MEE1024 Operations Research / Module II Tutorial Problems / Darla / SMEC / WS2017-18
2.1.A company has four warehouses W1, W2, W3 and W4. It is required to deliver a product from these warehouses to three customers C1, C2 and C3. The warehouses have the following amounts in stock:
Warehouse W1 W2 W3 W4
No. of units 15 16 12 13 and the customers’ requirements are:
Customer C1 C2 C3
No. of units 18 20 18
The table below shows the costs of transporting one unit from warehouse to the customer and stock of warehouse and requirement of customer.
C1 C2 C3
W1 8 6 3
W2 9 11 8
W3 6 5 7
W4 3 10 9
Determine the optimal solution to the problem.
2.2.Find an optimum basic feasible solution to the following T.P :
2.3.Solve the following transportation problem:
To
From
A B C
Availability I 50 30 220 1
II 90 45 170 3 III 250 200 50 4
4 2 2 Requirement
Warehouse
Factory
W1 W2 W3 W4
Factory capacity
F1 19 30 50 10 7
F2 70 30 40 60 9
F3 40 8 70 20 18
5 8 7 14
2.4.Solve the following transportation problem:
Consumers
A B C Availability Suppliers
I 6 8 4 14
II 4 9 8 12
III 1 2 6 5
Required 6 10 15 31
2.5.Given the following data:
Destinations
Sources
1 2 3 Capacities 1 2 2 3 10
2 4 1 2 15 3 1 3 - 40 Demands 20 15 30
The cost of shipment from third source to the third destination is not known. How many units should be transported from the sources to the destination so that the total cost of transporting all the units to their destinations is a minimum?
2.6.Solve the following transportation problem:
Source
Destination
1 2 3 4 Availability
1 21 16 25 13 11
2 17 18 14 23 13
3 32 27 18 41 19
Requirement 6 13 12 15 43
2.7.Solve the following transportation problem:
Origin
Destination
D1 D2 D3 D4 Availability
O1 1 2 1 4 30
O2 3 3 2 1 50
O3 4 2 5 9 20
Requirement 20 40 30 10 100
2.8.Solve the following transportation problem :
D1 D2 D3 availability
O1 4 8 8 76
O2 16 24 16 82
O3 8 16 24 77
2.9.Solve the following transportation problem where all cell entries are unit profits of transportation from any origin to any destination :
A B C D Availability
F1 8 9 6 3 170
F2 6 11 5 10 200
F3 3 8 7 9 180
Requirement 150 160 110 130
2.10. A company has four warehouses W1, W2, W3 and W4. It is required to deliver a product from these warehouses to three customers C1, C2 and C3. The warehouses have the following amounts in stock:
Warehouse W1 W2 W3
No. of units 15 25 5 and the customers’ requirements are:
Customer C1 C2 C3 C4
No. of units 5 15 15 10
The table below shows the costs of transporting one unit from warehouse to the customer and stock of warehouse and requirement of customer.
C1 C2 C3 C4
W 1
10 2 20 11
W 2
12 7 9 20
W 3
0 14 16 18
Use the VAM to find the starting solution and find the optimal solution to the problem
2.11. There are three sources or origins which store a given product. These sources supply these products to four dealers. The capacities of the sources and the demands of the dealers are given below :
Sources Demands
S1 150 D1 90
S2 40 D2 70
S3 80 D3 50
D4 60
The cost of transporting the products from various sources to various dealers is shown below:
D1 D2 D3 D4
S1 27 23 31 69
S2 10 45 40 32
S3 30 54 35 57
2.12. The following table represents a specific iteration of transportation technique used in the process of solution of transportation problem with cost values. The value in circle represents an allocation quantity. It is assumed that a very low quantity of transportation of goods represented as .
Develop the optimal solution.
2.13. An oil corporation has got three refineries P, Q, and R, and it has to send petrol to four different deports A, B, C and D. The cost of shipping 1 gallon of petrol from each refineries to each deport is given below: The requirements of deports and the available petrol at the refineries are also given.
Deport
Refinery
A B C D Available
P 10 12 15 8 130
Q 14 11 9 10 150
R 20 5 7 18 170
Required 90 100 140 120
Find the minimum cost of shipping after obtaining an initial solution by Vogel’s Approximation Method.
2.14. A company has four warehouses W1, W2 and W3. It is required to deliver a product from these warehouses to three customers C1, C2 and C3. The warehouses have the following amounts in stock:
D1 D2 D3 D4 Supply
O1 10
2
20 11 15
O2 12
7 9 20
25
O3
4
14 16
18
10
Demand 5 15 15 15
15 10
5 5
Customer C1 C2 C3 No. of units 75 20 50
The table below shows the costs of transporting one unit from the warehouse to the customer.
Suppose that the penalty costs per unit of unsatisfied demand are Rs.5, Rs.3 and Rs.2 for customers C1, C2 and C3 respectively. Use the VAM to find the starting solution and find the optimal solution to the problem.
C1 C2 C3
W1 5 1 7
W2 6 4 6
