6. Peculiar Outsourcing Company Ltd. has production centers at Mumbai, Chennai and Kolkata. The company has its distribution centers at Ahmedabad, Bhopal, Bangalore and Goa. Production costs are equal and fixed at all three production centers, however the variable cost are only the transportation costs. The monthly productions at Mumbai, Chennai and Kolkata are 10,000 units, 12,000 units and 5000 units respectively. The monthly demand at company’s four distribution centers viz. Ahmedabad, Bhopal, Bangalore and Goa are 12000 units, 8000 units, 4000 units and 3000 units respectively. The transportation cost per unit from different production centers to different distribution centers are given in the following table.
Production Centre 
Distribution Centres 

Ahmedabad 
Bhopal 
Bangalore 
Goa 

Mumbai 
6 
4 
14 
12 
Chennai 
14 
10 
4 
6 
Kolkata 
4 
10 
8 
10 
(a) Obtain an optimum transportation schedule so as to minimize the transportation cost.
(b) If the transportation cost from production centre Kolkata to distribution centre Bangalore is changed from ` 8 per unit to ` 12 per unit, what will be the affect on the transportation schedule? Will it change? If yes, state the reason.
(c) If the company wants to meet the requirement of at least 2000 units at its Goa distribution centre only from Mumbai, will the optimum solution obtained change? If so, find the new optimum transportation schedule and its effects on total cost?
7. The following table shows all necessary information on the availability of supply to each warehouse, the requirement of each market and the unit transportation cost from each warehouse to each market: (April 05)
Warehouse 
Market 
Supply 

P 
Q 
R 
S 

A 
6 
3 
5 
4 
22 
B 
5 
9 
2 
7 
15 
C 
5 
7 
8 
6 
8 
Requirement 
7 
12 
17 
9 

The shipping clerk has worked out the following schedule from experience: 12 units from A to Q, 1 unit from A to R, 9 units from A to S, 15 units from B to R, 7 units from C to P and 1 unit from C to R.
i) Check and see if the clerk has optimal schedule.
ii) Find the optimal schedule and the minimum total transportation cost.
iii) If the clerk is approached by a courier to route C to Q, who offers to reduce his rate in hope of getting some business, by how much the rate should be reduced that the clerk will offer him the business.
10. A company has 3 plants and 4 warehouses. The supply and demand in units and corresponding transportation costs in ` Per unit are given below. On the basis of past experience, following dispatch schedule has been finalized.
Plant 
Warehouse 
Supply 


I 
II 
III 
IV 

A 
5

10 
10 4 
5 
10

B 
20 6

8 
7 
5 2 
25 
C 
5 4

10 2  5 5 
7 
20 
Demand 
25 
10 
15 
5 
55 
Answer the following questions, giving brief answers:
i) Is this solution feasible?
ii) Is this solution degenerate?
iii) Is this solution optimum? If not find the optimum solution?
iv) Does the problem have alternate optimum solutions? If yes, give another optimum solution?
v) Calculate the total minimum transportation cost as per the optimal solution.
vi) If the transportation carrier offers 10% discount on route C to 3, should the management accept the offer? Analyze the optimal solution to find answer.
11. A company BMS PVT LTD. has three plants and four warehouses. The supply and demand in units and the corresponding transportation costs in rupees per unit are given. The table below has been taken from the solution procedure of the transportation problem.
PLANTS 
WAREHOUSES 
SUPPLY 

I 
II 
III 
IV 

A 
4 
5 
3 
6 
500 
B 
3 
6 
7 
3 
700 
C 
1 
4 
1 
2 
800 
DEMAND 
500 
400 
900 
200 

a) Find the Initial Feasible Solution (IFS) by Vogel’s Approximation Method to the above transportation problem.
b) Test the IFS for optimality and if required improve it to optimality and calculate minimum total transportation cost.
c) Is there any alternate optimal solution? Justify
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