find optimum solution with Vogel Approximation Method

1. V A M ( V O G E L ’ S A P R O X I M A T I O N M E T H O D )
English Mathematic

2. VAM (Vogel’s Approximation Method)
 The more easy and faster method for use in allocate
resources from multiple sources to multiple
destinations (market area)

3. For Example...
 a company X interested in transporting fertilizer
from three factories to three markets. Supplay
capacity, market demand in the third markets and
transport costs of unit are as follows
To
From
A B C SUPPLAY
W 20 5 8 90
H 15 20 10 60
P 25 10 19 50
DEMAND 50 110 40 200

4. Step 1 : constuct the matrix allocation of costs
TO
FROM
A B C SUPPLAY
W 90
H 60
P 50
DEMAND 50 110 40 200
20 5
15 20
25 10
8
10
19
x11
x21
x31 x32
x22
x12 x13
x23
x33

5. Step 2 : find the difference beetwen 2
smallest values at every row and column
To
From
A B C
Smallest
values of
row
W 20 5 8 8-5 =3
H 15 20 10 15-10 = 5
P 25 10 19 19-10 = 9
Smallest
values of
coulomb
20-15= 5 10-5=5 10-2=8

6. Step 3: choose the biggest difference
To
From
A B C
Smallest
values of
row
W 20 5 8 8-5 =3
H 15 20 10 15-10 = 5
P 25 10 19 19-10 = 9
Smallest
values of
coulomb
20-15= 5 10-5=5 10-2=8
Execution of value that was choosen (P row)

7. Step 4 : choose the square with lowest cost then
put it as much as you can
TO
FROM
A B C SUPPLAY
P
25 10 19
50
DEMAND 50 110 40 200
After that remove the row from table
5032
x
60

8. Step 5 : find the different again + execution again
To
From
A B C
Smallest
values of
row
W 20 5 8 8-5 =3
H 15 20 10 15-10 = 5
Smallest
values of
coulomb
20-15= 5 20-5=15 10-2=8
Remove this coulomb

9. Step 6 : find again....
To
From
A B C
Smallest
value of
row
Supplay
W 20 5 8 12 90
H 15 20 10 5 60
Smallest
value of
coulomb
5 8
Demand 50 60 40

10. Execution .........
To
From
A B C SUPPLAY
W
60 30
90
H 60
P
50
50
DEMAND
50 110 40
200
20 5
15 20
25 10
8
10
19

11. Finaalllllll.............
TO
FROM
A B C SUPPLAY
W 60 30
90
H 50 10
60
P 50
50
DEMAND 50 110 40
200
20 5
15 20
25 10
8
10
19
So the transportation cost = 60*5+30*8 + 50*15 + 10*10 + 50*10 = 1890