Advertisements
Advertisements
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 |
Advertisements
Solution
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.
APPEARS IN
RELATED QUESTIONS
Write mathematical form of transportation problem
Find an initial basic feasible solution of the following problem using the northwest corner rule.
| D1 | D2 | D3 | D4 | Supply | |
| O1 | 5 | 3 | 6 | 2 | 19 |
| O2 | 4 | 7 | 9 | 1 | 37 |
| O3 | 3 | 4 | 7 | 5 | 34 |
| Demand | 16 | 18 | 31 | 25 |
Explain Vogel’s approximation method by obtaining initial feasible solution of the following transportation problem.
| D1 | D2 | D3 | D4 | Supply | |
| O1 | 2 | 3 | 11 | 7 | 6 |
| O2 | 1 | 0 | 6 | 1 | 1 |
| O3 | 5 | 8 | 15 | 9 | 10 |
| Demand | 7 | 5 | 3 | 2 |
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 | ||
Find the initial basic feasible solution of the following transportation problem:
| I | II | III | Demand | |
| A | 1 | 2 | 6 | 7 |
| B | 0 | 4 | 2 | 12 |
| C | 3 | 1 | 5 | 11 |
| Supply | 10 | 10 | 10 |
Using Least Cost method
Find the initial basic feasible solution of the following transportation problem:
| I | II | III | Demand | |
| A | 1 | 2 | 6 | 7 |
| B | 0 | 4 | 2 | 12 |
| C | 3 | 1 | 5 | 11 |
| Supply | 10 | 10 | 10 |
Using Vogel’s approximation method
Choose the correct alternative:
In a degenerate solution number of allocations is
Choose the correct alternative:
Solution for transportation problem using ______ method is nearer to an optimal solution.
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 | ||
Determine an initial basic feasible solution to the following transportation problem by using least cost method
| 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 | ||
