Transportation Problems
Assignment II (Part – C)
Degeneracy Problems
Q1. A manufacturer wants to ship 8 loads to
his product as shown below. The matrix gives the kilometers from origin to the
destination.
|
Origin
|
|
Destination
|
|||
|
A
|
B
|
C
|
Supply
|
||
|
X
|
50
|
30
|
220
|
1
|
|
|
Y
|
90
|
45
|
170
|
3
|
|
|
Z
|
50
|
200
|
50
|
4
|
|
|
Demand
|
3
|
3
|
2
|
8
|
|
Shipping cost
Rs. 10 per load per kilometer. What shipping schedule should be used?
Answer: Total Optimal Cost for
transportation =385 x 10=3850
Q2. A company has three factories F1, F2 and
F3 which supply warehouses at W1, W2 & W3. Monthly factory capacities are
120 units, 80 units and 80 units respectively. Monthly warehouse requirement
are 150 units, 80 and 50 units respectively. Unit transportation Costs (in Rs.)
are as follow:
|
|
W1
|
W2
|
W3
|
Supply
|
|
F1
|
8
|
8
|
15
|
120
|
|
F2
|
15
|
10
|
17
|
80
|
|
F3
|
3
|
9
|
10
|
80
|
|
Demand
|
150
|
80
|
50
|
280
|
Determine the
optimal distribution for this company to minimize transportation cost.(Apply
NWCM & then test its optimality by applying MODI)
Answer: Total Optimal Cost for
transportation =2350
Q3. At the beginning of a sowing season, there
will be surplus of 6, 9, 7 and 5 tractors in four villages A, B, C and D while
three other villages X,Y and Z will require 8,7 and 12 tractors respectively
for faring purposes. The cost of moving tractors is directly proportional to
the distance between the surplus and deficit villages, and these distances are
given in the table
|
Surplus
Villages
|
Deficit Villages
|
|
|||
|
|
X
|
Y
|
Z
|
Supply
|
|
|
A
|
26
|
22
|
28
|
120
|
|
|
B
|
19
|
27
|
16
|
80
|
|
|
C
|
39
|
21
|
32
|
80
|
|
|
D
|
18
|
24
|
23
|
|
|
|
Demand
|
150
|
80
|
50
|
280
|
|
Determine the
optimal scheme for delivery of tractors from surplus villages to deficit
villages.
Answer: Total Optimal Cost for
transportation =543
Q4. Goods have to be transported from sources
S1, S2 and S3 to destination D1,D2 and
D3. The transportation cost per unit, capacities of the sources and the
requirements of the destination are given in the following table (APPLY NWCM AND MODI)
|
|
D1
|
D2
|
D3
|
Supply
|
|
S1
|
8
|
5
|
6
|
120
|
|
S2
|
15
|
10
|
12
|
80
|
|
S3
|
3
|
9
|
10
|
80
|
|
Demand
|
150
|
80
|
50
|
280
|
Answer: Total Optimal Cost for
transportation =1900
Q5. Obtain an optimal solution of
transportation problem
|
|
D1
|
D2
|
D3
|
D4
|
D5
|
D6
|
Supply
|
|
P1
|
9
|
12
|
9
|
6
|
9
|
10
|
5
|
|
P2
|
7
|
3
|
7
|
7
|
5
|
5
|
6
|
|
P3
|
6
|
5
|
9
|
12
|
3
|
11
|
2
|
|
P3
|
6
|
8
|
11
|
2
|
2
|
10
|
9
|
|
Demand
|
4
|
4
|
6
|
2
|
4
|
2
|
22
|
Determine optimal allocation of output.
Answer: Total Optimal Cost for
transportation =112
Q6. Obtain an optimal solution of
transportation problem
|
|
D1
|
D2
|
D3
|
D4
|
D5
|
D6
|
Supply
|
|
P1
|
5
|
3
|
7
|
3
|
8
|
5
|
3
|
|
P2
|
5
|
6
|
12
|
5
|
7
|
11
|
4
|
|
P3
|
2
|
1
|
3
|
4
|
8
|
2
|
2
|
|
P3
|
9
|
6
|
10
|
5
|
10
|
9
|
8
|
|
Demand
|
3
|
3
|
6
|
2
|
1
|
2
|
17
|
Determine optimal allocation of output.
Answer: Total Optimal Cost for
transportation =103
Q7. A steel Company has three open health
furnaces and five rolling mills. Transportation cost for shipping steel from
furnaces to rolling mills are shown in the following Table. What is the optimal
shipping schedule?
|
|
M1
|
M2
|
M3
|
M4
|
M5
|
Supply
|
|
F1
|
4
|
2
|
3
|
2
|
6
|
8
|
|
F2
|
5
|
4
|
5
|
2
|
1
|
12
|
|
F3
|
6
|
5
|
4
|
7
|
3
|
14
|
|
Demand
|
4
|
4
|
6
|
8
|
8
|
|
Q6. National Oil Company has three refineries
and 4 depots. Transportation Costs per ton & Requirement are given below
|
|
D1
|
D2
|
D3
|
D4
|
Supply
|
|
P1
|
5
|
7
|
13
|
10
|
700
|
|
P2
|
8
|
6
|
14
|
13
|
600
|
|
P3
|
12
|
10
|
9
|
11
|
800
|
|
Demand
|
300
|
600
|
700
|
400
|
|
Determine optimal allocation of output.
Answer: Total Optimal Cost for
transportation =15,400
