Test Paper: Transportation, Assignment & Project Scheduling
Section A: Transportation Problems (15 marks)
Q1. (5 marks)
Use the North-West Corner Method to find the initial feasible solution for the following transportation problem:
| Source / Destination | D1 | D2 | D3 | Supply |
|----------------------|----|----|----|--------|
| S1 | 2 | 3 | 1 | 20 |
| S2 | 5 | 4 | 2 | 30 |
| S3 | 3 | 6 | 4 | 25 |
| Demand | 10 | 35 | 30 |
Q2. (5 marks)
Find the optimal solution using the MODI method for the following initial feasible solution:
| Source / Destination | D1 | D2 | D3 | Supply |
|----------------------|----|----|----|--------|
| S1 | 4 | 8 | 6 | 20 |
| S2 | 5 | 2 | 7 | 25 |
| S3 | 6 | 4 | 5 | 15 |
| Demand | 10 | 30 | 20 |
Q3. (5 marks)
Explain the steps of the MODI Method used for optimality testing.
Section B: Assignment Problems (15 marks)
Q4. (5 marks)
Solve the following assignment problem using the Hungarian Method to minimize total cost:
| Task / Worker | W1 | W2 | W3 | W4 |
|---------------|----|----|----|----|
Section A: Transportation Problems (15 marks)
Q1. (5 marks)
Use the North-West Corner Method to find the initial feasible solution for the following transportation problem:
| Source / Destination | D1 | D2 | D3 | Supply |
|----------------------|----|----|----|--------|
| S1 | 2 | 3 | 1 | 20 |
| S2 | 5 | 4 | 2 | 30 |
| S3 | 3 | 6 | 4 | 25 |
| Demand | 10 | 35 | 30 |
Q2. (5 marks)
Find the optimal solution using the MODI method for the following initial feasible solution:
| Source / Destination | D1 | D2 | D3 | Supply |
|----------------------|----|----|----|--------|
| S1 | 4 | 8 | 6 | 20 |
| S2 | 5 | 2 | 7 | 25 |
| S3 | 6 | 4 | 5 | 15 |
| Demand | 10 | 30 | 20 |
Q3. (5 marks)
Explain the steps of the MODI Method used for optimality testing.
Section B: Assignment Problems (15 marks)
Q4. (5 marks)
Solve the following assignment problem using the Hungarian Method to minimize total cost:
| Task / Worker | W1 | W2 | W3 | W4 |
|---------------|----|----|----|----|
