Answer to Question #173567 in Operations Research for ANJU JAYACHANDRAN

Question

3. (a) A company has three factories 1 2 F ,F and F3

which supply goods to four warehouses

1 2 3 W ,W ,W and . W4

The daily factory capacities of 1 2 F ,F and F3

are, respectively, six

units, one unit and ten units. The demand of the warehouses 1 2 3 W ,W ,W and W4

are,

respectively, seven, five, three and two units. Unit transportation cost are as

follows: (5)

W1 W2 W3 W4

F1

2 3 11 7

F2

1 0 6 1

F3

5 8 15 9

Find an initial basic feasible solution by the Vogel’s approximation method.

Answer 1

: Since $\sum_{i=1}^4a_i=\sum_{j=1}^3 b_j,$ the given problem is balanced TP., Therefore there exists a

feasible solution.

 Step-1 Select the lowest and next to lowest cost for each row and each column, then the

difference between them for each row and column displayed them with in first bracket against

respective rows and columns. Here all the differences have been shown within first

compartment. Maximum difference is 15 which is occurs at the second column. Allocate min

(40,120) in the minimum cost cell (1,2).

Step -2: Appling the same techniques we obtained the initial BFS. Where all capacities and

demand have been exhausted.

The initial basic feasible solution is$x_{12}=40, x_{14}=40, x_{21}=10, x_{23}=30, x_{24}=30, x_{31}=50.$

and

minimum cost of transportation$=22 *40 + 4 * 80 + 24 * 10 + 9 *30 + 7 * 30 + 32 * 50 = 3520.$