Center of Gravity Method of Plant Location
The center of gravity method is used to find the optimal location for a distribution center that minimizes total transportation costs. This method takes into account factors such as markets, cost of goods, and cost of transportation. The center of gravity method aims at minimizing the total shipping cost, i.e. cost incurred for shipping from the distribution center to the different shipping points.
If the shipping quantities for all destination points are equal, the location at which the transportation cost will be minimum can be identified by taking the arithmetic averages of the X and Y coordinates of the destination. But if the shipping quantities are unequal, the location can be found using a weighted average approach (the quantities to be shipped are taken as weights).
The center of gravity of a geographical location can be identified by calculating the X and Y coordinate values of the location that would minimize transportation costs.
The coordinates of the center of gravity can be identified by
Where,
Xc = X coordinate of the center of gravity
Yc = Y coordinate of the center of gravity
Vi = Volume of items transported to and from location i
Xi = X coordinate of location i
Yi= Y coordinate of the location i
Problem
Figure shows the X and Y coordinates of seven retail locations of a retail chain. Information regarding the quantity to be shipped to each of the seven locations is given in Table 1. Using the center of gravity method, identify the coordinates of the optimal location for the warehouse.
Table 1
|
|
Retail Outlet
|
X
|
Y
|
VOLUME
|
|
A
|
4
|
10
|
80
|
|
B
|
3.5
|
15
|
100
|
|
C
|
4
|
6
|
120
|
|
D
|
10
|
2
|
130
|
|
E
|
16
|
6
|
100
|
|
F
|
8
|
5
|
150
|
|
G
|
14
|
13
|
90
|
Solution
Table 2
|
|
Retail Outlet
|
Xi
|
Yi
|
Volume (Vi)
|
ViXi
|
ViYi
|
|
A
|
4
|
10
|
80
|
320
|
800
|
|
B
|
3.5
|
15
|
100
|
350
|
1500
|
|
C
|
4
|
6
|
120
|
480
|
720
|
|
D
|
10
|
2
|
130
|
1300
|
260
|
|
E
|
16
|
6
|
100
|
1600
|
600
|
|
F
|
8
|
5
|
150
|
1200
|
750
|
|
G
|
14
|
13
|
90
|
1260
|
1170
|
|
|
|
|
|
|
|
From Table 2, we can get the value of
Substituting these values in the equation for
| Volume-weighted X coordinate = Xc= |
 |
| Volume-weighted Y coordinate = Yc = |
 |
The X and Y coordinates of the point of center of gravity are 8.45 and 7.53.
Figure 6.3 shows that the location of the warehouse is closest to the location of retail outlet F.
Figure: Location of Center of Gravity
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