Center of Gravity Method Assignment Help

Location Evaluation Methods - Center of Gravity Method

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

449_center of gravity formula.png

 

1543_center of gravity formula1.png

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

 

 

 

  158_center of gravity solution.png

  648_center of gravity solution1.png

  825_center of gravity solution2.png

 

1019_center of gravity solution6.png

From Table 2, we can get the value of

 

564_center of gravity solution3.png

Substituting these values in the equation for

Volume-weighted X coordinate = Xc=  325_center of gravity solution4.png

 

Volume-weighted Y coordinate = Yc 918_center of gravity solution5.png

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                          

1539_center of gravity solution7.png

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