 8) + (6 × 12)

= 6 + 11 + 8 + 28 + 4 + 24 + 72

= 153

Thus the minimum cost of the transportation problem by Northwest Comer rule is ₹ 153.