Question

Determine an initial basic feasible solution of the following transportation problem by north west corner method.

	Bangalore	Nasik	Bhopal	Delhi	Capacity
Chennai	6	8	8	5	30
Madurai	5	11	9	7	40
Trickly	8	9	7	13	50
Demand (Units/day)	35	28	32	25

Answer 1

Let B, N, Bh, D represent the destinations Bangalore, Nasik, Bhopal, and Delhi respectively.

Let C, M, T represent the starting places Chennai, Madurai, and Trichy respectively.

The given transportation table is

	Bangalore	Nasik	Bhopal	Delhi	Capacity (ai)
Chennai	6	8	8	5	30
Madurai	5	11	9	7	40
Trickly	8	9	7	13	50
Demand (bj)	35	28	32	25	120

Total capacity = Total Demand = 120.

So the given problem is a balanced transportation problem.

Hence there exists a feasible solution to the given problem.

First allocation:

	Bangalore	Nasik	Bhopal	Delhi	Capacity (ai)
Chennai	(30)6	8	8	5	30/0
Madurai	5	11	9	7	40
Trickly	8	9	7	13	50
Demand (bj)	35/5	28	32	25	120

Second allocation:

	Bangalore	Nasik	Bhopal	Delhi	(ai)
Chennai	(30)6	8	8	5	30/0
Madurai	(5)5	11	9	7	40/35
Trickly	8	9	7	13	50
(bj)	35/5/0	28	32	25	120

Third allocation:

	Bangalore	Nasik	Bhopal	Delhi	(ai)
Chennai	(30)6	8	8	5	30/0
Madurai	(5)5	(28)11	9	7	40/35/7
Trickly	8	9	7	13	50
(bj)	35/5/0	28/0	32	25	120

Fourth allocation:

	Bangalore	Nasik	Bhopal	Delhi	(ai)
Chennai	(30)6	8	8	5	30/0
Madurai	(5)5	(28)11	(7)9	7	40/35/7/0
Trickly	8	9	7	13	50
(bj)	35/5/0	28/0	32/25	25	120

Fifth allocation:

	Bangalore	Nasik	Bhopal	Delhi	(ai)
Chennai	(30)6	8	8	5	30/0
Madurai	(5)5	(28)11	(7)9	7	40/35/7/0
Trickly	8	9	(25)7	13	50/25
(bj)	35/5/0	28/0	32/25/0	25	120

Final allocation:

	Bangalore	Nasik	Bhopal	Delhi	(ai)
Chennai	(30)6	8	8	5	30/0
Madurai	(5)5	(28)11	(7)9	7	40/35/7/0
Trickly	8	9	(25)7	(25)13	50/25/0
(bj)	35/5/0	28/0	32/25/0	25/0	120

Transportation schedule: Chennai to Bangalore, Madurai to Bangalore, Madurai to Nasik, Madurai to Bhopal, Trichy to Bhopal, Trichy to Delhi.

i.e x₁₁ = 30

x₂₁ = 5

x₂₂ = 28

x₂₃ = 7

x₃₃ = 25

x₃₄ = 25

The total transportation cost = (30 × 6) + (5 × 5) + (28 × 11) + (7 × 9) + (25 × 7) + (25 × 13)

= 180 + 25 + 308 + 63 + 175 + 325

= 1076

Thus the minimum cost is ₹ 1076 by the northwest comer method.