Question

Using the center for gravity method, determine the optimal x-coordinate for a single facility location to serve the following 5 sites (R1-5) with the following given coordinates and daily demands. x* = []

F X Y W
R1 8 7 100
R2 2 4 220
R3 6 8 80
R4 4 7 180
R5 12 15 350

Answer 1

7.139

Step-by-step explanation:

From the given information:

By using the center of gravity method, we can calculate the optimal x-coordinate.

The center of gravity technique evaluates existing facilities, the distances and the length between them, and the amounts of products to be shipped when citing single facilities.

Center of gravity method can be expressed as:

`X - coordinate = (\sum X * W)/(\sum W)`

`\implies ((8 * 100)+(2* 220) + ( 6* 80)+(4 * 180) +(12* 350))/(100+220+80+180+350)`

`\implies ((800)+(440) + ( 480)+(720) +(4200))/(930)`

`\implies (6640)/(930)`

=7.139