Transportation Problem Using
1. North-West corner method
2. Least cost method
3. Vogel's approximation method
4. Row minima method
5. Column minima method
6. Russell's approximation method
7. Heuristic method-1
8. Heuristic method-2
9. optimal solution using MODI method
10. optimal solution using stepping stone method
1. A Company has 3 production facilities S1, S2 and S3 with production capacity of 7, 9 and 18 units (in 100's) per week of a product, respectively. These units are tobe shipped to 4 warehouses D1, D2, D3 and D4 with requirement of 5,6,7 and 14 units (in 100's) per week, respectively. The transportation costs (in rupees) per unit between factories to warehouses are given in the table below.
D
_{1}
D
_{2}
D
_{3}
D
_{4}
Capacity
S
_{1}
19
30
50
10
7
S
_{2}
70
30
40
60
9
S
_{3}
40
8
70
20
18
Demand
5
8
7
14
34
Find initial basic feasible solution for given problem by using
(a) North-West corner method
(b) Least cost method
(c) Vogel's approximation method
(d) obtain an optimal solution by MODI method
if the object is to minimize the total transportation cost.
2. Find an initial basic feasible solution for given transportation problem by using
(a) North-West corner method
(b) Least cost method
(c) Vogel's approximation method
D
_{1}
D
_{2}
D
_{3}
D
_{4}
Supply
S
_{1}
11
13
17
14
250
S
_{2}
16
18
14
10
300
S
_{3}
21
24
13
10
400
Demand
200
225
275
250
3. A company has factories at F1, F2 and F3 which supply to warehouses at W1, W2 and W3. Weekly factory capacities are 200, 160 and 90 units, respectively. Weekly warehouse requiremnet are 180, 120 and 150 units, respectively. Unit shipping costs (in rupess) are as follows:
W
_{1}
W
_{2}
W
_{3}
Supply
F
_{1}
16
20
12
200
F
_{2}
14
8
18
160
F
_{3}
26
24
16
90
Demand
180
120
150
450
Determine the optimal distribution for this company to minimize total shipping cost.
4. Find an initial basic feasible solution for given transportation problem by using
(a) North-West corner method
(b) Least cost method
(c) Vogel's approximation method
P
Q
R
S
Supply
A
6
3
5
4
22
B
5
9
2
7
15
C
5
7
8
6
8
Demand
7
12
17
9
45