1.         ABC firm has three plants located all over the country. The daily production at each factory is as follows.

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Factory I (F1) 18 units

Factory II (F2) 3 units

Factory III (F3) 30 units

Each day the firm must fulfill the needs of its four distribution centres. Minimum requirement at each centre is as follows.

Distribution Centre 1 – D1 : 21 units

Distribution Centre 2 – D1 : 15 units

Distribution Centre 3 – D1 : 9 units

Distribution Centre 4 – D1 : 6 units

Cost in ` of shipping one unit from each plant to each distribution centre is given in the following table in thousands of rupees.

D1

D2

D3

D4

F1

8

12

44

28

F2

4

0

24

4

F3

20

32

60

36

Obtain initial basic feasible solution by

(1)       North-west Corner rule

(2)       Least Cost Method

(3)       Vogel’s approximation method if the objective is to minimize the total transportation cost.

(Ans : NW = ` 1392, LC = ` 1344, VAM = ` 1224)

2.         A company has three factories F1, F2, F3 with production capacities of 11, 13 and 19 units (in thousands). It has four warehouses W1, W2, W3 and W4 with demands of 6, 10, 12 and 15 units (in thousands).

Unit cost of transportation is given from each factory to each warehouse.

             To

W1

W2

W3

W4

From

F1

42

32

50

26

F2

34

36

28

46

F3

64

54

36

82

Based on the above information,

(1)       Construct a Transportation table

(2)       Find Initial Feasible Solution by :

(a)         North – West Corner Method (NWCM)

(b)         Least Cost Method (LCM)

(c)         Vogel’s Approximation Method (VAM)

                                (Ans : NW = ` 21,90,000, LC = ` 18,44,000, VAM = ` 15,92,000)

3.         A company has three plants A, B, C for which capacities are 7, 10 and 18 units. It has four warehouses P, Q, R, S for which demands are 5, 8, 7 and 15 units. Unit transportation cost is given in `

           WH

P

Q

R

S

Plant

A

38

60

100

24

B

140

60

80

120

C

80

20

120

40

Find Initial Feasible Solution by :

(a)       North – West Corner Method(NWCM)

(b)       Least Cost Method (LCM)

(c)        Vogel’s Approximation Method (VAM)

(Ans : NW = ` 1950, LC = ` 1788, VAM = ` 1718)

 

4.         Supply, Demand & Unit transportation cost data is given. Find Initial Feasible Solution by NWCR, LCM & VAM

             To

W

X

Y

Supply

From

A

16

24

24

152

B

48

72

48

164

C

24

48

72

154

Demand

144

204

82

                                                  (Ans : NW = ` 21,744, LC = ` 16,848, VAM = ` 14,544)

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