Aalogistics Co. has just signed a contract to deliver products to three location
ID: 409429 • Letter: A
Question
Aalogistics Co. has just signed a contract to deliver products to three locations, and they are trying to decide where to put their new warehouse. The three delivery locations are Chicago, Kansas City, and Memphis. The x, y coordinates for the delivery locations are as follows:
Location x coordinate y coordinate
Chicago 92 42
Kansas City 85 39
Memphis 90 35
The total quantity to be delivered to each destination is: 400 to Chicago, 150 to Kansas City, and 100 to Memphis. Calculate the location (x and y coordinates) of the new warehouse using the Center of Gravity approach. Please show all work.
Explanation / Answer
Center of Gravity Method
The Center of Gravity Method is an approach that seeks to compute geographic coordinates for a potential single new facility that will minimize costs. It’s an approach where the main inputs that it considers are the following:
Markets
Volume of goods shipped
Shipping cost
Then, using the equations below,
We calculate the X and Y coordinates using these equations where Cx is the X (horizontal axis) coordinate for the new facility. Cy is the Y (vertical axis) coordinate for the new facility, dix is the X coordinate of the existing location, diy is the Y coordinate of the existing location, and Vi is the volume of goods moved to or from the ith location.
Once you have obtained the X and Y coordinates place that location on the map.
But, it doesn’t end there. As I mention earlier, there are other factors to consider. What this method allows is a point of departure – or, literally, a starting point of where (from the perspective of longitude and latitude) you options are for where to grow your fulfillment or logistics network.
Ware house 1 ( 92,42) , Warehouse 2(85,39),Warehouse 3 (90,35) on the below axis
On Y axis
100
75
50
25
0
On X Axis 25 50 75 100
Given the assumptions and grid coordinates above, we get the following:
Which gives us,
If we were to plot the new suggested warehouse coordinates on the grid, we would get:
New ware house values (X,Y) = 78 & 40