# Operations Research

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Operations Research (MTH601)
199
Table 71
Destination
Origin
1
2
3
4
1
-5
-19
2
54
67
3
50
17
(ui + vj) for unalloted cells
Table 72
Destination
Origin
1
2
3
4
1
61
67
2
28
14
3
49
54
Cell evaluation
In table 72 (matrix of cell evaluation) there is no negative entry indicating that the solution found in
table 66 is optimal.
The optimum cost = Rs. 6698
REVIEW QUESTIONS
1.
What do you understand by degeneracy in a transportation problem?
2.
What is degeneracy?
3.
Write a short note on degeneracy in a transportation problem.
4.
Explain how degeneracy in a transportation problem may be resolved.
5.
How the problem of degeneracy arises in a transportation problem?
6.
A company has three plants at locations A, B and C which supply to warehouses located at D, E, F, G
and H. Monthly plant capacities are 800, 500 and 900 units respectively. Monthly warehouse
requirements are 400, 400, 500, 400 and 800 units respectively. Unit transportation costs (in Rupees)
are given below.
To
D
E
F
G
H
A
5
8
6
6
3
B
4
7
7
6
5
C
8
4
6
6
4
Determine an optimum distribution for the company in order to minimize the total transportation cost.
199
Operations Research (MTH601)
200
7.
A company has four manufacturing plants and five warehouses. Each plant manufactures the same
product, which is sold at different prices at each warehouse area. The cost of manufacturing and cost of
raw materials are different in each plant due to various factors. The capacities of the plants are also
different. These data are given in the following table:
Item/Plants
1
2
3
4
Manufacturing
Cost (Rs.) per
12
10
8
7
unit
Raw material
Cost (Rs.) per
8
7
7
5
unit
Capacity  per
unit time
100
200
120
80
The company has five warehouses. The sale prices, transportation costs and demands are
given in the following table:
Transportation Cost (Rs.)
Sale Price
Warehouse
per unit
(Rs.) Per
Demand
Plants
Unit
1
2
3
4
80
30
A
4
7
4
3
120
32
B
8
9
7
8
150
28
C
2
7
6
10
70
34
D
10
7
5
8
90
30
E
2
5
8
9
(i) Formulate this into a transportation problem to maximize profit.
(ii) Find the solution using VAM method.
(iii) Test for optimality and find the optimal solution.
200