# Self Test Questions

#### Theory

1. Describe the transportation problem with its general mathematical formulation.

2. Explain the following:

• North west corner rule
• Matrix minimum method
• Vogel approximation method

3. Explain the following with the help of an example:

• Unbalanced transportation problem
• Maximization in a transportation problem
• Degeneracy
• Prohibited routes

4. Discuss the similarities and differences between the stepping stone method and the MODI method in solving a transportation problem.

##### 5. Fill in the blanks
1. The objective of a transportation problem is to …………………. the transportation cost.
2. The constraints of a transportation problem are ………………….
3. If a transportation problem has m factories and n retail shops the number of variables is …………………. and the number of constraints is …………………

#### Practical

1. A factory has three warehouses W1, W2 and W3 which supply to four stores S1, S2, S3 and S4. Monthly capacities of the warehouses are W1 = 100 units, W2 = 40 units and W3 = 60 units. Monthly demands at the stores are S1 = 30 units, S2 = 50 units, S3 = 65 units and S4= 55 units.
The shipping cost in terms of rupees from warehouses to stores is as given below:

Stores
Warehouses S1 S2 S3 S4
W1 14 16 12 20
W2 12 14 10 8
W3 10 16 8 15

The problem here is to determine the optimum distribution for the factory to minimize shipping costs.

#### 2. Solve the following transportation problems.

(a)

Stores
Factories 1 2 3 Supply
1 2 7 4 5
2 3 3 1 8
3 5 4 7 7
4 1 6 2 14
Demand 7 9 18 34

(b)

Use Horizontal Scrollbar to View Full Table Calculation.

Stores
Factories A B C D E F Supply
1 1 2 1 4 5 1 30
2 3 3 2 1 4 3 50
3 4 2 5 9 6 2 75
4 3 1 7 3 4 6 20
Demand 20 40 30 10 50 25

(c)

X Y Z ai
A 8 7 3 60
B 3 8 9 70
C 11 3 5 80
bj 50 80 80

(d)

D1 D2 D3 D4 ai
O1 10 7 3 6 3
O2 1 6 8 3 5
O3 7 4 5 3 7
bj 3 2 6 4 15

(e)

D1 D2 D3 ai
O1 7 3 3 4
O2 3 1 4 1
O3 4 3 6 5
bj 2 3 5 10

(f)

D1 D2 D3 D4 D5 D6 ai
O1 9 12 9 6 9 10 5
O2 7 3 7 7 5 5 6
O3 6 5 9 11 3 11 2
O4 6 8 11 2 2 10 2
bj 4 4 6 2 4 2

(g)

D1 D2 D3 D4 ai
O1 4 3 0 5 24
O2 1 2 6 1 17
O3 3 6 2 3 19
bj 15 19 18 8 60

3. Solve the following transportation problems by Stepping Stone Method and MODI method:

(a)

Distributor
Factory 1 2 3 Inventory
1 2 1 5 10
2 7 3 4 25
3 6 5 3 20
Order 15 22 18 55

(b)

Plant Market Available
A B C D
X 19 30 50 10 7
Y 70 30 40 60 9
Z 40 8 70 20 18
Required 5 8 7 14

(c)

Plant Market Available
A B C D
X 14 9 18 6 11
Y 10 11 7 16 13
Z 25 20 11 34 19
Required 6 10 12 15

(d)

Plant Market Available
A B C D
X 10 22 0 20 8
Y 15 20 12 8 13
Z 20 12 10 15 11
Required 5 11 8 8

(e)

D1 D2 D3 D4 D5 Total
O1 12 4 9 5 9 55
O2 8 1 6 6 7 45
O3 1 12 4 7 7 30
O4 10 15 6 9 1 50
Total 40 20 50 30 40

(f)

D1 D2 D3 Total
O1 2 4 1 40
O2 6 3 2 50
O3 4 5 6 20
O4 3 2 1 30
O5 5 2 5 10
Total 50 60 40 150

4. Solve the following transportation problem.

Furnaces Mills
M1 M2 M3 M4 M5 Total
F1 4 2 3 2 6 8
F2 5 4 5 2 1 12
F3 6 5 4 7 3 14
Requirement 4 4 6 8 8